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Lessons In Electric Circuits, Volume VI – Experiments
By Tony R. Kuphaldt First Edition, last update October 30, 2002
i c 2002-2003, Tony R. Kuphaldt This book is published under the terms and conditions of the Design Science License. These terms and conditions allow for free copying, distribution, and/or modification of this document by the general public. The full Design Science License text is included in the last chapter. As an open and collaboratively developed text, this book is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the Design Science License for more details. Available in its entirety as part of the Open Book Project collection at http://www.ibiblio.org/obp
PRINTING HISTORY • First Edition: Printed in April 2002. Source files written in SubML format. SubML is a simple A markup language designed to easily convert to other markups like L TEX, HTML, or DocBook using nothing but search-and-replace substitutions.
1 INTRODUCTION 1.1 Electronics as science . 1.2 Setting up a home lab 1.2.1 Work area . . . 1.2.2 Tools . . . . . 1.2.3 Supplies . . . . 1.3 Contributors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1 2 2 3 12 14 15 15 20 27 34 41 44 47 52 54 56 59 59 60 63 67 77 86 92 98 101 108 111 116 121
2 BASIC CONCEPTS AND TEST EQUIPMENT 2.1 Voltmeter usage . . . . . . . . . . . . . . . . . . . . 2.2 Ohmmeter usage . . . . . . . . . . . . . . . . . . . 2.3 A very simple circuit . . . . . . . . . . . . . . . . . 2.4 Ammeter usage . . . . . . . . . . . . . . . . . . . . 2.5 Ohm's Law . . . . . . . . . . . . . . . . . . . . . . 2.6 Nonlinear resistance . . . . . . . . . . . . . . . . . 2.7 Power dissipation . . . . . . . . . . . . . . . . . . . 2.8 Circuit with a switch . . . . . . . . . . . . . . . . . 2.9 Electromagnetism . . . . . . . . . . . . . . . . . . . 2.10 Electromagnetic induction . . . . . . . . . . . . . . 3 DC 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 CIRCUITS Introduction . . . . . . . . . . . . . Series batteries . . . . . . . . . . . Parallel batteries . . . . . . . . . . Voltage divider . . . . . . . . . . . Current divider . . . . . . . . . . . Potentiometer as a voltage divider Potentiometer as a rheostat . . . . Precision potentiometer . . . . . . Rheostat range limiting . . . . . . Thermoelectricity . . . . . . . . . . Make your own multimeter . . . . Sensitive voltage detector . . . . . Potentiometric voltmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
iv 3.14 3.15 3.16 3.17 3.18 4-wire resistance measurement . . A very simple computer . . . . . . Potato battery . . . . . . . . . . . Capacitor charging and discharging Rate-of-change indicator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4 AC CIRCUITS 4.1 Introduction . . . . . . . . . . . . . . . 4.2 Transformer – power supply . . . . . . 4.3 Build a transformer . . . . . . . . . . . 4.4 Variable inductor . . . . . . . . . . . . 4.5 Sensitive audio detector . . . . . . . . 4.6 Sensing AC magnetic fields . . . . . . 4.7 Sensing AC electric fields . . . . . . . 4.8 Automotive alternator . . . . . . . . . 4.9 Phase shift . . . . . . . . . . . . . . . 4.10 Sound cancellation . . . . . . . . . . . 4.11 Musical keyboard as a signal generator 4.12 PC Oscilloscope . . . . . . . . . . . . . 4.13 Waveform analysis . . . . . . . . . . . 4.14 Inductor-capacitor "tank" circuit . . . 4.15 Signal coupling . . . . . . . . . . . . . 5 DISCRETE SEMICONDUCTOR 5.1 Introduction . . . . . . . . . . . . 5.2 Commutating diode . . . . . . . 5.3 Half-wave rectifier . . . . . . . . 5.4 Full-wave center-tap rectifier . . 5.5 Full-wave bridge rectifier . . . . . 5.6 Rectifier/filter circuit . . . . . . . 5.7 Voltage regulator . . . . . . . . . 5.8 Transistor as a switch . . . . . . 5.9 Static electricity sensor . . . . . . 5.10 Pulsed-light sensor . . . . . . . . 5.11 Voltage follower . . . . . . . . . . 5.12 Common-emitter amplifier . . . . 5.13 Multi-stage amplifier . . . . . . . 5.14 Current mirror . . . . . . . . . . 5.15 JFET current regulator . . . . . 5.16 Differential amplifier . . . . . . . 5.17 Simple op-amp . . . . . . . . . . 5.18 Audio oscillator . . . . . . . . . . 5.19 Vacuum tube audio amplifier . .
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. . . . . . . 9. . . . . . . . .2 The use of SPICE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .7 Simple combination lock . . 8 ABOUT THIS BOOK 8. . . . . . . . . . . . .CONTENTS 6 ANALOG INTEGRATED CIRCUITS 6. . . . . 7. . . . . . . . . . . . . . . . . . . . . .2. . . . . . . . . . . . . . . . . . . .1 How to contribute to this book . . . . .8 7. . . . . . . . . . . . . . . . . . . . 6. . . . .2 Your name here . . . . . . . . . .7 6. . . .1 0. . . . . . . . . . . . . . . . . . . . . . . . . . 6. . . . . . . 7. . . . . . . Definitions . . . . . . . . . . . . . . . . .2 Basic gate function . . . . . . . . . . . . . . . . . . . . . . . . . . . 9. . . . . . . . . . . . . . . . . . . . . . . . .4 3. . . . . . . . . . . . . . . . . . . . . . 7. .9 PWM power controller . . . . . . . . . . . 6. 9. . . . . . . . . . . .3 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. . . . . . . . . . . . . . . . . . . . . . .2. . . . . . . .1 Introduction . . . . . . . . .2. . . . . . Modification . . . . . . . . . . . . . . . . . . . . .3 NOR gate S-R latch . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. 10. . . . . . . . . . . . . . . . . . 6. . . . . . . . . . . . . . . . . . . . . . . . . . . .2 Voltage comparator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . No restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. . . . . . . . . . .3 Precision voltage follower . . .9 8.6 Integrator . . . . . . .8 3-bit binary counter . . . . . . . . . . 10. . . . . . . . . . . . Rights and copyright . . . . . Disclaimer of liability . . . . . . . . . . . . . . . . . . . 7. .7 555 audio oscillator . . . .4 NAND gate S-R enabled latch . .8 555 ramp generator . . . . . .3 Typo corrections and other "minor" contributions 10 DESIGN SCIENCE LICENSE 10. . . . . . . . 6. . . . . . . . . . . . . . . . . . . .6 5. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 DIGITAL INTEGRATED CIRCUITS 7. . . . . . . . . . . . . . . .4 Noninverting amplifier .2 Credits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2 1. . . . . 7. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6 LED sequencer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7. . . . . . . . . . . . . .10 Class B audio amplifier . . . . . . . . . . . . . . . . . . . . .1 Introduction .3 2. . . . . . . . . . . . . . . . . 10. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .9 7-segment display . . . . . 8. . . . . . . . . . . . . . 6. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .5 High-impedance voltmeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6. . . . . . . . . . . . . . . . . Preamble . . . 6. . . . . . . . . 7. . . . . . . . 10. . . . . . . . . . . . 9. . . . . . . . . . . . . . . . . . . . . . . . . . .1 Purpose . . . . . . . Copying and distribution . . . . . . . Kuphaldt . . . . . . . . . .5 NAND gate S-R flip-flop . . . . . 9 CONTRIBUTOR LIST 9. . . . . . . . . . . 8. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10. . . . . 7. . Acceptance . . . . . . . . . . . . . . . . . . . . v 277 277 278 281 285 288 292 298 301 304 308 317 317 319 323 327 329 333 342 345 347 351 351 352 353 355 355 356 356 356 357 359 359 359 360 360 361 361 361 361 362 . . . . .1 Tony R. . . .5 4. . . . . . . . 6. . . . . . . . . . . . . . . . . . . . . . No warranty . . . . . . . . . . . . . . . . . .
and a very accessible science at that. A process of assessment. it is impractical for me to present a complete laboratory course here. is also vital to guarantee that a certain level of learning has taken place. and usually must be based around specific parts and equipment so that the experiments will be sufficient detailed. The experiments in this volume begin at a level appropriate for someone with no electron1 . so that the individual learning on their own has a resource to guide their experimental adventures. Not so with electronics. In order for someone to teach themselves a science such as electronics. and my intent is to honor their service and love by giving back to the world what they gave to me. Many people selflessly volunteered their time and expertise in helping me learn electronics when I was younger. I must include a guide to experimentation along with the text(s) on theory. and helps to improve the quality of learning. I am forced to design the experiments at a lower level than what would be expected for a college lab course. Peer review (comparison of experimental results with the work of others) is another important component of college-level laboratory study. When I starting writing Lessons In Electric Circuits. with results sufficiently precise to allow for rigorous comparison between experimental and theoretical data. they must engage in handson experimentation.Chapter 1 INTRODUCTION 1. Many advanced concepts may be explored using parts and equipment totaling under a few hundred US dollars.1 Electronics as science Electronics is a science. especially in scientific endeavors. This is good. A formal laboratory course for college electronics study requires an enormous amount of work to prepare. In the interest of keeping this experiment guide reasonably low-cost for people to follow. articulated through a qualified instructor. being mostly self-taught in electronics myself. expensive equipment is generally required to perform any non-trivial experiments. With other areas of scientific study. Since I cannot meet these criteria through the medium of a book. If my contribution to society is to be complete. because hands-on experimentation is vital to gaining scientific knowledge about any subject. my intent was to create a textbook suitable for introductory college use. I knew the value of a good textbook to hobbyists and experimenters not enrolled in any formal electronics course. Knowledge gleaned from books alone has limited use. However. and practical for deployment over the internet.
" it is this one: I fully intend to continue adding experiments ad infinitum so as to provide the experimenter or hobbyist with a wealth of ideas to explore the science of electronics. I take efforts to direct the reader's attention toward it. I strongly recommend that experimenters obtain some of the more expensive components such as transformers (see the AC chapter) by salvaging them from discarded electrical appliances. This is one of the most important reasons why experimentation is so vital to your scientific education: the real problems you will invariably encounter in experimentation challenge you to develop practical problem-solving skills. hazards do exist building anything with your own two hands. feel free to explore by trying different circuit construction and measurement techniques. Where there is a greaterthan-normal level of danger in an experiment. although they could serve as templates for more rigorous coursework. from the mis-handling of electricity by the experimenter. It doesn't take a tremendous effort to describe an experiment or two. If something isn't working as the text describes it should. as well as a few tools and critical supplies. All experiments shown in this book are designed with safety in mind.2. In many of these experiments. giving you full credit for the work. and progress to higher levels. I offer part numbers for Radio Shack brand components. and any test equipment. but the knowledge gained by "troubleshooting" a circuit yourself is at least as important as the knowledge gained by a properly functioning experiment. Often times. They stress qualitative knowledge over quantitative knowledge.1 Work area A work area should consist of a large workbench. and I will gladly include it if you email it to me. This section describes the setup of a home electronics laboratory. When performing these experiments.2 Setting up a home lab In order to build the circuits described in this volume. However. lesser-known supply houses. INTRODUCTION ics knowledge. It is nearly impossible to shock or otherwise hurt yourself by battery-powered experiments or other circuits of low voltage. it is unfortunately necessary in this litigious society to disclaim any and all liability for the outcome of any experiment presented here.2 CHAPTER 1. don't give up! It's probably due to a simple problem in construction (loose wire. 1. Inexpensive desks intended for computer use function very well for this purpose. desk. wrong component value) or test equipment setup. It can be frustrating working through these problems on your own. with household electrical power (120 volts AC) readily accessible to power soldering equipment. or table (preferably wooden) for performing circuit assembly. However. Neither myself nor any contributors bear responsibility for injuries resulting from the construction or use of any of these projects. power supplies. Perform these experiments at your own risk! 1. as the electrical conductivity of a . you will need a small work area. If there is any portion of Lessons In Electric Circuits that will remain "incomplete. Avoid a metal-surface desk. Refer to Appendix 2 for details on contributing to this book. This volume of the book series is also the easiest to contribute to. This is not an endorsement of Radio Shack. or from any other unsafe practices leading to injury. for those who would like to help me in providing free information to people learning electronics. both for economic and ecological reasons. but simply a convenient reference to an electronic supply company well-known in North America. components of better quality and lower price may be obtained through mail-order companies and other.
If you cannot obtain a wooden-surface workbench. This is an electrical instrument designed to measure voltage. As you can tell from the photographs. you might want to search for them at thrift stores and pawn shops before buying them new.1. Vinyl and plastic bench surfaces are to be avoided for their ability to generate and store large static-electric charges. Multimeters are manufactured in both digital and analog form. some of my own tools are rather old but function well nonetheless.2 Tools A few tools are required for basic electronics work. First and foremost in your tool collection is a multimeter. these materials melt easily when exposed to hot soldering irons and molten solder droplets. If you are reasonably skilled with woodworking tools. current. The work area should be well-lit and comfortable. you may turn any form of table or desk into one by laying a piece of plywood on top. If you desire to keep the cost as low as possible. A digital multimeter is preferred for precision work.2. SETTING UP A HOME LAB 3 metal surface creates both a shock hazard and the very distinct possibility of unintentional "short circuits" developing from circuit components touching the metal tabletop. but analog meters are also useful for gaining an intuitive understanding of instrument sensitivity and range.2. Also. and often other variables as well. I have a small radio set up on my own workbench for listening to music or news as I experiment. It is convenient to have a single switch for shutting off all power in case of an accidental short-circuit! 1. you may construct your own desk using plywood and 2x4 boards. purchased in 1987: Digital multimeter Most analog multimeters sold today are quite inexpensive. resistance. and not necessarily precision test . My own workbench has a "power strip" receptacle and switch assembly mounted to the underside. into which I plug all 120 volt devices. My own digital multimeter is a Fluke model 27. which may damage sensitive electronic components. Most of these tools are inexpensive and easy to obtain.
DC or AC. and they can be unplugged from it. I recommend having both digital and analog meter types in your tool collection. Even some of the internal components were salvaged from scrap (the step-down transformer and headphone jack were taken from an old radio. you might justify the purchase of more expensive. one could take much greater care in choosing construction materials (metal box. the greater the "dB" rating of the headphones. shielded test probe cable). because it allows you to listen to an electronic signal. The single most influential component with regard to detector sensitivity is the headphone assembly: generally speaking. purchased in non-working condition from a thrift store). The entire thing. Since the headphones need not be modified for use in the detector circuit. Sensitive voltage/audio detector As you can see. Few tools engender an intuitive comprehension of frequency and amplitude as this! I cite its use in many of the experiments shown in this volume. cost no more than $15 to build. and thereby determine something of its nature. this is a most valuable tool. spending as little money as possible on the analog multimeter and investing in a good-quality digital multimeter (I highly recommend the Fluke brand).4 CHAPTER 1. so I strongly encourage that you build your own. ====================================== A test instrument I have found indispensable in my home work is a sensitive voltage detector. but it probably wouldn't improve its performance significantly. or sensitive audio detector. In the absence of an oscilloscope. the better they will function for this purpose. equipped with an attenuator (volume control) and limiting diodes to limit sound intensity from strong signals. including the headphones purchased second-hand. it is the most useful piece of test equipment in the collection of the budget electronics experimenter. Of course. INTRODUCTION instruments. Its purpose is to audibly indicate the presence of low-intensity voltage signals. section of brown lamp cord for the test leads). . Second only to a multimeter. It is nothing more than a sensitized set of audio headphones. high-quality headphones by using them as part of a home entertainment (audio/video) system. I built my detector using scrap parts (household electrical switch/receptacle box for the enclosure. described in nearly identical experiments in two chapters of this book volume.
for a multitude of wire sizes. sometimes called a prototyping board. This device allows you to quickly join electronic components to one another without having to solder component terminals and wires together.1.2. and it is a special form of plier with several knife-edged holes in the jaw area sized just right for cutting through the plastic insulation and not the copper. SETTING UP A HOME LAB ====================================== 5 Also essential is a solderless breadboard. or gauges. Shown here are two different sizes of wire stripping pliers: Wire stripping pliers . you need a tool to "strip" the plastic insulation off the ends so that bare copper metal is exposed. Solderless breadboard ====================================== When working with wire. or proto-board. This tool is called a wire stripper.
These may be purchased complete.6 CHAPTER 1. Jumper wires (as sold by Radio Shack) Jumper wires (home-made) . INTRODUCTION ====================================== In order to make quick. or assembled from clips and wires. temporary connections between some electronic components. you need jumper wires with small "alligator-jaw" clips at each end.
uninsulated (bare metal) alligator clips are okay to use so long as care is taken to avoid any unintentional contact between the bare clips and any other wires or components.2. ====================================== Needle-nose pliers are designed to grasp small objects. and are especially useful for pushing wires into stubborn breadboard holes. SETTING UP A HOME LAB 7 The home-made jumper wires with large.1. jumper wires with insulated (rubber-covered) clips like the jumper shown from Radio Shack are much preferred. For use in crowded breadboard circuits. Needle-nose pliers ====================================== .
Do not use "acid-core" solder! Acid-core solder is intended for the soldering of copper tubes (plumbing). and the thinnest solder you can find.8 CHAPTER 1. INTRODUCTION No tool set would be complete without screwdrivers. Also. Soldering iron and solder ("rosin core") . you should avoid solder containing the metal lead. You may later find it useful to invest in a set of jeweler's screwdrivers for work with very small screws and screw-head adjustments. the residual acid will cause wires to corrode. no larger for printed circuit board work. If used for electrical work. to prevent bits of molten solder from accidently landing in your eye should a wire release from the joint during the soldering process and fling bits of solder toward you. opting instead for silver-alloy solder. If you do not already wear glasses. Screwdrivers ====================================== For projects involving printed-circuit board assembly or repair. a small soldering iron and a spool of "rosin-core" solder are essential tools. and I recommend a complementary pair (3/16 inch slotted and #2 Phillips) as the starting point for your collection. a pair of safety glasses is highly recommended while soldering. where a small amount of acid helps to clean the copper of surface impurities and provide a stronger bond. I recommend a 25 watt soldering iron.
Soldering gun ====================================== Knives. SETTING UP A HOME LAB 9 ====================================== Projects requiring the joining of large wires by soldering will necessitate a more powerful heat source than a 25 watt soldering iron. A soldering gun is a practical option. are essential tools for all kinds of work.2. Utility knife . For safety's sake.1. I recommend a "utility" knife with retracting blade. These knives are also advantageous to have for their ability to accept replacement blades. like screwdrivers.
Slip-joint pliers Adjustable-joint pliers .10 CHAPTER 1. Two types I recommend are slip-joint and adjustable-joint ("Channel-lock"). INTRODUCTION ====================================== Pliers other than the needle-nose type are useful for the assembly and disassembly of electronic device chassis.
SETTING UP A HOME LAB 11 ====================================== Drilling may be required for the assembly of large projects. wood. It is certainly safer and quieter than a power drill.2. and most metals.1. Although power drills work well. and costs quite a bit less. Hand drill As the wear on my drill indicates. I have found that a simple hand-crank drill does a remarkable job drilling through plastic. it is an often-used tool around my home! ====================================== Some experiments will require a source of audio-frequency voltage signals. Normally. this type of signal is generated in an electronics laboratory by a device called a signal generator or function .
and oscilloscopes are usually outside the budgetary range of the home experimenter.2. ====================================== An alternative to solderless breadboard circuit construction is wire-wrap. it often requires the use of an oscilloscope to fine-tune. Wire-wrap wire and wrapping tool . You need not be a musician to operate one for the purposes of generating an audio signal (just press any key on the board!). in different insulation colors. and the connections made are at least as durable as soldered connections. Insulation color has no bearing on the wire's performance.3 Supplies Wire used in solderless breadboards must be 22-gauge. No soldering is required. INTRODUCTION generator. More details regarding the use of a "Musical Keyboard as a Signal Generator" may be found in the experiment of that name in chapter 4 (AC). solid copper. solid copper wire Note how the last 1/4 inch or so of the copper wire protruding from the spool has been "stripped" of its plastic insulation. A relatively inexpensive alternative to a commercial signal generator is an electronic keyboard of the musical type.12 CHAPTER 1. perhaps more. and a special wrapping tool. but different colors are sometimes useful for "colorcoding" wire functions in a complex circuit. Spool of 22-gauge. Wire-wrapping requires a spool of this very thin wire. Spools of this wire are available from electronic supply stores and some hardware stores. The electronic signal generated by the keyboard is conducted to your circuit via a headphone cable plugged into the "headphones" jack. 1. where 30-gauge (very thin!) solid copper wire is tightly wrapped around the terminals of components inserted through the holes of a fiberglass board. While building such a device is not impossible (nor difficult!). and they may be obtained quite readily at second-hand stores for substantially less than new price. the simplest kind resembling a small screwdriver.
and green. Extension cord. This is especially true if the cord is purchased on sale! Also. SETTING UP A HOME LAB 13 ====================================== Large wire (14 gauge and bigger) may be needed for building circuits that carry significant levels of current. Typically comprised of three wires colored white. extension cords are often sold at prices less than the retail cost of the constituent wire alone. Though electrical wire of practically any gauge may be purchased on spools. available at any hardware store: cheap extension cords.1. copper wire. I have found a very inexpensive source of stranded (flexible). in package . an extension cord provides you with a pair of 120 volt connectors: male (plug) and female (receptacle) that may be used for projects powered by 120 volts. black.2.
Michael Warner (April 9. See Appendix 2 (Contributor List) for dates and contact information. Component box In this view of one of my component boxes. carefully cut the outer layer of plastic insulation away using a utility knife. This is. One technique for keeping these components organized is to keep them in a plastic "organizer" box like the type used for fishing tackle.3 Contributors Contributors to this chapter are listed in chronological order of their contributions. INTRODUCTION To extract the wires. both for safety's sake and for the sake of avoiding cuts in the individual wires' insulation. you can see plenty of 1/8 watt resistors. much preferable to slicing the entire length of the insulation with a knife. you will accumulate a large number of small components. from most recent to first. ====================================== During the course of building many circuits. then grasping the wires with one hand and the insulation with the other and pulling them apart. 2002): Suggestions for a section describing home laboratory setup. and even a few 8-pin integrated circuits ("chips"). of course. 1. transistors. With practice. Labels for each compartment were made with a permanent ink marker. diodes. . you may find you can peel away the outer insulation by making a short cut in it at one end of the cable.14 CHAPTER 1.
Volume 1. digital or analog • Assorted batteries • One light-emitting diode (Radio Shack catalog # 276-026 or equivalent) • Small "hobby" motor. chapter 8: "DC Metering Circuits" LEARNING OBJECTIVES • How to measure voltage 15 . 278-1157. or equivalent) A multimeter is an electrical instrument capable of measuring voltage. but to eventually have both in your tool kit for these experiments. or resistance. for indicating the quantity of voltage. Digital multimeters have numerical displays. like digital clocks. current. permanent-magnet type (Radio Shack catalog # 273-223 or equivalent) • Two jumper wires with "alligator clip" ends (Radio Shack catalog # 278-1156. chapter 1: "Basic Concepts of Electricity" Lessons In Electric Circuits. Volume 1. Analog multimeters tend to be less expensive than digital multimeters. Analog multimeters indicate these quantities by means of a moving pointer over a printed scale. current. and resistance. CROSS-REFERENCES Lessons In Electric Circuits.1 Voltmeter usage PARTS AND MATERIALS • Multimeter. I strongly recommend purchasing an analog multimeter before purchasing a digital multimeter.Chapter 2 BASIC CONCEPTS AND TEST EQUIPMENT 2. and more beneficial as learning tools for the first-time student of electricity.
16 CHAPTER 2. BASIC CONCEPTS AND TEST EQUIPMENT • Characteristics of voltage: existing between two points • Selection of proper meter range ILLUSTRATION Digital multimeter V V OFF A A Analog multimeter A COM + Test leads Test leads Test probes Test probes .
you will be using some sort of test equipment to measure aspects of electricity you cannot directly see. Read them well! If your multimeter is digital. Reverse the test probe connections to the battery if the meter's indication is negative (on an analog meter. mathematically defined as joules per coulomb. Multimeters indicate the presence of. An autoranging meter has only a few selector switch (dial) positions. several for current. in which case you need to set the switch to that one position. a negative value is indicated by the pointer deflecting left instead of right). Some digital multimeters are autoranging. it will require a small battery to operate. or smell.5-volt "D-cell" battery INSTRUCTIONS In all the experiments in this book. VOLTMETER USAGE 17 + - Light-emitting diode ("LED") 6-volt "lantern" battery Permanentmagnet motor 1. In this experiment. . The meter should now provide you with some sort of indication. hear. it is the specific energy per unit charge. and the black test probe to the negative (-) side of the same battery. Electricity – at least in small. you will familiarize yourself with the measurement of voltage. Set your multimeter's selector switch to the highest-value "DC volt" position available.2. Your most fundamental "eyes" in the world of electricity and electronics will be a device called a multimeter. Touch the red test probe to the positive (+) side of a battery. and is to manual ranging as an automatic transmission is to a manual transmission in a car. An autoranging meter "shifts gears" automatically to find the best measurement range to display the particular quantity being measured. current. It is analogous to pressure in a fluid system: the force that moves fluid through a pipe. and several for resistance. Autoranging is usually found on only the more expensive digital meters. If it is analog. it does not need a battery to measure voltage. and measure the quantity of. and resistance.1. Your multimeter should come with some basic instructions. Manual-ranging meters have several different selector positions for each basic quantity: several for voltage. safe quantities – is insensible by our human bodies. taste. and is measured in the unit of the Volt (V). In scientific terms. electrical properties such as voltage. Voltage is the measure of electrical "push" ready to motivate electrons to move through a conductor. feel. Autoranging multimeters may only have a single position for DC voltage.
as indicated by a greater deflection of the analog meter pointer (needle). and note the meter's indication: Light source LED - + Batteries develop electrical voltage through chemical reactions." it has exhausted its original store of chemical "fuel. When a battery "dies. but LEDs also happen to generate DC voltage when exposed to light. The small electric motor specified in the "Parts and Materials" list functions as an electrical generator if its shaft is turned by a mechanical force. and learn how to select the best voltage range on the multimeter to give you maximum indication without over-ranging. move the selector switch to the lowest-range setting that does not "over-range" the meter. past the full-range scale value. If you find it difficult to maintain both meter test probes in connection with the motor's terminals while simultaneously spinning the shaft with your fingers. An over-ranged analog meter is said to be "pegged. the indication will be small. Now switch your multimeter to the lowest DC voltage range available. or a series of dashed lines. and the selector switch has been set to a high-range position. and touch the meter's test probes to the terminals (wire leads) of the light-emitting diode (LED)." The LED. or more active digits on the digital meter display. Connect your voltmeter (your multimeter. you may use alligator clip "jumper" wires . it will produce voltage." as the needle will be forced all the way to the right-hand side of the scale. This indication is manufacturer-specific. Another source of voltage through energy conversion a generator. The indication should be stronger now. What happens if you only touch one meter test probe to one end of a battery? How does the meter have to connect to the battery in order to provide an indication? What does this tell us about voltmeter use and the nature of voltage? Is there such a thing as voltage "at" a single point? Be sure to measure more than one size of battery. So long as there is light to illuminate the LED. Point the LED toward a bright source of light with your multimeter connected to it. Move the selector switch to the next lower DC voltage range setting and reconnect to the battery.18 CHAPTER 2. An LED is designed to produce light when powered by a small amount of electricity. somewhat like a solar cell. The meter should indicate voltage by means of needle deflection (analog) or numerical readout (digital). BASIC CONCEPTS AND TEST EQUIPMENT If your meter is a manual-range type. rather. however. it converts optical energy into electrical energy. and spin the shaft with your fingers. For the best results. An over-ranged digital meter sometimes displays the letters "OL". set to the "volt" function) to the motor's terminals just as you connected it to the LED's terminals. does not rely on an internal "fuel" to generate voltage.
1. If the applied voltage is of the reverse polarity (negative on red and positive on black)." . the meter will register voltage in the normal direction. The voltmeter indicates polarity by direction of needle direction (analog) or sign of numerical indication (digital). the meter will indicate "backwards.2. VOLTMETER USAGE like this: 19 Jumper wire Alligator clip + Motor Determine the relationship between voltage and generator shaft speed? Reverse the generator's direction of rotation and note the change in meter indication. When the red test lead is positive (+) and the black test lead negative (-). you change the polarity of the voltage created by the generator. When you reverse shaft rotation.
CROSS-REFERENCES Lessons In Electric Circuits. You need not possess all items listed above in order to effectively learn about resistance. chapter 1: "Basic Concepts of Electricity" Lessons In Electric Circuits. However. Volume 1. do not attempt to measure the resistance of a battery or any other source of substantial voltage using a multimeter set to the resistance ("ohms") function.2 Ohmmeter usage PARTS AND MATERIALS • Multimeter. be sure to never measure the resistance of any electrically "live" object or circuit. Conversely. Failing to heed this warning will likely result in meter damage and even personal injury. Radio Shack catalog # 276-1101) • Cadmium Sulphide photocell (Radio Shack catalog # 276-1657) • Breadboard (Radio Shack catalog # 276-174 or equivalent) • Jumper wires • Paper • Pencil • Glass of water • Table salt This experiment describes how to measure the electrical resistance of several objects. Volume 1. chapter 8: "DC Metering Circuits" LEARNING OBJECTIVES • Determination and comprehension of "electrical continuity" • Determination and comprehension of "electrically common points" • How to measure resistance • Characteristics of resistance: existing between two points • Selection of proper meter range • Relative conductivity of various components and materials . In other words. digital or analog • Assorted resistors (Radio Shack catalog # 271-312 is a 500-piece assortment) • Rectifying diode (1N4001 or equivalent.20 CHAPTER 2. you need not limit your experiments to these items. BASIC CONCEPTS AND TEST EQUIPMENT 2.
the meter should register 0 ohms of resistance. and return to its resting position when the probes are pulled apart. What would we say about a piece of wire if the ohmmeter needle didn't move at all when the probes were connected to opposite ends? Digital multimeters set to the "resistance" mode indicate non-continuity by displaying some non-numerical indication on the display. Use your meter to determine continuity between the holes on a breadboard : a device used for temporary construction of circuits." that unit symbolized by the capital Greek letter omega (Ω). or sometimes by the word "ohms. The resistance scale on an analog multimeter is reverse-printed from the other scales: zero resistance in indicated at the far right-hand side of the scale. OHMMETER USAGE ILLUSTRATION 21 Incandescent lamp Diode Photocell Resistor Resistor INSTRUCTIONS Resistance is the measure of electrical "friction" as electrons move through a conductor. inserted into the holes of the breadboard. while others display dashed lines. Touch the test probes together and move this adjustment until the needle exactly points to zero at the right-hand end of the scale. you will notice the needle deflect full-scale when the probes are touched together. to connect the meter to these spring clips so that you can test for continuity: . Use small pieces of 22-gauge solid copper wire. for instance." Touch the two test probes of your meter together. When you do. You can. where component terminals are inserted into holes on a plastic grid.2. test the continuity of a piece of wire by connecting the meter probes to opposite ends of the wire and checking to see the the needle moves full-scale. There should also be a small adjustment knob or "wheel" on the analog multimeter to calibrate it for "zero" ohms of resistance. Some models say "OL" (Open-Loop). metal spring clips underneath each hole connecting certain holes to others. and infinite resistance is indicated at the far left-hand side. Although your multimeter is capable of providing quantitative values of measured resistance. If you are using an analog meter. The resistance function is usually denoted by the unit symbol for resistance: the Greek letter omega (Ω). Set your multimeter to the highest resistance range available. It is measured in the unit of the "Ohm.2. it is also useful for qualitative tests of continuity: whether or not there is a continuous electrical connection from one point to another.
22 CHAPTER 2. BASIC CONCEPTS AND TEST EQUIPMENT Continuity! Analog meter - + 22-gauge wire 22-gauge wire Breadboard .
while commonality describes how the points themselves relate to each other. Black. is that of points being electrically common to each other. commonality is a qualitative assessment. Other resistors use five color bands to denote their value and precision. the first one being that there will never be substantial voltage dropped between points that are electrically common to each other. that points within a breadboard column (vertical in the illustrations) are electrically common to each other. because there are certain facts regarding voltage in relation to electrically common points that are valuable in circuit analysis and troubleshooting. Conversely. and a fifth color for . because there is no continuity between them. Select a 10. which marks them as +/.2. in which case the colors for a 10 kΩ resistor will be Brown. closely related to electrical continuity. Gold (+/. Black. because there is electrical continuity between them.000 ohm (10 kΩ) resistor from your parts assortment. We could say.20%. Electrically common points are points of contact on a device or in a circuit that have negligible (extremely small) resistance between them. Red. breadboard points within a row (horizontal in the illustrations) are not electrically common. based on a relative comparison of resistance between other points in a circuit. Like continuity. Black. Orange. Continuity describes what is between points of contact.10%). This resistance value is indicated by a series of color bands: Brown. It is an important concept to grasp. then. OHMMETER USAGE 23 No continuity Analog meter - + 22-gauge wire 22-gauge wire Breadboard An important concept in electricity.5%) or Silver (+/. Some resistors have no color for precision. and then another color representing the precision of the resistor.2.
Connect the meter's test probes across the resistor as such. BASIC CONCEPTS AND TEST EQUIPMENT precision. as they are often sharpened to a needle-point. but it may be more severe when measuring other values of resistor. you should see a numerical figure close to 10 shown on the display. you will be measuring the parallel combination of the resistor and your own body.24 CHAPTER 2. Try wetting your fingers with water and re-measuring resistance with the meter. Try reversing the test probe connections on the resistor. Some digital meters are manually-ranged. as your body resistance tends to be greater than 10. try not to touch both probe tips to your fingers. and the other probe tip with the fingers of the other hand. just as you needed to select an appropriate voltage range when reading the voltage of a battery. What impact does this . Does this change the meter's indication at all? What does this tell us about the resistance of a resistor? What happens when you only touch one probe to the resistor? What does this tell us about the nature of resistance. this error will be minimal. you need to select a lower resistance range on the meter. experiment with different range switch positions and see which one gives you the best indication. If yours is like this. and require appropriate range selection just as the analog meter. with a small "k" symbol on the right-hand side denoting the metric prefix for "kilo" (thousand). If you do.000 ohms hand-to-hand. Note: be very careful with the probes. and how it is measured? How does this compare with voltage measurement. not at the very points! You may need to adjust the meter range again after measuring the 10 kΩ resistor. If you are using a digital multimeter. and what happened when we tried to measure battery voltage by touching only one probe to the battery? When you touch the meter probes to the resistor terminals. which will tend to make the meter indication lower than it should be! When measuring a 10 kΩ resistor. You may safely measure the resistance of your own body by holding one probe tip with the fingers of one hand. and note its indication on the resistance scale: Analog meter Resistor - + If the needle points very close to zero. Hold the probe tips along their length.
OHMMETER USAGE 25 have on the indication? Try wetting your fingers with saltwater prepared using the glass of water and table salt. The less resistance there is between two points. Does it increase or decrease with decreased probe spacing? If the results are inconsistent. Measure resistance on the black strip with your meter.2. especially in contrast to the resistor? Take a piece of paper and draw a very heavy black mark on it with a pencil (not a pen!). and increased body resistance acts as a safeguard by making it more difficult for electrons to flow through us.2. What impact does this have on your body's resistance as measured by the meter? Resistance is the measure of friction to electron flow through an object. What does this teach you about resistance versus length of a conductive material? . the harder it is for electrons to move (flow) between those two points. Try reversing the test probe connections to the diode and re-measure resistance. what can we ascertain about electrical safety from the resistance readings obtained with wet fingers? Does water increase or decrease shock hazard to people? Measure the resistance of a rectifying diode with an analog meter. What strikes you as being remarkable about the diode. so that it is consistent in its density. and re-measuring resistance. placing the probe tips at each end of the mark like this: - + Mark made with pencil Paper Move the probe tips closer together on the black mark and note the change in resistance value. Given that electric shock is caused by a large flow of electrons through a person's body. you need to redraw the mark with more and heavier pencil strokes.
you may want to use alligator-clip jumper wires to make connection with the component. Just as with the light-emitting diode (LED) of the voltmeter experiment. clean water. rubber. dirty water. salt water. wood. .26 CHAPTER 2. paper. diamond (on a diamond ring or other piece of jewelry). just be sure not to try measure anything that produces substantial voltage. and oil. metal. leaving your hands free to hold the photocell to a light source and/or change meter ranges: Light source Photocell - + Experiment with measuring the resistance of several different types of materials. plastic. like a battery. BASIC CONCEPTS AND TEST EQUIPMENT Connect your meter to the terminals of a cadmium-sulphide (CdS) photocell and measure the change in resistance created by differences in light exposure. Suggestions for materials to measure are: fabric. glass.
Volume 1. In all subsequent illustrations. chapter 1: "Basic Concepts of Electricity" LEARNING OBJECTIVES • Essential configuration needed to make a circuit • Normal voltage drops in an operating circuit • Importance of continuity to a circuit • Working definitions of "open" and "short" circuits • Breadboard usage • Terminal strip usage SCHEMATIC DIAGRAM Battery Lamp ILLUSTRATION .3. a digital multimeter will be shown instead of an analog meter unless there is some particular reason to use an analog meter. You are encouraged to use both types of meters to gain familiarity with the operation of each in these experiments. a multimeter is assumed to be necessary and will not be included in the required list of parts and materials. A VERY SIMPLE CIRCUIT 27 2. CROSS-REFERENCES Lessons In Electric Circuits.2.3 A very simple circuit PARTS AND MATERIALS • 6-volt battery • 6-volt incandescent lamp • Jumper wires • Breadboard • Terminal strip From this experiment on.
This is not true! + Battery - No light! Lamp break in circuit + Battery - break in circuit No light! Lamp . assuming the battery and lamp are both in good condition and they are matched to one another in terms of voltage. that the wire connecting the negative terminal of the battery to the lamp is more important to circuit operation than the other wire providing a return path for electrons back to the battery. the lamp will fail to light. If there is a "break" (discontinuity) anywhere in the circuit. Connect the lamp to the battery as shown in the illustration.28 CHAPTER 2. It does not matter where such a break occurs! Many students assume that because electrons leave the negative (-) side of the battery and continue through the circuit to the positive (+) side. BASIC CONCEPTS AND TEST EQUIPMENT + Battery Lamp INSTRUCTIONS This is the simplest complete circuit in this collection of experiments: a battery and an incandescent lamp. and the lamp should light.
and across each jumper wire. Now. measure voltage across the battery.3. "break" the circuit at one point and re-measure voltage between the same sets of points.2. A VERY SIMPLE CIRCUIT 29 break in circuit + Battery No light! Lamp break in circuit + Battery No light! Lamp Using your multimeter set to the appropriate "DC volt" range. additionally measuring voltage across the break like this: . across the lamp. Familiarize yourself with the normal voltages in a functioning circuit.
Construct the same circuit on a breadboard. taking care to place the lamp and wires into the breadboard in such a way that continuity will be maintained. and break the circuit in another place. as indicated by the meter? Re-connect the jumper wire to the lamp. BASIC CONCEPTS AND TEST EQUIPMENT V V OFF A A A COM + Battery - No light! Lamp What voltages measure the same as before? What voltages are different since introducing the break? How much voltage is manifest.30 CHAPTER 2. The example shown here is only that: an example. not the only way to build a circuit on a breadboard: . Measure all voltage "drops" again. or dropped across the break? What is the polarity of the voltage drop across the break. familiarizing yourself with the voltages of an "open" circuit.
Experiment with different configurations on the breadboard, plugging the lamp into different holes. If you encounter a situation where the lamp refuses to light up and the connecting wires are getting warm, you probably have a situation known as a short circuit, where a lower-resistance path than the lamp bypasses current around the lamp, preventing enough voltage from being dropped across the lamp to light it up. Here is an example of a short circuit made on a breadboard:
No light!
"shorting" wire
Here is an example of an accidental short circuit of the type typically made by students unfamiliar with breadboard usage:
No light!
Here there is no "shorting" wire present on the breadboard, yet there is a short circuit, and the lamp refuses to light. Based on your understanding of breadboard hole connections, can you determine where the "short" is in this circuit? Short circuits are generally to be avoided, as they result in very high rates of electron flow, causing wires to heat up and battery power sources to deplete. If the power source is substantial enough, a short circuit may cause heat of explosive proportions to manifest, causing equipment damage and hazard to nearby personnel. This is what happens when a tree limb "shorts" across wires on a power line: the limb – being composed of wet wood – acts as a low-resistance path to electric current, resulting in heat and sparks. You may also build the battery/lamp circuit on a terminal strip: a length of insulating material with metal bars and screws to attach wires and component terminals to. Here is an example of how this circuit might be constructed on a terminal strip:
Terminal strip
Ammeter usage
PARTS AND MATERIALS • 6-volt battery • 6-volt incandescent lamp Basic circuit construction components such as breadboard, terminal strip, and jumper wires are also assumed to be available from now on, leaving only components and materials unique to the project listed under "Parts and Materials."
CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 1: "Basic Concepts of Electricity" Lessons In Electric Circuits, Volume 1, chapter 8: "DC Metering Circuits"
LEARNING OBJECTIVES • How to measure current with a multimeter • How to check a multimeter's internal fuse • Selection of proper meter range
Ammeter A Battery Lamp
+ Battery
INSTRUCTIONS Current is the measure of the rate of electron "flow" in a circuit. It is measured in the unit of the Ampere, simply called "Amp," (A). The most common way to measure current in a circuit is to break the circuit open and insert an "ammeter" in series (in-line) with the circuit so that all electrons flowing through the circuit also have to go through the meter. Because measuring current in this manner requires the meter be made part of the circuit, it is a more difficult type of measurement to make than either voltage or resistance. Some digital meters, like the unit shown in the illustration, have a separate jack to insert the red test lead plug when measuring current. Other meters, like most inexpensive analog meters, use the same jacks for measuring voltage, resistance, and current. Consult your owner's manual on the particular model of meter you own for details on measuring current. When an ammeter is placed in series with a circuit, it ideally drops no voltage as current goes through it. In other words, it acts very much like a piece of wire, with very little resistance from one test probe to the other. Consequently, an ammeter will act as a short circuit if placed in parallel (across the terminals of) a substantial source of voltage. If this is done, a surge in current will result, potentially damaging the meter:
current surge + Battery SHORT CIRCUIT ! current surge
Ammeters are generally protected from excessive current by means of a small fuse located inside the meter housing. If the ammeter is accidently connected across a substantial voltage source, the resultant surge in current will "blow" the fuse and render the meter incapable of measuring current until the fuse is replaced. Be very careful to avoid this scenario!
You may test the condition of a multimeter's fuse by switching it to the resistance mode and measuring continuity through the test leads (and through the fuse). On a meter where the same test lead jacks are used for both resistance and current measurement, simply leave the test lead plugs where they are and touch the two probes together. On a meter where different jacks are used, this is how you insert the test lead plugs to check the fuse:
Low resistance indication = good fuse High resistance indication = "blown" fuse V V
Internal location of fuse
touch probes together
Build the one-battery, one-lamp circuit using jumper wires to connect the battery to the lamp, and verify that the lamp lights up before connecting the meter in series with it. Then, break the circuit open at any point and connect the meter's test probes to the two points of the break to measure current. As usual, if your meter is manually-ranged, begin by selecting the highest range for current, then move the selector switch to lower range positions until the strongest indication is obtained on the meter display without over-ranging it. If the meter indication is "backwards," (left motion on analog needle, or negative reading on a digital display), then reverse the test probe connections and try again. When the ammeter indicates a normal reading (not "backwards"), electrons are entering the black test lead and exiting the red. This is how you determine direction of current using a meter. For a 6-volt battery and a small lamp, the circuit current will be in the range of thousandths of an amp, or milliamps. Digital meters often show a small letter "m" in the right-hand side of the display to indicate this metric prefix. Try breaking the circuit at some other point and inserting the meter there instead. What do you notice about the amount of current measured? Why do you think this is? Re-construct the circuit on a breadboard like this:
. • Insert a spare piece of wire into the hole you just pulled the other wire or terminal out of.38 CHAPTER 2. Leave it hanging in mid-air. You are now assured of measuring current through the wire or terminal initially identified. • Connect the ammeter between the two unconnected wire ends (the two that were hanging in mid-air). • Pull that wire or terminal out of the breadboard hole. BASIC CONCEPTS AND TEST EQUIPMENT + - Breadboard Students often get confused when connecting an ammeter to a breadboard circuit. Leave the other end of this wire hanging in mid-air. How can the meter be connected so as to intercept all the circuit's current and not create a short circuit? One easy method that guarantees success is this: • Identify what wire or component terminal you wish to measure current through.
2. following the same connection procedure outlined above. What do you notice about these current measurements? The results in the breadboard circuit should be the same as the results in the free-form (no breadboard) circuit.4. AMMETER USAGE 39 m V wire pulled out of breadboard + A COM A A OFF V spare wire Again. measure current through different wires in this circuit. Building the same circuit on a terminal strip should also yield similar results: .
If the current for your circuit is a different value.70 mA) shown in the illustrations is an arbitrary quantity. If the lamp refuses to light when the meter is connected to the circuit. . that is okay.70 milliamps (24. reasonable for a small incandescent lamp.40 CHAPTER 2. If your lamp refuses to light when the meter is connected in the circuit. Check the condition of your meter's fuse as described previously in this section and replace the fuse if necessary. and the meter registers a much greater reading. you've probably blown the fuse inside the meter. and the meter registers zero current. you probably have a short-circuit condition through the meter. so long as the lamp is functioning when the meter is connected. BASIC CONCEPTS AND TEST EQUIPMENT m V + V OFF A A A COM Terminal strip The current figure of 24.
2. OHM'S LAW 41 2. the internal resistance of the voltmeter substantially changing circuit resistance when it is connected in parallel with a high-value resistor. but not enough to cause serious disagreement with calculated values.5. At the recommended resistance values. there will still be a small amount of measurement error due to the "impact" of the meter. Very high resistance values can cause problems for voltage measurement. the internal resistance of the ammeter has a significant impact on measurement accuracy.5 Ohm's Law PARTS AND MATERIALS • Calculator (or pencil and paper for doing arithmetic) • 6-volt battery • Assortment of resistors between 1 KΩ and 100 kΩ in value I'm purposely restricting the resistance values between 1 kΩ and 100 kΩ for the sake of obtaining accurate voltage and current readings with your meter. With very low resistance values. Volume 1. CROSS-REFERENCES Lessons In Electric Circuits. chapter 2: "Ohm's Law" LEARNING OBJECTIVES • Voltmeter use • Ammeter use • Ohmmeter use • Use of Ohm's Law SCHEMATIC DIAGRAM Ammeter A Battery Resistor V Voltmeter ILLUSTRATION .
Be sure not to hold the resistor terminals when measuring resistance. one-resistor circuit. Build a one-battery. Set your multimeter to the appropriate voltage range and measure voltage across the resistor as it is being powered by the battery. BASIC CONCEPTS AND TEST EQUIPMENT Ammeter V + V OFF A A A COM Terminal strip Resistor V V OFF A A Voltmeter A COM INSTRUCTIONS Select a resistor from the assortment. or else your hand-to-hand body resistance will influence the measurement! Record this resistance value for future use. Record this voltage value along with the resistance value previously measured. but any form of circuit construction is okay. Select the best current range: whichever one gives the strongest meter indication without . A terminal strip is shown in the illustration. Break the circuit and connect the ammeter within that break. and measure its resistance with your multimeter set to the appropriate resistance range.42 CHAPTER 2. in series with the battery and resistor. so it becomes a part of the circuit. Set your multimeter to the highest current range available.
These differences should be rather small. voltage. are more accurate than others! Substitute different resistors in the circuit and re-take all resistance. Record this current value along with the resistance and voltage values previously recorded. because it is the nature of a battery to maintain voltage at a constant level. OHM'S LAW 43 over-ranging the meter. use the Ohm's Law equation to calculate circuit current. no more than several percent. you need not bother with setting ranges. Compare this calculated figure with the measured figure for circuit voltage: Ohm's Law (solving for voltage) E = IR There should be close agreement between all measured and all calculated figures. Some meters. and current measurements. Taking the measured figures for voltage and resistance. If your multimeter is autoranging.2. of course. Compare this calculated figure with the measured figure for circuit current: Ohm's Law (solving for current) I= Where. Compare this calculated figure with the measured figure for circuit resistance: E R Ohm's Law (solving for resistance) R= E I Finally.5. Voltage should remain approximately the same for any resistor size inserted into the circuit. current. Any differences in respective quantities of voltage. use the Ohm's Law equation to calculate circuit voltage. Re-calculate these figures and check for agreement with the experimental data (measured quantities). of course. taking the measured figures for resistance and current. E = Voltage in volts I = Current in amps R = Resistance in ohms Taking the measured figures for voltage and current. or resistance are most likely due to meter inaccuracies. use the Ohm's Law equation to calculate circuit resistance. . Also note the simple mathematical relationship between changes in resistor value and changes in circuit current.
44 CHAPTER 2.6 Nonlinear resistance PARTS AND MATERIALS • Calculator (or pencil and paper for doing arithmetic) • 6-volt battery • Low-voltage incandescent lamp (Radio Shack catalog # 272-1130 or equivalent) CROSS-REFERENCES Lessons In Electric Circuits. BASIC CONCEPTS AND TEST EQUIPMENT 2. Volume 1. chapter 2: "Ohm's Law" LEARNING OBJECTIVES • Voltmeter use • Ammeter use • Ohmmeter use • Use of Ohm's Law • Realization that some resistances are unstable! • Scientific method SCHEMATIC DIAGRAM Ammeter A Battery Lamp V Voltmeter ILLUSTRATION .
you need not bother with setting ranges. NONLINEAR RESISTANCE 45 Ammeter V + V OFF A A A COM Terminal strip Lamp V V OFF A Voltmeter A A COM INSTRUCTIONS Measure the resistance of the lamp with your multimeter. Record this resistance value for future use. so it becomes a part of the circuit. Build a one-battery. Select the best current range: whichever one gives the strongest meter indication without overranging the meter.6. but less than any of the resistors from the last experiment. Record this current value along with the resistance and voltage values previously recorded. Break the circuit and connect the ammeter within that break.2. in series with the battery and lamp. Record this voltage value along with the resistance value previously measured. If your multimeter is autoranging. Set your multimeter to the highest current range available. It has substantially more resistance than a jumper wire. This resistance figure is due to the thin metal "filament" inside the lamp. Set your multimeter to the appropriate voltage range and measure voltage across the lamp as it is energized (lit). of course. . one-lamp circuit.
or between resistance measurements taken with different types of meters? This problem is a good test case for the application of scientific method. Usually. try measuring the lamp's resistance again. Compare this calculated figure with the measured figure for circuit current: Ohm's Law (solving for current) I= Where. BASIC CONCEPTS AND TEST EQUIPMENT Taking the measured figures for voltage and resistance. If not. You will need to disconnect the lamp from the battery circuit in order to obtain a resistance reading. and that this accounts for the difference between the measured and calculated circuit currents. E = Voltage in volts I = Current in amps R = Resistance in ohms What you should find is a marked difference between measured current and calculated current: the calculated figure is much greater. If you measure substantial resistance change as a result of light exposure. when lit). because voltages outside of the meter interfere with resistance measurement.46 CHAPTER 2. then your hypothesis has some evidential support. Once you've thought of a possible reason for the lamp's resistance changing between lit and unlit conditions. and how might those factors be different between conditions of lit and unlit. Why? What factor(s) might influence the resistance of the lamp filament. This is a general rule that should be remembered: measure resistance only on an unpowered component! Using a different ohmmeter. For example. try to duplicate that cause by some other means. Why is this? To make things more interesting. E R . analog meters give higher lamp resistance readings than digital meters. then your hypothesis has been falsified. This behavior is very different from that of the resistors in the last experiment. try exposing the lamp to an external source of light while measuring its resistance. and another cause must be responsible for the change in circuit current. the lamp will probably register as a different value of resistance. this time using a different model of meter. use the Ohm's Law equation to calculate circuit current. if you think the lamp resistance might change as it is exposed to light (its own light.
7. the type used to take body temperature. Black. but within five percent of the figures specified (+/. Black.5 Ω for the 10 Ω resistor. Do not use any battery size other than 6 volts for this experiment. Brown. I recommend a medical thermometer. • Small thermometer The resistor values need not be exact. Orange. Color codes for 5% tolerance 10 Ω and 330 Ω resistors are as follows: Brown. +/. Gold (330.0.5%). to facilitate rapid detection of heat produced by the resistor. chapter 2: "Ohm's Law" LEARNING OBJECTIVES • Voltmeter use • Ammeter use • Ohmmeter use • Use of Joule's Law • Importance of component power ratings • Significance of electrically common points SCHEMATIC DIAGRAM ILLUSTRATION . POWER DISSIPATION 47 2. Volume 1. The thermometer should be as small as possible.7 Power dissipation PARTS AND MATERIALS • Calculator (or pencil and paper for doing arithmetic) • 6 volt battery • Two 1/4 watt resistors: 10 Ω and 330 Ω.16. +/. +/. Gold (10. CROSS-REFERENCES Lessons In Electric Circuits.5 Ω for the 330 Ω resistor).2.5%). and Orange.
and the other side of the resistor is directly connected to the other side of the battery. Voltage may be measured directly across the battery. You might be wondering why I advise no bodily contact with the powered resistor. . since those two components share the same set of electrically common points: one side of the resistor is directly connected to one side of the battery. or directly across the resistor. measure voltage with a voltmeter. BASIC CONCEPTS AND TEST EQUIPMENT Thermometer - + Caution: do not hold resistor with your fingers while powered! INSTRUCTIONS Measure each resistor's resistance with your ohmmeter.48 CHAPTER 2. This is because it will become hot when powered by the battery. Battery voltage is the same as resistor voltage in this circuit. You will use the thermometer to measure the temperature of each resistor when powered. noting the exact values on a piece of paper for later reference. With the 330 Ω resistor connected to the battery. Connect the jumper wires to the resistor terminals before connecting the other ends to the battery. Connect the 330 Ω resistor to the 6 volt battery using a pair of jumper wires as shown in the illustration. there is more than one way to obtain a proper reading. In measuring voltage. This will ensure your fingers are not touching the resistor when battery power is applied.
measure current through the circuit. however. make a break in the circuit. there is no one "correct" way to measure current. Voltage measured between any point on the upper wire and any point on the lower wire should be the same. Again. All points of contact along the lower wire (colored black) are likewise electrically common to each other. One viable option is shown in the following illustration: .2.7. and place the ammeter within that break: connect the two test probes to the two wire or terminal ends left open from the break. To do this. should be zero. Voltage measured between any two common points. POWER DISSIPATION 49 V V OFF A A A COM lly common ec tr i point ca s ele + - el ctr ica lly co mm on points All points of contact along the upper wire in the illustration (colored red) are electrically common to each other. so long as the ammeter is placed within the flow-path of electrons through the resistor and not across a source of voltage. Using an ammeter.
Whereas voltage is the measure of electrical "push" motivating electrons to move through a circuit. power is symbolized by the letter "P" and measured in the unit of the Watt (W). Any way you calculate it. BASIC CONCEPTS AND TEST EQUIPMENT V V OFF A A A COM + - Now that you've measured and recorded resistor resistance. the power dissipation figure should be roughly the same. current. . and current is the measure of electron flow rate. power is the measure of work-rate: how fast work is being done in the circuit. Power may be calculated by any one of three equations – collectively referred to as Joule's Law – given any two out of three quantities of voltage. In mathematical equations.50 CHAPTER 2. and power is a description of how rapidly that work is taking place. current. using the three measured values of voltage. It takes a certain amount of work to push electrons through a resistance. circuit voltage. and circuit current. and resistance. you are ready to calculate power dissipation. and resistance: Joule's Law (solving for power) P = IE P = I2R P= E2 R Try calculating power in this circuit.
The power rating of any electrical component does not tell us how much power it will dissipate. it is more than capable of sustaining this level of power dissipation. we find that a 10 Ω resistor connected to a 6 volt battery dissipates about 3. that component will increase temperature to the point of damage. disconnect the 330 Ω resistor and replace it with the 10 Ω resistor. to use a metric prefix. Performing some Joule's Law calculations for resistor power again. avoid touching the resistor once the circuit is complete. as it will heat up rapidly. then disconnect the 330 Ω resistor from the two alligator clips.5 Ω). then connect the 10 Ω resistor between the two clips. but simply how much power it may dissipate without sustaining damage.0909 milli-watts (mW). and finally reconnect the jumper wire back to the battery terminal. Caution: keep the 10 Ω resistor away from any flammable materials when it is powered by the battery! You may not have enough time to take voltage and current measurements before the resistor begins to smoke. cooling it down again.4 times its rated power dissipation. or 250 mW).2.6 watts of power. Little wonder it smokes so quickly after connection to the battery! . re-connect the jumper wire and let it smoke a bit more. or 109. as an increased resistance results in less current and (generally) less power dissipation.25 watts. If the actual amount of dissipated power exceeds a component's power rating. disconnect one of the jumper wires from a battery terminal to interrupt circuit current. This is often a self-protective mode of failure. Touch the thermometer end to the middle of the resistor and see how warm it gets.7. about 14. and give the resistor a few moments to cool down. measure the resistor's resistance with an ohmmeter and note any substantial deviation from its original value.1090909 watts. What trend do you notice with the resistor's value as it is damaged more and more by overpowering? It is typical of resistors to fail with a greater-than-normal resistance when overheated. At the first sign of distress.000 volts and a resistor of exactly 330 Ω. the resistor should become noticeably warm but it should not over heat. Again.5% of its advertised value (between 9. the resistor's normal resistance value will not return if sufficiently damaged. POWER DISSIPATION 51 Assuming a battery with 6. To illustrate. Since the resistor has a power rating of 1/4 watt (0.5 and 10. the power dissipation will be 0. The safest way to do this is to disconnect one jumper wire from a battery terminal. Because the actual power level is almost half the rated power. If the resistor still measures within +/. However. With power still disconnected.
22-gauge or larger • Household light switch (these are readily available at any hardware store) Household light switches are a bargain for students of basic electricity. and almost impossible to damage with battery power.8 Circuit with a switch PARTS AND MATERIALS • 6-volt battery • Low-voltage incandescent lamp (Radio Shack catalog # 272-1130 or equivalent) • Long lengths of wire. just the simple on-off "toggle" variety used for ordinary household wall-mounted light controls. Do not get "dimmer" switches. very inexpensive. BASIC CONCEPTS AND TEST EQUIPMENT 2.52 CHAPTER 2. CROSS-REFERENCES Lessons In Electric Circuits. chapter 1: "Basic Concepts of Electricity" LEARNING OBJECTIVES • Switch behavior • Using an ohmmeter to check switch action SCHEMATIC DIAGRAM Switch ILLUSTRATION Switch + - . Volume 1. They are readily available.
Measure voltage across the battery. as it shows how the switch is able to control circuit current no matter how physically large the circuit may be.8. and across the lamp with the switch in both positions. any break in the circuit at any location causes the lamp to immediately de-energize (darken). one-lamp circuit as shown in the schematic diagram and in the illustration. As before. This circuit is most impressive when the wires are long. across the switch (measure from one screw terminal to another with the voltmeter). . When the switch is turned off. CIRCUIT WITH A SWITCH 53 INSTRUCTIONS Build a one-battery. and the lamp will go out just the same as if a wire were pulled loose from a terminal. one-switch.2. it is said to be open.
CROSS-REFERENCES Lessons In Electric Circuits. You will need enough magnet wire to wrap hundreds of turns around the bolt. chapter 14: "Magnetism and Electromagnetism" LEARNING OBJECTIVES • Application of the left-hand rule • Electromagnet construction SCHEMATIC DIAGRAM ILLUSTRATION . Stainless steel. for example.9 Electromagnetism PARTS AND MATERIALS • 6-volt battery • Magnetic compass • Small permanent magnet • Spool of 28-gauge magnet wire • Large bolt. nail. but any commonly available steel will suffice. Be sure to select a bolt. nail. or steel rod • Electrical tape Magnet wire is a term for thin-gauge copper wire with enamel insulation instead of rubber or plastic insulation.54 CHAPTER 2. nail. Volume 1. or other rod-shaped steel form. or rod that is magnetic. is non-magnetic and will not function for the purpose of an electromagnet coil! The ideal material for this experiment is soft iron. Its small size and very thin insulation allow for many "turns" to be wound in a compact coil. BASIC CONCEPTS AND TEST EQUIPMENT 2.
Electromagnetism has many applications. even manner.9. or mail) to protect the wire from abrasion. solenoids. including relays. it will produce a strong magnetic field: one "pole" at each end of the rod. This phenomenon will be explored in greater detail in the next chapter (DC Circuits). The only rule you must follow is that all turns must be wrapped around the bar in the same direction (no reversing from clockwise to counter-clockwise!). Scrape the enamel insulation off the ends of the coil wires for connection to jumper leads. . You might notice a significant spark whenever the battery is disconnected from the electromagnet coil: much greater than the spark produced if the battery is simply short-circuited. wrap a layer or two of electrical tape over the wire coil to secure the wire in place. computer printer mechanisms. place a permanent magnet near one pole and note whether there is an attractive or repulsive force. The effect is known as inductive "kickback" and is capable of delivering a small but harmless electric shock! To avoid receiving this shock. and magnetic media "write" heads (tape recorders.2. This spark is the result of a high-voltage surge created whenever current is suddenly interrupted through the coil. and it is okay to wrap in the same style that a fishing reel wraps line around the spool. When electric current goes through the coil. doorbells. then turn the drill motor on at a slow speed and let it do the wrapping! This allows you to feed wire onto the rod in a very steady. ELECTROMAGNETISM 55 Compass N W E S Electromagnet (wire coil wrapped around steel bar) + - INSTRUCTIONS Wrap a single layer of electrical tape around the steel bar (or bolt. This phenomenon is known as electromagnetism. making the coil as even as possible. Proceed to wrap several hundred turns of wire around the steel bar. buzzers. then connect the coil to a battery. After you've wrapped several hundred turns of wire around the rod. I find that a drill press works as a great tool for coil winding: clamp the rod in the drill's chuck as if it were a drill bit. do not place your body across the break in the circuit when de-energizing! Use one hand at a time when un-powering the coil and you'll be perfectly safe. It is okay to overlap wire. Reverse the orientation of the permanent magnet and note the difference in force. The magnetic compass is used to identify the "North" and "South" poles of the electromagnet. With the electromagnet energized (connected to the battery). disk drives). electric motors.
56 CHAPTER 2.10 Electromagnetic induction PARTS AND MATERIALS • Electromagnet from previous experiment • Permanent magnet See previous experiment for instructions on electromagnet construction. BASIC CONCEPTS AND TEST EQUIPMENT 2. CROSS-REFERENCES Lessons In Electric Circuits. Volume 1. chapter 14: "Magnetism and Electromagnetism" LEARNING OBJECTIVES • Relationship between magnetic field strength and induced voltage SCHEMATIC DIAGRAM + Voltmeter V ILLUSTRATION V V OFF A A Electromagnet A COM Magnet N S INSTRUCTIONS .
we produce electricity from a magnetic field.2. ELECTROMAGNETIC INDUCTION 57 Electromagnetic induction is the complementary phenomenon to electromagnetism. Move the magnet slowly to and from one end of the electromagnet. Try the other end of the coil and compare results. Instead of producing a magnetic field from electricity. electromagnetic induction requires motion between the magnet and the coil to produce a voltage.10. . There is one important difference. as the magnetic field from the permanent magnet may affect the meter's operation and produce false readings. Try the other end of the permanent magnet and compare. Experiment with moving the magnet. Digital meters are unaffected by magnetic fields. Connect the multimeter to the coil. though: whereas electromagnetism produces a steady magnetic field from a steady electric current. and discover for yourself what factor(s) determine the amount of voltage induced. noting the polarity and magnitude of the induced voltage. and set it to the most sensitive DC voltage range available. If using an analog multimeter. be sure to use long jumper wires and locate the meter far away from the coil.
which can refer to either voltage or current in a constant polarity or direction. 59 . respectively.1 Introduction "DC" stands for Direct Current.Chapter 3 DC CIRCUITS 3. These experiments are designed to introduce you to several important concepts of electricity related to DC circuits.
any size batteries will suffice for this experiment. Volume 1. DC CIRCUITS 3. chapter 5: "Series and Parallel Circuits" Lessons In Electric Circuits. Volume 1. but it is recommended to have at least two different voltages available to make it more interesting.60 CHAPTER 3. CROSS-REFERENCES Lessons In Electric Circuits. chapter 11: "Batteries and Power Systems" LEARNING OBJECTIVES • How to connect batteries to obtain different voltage levels SCHEMATIC DIAGRAM + + + V Voltmeter - ILLUSTRATION .2 Series batteries PARTS AND MATERIALS • Two 6-volt batteries • One 9-volt battery Actually.
3. Measure the voltage across each battery individually as they are connected. then measure the total voltage across them both. SERIES BATTERIES 61 + - V V OFF A A A COM + - INSTRUCTIONS Connecting components in series means to connect them in-line with each other. like this: . so that there is but a single path for electrons to flow through them all.2. you will find that their respective voltages add. If you connect batteries so that the positive of one connects to the negative of the other.
Can you predict what the overall voltage polarity will be. black=positive). for instance a 6-volt battery with a 9-volt battery. What is the total voltage in this case? Try reversing the terminal connections of just one of these batteries. DC CIRCUITS V V OFF A A A COM + Measuring first battery Measuring total voltage + V V OFF A A A COM + - + + Measuring second battery V V OFF - A A A COM + - Try connecting batteries of different sizes in series with each other. if the indication is a negative number.62 CHAPTER 3. knowing the polarities of the individual batteries and their respective strengths? + V Voltmeter - . if the meter's digital indication is a positive number. Analog meters simply will not read properly if reverseconnected. so that they are opposing each other like this: + Seriesopposing + How does the total voltage compare in this situation to the previous one with both batteries "aiding?" Note the polarity of the total voltage as indicated by the voltmeter indication and test probe orientation. the red probe is positive (+) and the black probe negative (-). Remember. because the needle tries to move the wrong direction (left instead of right). the polarity is "backward" (red=negative.
CROSS-REFERENCES Lessons In Electric Circuits. PARALLEL BATTERIES 63 3.3 Parallel batteries PARTS AND MATERIALS • Four 6-volt batteries • 12-volt light bulb. chapter 5: "Series and Parallel Circuits" Lessons In Electric Circuits. 25 or 50 watt • Lamp socket High-wattage 12-volt lamps may be purchased from recreational vehicle (RV) and boating supply stores. Common sizes are 25 watt and 50 watt.3. Volume 1. This lamp will be used as a "heavy" load for your batteries (heavy load = one that draws substantial current). chapter 11: "Batteries and Power Systems" LEARNING OBJECTIVES • Voltage source regulation • Boosting current capacity through parallel connections SCHEMATIC DIAGRAM + - + - + - + - ILLUSTRATION + - + - + - + - INSTRUCTIONS . Volume 1. A regular household (120 volt) lamp socket will work just fine for these low-voltage "RV" lamps.3.
DC CIRCUITS Begin this experiment by connecting one 6-volt battery to the lamp. you will measure a low voltage there as well.64 CHAPTER 3. noting the lamp voltage with the addition of each new. should glow dimly when powered by the 6-volt battery. Add one battery at a time in parallel. The lamp. Use your voltmeter to read voltage across the lamp like this: + V V OFF - A A A COM The voltmeter should register a voltage lower than the usual voltage of the battery. and all negative (-) terminals common to each other as well. If you use your voltmeter to read the voltage directly at the battery terminals. parallel-connected battery: . so that each battery only has to supply a fraction of the total current demanded by the lamp. We may overcome this problem by connecting batteries in parallel with each other. Parallel connections involve making all the positive (+) battery terminals electrically common to each other by connection through jumper wires. designed to operate on 12 volts." due to voltage dropped across resistance internal to the battery. Why is this? The large current drawn by the high-power lamp causes the voltage at the battery terminals to "sag" or "droop.
Measuring total current involves a similar procedure: make a break somewhere in the path that total current must take. additional batteries . Shown here is the easiest way to measure single-battery current: V V OFF A A A COM + - + - + - + - By breaking the circuit for just one battery. .3. . Try measuring the current of one battery and comparing it to the total current (light bulb current). + + + + - V V OFF A A A COM There should also be a noticeable difference in light intensity as the voltage "sag" is improved. PARALLEL BATTERIES 65 .3. . . then insert the ammeter within than break: . we intercept the current of that one battery and are therefore able to measure it. and inserting our ammeter within that break.
To obtain maximum brightness from the light bulb.66 CHAPTER 3. a series-parallel connection is required. DC CIRCUITS + - + - + - + - V V OFF A A A COM Note the difference in current between the single-battery and total measurements. Two 6-volt batteries connected series-aiding will provide 12 volts. Connecting two of these seriesconnected battery pairs in parallel improves their current-sourcing ability for minimum voltage sag: + - + - + - + - .
With very low resistance values. the internal resistance of the ammeter has a significant impact on measurement accuracy.4 Voltage divider PARTS AND MATERIALS • Calculator (or pencil and paper for doing arithmetic) • 6-volt battery • Assortment of resistors between 1 KΩ and 100 kΩ in value I'm purposely restricting the resistance values between 1 kΩ and 100 kΩ for the sake of obtaining accurate voltage and current readings with your meter.4. Volume 1. CROSS-REFERENCES Lessons In Electric Circuits. the internal resistance of the voltmeter substantially changing circuit resistance when it is connected in parallel with a high-value resistor. Very high resistance values may cause problems for voltage measurement. chapter 6: "Divider Circuits and Kirchhoff's Laws" LEARNING OBJECTIVES • Voltmeter use • Ammeter use • Ohmmeter use • Use of Ohm's Law • Use of Kirchhoff's Voltage Law ("KVL") • Voltage divider design SCHEMATIC DIAGRAM R1 + R2 V Voltmeter - R3 . VOLTAGE DIVIDER 67 3.3.
DC CIRCUITS R1 R2 + - R3 Breadboard + - R2 Terminal strip R1 R3 .68 ILLUSTRATION CHAPTER 3.
Use Ohm's Law (I=E/R) to calculate circuit current." measuring battery voltage under load is a good scientific practice because it provides more realistic data. then verify this calculated value by measuring current with an ammeter like this ("terminal strip" version of the circuit shown as an arbitrary choice in construction method): . noting this voltage figure on paper as well. but appropriate for a simple experiment such as this. We saw this effect exaggerated in the "parallel battery" experiment while powering a high-wattage lamp: battery voltage tends to "sag" or "droop" under load. and "free-form. VOLTAGE DIVIDER 69 R1 R2 R3 + - "Free-form" construction INSTRUCTIONS Shown here are three different methods of circuit construction: on a breadboard. on a terminal strip. but is quite temporary. Breadboard construction is versatile and allows for high component density (many parts in a small space). Select three resistors from your resistor assortment and measure the resistance of each one with an ohmmeter. as shown in the illustrations.3. Terminal strips offer a much more permanent form of construction at the cost of low component density. It is advisable to measure battery voltage while it's powering the resistor circuit because this voltage may differ slightly from a no-load condition. for reference in your circuit calculations.4. and to the 6-volt battery. The "free-form" method – where all components are connected together with "alligator-" style jumper wires – is the least professional. Note these resistance values with pen and paper. Although this three-resistor circuit should not present a heavy enough load (not enough current drawn) to cause significant voltage "sag. Measure battery voltage with a voltmeter after the resistors have been connected to it." Try building the same circuit each way to familiarize yourself with the different construction techniques and their respective merits. Connect the three resistors in series.
there should be close agreement between the calculated and measured voltage figures. verifying the accuracy of your predictions. In the illustration. Switch you multimeter to the "voltage" mode and measure the voltage dropped across each resistor. or 3 volts. This fractional value is determined by the resistance of the particular resistor and the total resistance. An example using the numbers 0 through 3 is shown here in both illustrative and schematic form. Now. the meter may show the appropriate metric prefix symbol (m or µ) in some corner of the display. so pay close attention! The measured value of current should agree closely with your Ohm's Law calculation.70 CHAPTER 3. take that calculated value for current and multiply it by the respective resistances of each resistor to predict their voltage drops (E=IR). Each resistor voltage drop will be some fraction or percentage of the total voltage. These metric prefix telltales are easy to overlook when reading the display of a digital meter. Points that are electrically common (directly connected to each other with insignificant resistance between) must bear the same number. If a resistor drops 50% of the total battery voltage in a voltage divider circuit. The next part of this experiment is a validation of Kirchhoff's Voltage Law. DC CIRCUITS V V OFF A A A COM + - R2 R1 R3 If your resistor values are indeed between 1 kΩ and 100 kΩ. I show how points in the circuit may be labeled with small pieces of tape. in the milliamp (mA) or microamp (µA) range. For this. hence the name voltage divider given to this circuit. numbers . the current should be a very small value. that resistor will drop 10 volts. or 50% of 20 volts. and the battery voltage approximately 6 volts. the voltage across that resistor will be 50% of 6. Again. if the total voltage is 6 volts. When you measure current with a digital meter. So. If the total voltage is 20 volts. that proportion of 50% will remain the same as long as the resistor values are not altered. you need to identify each unique point in the circuit with a number.
Write on paper each of these voltages. VOLTAGE DIVIDER written on the tape: 71 0 3 + 3 R2 2 1 0 Terminal strip 3 R1 2 1 R3 0 3 R1 3 2 R2 1 R3 0 0 Using a digital voltmeter (this is important!). along with its respective sign as indicated by the meter." Mathematical sign is very significant in this phase of the experiment! Here is a sequence of illustrations showing how to "step around" the circuit loop.325 volts. In other words. starting and ending at point 0: . Do not reverse the meter probe connections with the circuit to make the number read "correctly.3. you should write that figure as a negative number. if the voltmeter registers a negative voltage such as -1. measure voltage drops around the loop formed by the points 0-1-2-3-0.4.
DC CIRCUITS Measure voltage from 1 to 0 0 3 + 3 R2 2 1 0 V V OFF A A A COM 3 R1 2 1 R3 0 Measure voltage from 2 to 1 0 3 + 3 R2 2 1 0 V V OFF A A A COM 3 R1 2 1 R3 0 .72 CHAPTER 3.
4. VOLTAGE DIVIDER 73 Measure voltage from 3 to 2 0 3 + 3 R2 2 1 0 V V OFF A A A COM 3 R1 2 1 R3 0 Measure voltage from 0 to 3 0 3 + 3 R2 2 1 0 V V OFF A A A COM 3 R1 2 1 R3 0 Using the voltmeter to "step" around the circuit in this manner yields three positive voltage figures and one negative: .3.
so long as it begins and ends with the same point. or even a legitimate current path at all. should equal zero. It is important to realize that the "loop" stepped around does not have to be the same path that current takes in the circuit. This is the fundamental principle of Kirchhoff's Voltage Law: that the algebraic sum of all voltage drops in a "loop" add to zero. algebraically added ("algebraically" = respecting the signs of the numbers). The loop in which we tally voltage drops can be any collection of points. we may measure and add the voltages in the loop 1-2-3-1. and they will form a sum of zero as well: 3 3-2 (+) 2-1 (+) 3 R1 2 R2 1 R3 1-3 (-) 0 0 . For example.74 CHAPTER 3. DC CIRCUITS 3 3-2 (+) 2-1 (+) 1-0 (+) 0 3 R1 2 R2 1 R3 0 0-3 (-) These figures.
4. VOLTAGE DIVIDER 75 Measure voltage from 2 to 1 0 3 + 3 R2 2 1 0 V V OFF A A A COM 3 R1 2 1 R3 0 Measure voltage from 3 to 2 0 3 + 3 R2 2 1 0 V V OFF A A A COM 3 R1 2 1 R3 0 .3.
2) v(0. and R3 . . and/or the resistor values.end This computer simulation is based on the point numbers shown in the previous diagrams for illustrating Kirchhoff's Voltage Law (points 0 through 3).print dc v(2. This experiment is intended to give empirical evidence for and a deep understanding of Kirchhoff's Voltage Law as a general principle. verbatim): Voltage divider v1 3 0 r1 3 2 5k r2 2 1 3k r3 1 0 2k . DC CIRCUITS Measure voltage from 1 to 3 0 3 + 3 R2 2 1 0 V V OFF A A A COM 3 R1 2 1 R3 0 Try stepping between any set of points.0) v(2.1) v(3. This Law holds true no matter what the configuration of the circuit: series. 30%. and 20% proportions of total voltage across R1 . around your circuit and see for yourself that the algebraic sum always equals zero.76 CHAPTER 3.2) v(1.dc" line.3) * Voltages around 1-2-3-1 loop algebraically add to zero: . Feel free to modify the voltage source value (in the ". then another line of text containing three voltage figures.print dc v(1. COMPUTER SIMULATION Netlist (make a text file containing the following text. SPICE will print a line of text containing four voltage figures.1) v(3. or even an irreducible network. R2 . When run. Add the voltage figures in each line to see that the sum is zero. allowing us to predict the magnitude and polarity of voltages in a circuit by developing mathematical equations for analysis based on the truth of all voltages in a loop adding up to zero. Resistor values were chosen to provide 50%. shown here as 6 volts). Kirchhoff's Voltage Law is a powerful concept.3) . respectively. series-parallel. in any order. along with lots of other text lines describing the analysis process. parallel.dc v1 6 6 1 * Voltages around 0-1-2-3-0 loop algebraically add to zero: .
CURRENT DIVIDER 77 3.5 Current divider PARTS AND MATERIALS • Calculator (or pencil and paper for doing arithmetic) • 6-volt battery • Assortment of resistors between 1 KΩ and 100 kΩ in value CROSS-REFERENCES Lessons In Electric Circuits.5. Volume 1.3. chapter 6: "Divider Circuits and Kirchhoff's Laws" LEARNING OBJECTIVES • Voltmeter use • Ammeter use • Ohmmeter use • Use of Ohm's Law • Use of Kirchhoff's Current Law (KCL) • Current divider design SCHEMATIC DIAGRAM R1 R2 R3 + A Ammeter - ILLUSTRATION .
In this illustration. This is done for the ease of proving a concept (of current summing at a circuit node). it is considered improper to secure more than two wires under a single terminal strip screw. DC CIRCUITS + - R1 R2 R3 Breadboard + - Terminal strip R1 R2 R3 Normally. I show three wires joining at the top screw of the rightmost lug used on this strip. .78 CHAPTER 3. and does not represent professional assembly technique.
Measure voltage across each of the three resistors. I show different methods of constructing the same circuit: breadboard. Measure battery voltage with a voltmeter after the resistors have been connected to it. as shown in the illustrations. noting this voltage figure on paper as well. In a parallel circuit. and with the 6-volt battery.3. and "free-form. CURRENT DIVIDER 79 Piece of stiff wire serves as a connection point "Free-form" construction + R1 R2 R3 The non-professional nature of the "free-form" construction method merits no further comment." Experiment with all these construction formats and become familiar with their respective advantages and disadvantages. connecting the meter's black probe to the lifted wire. INSTRUCTIONS Once again. Select three resistors from your resistor assortment and measure the resistance of each one with an ohmmeter.5. In this manner. What do you notice? In a series circuit. Place the red probe of the ammeter at the point where the positive (+) ends of the resistors connect to each other and lift one resistor wire at a time. Use Ohm's Law (I=E/R) to calculate current through each resistor. measure each resistor current. Note these resistance values with pen and paper. current is equal through all components at any given time. In these illustrations. voltage is the common variable between all components. noting both the magnitude of the current and the polarity. Connect the three resistors in parallel to and each other. for reference in your circuit calculations. It is advisable to measure battery voltage while it's powering the resistor circuit because this voltage may differ slightly from a no-load condition. terminal strip. I show an ammeter used to measure the current through R1 : . then verify this calculated value by measuring current with a digital ammeter.
80 CHAPTER 3. DC CIRCUITS V V OFF A A A COM + - R1 R2 R3 Breadboard .
not negative.3. all three indications should be positive. comparing with the current figures calculated previously. Now. With the digital ammeter connected as shown. CURRENT DIVIDER 81 V V OFF A A A COM + - Terminal strip R1 R2 R3 Measure current for each of the three resistors.5. but disconnecting the wire leading to the positive (+) side of the battery and touching the black probe to it: . measure total circuit current. keeping the ammeter's red probe on the same point of the circuit.
82 CHAPTER 3. DC CIRCUITS V V OFF A A A COM + - R1 R2 R3 Breadboard .
5. This is why a parallel resistor circuit is often called a current divider. CURRENT DIVIDER 83 V V OFF A A A COM + - Terminal strip R1 R2 R3 Note both the magnitude and the sign of the current as indicated by the ammeter. Along with Kirchhoff's Voltage Law. if you consider the points in a parallel circuit in terms of electrical commonality. and measure resistance across the parallel resistors. Now consider the four current measurements as all positive numbers: the first three representing the current through each resistor. it allows us to generate equations describing several variables in a circuit. It makes sense. You may read total resistance across any of the individual resistors' terminals and obtain the same indication: it will be a value less than any of the individual resistor values. This Law is also very useful in the mathematical analysis of circuits. This is often surprising to new students of electricity. All parallel components are connected between two sets of electrically common points. or percentage. to read resistance . Disconnect the battery from the rest of the circuit.3. which may then be solved using a variety of mathematical techniques. just as Kirchhoff's Voltage Law is to voltages adding in a series loop: in both cases. What do you notice about the result that is similar to the Kirchhoff's Voltage Law experiment? Kirchhoff's Current Law is to currents "summing" at a point (node) in a circuit. and the fourth representing total circuit current as a positive sum of the three "branch" currents. of the total current. Add this figure (algebraically) to the three resistor currents. the algebraic sum is equal to zero. Each resistor (branch) current is a fraction. that you read the exact same (total) resistance figure when connecting an ohmmeter across any one of a set of parallel-connected resistors. Since the meter cannot distinguish between points common to each other by way of direct connection. though.
across one resistor is to read the resistance of them all. The same is true for voltage, which is why battery voltage could be read across any one of the resistors as easily as it could be read across the battery terminals directly. If you divide the battery voltage (previously measured) by this total resistance figure, you should obtain a figure for total current (I=E/R) closely matching the measured figure. The ratio of resistor current to total current is the same as the ratio of total resistance to individual resistance. For example, if a 10 kΩ resistor is part of a current divider circuit with a total resistance of 1 kΩ, that resistor will conduct 1/10 of the total current, whatever value that current total happens to be. COMPUTER SIMULATION Schematic with SPICE node numbers:
2 Vitotal 1 V1 Vir1
2 Vir3
Vir2 3 4 R2
Ammeters in SPICE simulations are actually zero-voltage sources inserted in the paths of electron flow. You will notice the voltage sources Vir1 , Vir2 , and Vir3 are set to 0 volts in the netlist. When electrons enter the negative side of one of these "dummy" batteries and out the positive, the battery's current indication will be a positive number. In other words, these 0-volt sources are to be regarded as ammeters with the red probe on the long-line side of the battery symbol and the black probe on the short-line side. Netlist (make a text file containing the following text, verbatim): Current divider v1 1 0 r1 3 0 2k r2 4 0 3k r3 5 0 5k vitotal 2 1 dc 0 vir1 2 3 dc 0 vir2 2 4 dc 0 vir3 2 5 dc 0 .dc v1 6 6 1 .print dc i(vitotal) i(vir1) i(vir2) i(vir3) .end
When run, SPICE will print a line of text containing four current figures, the first current representing the total as a negative quantity, and the other three representing currents for resistors R1 , R2 , and R3 . When algebraically added, the one negative figure and the three positive figures will form a sum of zero, as described by Kirchhoff's Current Law.
Potentiometer as a voltage divider
PARTS AND MATERIALS • Two 6-volt batteries • Carbon pencil "lead" for a mechanical-style pencil • Potentiometer, single turn, 5 kΩ to 50 kΩ, linear taper (Radio Shack catalog # 271-1714 through 271-1716) • Potentiometer, multi turn, 1 kΩ to 20 kΩ, (Radio Shack catalog # 271-342, 271-343, 900-8583, or 900-8587 through 900-8590) Potentiometers are variable voltage dividers with a shaft or slide control for setting the division ratio. They are manufactured in panel-mount as well as breadboard (printed-circuit board) mount versions. Any style of potentiometer will suffice for this experiment. If you salvage a potentiometer from an old radio or other audio device, you will likely be getting what is called an audio taper potentiometer. These potentiometers exhibit a logarithmic relationship between division ratio and shaft position. By contrast, a linear potentiometer exhibits a direct correlation between shaft position and voltage division ratio. I highly recommend a linear potentiometer for this experiment, and for most experiments in general. CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 6: "Divider Circuits and Kirchhoff's Laws" LEARNING OBJECTIVES • Voltmeter use • Ohmmeter use • Voltage divider design and function • How voltages add in series
Potentiometer + V ILLUSTRATION
Pencil "lead" V V + A OFF
Begin this experiment with the pencil "lead" circuit. Pencils use a rod made of a graphite-clay mixture, not lead (the metal), to make black marks on paper. Graphite, being a mediocre electrical conductor, acts as a resistor connected across the battery by the two alligator-clip jumper wires. Connect the voltmeter as shown and touch the red test probe to the graphite rod. Move the red probe along the length of the rod and notice the voltmeter's indication change. What probe position gives the greatest voltage indication?
Essentially, the rod acts as a pair of resistors, the ratio between the two resistances established by the position of the red test probe along the rod's length:
Pencil "lead"
equivalent to
Now, change the voltmeter connection to the circuit so as to measure voltage across the "upper resistor" of the pencil lead, like this:
Pencil "lead"
Move the black test probe position along the length of the rod, noting the voltmeter indication. Which position gives the greatest voltage drop for the meter to measure? Does this differ from the previous arrangement? Why? Manufactured potentiometers enclose a resistive strip inside a metal or plastic housing, and provide some kind of mechanism for moving a "wiper" across the length of that resistive strip. Here is an illustration of a rotary potentiometer's construction:
Rotary potentiometer construction
Wiper Resistive strip
Some rotary potentiometers have a spiral resistive strip, and a wiper that moves axially as it rotates, so as to require multiple turns of the shaft to drive the wiper from one end of the potentiometer's range to the other. Multi-turn potentiometers are used in applications where precise setting is important. Linear potentiometers also contain a resistive strip, the only difference being the wiper's direction of travel. Some linear potentiometers use a slide mechanism to move the wiper, while others a screw, to facilitate multiple-turn operation:
Linear potentiometer construction Wiper Resistive strip
It should be noted that not all linear potentiometers have the same pin assignments. On some, the middle pin is the wiper. Set up a circuit using a manufactured potentiometer, not the "home-made" one made from a pencil lead. You may use any form of construction that is convenient. Measure battery voltage while powering the potentiometer, and make note of this voltage figure on paper. Measure voltage between the wiper and the potentiometer end connected to the negative (-) side of the battery. Adjust the potentiometer mechanism until the voltmeter registers exactly
For a 6-volt battery. Now. . connect two batteries in a series-aiding configuration. and then measure the voltage between the same two points on the potentiometer (wiper and negative side). Divide the potentiometer's measured output voltage by the measured total voltage. to provide approximately 12 volts across the potentiometer. this will be approximately 2 volts. the same voltage division ratio as was set previously: V V + A OFF A A COM + Voltmeter measuring output of potentiometer.6. The quotient should be 1/3. Measure the total battery voltage.3. POTENTIOMETER AS A VOLTAGE DIVIDER 91 1/3 of total voltage.
linear taper (Radio Shack catalog # 271-1714) • Small "hobby" motor. permanent-magnet type (Radio Shack catalog # 273-223 or equivalent) For this experiment. CROSS-REFERENCES Lessons In Electric Circuits. you will need a relatively low-value potentiometer. certainly not more than 5 kΩ.7 Potentiometer as a rheostat PARTS AND MATERIALS • 6 volt battery • Potentiometer. 5 kΩ. single turn. DC CIRCUITS 3. chapter 2: "Ohm's Law" LEARNING OBJECTIVES • Rheostat use • Wiring a potentiometer as a rheostat • Simple motor speed control • Use of voltmeter over ammeter to verify a continuous circuit SCHEMATIC DIAGRAM Mtr ILLUSTRATION . Volume 1.92 CHAPTER 3.
but merely a variable resistor: a two-terminal device. a variable resistor is known as a rheostat. where shaft position determines a specific voltage division ratio. In its simplest configuration.3. POTENTIOMETER AS A RHEOSTAT 93 + optional Motor Potentiometer INSTRUCTIONS Potentiometers find their most sophisticated application as voltage dividers.7. but potentiometers can be made to function as rheostats quite easily. the third terminal left unconnected and unused: Mtr . Technically. there are applications where we don't necessarily need a variable voltage divider. However. a potentiometer may be used as a rheostat by simply using the wiper terminal and one of the other terminals.
The direction of motion required to increase or decrease resistance may be changed by using a different set of terminals: Less resistance when turned clockwise More resistance when turned clockwise Wiper Resistive strip Wiper Resistive strip Be careful. that you don't use the two outer terminals. though.94 CHAPTER 3. as this will result in no change in resistance as the potentiometer shaft is turned. In other words. it will no longer function as a variable resistance: . DC CIRCUITS + - Motor Potentiometer Moving the potentiometer control in the direction that brings the wiper closest to the other used terminal results in a lower resistance.
As you can see. A much more efficient means of motor control relies on fast "pulsing" of power to the motor. Experiment with different terminal connections on the potentiometer. motor speed may be made variable using a series-connected rheostat to change total circuit resistance and limit total current. using a high-speed switching device such as a transistor. the "unused" terminal is often connected to the wiper terminal. this seems rather pointless. noting the changes in motor speed control. is inefficient. and see how motor speed may be controlled by adjusting shaft position. You may verify this fact for yourself by inserting another wire in your circuit and comparing motor behavior before and after the change: . This simple method of motor speed control. these techniques are much too sophisticated to explore at this point in the experiments. the motor might not move at all until the wiper is brought very close to the connected outer terminal. using just two terminals on the potentiometer. as it has no impact on resistance control. If your potentiometer has a high resistance (as measured between the two outer terminals). as it results in substantial amounts of power being dissipated (wasted) by the rheostat. POTENTIOMETER AS A RHEOSTAT 95 No resistance change when wiper moves! Build the circuit as shown in the schematic and illustration.3. however. A similar method of power control is used in household light "dimmer" switches. Unfortunately.7. like this: Mtr At first. When a potentiometer is used as a rheostat.
this connection ensures the circuit does not completely open: that there will still be a resistive path for current through the motor. however small: . and if a circuit cannot tolerate the complete loss of continuity (infinite resistance) created by this condition. However. if the wiper ever loses contact with the resistive strip inside the potentiometer. this additional wire makes no difference whatsoever. this may be an important. You may simulate such a wiper contact "failure" by disconnecting the potentiometer's middle terminal from the terminal strip. Old potentiometers tend to suffer from intermittent losses of contact between the wiper and the resistive strip.96 CHAPTER 3. In some applications. that "extra" wire provides a measure of protection by maintaining circuit continuity. DC CIRCUITS + add wire Motor Potentiometer If the potentiometer is in good working order. measuring voltage across the motor to ensure there is still power getting to it.
there is risk of causing a short circuit by connecting it across a substantial voltage source.3. possibly resulting in instrument damage or personal injury. and so whenever a voltage measurement may be made instead of a current measurement to verify the same thing. POTENTIOMETER AS A RHEOSTAT 97 + - break connection V V OFF A A A COM It would have been valid to measure circuit current instead of motor voltage to verify a completed circuit. it is the wiser choice.7. but this is a safer method because it does not involve breaking the circuit to insert an ammeter in series. . Voltmeters lack this inherent safety risk. Whenever an ammeter is used.
linear-taper potentiometer. Suppliers such as Radio Shack offer nice project boxes. A brief inspection of any binding post will clarify this verbal description. DC CIRCUITS 3. but boxes purchased at a general hardware store are much less expensive.8 Precision potentiometer PARTS AND MATERIALS • Two single-turn. for connection to potentiometer circuit (Radio Shack catalog # 274-662 or equivalent) This is a project useful to those who want a precision potentiometer without spending a lot of money. 50 kΩ (Radio Shack catalog # 271-1716) • Plastic or metal mounting box • Three "banana" jack style binding posts. I recommend building it in permanent form using some form of project enclosure. The sleeve is used as a nut to secure a wire wrapped around the post. or inserted through a perpendicular hole drilled through the post. The ultimate in low cost for a new box are the plastic boxes sold as light switch and receptacle boxes for household electrical wiring. Binding posts have screw-on sleeves that fit over a metal post. which maintain firm contact with the jack walls when inserted. Some banana jacks are called binding posts because they also allow plain wires to be firmly attached. multi-turn potentiometers are used to obtain precise voltage division ratios. or other terminal hardware. linear-taper potentiometers. Ordinarily. Banana plugs are so named because of their oblong appearance formed by spring steel strips. Because this is a useful project. CROSS-REFERENCES Lessons In Electric Circuits. 5 kΩ each (Radio Shack catalog # 271-1714) • One single-turn. Most multimeter test leads have this style of plug for insertion into the meter jacks. single-turn (sometimes called "3/4-turn") potentiometers connected together in a compound divider network. Volume 1. but a cheaper alternative exists using multiple. if a bit ugly. "Banana" jacks allow for the temporary connection of test leads and jumper wires equipped with matching "banana" plug ends.98 CHAPTER 3. chapter 6: "Divider Circuits and Kirchhoff's Laws" LEARNING OBJECTIVES • Soldering practice • Potentiometer function and operation SCHEMATIC DIAGRAM .
the resistance of all wiring connections must be carefully controlled to a bare minimum. Since potentiometer action is dependent on resistance.8. from a 6-volt battery. The circuit works on the principle of compressed range: the voltage output range of this circuit available by adjusting potentiometer R3 is restricted between the limits set by potentiometers R1 and R2 . respectively. When the circuit is assembled. Soldering ensures a condition of low resistance between joined conductors. In other words. This voltmeter will measure the "output" of the circuit. the range of output voltages obtainable by adjusting R3 would be restricted from 3 to . if R1 and R2 were set to output 5 volts and 3 volts. and also provides very good mechanical strength for the connections. Connect a voltmeter between the "wiper" post and the battery's negative (-) terminal. connect a 6-volt battery to the outer two binding posts. PRECISION POTENTIOMETER 99 R1 5 kΩ R3 R2 5 kΩ 50 kΩ V - + ILLUSTRATION V V OFF A A + - R1 5 kΩ 5 kΩ R2 R3 A COM 50 kΩ INSTRUCTIONS It is essential that the connecting wires be soldered to the potentiometer terminals.3. not twisted or taped.
The "range compression" afforded by this circuit allows for more precise voltage adjustment than would be normally obtainable using a single potentiometer.000 volts from a 6 volt battery. The reason that R1 and R2 were specified as 10 times less resistance than R3 is to minimize this effect. In other words. Adjust potentiometer R1 until the upper voltage limit is reached.100 CHAPTER 3. it interferes with the prior setting of the other. the interaction between R 1 and R2 would be more severe. this phenomenon of one adjustment affecting the other is known as interaction. Adjust potentiometer R2 until the lower voltage limit is reached. DC CIRCUITS 5 volts for the full rotation of that potentiometer. then turn R3 fully counter-clockwise to read and adjust the voltage of R2 . Once the upper and lower voltage limits have been set. if R1 is initially adjusted to provide an upper voltage limit of 5. turn R3 fully clockwise to read and adjust the voltage of R1 . so that its wiper is in the full "down" position as referenced to the schematic diagram (electrically "closest" to R2 's wiper terminal). To begin. If only a single potentiometer were used instead of this three-potentiometer circuit. so that its wiper is in the full "up" position as referenced to the schematic diagram (electrically "closest" to R1 's wiper terminal). When either the R1 or the R2 potentiometer is adjusted. as indicated by the voltmeter. turn the R3 potentiometer fully clockwise. though manageable with patience.000 volts. Turn the R3 potentiometer fully counter-clockwise. repeating as necessary. Technically. R1 will no longer be set to 5. we will enjoy greater precision than a single potentiometer could provide. If all three potentiometers were of equal resistance value. Operating this potentiometer network is more complex than using a single potentiometer. So long as R3 's adjustment range is compressed to some lesser value than full battery voltage. and then R2 is adjusted to provide some lower limit voltage different from what it was before. full rotation would produce an output voltage from 0 volts to full battery voltage. . and it is usually undesirable due to the extra effort required to set and re-set the adjustments. To obtain precise upper and lower voltage limits. Bear in mind that the upper and lower voltage limits need not be set precisely in order for this circuit to achieve its goal of increased precision. potentiometer R3 may be adjusted to produce an output voltage anywhere between those limits. as indicated by the voltmeter.
chapter 7: "Series-Parallel Combination Circuits" Lessons In Electric Circuits. chapter 8: "DC Metering Circuits" LEARNING OBJECTIVES • Series-parallel resistances • Calibration theory and practice SCHEMATIC DIAGRAM Rtotal ILLUSTRATION . RHEOSTAT RANGE LIMITING 101 3. chapter 5: "Series and Parallel Circuits" Lessons In Electric Circuits. Volume 1. Volume 1.9. linear taper (Radio Shack catalog # 271-1715) CROSS-REFERENCES Lessons In Electric Circuits.3. Volume 1.9 Rheostat range limiting PARTS AND MATERIALS • Several 10 kΩ resistors • One 10 kΩ potentiometer.
000 Ω: . Adjusting the potentiometer through its full range of travel should result in a resistance that varies smoothly from 0 Ω to 10.102 CHAPTER 3. To begin. connect a 10 kΩ potentiometer as a rheostat with no other resistors connected. DC CIRCUITS V V OFF A A A COM INSTRUCTIONS This experiment explores the different resistance ranges obtainable from combining fixed-value resistors with a potentiometer connected as a rheostat.
Add one to the circuit as shown and re-measure total resistance while adjusting the potentiometer: . RHEOSTAT RANGE LIMITING 103 V V OFF A A A COM Suppose we wanted to elevate the lower end of this resistance range so that we had an adjustable range from 10 kΩ to 20 kΩ with a full sweep of the potentiometer's adjustment.3. This could be easily accomplished by adding a 10 kΩ resistor in series with the potentiometer.9.
We could replace the potentiometer with one of another value. though: a range of 10 kΩ to 20 kΩ has the same 10. If we wish to shift the span of this rheostat circuit as well. Add a 10 kΩ resistor in parallel with the potentiometer.000 Ω.104 CHAPTER 3. in metrological terms. Now the calibrated resistance range of this circuit will be 10 kΩ to 15 kΩ: . With the addition of a series 10 kΩ resistor. This will decrease the span of the circuit from 10 kΩ to something less. to reduce the span to one-half of its former value: from 10 KΩ to 5 kΩ. or we could simulate a lowervalue potentiometer by placing a resistor in parallel with it. The difference between high and low ends of a range – called the span of the circuit – has not changed. diminishing its maximum obtainable resistance.000 Ω span as a range of 0 Ω to 10 kΩ. we must change the range of the potentiometer itself. DC CIRCUITS V V OFF A A A COM A shift in the low end of an adjustment range is called a zero calibration. the "zero point" was shifted upward by 10.
we can create a range of 7. However. there is no such restriction with calibrating the zero point of this circuit. For instance. short of replacing the potentiometer with another of greater total resistance. as it began at 0 Ω and may be made as great as we wish by adding resistance in series. A multitude of resistance ranges may be obtained using only 10 KΩ fixed-value resistors.5 kΩ to 10 kΩ by building the following circuit: . RHEOSTAT RANGE LIMITING 105 V V OFF A A A COM There is nothing we can do to increase the span of this rheostat circuit. Adding resistors in parallel can only decrease the span.9.3. if we are creative with series-parallel combinations of them.
If an instrument's internal resistance values are not precise. especially meter circuits. neither will its indications be. In many electrical instruments – multimeters especially – resistance is the determining factor for the instrument's range of measurement.106 CHAPTER 3.5 kΩ 2.5 kΩ 5 kΩ All resistors = 10 kΩ V V OFF A A A COM Creating a custom resistance range from fixed-value resistors and a potentiometer is a very useful technique for producing precise resistances required for certain circuits. Finding a fixed-value resistor of just the right resistance for placement . DC CIRCUITS Rtotal 0 to 2.
Experiment with different resistor "networks" and note the effects on total resistance range. so that precise adjustment is possible and so that accidental movement of its mechanism will not result in severe calibration errors. so custom resistance "networks" may need to be built to provide the desired resistance.9. RHEOSTAT RANGE LIMITING 107 in an instrument circuit design is unlikely.3. Having a potentiometer as part of the resistor network provides a means of correction if the network's resistance should "drift" from its original value. Designing the network for minimum span ensures that the potentiometer's effect will be small. .
10 Thermoelectricity PARTS AND MATERIALS • Length of bare (uninsulated) copper wire • Length of bare (uninsulated) iron wire • Candle • Ice cubes Iron wire may be obtained from a hardware store. DC CIRCUITS 3. If some cannot be found.108 CHAPTER 3. Volume 1. chapter 9: "Electrical Instrumentation Signals" LEARNING OBJECTIVES • Thermocouple function and purpose SCHEMATIC DIAGRAM Thermocouple + V Voltmeter ILLUSTRATION . aluminum wire also works. CROSS-REFERENCES Lessons In Electric Circuits.
touch the thermocouple tip to an ice cube and note the voltage indicated by the meter. A thermocouple is an application of the Seebeck effect: the production of a small voltage proportional to a temperature gradient along the length of a wire. It may take a short while to reach body temperature. Set your voltmeter to its most sensitive range and connect it to the terminals where the wires attach. THERMOELECTRICITY 109 V V OFF A A A COM iron wire copper wire Candle INSTRUCTIONS Twist one end of the iron wire together with one end of the copper wire. When the tip is at a temperature equal to the terminal strip.3. there will be no voltage produced. What you have just constructed is a thermocouple: a device which generates a small voltage proportional to the temperature difference between the tip and the meter connection points. This voltage is dependent upon . Connect the free ends of these wires to respective terminals on a terminal strip. The meter should indicate nearly zero voltage. Now. and thus no indication seen on the voltmeter. Remove the thermocouple tip from the flame and let cool until the voltmeter indication is nearly zero again. You should notice an indication on your voltmeter. Light a candle and insert the twisted-wire tip into the flame. Is it a greater or lesser magnitude than the indication obtained with the flame? How does the polarity of this voltage compare with that generated by the flame? After touching the thermocouple tip to the ice cube.10. so be patient while observing the voltmeter's indication. warm it by holding it between your fingers.
and so will not be attempted in this experiment. The resultant voltage between the two free wire ends is the difference between the two Seebeck voltages: iron wire voltage HOT COOL copper wire voltage Resultant voltage Thermocouples are widely used as temperature-sensing devices because the mathematical relationship between temperature difference and resultant voltage is both repeatable and fairly linear. Directly measuring the Seebeck voltage produced along a length of continuous wire from a temperature gradient is quite difficult. being made of two dissimilar metals joined at one end.110 CHAPTER 3. DC CIRCUITS the magnitude of the temperature difference and the type of wire. . it is possible to infer temperature. Different ranges of temperature measurement are possible by selecting different metal pairs to be joined together. produce a voltage proportional to the temperature of the junction. The temperature gradient along both wires resulting from a constant temperature at the junction produces different Seebeck voltages along those wires' lengths. By measuring voltage. Thermocouples. because the wires are made of different metals.
preferably high-precision metal film or wire-wound types (Radio Shack catalog # 271-309 is an assortment of metal-film resistors. Of course. The model recommended in the parts list is sold as a voltmeter with a 0-15 volt range. the goal here is learning. not meter function. 1 kΩ and 10 kΩ "trimmer" units. as these depend on the particular meter movement and measurement ranges chosen. The ideal meter movement is physically large (for ease of viewing) and as sensitive as possible (requires minimal current to produce full-scale deflection of the needle). or other terminal hardware. Be sure to use high-precision fixed-value resistors rather than carbon-composition resistors. if you don't care about the long-term stability of this meter but are building it just for the learning experience.11 Make your own multimeter PARTS AND MATERIALS • Sensitive meter movement (Radio Shack catalog # 22-410) • Selector switch. those values will change or "drift" over time due to aging and temperature fluctuations. but is actually a milliammeter with a range ("multiplier") resistor included separately. It may be cheaper to purchase an inexpensive analog meter and disassemble it for the meter movement alone. Although the thought of destroying a working multimeter in order to have parts to make your own may sound counter-productive. resistor precision matters little. PCB mount (Radio Shack catalog # 271-342 and 271-343 are 15turn. Even if you happen to find carbon-composition resistors of just the right value(s). High-quality meter movements are expensive. 6-position unit that works well) • Multi-turn potentiometers. break-before-make (Radio Shack catalog # 275-1386 is a 2-pole. respectively) • Assorted resistors.11.1% tolerance) • Plastic or metal mounting box • Three "banana" jack style binding posts. MAKE YOUR OWN MULTIMETER 111 3. multi-throw. chapter 8: "DC Metering Circuits" LEARNING OBJECTIVES • Voltmeter design and use • Ammeter design and use • Rheostat range limiting • Calibration theory and practice . Volume 1. CROSS-REFERENCES Lessons In Electric Circuits. single-pole. I cannot specify resistor values for this experiment.3. but Radio Shack carries some of acceptable quality that are reasonably priced. +/. for connection to potentiometer circuit (Radio Shack catalog # 274-662 or equivalent) The most important and expensive component in a meter is the movement: the actual needleand-scale mechanism whose task it is to translate an electrical current into mechanical displacement where it may be visually interpreted.
DC CIRCUITS SCHEMATIC DIAGRAM Movement + Off Rshunt Rmultiplier1 Rmultiplier2 Rmultiplier3 V V V "Common" jack A V/mA A mA "Rmultiplier" resistors are actually rheostat networks Rmultiplier ILLUSTRATION .112 • Soldering practice CHAPTER 3.
MAKE YOUR OWN MULTIMETER 113 Meter movement Common Rshunt - + A V/mA Selector switch INSTRUCTIONS First. Adjust the potentiometer until the meter movement is deflected exactly to full-scale. you need to determine the characteristics of your meter movement.11. battery. Most important is to know the full scale deflection in milliamps or microamps. and digital ammeter in series. To determine this. a potentiometer.3. connect the meter movement. Read the ammeter's display to find the fullscale current value: .
we subtract the movement's internal resistance. the more sensitive it is. If we wanted to determine the necessary range resistance ("Rmultiplier ") to give this movement a range of 0 to 15 volts. DC CIRCUITS Meter movement - + Potentiometer + - V V OFF A A A COM Be very careful not to apply too much current to the meter movement. A simple rheostat network to produce 14. and begin testing with the potentiometer turned to maximum resistance. Record this resistance figure along with the full-scale current figure obtained in the last procedure. After determining the full-scale current rating of your meter movement. as movements are very sensitive devices and easily damaged by overcurrent.6 kΩ (adjustable) would be a 10 kΩ potentiometer in parallel with a 10 kΩ fixed resistor. disconnect all components from the previous testing circuit and connect your digital ohmmeter across the meter movement terminals. so choose a potentiometer value high enough to limit current appropriately. leaving 14. that total resistance is 15 kΩ. you must accurately measure its internal resistance. but an example is given here. The calculations are outlined in chapter 8 of volume 1 ("Metering Circuits"). Suppose your meter movement had a full-scale rating of 1 mA and an internal resistance of 400 Ω.6 kΩ for the range resistor value. The lower the full-scale current rating of a movement. Most meter movements have full-scale deflection current ratings of 1 mA or less. all in series with another 10 kΩ fixed resistor: . For this example. Perhaps the most challenging portion of this project is determining the proper range resistance values and implementing those values in the form of rheostat networks. From this total resistance figure. To do this.114 CHAPTER 3. we would have to divide 15 volts (total applied voltage) by 1 mA (full-scale current) to obtain the total probe-to-probe resistance of the voltmeter (R=E/I).
Radio Shack sells printed circuit boards that have the same layout as a breadboard. careful amounts. it is an excellent project to assist learning fundamental instrument principles and circuit function. I strongly recommend that you mount the circuit board and all components in a sturdy box. Remember that you can always approach the exact value in slower and slower steps (file strokes). To calibrate a home-made shunt resistor. You will definitely not be using any 1/4 watt resistors for this. you will need to connect the your multimeter assembly to a calibrated source of high current. I recommend using a thick piece of wire or even a skinny piece of sheet metal as the "resistor." suitably filed or notched to provide just the right amount of resistance. For final construction. the meter is a sensitive ammeter with a range equal to the full-scale current rating of the meter movement. but you cannot go "backward" and decrease the shunt resistance! Build the multimeter circuit on a breadboard first while determining proper range resistance values. or a high-current source in series with a digital ammeter for reference.3. causing the meter movement to deflect more strongly. for convenience (catalog # 276-170). Feel free to alter the component layout from what is shown. and it "dampens" the needle mechanism to further guard against mechanical shock. Use a small metal file to shave off shunt wire thickness or to notch the sheet metal strip in small. MAKE YOUR OWN MULTIMETER 115 ≈ 15 kΩ. so save the parts and pieces for a later experiment! . inability to measure alternating current. In this position. If you plan on having an ammeter range in excess of 1 amp. This protects the meter from electrical damage by isolating it from the red test probe. solder the components on to a printed-circuit board. The resistance of your shunt will increase with every stroke of the file. The shunt resistor (Rshunt ) necessary for a high-current ammeter function needs to be a lowresistance unit with a high power dissipation. unless you form a resistance network with several smaller resistors in parallel combination. adjustable 10 kΩ 10 kΩ 10 kΩ One position of the selector switch directly connects the meter movement between the black Common binding post and the red V/mA binding post. Despite the limitations of this multimeter (no resistance function.11. A far more accurate and versatile multimeter may be constructed using many of the same parts if an amplifier circuit is added to it. so that the meter is durably finished. and perform all calibration adjustments there. and lower precision than most purchased analog multimeters). The far clockwise position of the switch disconnects the positive (+) terminal of the movement from either red binding post and shorts it directly to the negative (-) terminal.
the transformer used in this type of application (audio speaker impedance matching) is called an "audio transformer. Volume 2. An audio transformer will work. The tolerance (precision) rating for the 1 kΩ resistor is irrelevant. it is not necessary. or other terminal hardware. chapter 12: "AC Metering Circuits" . you should try a few different headphone models at a high-quality audio store and "listen" for which ones produce an audible sound for the lowest volume setting on a radio or CD player. Volume 1. but listening is believing: if you're serious about building a detector with maximum sensitivity for small electrical signals. using the 6-volt secondary winding tap) • Two 1N4001 rectifying diodes (Radio Shack catalog # 276-1101) • 1 kΩ resistor • 100 kΩ potentiometer (Radio Shack catalog # 271-092) • Two "banana" jack style binding posts. It is not important that you understand its intended function in this experiment. the better. as it gives the user control over the loudness for any given signal. but I've found small step-down power transformers of 120/6 volt ratio to be perfectly adequate for the task. chapter 9: "Transformers" Lessons In Electric Circuits. and far more rugged. Volume 2. as you could spend hundreds of dollars on a pair of headphones to get the absolute best sensitivity! Take heart. used to convert high-voltage AC power into low-voltage AC power. The 100 kΩ potentiometer is a recommended option for incorporation into this project. for connection to potentiometer circuit (Radio Shack catalog # 274-662 or equivalent) • Plastic or metal mounting box Regarding the headphones. Beware. chapter 8: "DC Metering Circuits" Lessons In Electric Circuits." with its primary and secondary windings represented by impedance values (1000 Ω : 8 Ω) instead of voltages. DC CIRCUITS 3. A linear-taper potentiometer works quite well. Volume 1. so you don't need to buy the best. A transformer is a device normally used with alternating current ("AC") circuits. cheaper (especially when taken from an old thrift-store alarm clock radio). and for many other purposes. the higher the "sensitivity" rating in decibels (dB). Normally.12 Sensitive voltage detector PARTS AND MATERIALS • High-quality "closed-cup" audio headphones • Headphone jack: female receptacle for headphone plug (Radio Shack catalog # 274-312) • Small step-down power transformer (Radio Shack catalog # 273-1365 or equivalent. though: I've used an old pair of Radio Shack "Realistic" brand headphones with perfectly adequate results. other than it makes the headphones become more sensitive to low-current electrical signals. chapter 10: "DC Network Analysis" (in regard to the Maximum Power Transfer Theorem) Lessons In Electric Circuits. CROSS-REFERENCES Lessons In Electric Circuits. Even though an audio-taper potentiometer would be appropriate for this application.116 CHAPTER 3.
I've found the series connection to work best. most likely being stereo units (separate left and right speakers) will have a three-contact plug. If you only have a "mono" headphone set with a two-contact plug.3. that is. SENSITIVE VOLTAGE DETECTOR LEARNING OBJECTIVES • Soldering practice • Detection of extremely small electrical signals • Using a potentiometer as a voltage divider/signal attenuator • Using diodes to "clip" voltage at some maximum level 117 SCHEMATIC DIAGRAM headphones test lead 1 kΩ diodes transformer jack plug test lead ILLUSTRATION headphones resistor Binding posts diodes 120 V 6V transformer jack plug INSTRUCTIONS The headphones.12. to produce the most sound from a small signal: . just connect to those two contact points. You may either connect the two stereo speakers in series or in parallel. You will be connecting to only two of those three contact points.
It is also valuable in that it allows you to use a different bodily sense in interpreting the behavior of a circuit. potentiometric (null-balance) voltmeter circuits. This may be accomplished by connecting a voltage divider to the "front" of the circuit: SCHEMATIC DIAGRAM test lead 1 kΩ 100 kΩ test lead ILLUSTRATION . once the detector components are mounted inside a box.118 CHAPTER 3. The system will work without the diodes and resistor in place. You may use ordinary multimeter probes. and detect extremely low-amplitude AC ("alternating current") signals in the audio frequency range. and the resulting sound caused by accidently connecting the test leads across a substantial voltage source (like a battery) can be deafening! Binding posts provide points of connection for a pair of test probes with banana-style plugs. and any loose wire connections in the circuit will add unwanted noise to the sounds produced by the measured voltage signal. especially for the low-budget experimenter without an oscilloscope. work together to prevent any more than about 0. For connection across any non-trivial source of voltage (1 volt and greater). the detector's extremely high sensitivity should be attenuated. DC CIRCUITS To transformer To transformer common right left Speakers in series common right left Speakers in parallel Solder all wire connections well. or make your own probes with alligator clips at the ends for secure connection to a circuit. along with the series-connected 1 kΩ resistor. This does one thing and one thing only: limit the amount of sound the headphones can produce. This detector system is extremely sensitive. It is a valuable piece of test equipment. The two diodes (arrow-like component symbols) connected in parallel with the transformer's primary winding.7 volts from being dropped across the primary coil of the transformer. Detectors are intended to be used for balancing bridge measurement circuits. but there will be no limit to sound volume in the circuit.
impedance is measured in the unit of the Ohm (Ω). it might look something like this: . As the Maximum Power Transfer Theorem predicts. If the sound is too loud. Like resistance. Headphone speakers are "low impedance" devices: they require low voltage and "high" current to deliver substantial sound power. by comparison. Most small signal sources have high internal impedances. We use the term "impedance" to describe the headphone's opposition to current because it is primarily AC signals that headphones are normally subjected to. but enough to produce soft "clicking" sounds every time the leads make and break contact on the wet skin of your tongue. but it is symbolized in equations by the capital letter "Z" rather than the capital letter "R". some much higher than the nominal 8 Ω of the headphone speakers. is a strictly measure of opposition to direct current (DC). I've been able to detect currents of less than 1/10 of a microamp (¡ 0. turn the potentiometer down and try again. The transformer does this. Try unplugged the headphone plug from the jack (receptacle) and similarly touching it to the end of your tongue.12. Impedance is a measure of opposition to any and all forms of electric current. with the sensitivity adjustment set to maximum. Constructed as such. turn it up and try again. maximum sound power will be delivered by the headphone speakers when their impedance is "matched" to the impedance of the voltage source. The transformer also helps aid the detection of small DC signals by producing inductive "kickback" every time the test lead circuit is broken. The detector produces a "click" sound whenever the test leads make or break contact with the voltage source under test. This is a technical way of saying that they are incapable of supplying substantial amounts of current. You should still hear soft clicking sounds. A good demonstration of the detector's sensitivity is to touch both test leads to the end of your tongue. not DC.1 µA). thus "amplifying" the signal by magnetically storing up electrical energy and suddenly releasing it to the headphone speakers.3. With my cheap headphones. including alternating current (AC). The voltage produced by metalto-electrolyte contact (called galvanic voltage) is very small. SENSITIVE VOLTAGE DETECTOR 119 potentiometer Adjust the 100 kΩ voltage divider potentiometer to about mid-range when initially sensing a voltage signal of unknown magnitude. but they will be much smaller in amplitude. If too soft. and providing nice test lead wires) so it may be easily used in the future. I recommend building this detector in a permanent fashion (mounting all components inside of a box. Resistance.
120 CHAPTER 3. DC CIRCUITS headphones Test leads Sensitivity plug .
it is recommended that you use it in this experiment. CROSS-REFERENCES Lessons In Electric Circuits. If you have not yet built the sensitive voltage detector. If you have built the "precision potentiometer" described earlier in this chapter. the greater the value. POTENTIOMETRIC VOLTMETER 121 3. but the headphone-based voltage detector is more appropriate because it demonstrates how you can make precise voltage measurements without using expensive or advanced meter equipment. They need not be precisely equal value. Likewise. You can use a digital multimeter set to the "DC millivolt" (DC mV) range in lieu of a voltage detector. the better the results. I recommend using your home-made multimeter for the same reason.13 Potentiometric voltmeter PARTS AND MATERIALS • Two 6 volt batteries • One potentiometer. Volume 1. yet simple. In this particular experiment. either. single turn.3. although any voltmeter will suffice for this experiment. the actual values of the resistors are not critical. it is recommended that you build one before proceeding with this experiment! It is a very useful. linear taper (Radio Shack catalog # 271-1715) • Two high-value resistors (at least 1 MΩ each) • Sensitive voltage detector (from previous experiment) • Analog voltmeter (from previous experiment) The potentiometer value is not critical: anything from 1 kΩ to 100 kΩ is acceptable. chapter 8: "DC Metering Circuits" LEARNING OBJECTIVES • Voltmeter loading: its causes and its solution • Using a potentiometer as a source of variable voltage • Potentiometric method of voltage measurement SCHEMATIC DIAGRAM 1 MΩ 6V 1 MΩ measure voltage between these two test points null Test probes + V Potentiometric voltmeter 6V . piece of test equipment that you should not be without. 10 kΩ.13.
there is so little air released from the tire during the act of measurement that the reduction in pressure is negligible. series voltage drops add to equal the total applied voltage. the act of measuring tire pressure alters the tire's pressure. In other words. This affects the pressure in the tire. Do you notice anything unusual about the voltmeter's readings? Normally. it releases some air out of the tire. but in this case you will notice a serious discrepancy. Voltmeters similarly impact the voltage they measure. though. In this circuit. with approximately 3 volts dropped across each resistor. the effect is very pronounced. If the two high-value resistors are of equal value. by bypassing some current around the component whose voltage drop is being measured. Measure the battery voltage directly with a voltmeter. I like to use the analogy of an air pressure gauge used to check the pressure of a pneumatic tire. Why is this? Try replacing the two highvalue resistors with two of 100 kΩ value each and repeat the experiment. This affects the voltage drop. but the effect is so slight that you usually don't notice it. the voltmeter itself alters the circuit so that the voltage is not the same as with no meter connected. DC CIRCUITS + Test probes Potentiometric voltmeter circuit + - headphones - + Sensitivity plug INSTRUCTIONS Build the two-resistor voltage divider circuit shown on the left of the schematic diagram and of the illustration. Replace those resistors with two 10 KΩ units and repeat. and so the gauge reads a slightly lower pressure than what was in the tire before the gauge was connected. What do you notice about the voltage readings with lower-value resistors? What does this tell you about voltmeter "impact" on a circuit in relation to that circuit's . the battery's voltage should be split in half. When a gauge is connected to the tire's fill valve. then measure each resistor's voltage drop. Is Kirchhoff's Voltage Law untrue? Is this an exception to one of the most fundamental laws of electric circuits? No! What is happening is this: when you connect a voltmeter across either resistor. Hopefully.122 ILLUSTRATION Test circuit CHAPTER 3. though.
If you happen to have two voltmeters. POTENTIOMETRIC VOLTMETER 123 resistance? Replace any low-value resistors with the original. What do you notice about the digital meter's readings versus the analog meter's? Digital voltmeters typically have greater internal (probe-to-probe) resistance. and the other voltmeter across the other resistor. and thus suffer no voltage "impact" problems.3. When the two voltages are equal. as indicated by a very sensitive null detector. the adjustable voltage source is measured with an ordinary voltmeter. measuring the adjustable source is the same as measuring across the test circuit. Is there any way to make a "perfect" voltmeter: one that has infinite resistance and draws no current from the circuit under test? Modern laboratory voltmeters approach this goal by using semiconductor "amplifier" circuits. A much simpler and much older technique is called the potentiometric or nullbalance method. though. An ideal voltmeter would draw zero current from the circuit under test. even though they're different from the readings obtained from a single meter used twice. This involves using an adjustable voltage source to "balance" the measured voltage. except that there is no "impact" error because the adjustable source provides any current needed by the voltmeter. allowing measurement of its true voltage drop. try this: connect one voltmeter across one resistor. Because the two voltage sources are equal to each other. Consequently. This can be any arbitrarily sensitive meter movement or voltage indicator. and the more precisely that test voltage may be measured. Its sole purpose in this circuit is to indicate when there is zero voltage: when the adjustable voltage source (potentiometer) is precisely equal to the voltage drop in the circuit under test. Try measuring voltage across the two high-value resistors – one at a time – with a digital voltmeter instead of an analog voltmeter. but this method is too technologically advanced for the student or hobbyist to duplicate. . no matter what the resistor values are. it is unlikely that the voltage readings obtained this way are equal to the true voltage drops with no meters connected. the more precisely the adjustable source may be adjusted to equal the voltage under test. The more sensitive this null detector is. Unfortunately. Examine the following schematic to see how the potentiometric voltmeter method is implemented: 1 MΩ 6V + 1 MΩ Test circuit V Potentiometric voltmeter null + 6V The circle symbol with the word "null" written inside represents the null detector. meaning they draw less current than a comparable analog voltmeter when measuring the same voltage source. the circuit under test remains unaffected. high-value (>= 1 MΩ) resistors before proceeding. The voltage readings you get will add up to the total voltage this time. and so it is not a practical solution to the problem.13.
and a useful technique for the hobbyist who may lack expensive instrumentation in their home laboratory. It may be easier to use a regular multimeter as a null detector at first. you will need to intermittently make and break contact with the circuit under test and listen for "clicking" sounds. A multi-turn potentiometer may be used instead of the single-turn unit for greater adjustment precision. and is considered obsolete for all but the most precise measurement applications. You may find that a single-turn ("3/4 turn") potentiometer is too coarse of an adjustment device to accurately "null" the measurement circuit. This indicates a "null" or "balanced" condition. Do this by firmly securing one of the test probes to the test circuit and momentarily touching the other test probe to the other point in the test circuit again and again. until you become familiar with the process of adjusting the potentiometer for a "null" indication. or the "precision potentiometer" circuit described in an earlier experiment may be used. verbatim): . Although the potentiometric method requires more skill to use than simply connecting a modern digital voltmeter across a component. DC CIRCUITS Build this circuit as shown in the illustration and test its operation measuring the voltage drop across one of the high-value resistors in the test circuit. Even now. COMPUTER SIMULATION Schematic with SPICE node numbers: 1 1 MΩ V1 2 + 1 MΩ 0 1 R1 2 R2 3 + V 0 0 0 3 V2 null Netlist (make a text file containing the following text. it is still a valuable learning process for the new student of electronics. If you are using the headphone-based voltage detector as your null meter. and you may read the voltmeter indication to see how much voltage is dropped across the test circuit resistor. the potentiometric method was the only method for making highly accurate voltage measurements. then reading the voltmeter connected across the potentiometer. or less than the test circuit voltage. electrical standards laboratories make use of this technique along with the latest meter technology to minimize meter "impact" errors and maximize measurement accuracy. Unfortunately. the headphone-based null detector provides no indication of whether the potentiometer voltage is greater than. listening for sounds in the headphones indicating a difference of voltage between the test circuit and the potentiometer.124 CHAPTER 3. Adjust the potentiometer until no clicking sounds can be heard from the headphones. so you will have to listen for decreasing "click" intensity while turning the potentiometer to determine if you need to adjust the voltage higher or lower. Prior to the advent of amplified voltmeter technology.
3) v(3. you will notice that the voltage across R 2 is impacted significantly when the measurement circuit is unbalanced.000 volts: precisely equal to the (unaffected) test circuit voltage drop.3. POTENTIOMETRIC VOLTMETER Potentiometric voltmeter v1 1 0 dc 6 v2 3 0 r1 1 2 1meg r2 2 0 1meg rnull 2 3 10k rmeter 3 0 50k .0) .end 125 This SPICE simulation shows the actual voltage across R2 of the test circuit. of course. At that point.5 . and the voltage across the adjustable voltage source.print dc v(2. the adjustable voltage source is at a value of 3.dc v2 0 6 0. the null detector's voltage.5 volt steps.13. In the output of this simulation. returning to its true voltage only when there is practically zero voltage across the null detector. as that source is adjusted from 0 volts to 6 volts in 0.0) v(2. What is the lesson to be learned from this simulation? That a potentiometric voltmeter avoids impacting the test circuit only when it is in a condition of perfect balance ("null") with the test circuit! .
and your ammeter needs to be capable of measuring it without blowing a fuse or sustaining other damage. or a large spool of wire It would be ideal in this experiment to have two meters: one voltmeter and one ammeter. Whatever ammeter is used should be capable measuring at least a few amps of current. this may not be possible. Make sure the highest current range on the meter is at least 5 amps! CROSS-REFERENCES Lessons In Electric Circuits.14 4-wire resistance measurement PARTS AND MATERIALS • 6-volt battery • Electromagnet made from experiment in previous chapter. A 6-volt "lantern" battery essentially short-circuited by a long piece of wire may produce currents of this magnitude.126 CHAPTER 3. chapter 8: "DC Metering Circuits" LEARNING OBJECTIVES • Operating principle of Kelvin (4-wire) resistance measurement • How to measure low resistances with common test equipment SCHEMATIC DIAGRAM + A + V Runknown ILLUSTRATION . Volume 1. DC CIRCUITS 3. For experimenters on a budget.
and indeed is shown as such in the schematic diagram and illustration. 4-WIRE RESISTANCE MEASUREMENT 127 V V OFF A A V V OFF A A A COM A COM + - Runknown INSTRUCTIONS Although this experiment is best performed with two meters. Imagine trying to measure the diameter of a cotton thread with a yardstick. Being part of the measurement circuit. one multimeter is sufficient. as a low resistance specimen may be of much smaller resistance value than the meter circuitry itself. This presents a problem for measurement of low resistances. Except in special cases such as the megger. incurring significant measurement error by their presence: . Most ohmmeters operate on the principle of applying a small voltage across an unknown resistance (Runknown ) and inferring resistance from the amount of current drawn by it. or measuring the weight of a coin with a scale built for weighing freight trucks. and you will appreciate the problem at hand. both the voltage and current quantities employed by the meter are quite small. One of the many sources of error in measuring small resistances with an ordinary ohmmeter is the resistance of the ohmmeter's own test leads.3. the test leads may contain more resistance than the resistance of the test specimen.14.
or 4-wire. If you have a second meter. It involves the use of an ammeter and voltmeter. Because only the voltage dropped by the unknown resistance is factored into the calculation – not the voltage dropped across the ammeter's test leads or any other connecting wires carrying the main current – errors otherwise caused by these stray resistances are completely eliminated. with an ammeter connected in series. connect it across the specimen's connection points. I suggest the electromagnet coil specified in the last chapter. The voltage dropped across the resistance is measured by the voltmeter. quickly noting the voltage indication. so that it will not be damaged by the (possibly) high current generated in this near-short circuit condition. recording its indication as quickly as possible. and resistance calculated using Ohm's Law (R=E/I).128 CHAPTER 3. If you have only one meter. then immediately opening (breaking) the circuit. use it to measure current first.5 Ω One solution is called the Kelvin. select a suitably low resistance specimen to use in this experiment. WARNING: the ammeter used should be capable of measuring at least 5 amps of current. as it will begin to rapidly discharge due to the high circuit current. thus compromising measurement accuracy when the meter is re-configured and . as shown in the illustration.25 Ω COM A Lead resistance: 0. You don't want to leave the battery connected to the specimen for any longer than necessary for obtaining meter measurements. Very small resistances may be measured easily by using large current. Switch the meter to its voltage mode. providing a more easily measured voltage drop from which to infer resistance than if a small current were used. First. DC CIRCUITS Ω V V OFF A A Lead resistance: 0. use it to measure voltage across the specimen's connection points. Connect a 6-volt battery to this specimen.25 Ω 1. and re-connect the battery. and record both meters' indications. resistance measurement method. determining specimen resistance by Ohm's Law calculation. or a spool of wire where both ends may be accessed. A current is passed through the unknown resistance and measured.
3. The quotient will be equal to the specimen's resistance in ohms. . Take the voltage measurement and divide it by the current measurement. When two meters are used. this is not as significant an issue. 4-WIRE RESISTANCE MEASUREMENT 129 the circuit closed once more for the next measurement.14. because the current and voltage indications may be recorded simultaneously.
chapter 10: "DC Network Analysis" LEARNING OBJECTIVES • How a resistor network can function as a voltage signal averager • Application of Millman's Theorem SCHEMATIC DIAGRAM R1 R2 R3 + V - ILLUSTRATION . Precision is very important for this experiment! CROSS-REFERENCES Lessons In Electric Circuits.130 CHAPTER 3. between 10 kΩ and 47 kΩ each When selecting resistors. DC CIRCUITS 3. Volume 1. each one with a different voltage • Three equal-value resistors. measure each one with an ohmmeter and choose three that are the closest in value to each other.15 A very simple computer PARTS AND MATERIALS • Three batteries.
it should register the algebraic average of the three batteries' voltages. Polarity is important here! You will notice one battery in the schematic diagram connected "backward" to the other two.132 CHAPTER 3. If the resistor values . DC CIRCUITS V V OFF A A A COM + - + - INSTRUCTIONS This deceptively crude circuit performs the function of mathematically averaging three voltage signals together. divided by three). it is a computer that can only do one mathematical operation: averaging three quantities together. and so fulfills a specialized computational role. In other words. Build this circuit as shown and measure all battery voltages with a voltmeter. the other batteries measuring positive. Write these voltage figures on paper and average them together (E1 + E2 + E3 ." This battery's voltage should read as a negative quantity when measured by a properly connected digital meter. negative side "up. When you measure each battery voltage. and touch the red probe to the other battery terminal. keep the black test probe connected to the "ground" point (the side of the battery directly joined to the other batteries by jumper wires). When the voltmeter is connected to the circuit at the point shown in the schematic and illustrations.
and as such may be used to simulate the behavior of complex mechanical. electrical. perform mathematical operations in a series of discrete steps. and even chemical systems. Analog computers perform calculations in continuous fashion. At one time. the output voltage will equal the average voltage of the remaining batteries. Such analog computers excel at performing the calculus operations of numerical differentiation and integration." but it undeniably performs the mathematical function of averaging. but it performs it much faster than any modern digital computer can! Digital computers. at the speed of light!). If one battery is disconnected.15. Not only does it perform this function. such as personal computers (PCs) and pushbutton calculators. With the addition of circuits called amplifiers. A VERY SIMPLE COMPUTER 133 are chosen to match each other very closely. the circuit will average the two remaining voltages together with 0 volts. voltage signals in analog computer networks may be boosted and re-used in other networks to perform a wide variety of mathematical functions.3. the "answer" computed as fast as voltage propagates through the circuit (ideally. producing a smaller output signal: V V OFF A A A COM + - + - The sheer simplicity of this circuit deters most people from calling it a "computer. If the jumper wires formerly connecting the removed battery to the averager circuit are connected to each other. analog computers were the ultimate tool for engineering . the "output" voltage of this circuit should match the calculated average very closely as well. exploiting Ohm's and Kirchhoff's Laws for an arithmetic purpose.
134 CHAPTER 3. DC CIRCUITS research.0) . but rather to learn more about circuits and more about computer simulation of circuits! . verbatim): Voltage averager v1 1 0 v2 0 2 dc 9 v3 3 0 dc 1.dc v1 6 6 1 . but since then have been largely supplanted by digital computer technology. Digital computers enjoy the advantage of performing mathematical operations with much better precision than analog computers. COMPUTER SIMULATION Schematic with SPICE node numbers: 4 4 4 4 R1 1 V1 0 R2 2 V2 R3 + 3 V3 0 V - 0 0 Netlist (make a text file containing the following text. we aren't doing this for the practical task of averaging numbers. we can force a digital computer to simulate and analog computer.5 r1 1 4 10k r2 2 4 10k r3 3 4 10k . albeit at much slower theoretical speeds. which averages three numbers together.end With this SPICE netlist.print dc v(4. Obviously.
Volume 1. POTATO BATTERY 135 3. but many fruits and vegetables work as potential batteries! For the zinc electrode.16.3. or galvanized metal • Piece of thick copper wire The basic experiment is based on the use of a potato. chapter 11: "Batteries and Power Systems" LEARNING OBJECTIVES • The importance of chemical activity in battery operation • How electrode surface area affects battery operation ILLUSTRATION V V OFF A Galvanized nail A Potato COM Copper wire A INSTRUCTIONS .16 Potato battery PARTS AND MATERIALS • One large potato • One lemon (optional) • Strip of zinc. CROSS-REFERENCES Lessons In Electric Circuits. rough zinc texture are preferable to galvanized nails that are smooth. Nails with a thick. a large galvanized nail works well.
electrode depths. It can be difficult to power a load with a single "potato" battery. . parallel. and electrode spacings to obtain the greatest voltage possible from the potato. DC CIRCUITS Push both the nail and the wire deep into the potato. Measure voltage output by the potato battery with a voltmeter. though. Try other vegetables or fruits and compare voltage output with the same electrode metals. wasn't that easy? Seriously. or seriesparallel arrangement. experiment with different metals.136 CHAPTER 3. it is possible to obtain enough voltage and current capacity to power a small load. Now. Even if the voltage output is adequate. a potato battery has a fairly high internal resistance which causes its voltage to "sag" badly under even a light load. With multiple potato batteries connected in series. though. so don't expect to light up an incandescent lamp or power a hobby motor or do anything like that.
spewing caustic chemicals and emitting foul odors.17. chapter 16: "RC and L/R Time Constants" LEARNING OBJECTIVES • Capacitor charging action • Capacitor discharging action • Time constant calculation • Series and parallel capacitance SCHEMATIC DIAGRAM . When electrolytic capacitors fail. try to avoid this! I recommend a household light switch for the "SPST toggle switch" specified in the parts list. SPST ("Single-Pole.3. Volume 1. Very large capacitors are often polarity-labeled by a positive (+) marking next to one terminal. Single-Throw") Large-value capacitors are required for this experiment to produce time constants slow enough to track with a voltmeter and stopwatch. Usually capacitors of the size specified have a negative (-) marking or series of negative markings pointing toward the negative terminal.17 Capacitor charging and discharging PARTS AND MATERIALS • 6 volt battery • Two large electrolytic capacitors. Please. CROSS-REFERENCES Lessons In Electric Circuits. even with a source voltage as low as 6 volts. 1000 µF minimum (Radio Shack catalog # 272-1019. Be warned that most large capacitors are of the "electrolytic" type. Volume 1. CAPACITOR CHARGING AND DISCHARGING 137 3. chapter 13: "Capacitors" Lessons In Electric Circuits. 2721032. and they are polarity sensitive! One terminal of each capacitor should be marked with a definite polarity sign. Failure to heed proper polarity will almost surely result in capacitor failure. or equivalent) • Two 1 kΩ resistors • One toggle switch. they typically explode.
138 CHAPTER 3. DC CIRCUITS + V - Charging circuit + V - Discharging circuit ILLUSTRATION + Charging circuit .
2% from its present value to its final value: the voltage of the battery. and/or changing the total circuit capacitance.17. we must find a way of slowing it down. the time constant should be 1 second.3. You should already know by now how multiple resistors need to be connected to form a greater total resistance. experiment with various series and parallel combinations to obtain the slowest charging action. though. rather than suddenly as would be the case with a resistor. It is educational to plot the voltage of a charging capacitor over time on a sheet of graph paper. Just be sure that you insert the capacitor(s) in the proper direction: with the ends labeled negative (-) electrically "closest" to the battery's negative terminal! The discharging circuit provides the same kind of changing capacitor voltage. The "time constant" (τ ) of a resistor capacitor circuit is calculated by taking the circuit resistance and multiplying it by the circuit capacitance. Experiment once again with different combinations of resistors and capacitors. to see how the inverse exponential curve develops. In order to plot the action of this circuit. Given a pair of identical resistors and a pair of identical capacitors. but what about capacitors? This circuit will demonstrate to you how capacitance changes with series and parallel capacitor connections. For a 1 kΩ resistor and a 1000 µF capacitor. CAPACITOR CHARGING AND DISCHARGING 139 + Discharging circuit INSTRUCTIONS Build the "charging" circuit and measure voltage across the capacitor when the switch is closed. making sure as always that the capacitor's polarity is correct. Notice how it increases slowly over time. A one-second time constant doesn't provide much time to take voltmeter readings! We can increase this circuit's time constant two different ways: changing the total circuit resistance. except this time the voltage jumps to full battery voltage when the switch closes and slowly falls when the switch is opened. COMPUTER SIMULATION Schematic with SPICE node numbers: . You can "reset" the capacitor back to a voltage of zero by shorting across its terminals with a piece of wire. This is the amount of time it takes for the capacitor voltage to increase approximately 63.
verbatim): Capacitor charging circuit v1 1 0 dc 6 r1 1 2 1k c1 2 0 1000u ic=0 .1 5 uic .0) . DC CIRCUITS 1 V1 0 R1 2 C1 0 Netlist (make a text file containing the following text.end .140 CHAPTER 3.tran 0.plot tran v(2.
18 Rate-of-change indicator PARTS AND MATERIALS • Two 6 volt batteries • Capacitor. chapter 13: "Capacitors" LEARNING OBJECTIVES • How to build a differentiator circuit • Obtain an empirical understanding of the derivative calculus function SCHEMATIC DIAGRAM 6V 5 kΩ 0.3.18. in theory. 0. RATE-OF-CHANGE INDICATOR 141 3. work better for this experiment than high-resistance units.1 µF (Radio Shack catalog # 272-135) • 1 MΩ resistor • Potentiometer. 5 kΩ.1 µF + 6V 1 MΩ V - ILLUSTRATION . linear taper (Radio Shack catalog # 271-1714) The potentiometer value is not especially critical. although lower-resistance units will. CROSS-REFERENCES Lessons In Electric Circuits. single turn. Volume 1. I've used a 10 kΩ potentiometer for this circuit with excellent results.
Now. and you can see how it smoothly varies between zero and 12 volts as the potentiometer control is turned full-range. it is called a differentiator circuit.142 CHAPTER 3. What kind of potentiometer motion provides the steadiest voltage across the 1 MΩ resistor? In calculus. a function representing the rate of change of one variable as compared to another is called the derivative. What difference do you see between the two different directions of potentiometer control motion? Try moving the potentiometer in such a way that the voltmeter gives a steady. A digital voltmeter is highly recommended. Turn the potentiometer slowly counter-clockwise and note the voltmeter's indication. this behavior should be unsurprising to you. Because this circuit performs the calculus function of differentiation with respect to time (outputting the time-derivative of an incoming signal). and I advise setting it to a very sensitive (millivolt) range to obtain the strongest indications. What does the voltmeter indicate while the potentiometer is not being moved? Turn the potentiometer slowly clockwise and note the voltmeter's indication. Since the potentiometer is used here as a voltage divider. . DC CIRCUITS V V OFF A A A COM + - + - INSTRUCTIONS Measure voltage between the potentiometer's wiper terminal and the "ground" point shown in the schematic diagram (the negative terminal of the lower 6-volt battery). measure voltage across the 1 MΩ resistor while moving the potentiometer control. small indication. This is the input voltage for the circuit. This simple circuit illustrates the concept of the derivative by producing an output voltage proportional to the input voltage's rate of change over time.
More accurate differentiator circuits may be built by combining resistor-capacitor networks with electronic amplifier circuits. RATE-OF-CHANGE INDICATOR 143 Like the averager circuit shown earlier in this chapter. so this circuit is an excellent demonstration of the elegance of analog circuitry in performing mathematical computations. especially when implemented in a digital computer. the differentiator circuit is a kind of analog computer.3. Differentiation is a far more complex mathematical function than averaging. For more detail on computational circuitry. . go to the "Analog Integrated Circuits" chapter in this Experiments volume.18.
145 . consisting of a transformer that steps the hazardous voltage (110 to 120 volts AC. A convenient source of AC voltage is household wall-socket power. a small power supply will be the first project. RMS) down to 12 volts or less. which presents significant shock hazard. but rather as a power converter. These experiments are designed to introduce you to several important concepts specific to AC. respectively.1 Introduction "AC" stands for Alternating Current. This device does not really act as a source or supply of power. to reduce the hazardous voltage of wall-socket power to a much safer level. The title of "power supply" is somewhat misleading. which can refer to either voltage or current that alternates in polarity or direction.Chapter 4 AC CIRCUITS 4. In order to minimize this hazard while taking advantage of the convenience of this source of AC.
you should purchase one from an electronics supply store. Volume 2. and these transient currents will blow a fast-acting fuse. AC CIRCUITS 4. • Fuse and fuse holder (optional). chapter 9: "Transformers" LEARNING OBJECTIVES • Transformer voltage step-down behavior. If you decide to equip your power supply with a fuse. If you want to be absolutely sure what kind of transformer you're getting. • Box (optional). The radio would also provide the power cord and plug necessary for this project. • Household wall-socket power plug and cord. or slow-blow fuse. Determine the proper current rating of the fuse by dividing the transformer's "VA" rating by 120 volts: in other words. • Line cord switch. CROSS-REFERENCES Lessons In Electric Circuits. 120VAC step-down to 12VAC. or 273-1511). Line cord switches may be obtained from a hardware store. Volume 2. though. calculate the full allowable primary winding current and size the fuse accordingly. SCHEMATIC DIAGRAM . • Safe wiring techniques for power cords.2 Transformer – power supply PARTS AND MATERIALS • Power transformer. Power transformers may be obtained from old radios. • Purpose of tapped windings. • Terminal strip with at least three terminals. Transformers may draw high "surge" currents when initially connected to an AC source. be sure to get a slow-acting. with center-tapped secondary winding (Radio Shack catalog # 273-1365. chapter 1: "Basic AC Theory" Lessons In Electric Circuits. which can usually be obtained from a thrift store for a few dollars (or less!).146 CHAPTER 4. 273-1352.
If you wish to enclose the transformer inside of a box. which is dangerous! . scotch tape. you may use an electrical "junction" box. a three-prong plug should be used. You must make sure all highvoltage (120 volt household power) conductors are safely insulated from accidental contact. obtained from a hardware store or electrical supply house. Be sure to solder all wire connections so that they're secure. TRANSFORMER – POWER SUPPLY 147 Box (optional) Switch Fuse Plug (optional) Transformer ILLUSTRATION Terminal strip wires soldered and taped with electrical tape 12 / 6 volts CT Transformer plug 120 volts wires soldered and taped with electrical tape 2-conductor "zip" cord line switch "zip" cord split into separate wires INSTRUCTIONS Warning! This project involves the use of dangerous voltages. If the enclosure used is metal rather than plastic. and use real electrical tape (not duct tape. With the line switch in the "on" position. No bare wires should be seen anywhere on the "primary" side of the transformer circuit. measure resistance between either plug prong and the transformer case. Before plugging the plug into a wall socket. If the meter registers continuity (some resistance value less than infinity). or any other kind!) to insulate your soldered connections. packing tape. then you have a "short" between one of the power conductors and the case.2. do a safety check with an ohmmeter. There should be infinite (maximum) resistance.4. with the "ground" prong (the longest one on the plug) connected directly to the metal case for maximum safety.
148 CHAPTER 4. You should be able to measure AC voltage at the secondary side of the transformer.999 . you should measure half that. you should measure about 12 volts. verbatim): transformer with center-tap secondary v1 1 0 ac 120 sin rbogus1 1 2 1e-3 l1 2 0 10 l2 5 4 0. It would be advisable to keep this project assembled for use in powering other experiments shown in this book. there should be a small amount of resistance between the two plug prongs. Why is this? Plug the cord into a wall socket and turn the switch on. When the switch is turned "off. These secondary windings should register much lower resistances than the primary. Between either of these two terminals and the third terminal. check the transformer windings themselves for continuity.999 k2 l2 l3 0.025 k1 l1 l2 0. Measure resistance between pairs of wires on the secondary side. With the line switch in the "on" position. AC CIRCUITS Next. This third wire is the "center-tap" wire of the secondary winding. Between two of these terminals. between pairs of terminals. From here on." the resistance indication should increase to infinity (open circuit – no continuity).025 l3 4 3 0. I will designate this "low-voltage AC power supply" using this illustration: Low-voltage AC power supply 12 6 6 COMPUTER SIMULATION Schematic with SPICE node numbers: 1 Rbogus1 1 mΩ 2 L2 5 4 3 Rload1 Rload2 120 V L1 L3 0 0 1 TΩ Rbogus2 Netlist (make a text file containing the following text.
print ac v(5.999 rbogus2 3 0 1e12 rload1 5 4 1k rload2 4 3 1k * Sets up AC analysis at 60 Hz: .2. TRANSFORMER – POWER SUPPLY k3 l1 l3 0.3) .4) * Prints (bottom) secondary voltage between nodes 4 and 3: .4.print ac v(2.ac lin 1 60 60 * Prints primary voltage between nodes 2 and 0: .3) * Prints (total) secondary voltage between nodes 5 and 3: .print ac v(4.end 149 .0) * Prints (top) secondary voltage between nodes 5 and 4: .print ac v(5.
but 28 gauge is recommended so as to make a coil with as many turns as possible in a small diameter.150 CHAPTER 4. Any gauge of wire will work.3 Build a transformer PARTS AND MATERIALS • Steel flatbar. chapter 9: "Transformers" LEARNING OBJECTIVES • Effects of electromagnetism. AC CIRCUITS 4. SCHEMATIC DIAGRAM Transformer ILLUSTRATION . 4 pieces • Miscellaneous bolts. Volume 2. • Effects of winding turns on "step" ratio. • Effects of magnetic coupling on voltage regulation. CROSS-REFERENCES Lessons In Electric Circuits. washers • 28 gauge "magnet" wire • Low-voltage AC power supply "Magnet wire" is small-gauge wire insulated with a thin enamel coating. because many "turns" of wire may be wrapped in a relatively smalldiameter coil. • Effects of electromagnetic induction. It is intended to be used to make electromagnets. nuts.
3. as your home-made windings really aren't rated for any significant voltage! Measure the output voltage (secondary winding) of your transformer with an AC voltmeter. Do not power your transformer directly from wall-socket voltage (120 volts). thus increasing the reluctance (analogous to resistance) of the magnetic "circuit" coupling the two windings together. Power your transformer with the low-voltage output of the "power supply" described at the beginning of this chapter. depending on whether or not you want the transformer to be able to "step" voltage up or down. try it in step-up versus step-down mode. You may make these windings with an equal or unequal number of turns. There should be no continuity (infinite resistance) between the winding and the steel bar. Check for continuity between winding ends to ensure that the wire isn't broken open somewhere within the coil. If either resistance measurements indicate a problem. I recommend equal turns to begin with. Use bolts to secure the bars together (it is recommended that you drill bolt holes through the bars before you wrap wire around them). . Check for shorted windings (ohmmeter reading between wire ends and steel bar) after you're finished wrapping the windings. Note the effect on output voltage and voltage "sag" under load. Wrap several hundred turns of magnet wire around these two bars. bars of steel. the winding must be re-made. equal-length bars of steel with a thin layer of electrically-insulating tape. powering different AC loads. then experiment later with coils of unequal turn count. Connect a load of some kind (light bulbs are good!) to the secondary winding and re-measure voltage. Note the degree of voltage "sag" at the secondary winding as load current is increased. If you've made your transformer with unequal-turn windings.4. Join those bars together in a rectangle with two other. shorter. BUILD A TRANSFORMER 151 bolt wire coil wire coil steel "flatbar" INSTRUCTIONS Wrap two. Loosen or remove the connecting bolts from one of the short bar pieces.
rated for power supply voltage CROSS-REFERENCES Lessons In Electric Circuits. large enough to almost fill diameter of paper tube • 28 gauge "magnet" wire • Low-voltage AC power supply • Incandescent lamp.4 Variable inductor PARTS AND MATERIALS • Paper tube. Volume 2. Volume 1. chapter 14: "Magnetism and Electromagnetism" Lessons In Electric Circuits. from a toilet-paper roll • Bar of iron or steel. chapter 15: "Inductors" Lessons In Electric Circuits. SCHEMATIC DIAGRAM Variable inductor Lamp ILLUSTRATION .152 CHAPTER 4. AC CIRCUITS 4. chapter 3: "Reactance and Impedance – Inductive" LEARNING OBJECTIVES • Effects of magnetic permeability on inductance. • How inductive reactance can control current in an AC circuit. Volume 1.
such as copper and stainless steel. Not all metals have the same effect. Try using bars of different materials. the lamp should glow brightly.4. . the lamp dims from increased inductance (L) and consequently increased inductive reactance (XL ). if available. VARIABLE INDUCTOR wire coil 153 Steel bar Paper tube Low-voltage AC power supply 12 6 6 INSTRUCTIONS Wrap hundreds of turns of magnet wire around the paper tube. due to differences in magnetic permeability. When the steel bar is inserted in the tube. Connect this home-made inductor in series with an AC power supply and lamp to form a circuit.4. When the tube is empty.
the higher the "sensitivity" rating in decibels (dB). The tolerance (precision) rating for the 1 kΩ resistor is irrelevant. for connection to potentiometer circuit (Radio Shack catalog # 274-662 or equivalent) • Plastic or metal mounting box Regarding the headphones. AC CIRCUITS 4. but listening is believing: if you're serious about building a detector with maximum sensitivity for small electrical signals. chapter 9: "Transformers" Lessons In Electric Circuits. and far more rugged. so you don't need to buy the best.5 Sensitive audio detector PARTS AND MATERIALS • High-quality "closed-cup" audio headphones • Headphone jack: female receptacle for headphone plug (Radio Shack catalog # 274-312) • Small step-down power transformer (Radio Shack catalog # 273-1365 or equivalent. chapter 8: "DC Metering Circuits" Lessons In Electric Circuits. Beware. the transformer used in this type of application (audio speaker impedance matching) is called an "audio transformer. Even though an audio-taper potentiometer would be appropriate for this application. as it gives the user control over the loudness for any given signal. Volume 2. Normally. though: I've used an old pair of Radio Shack "Realistic" brand headphones with perfectly adequate results. The 100 kΩ potentiometer is a recommended option for incorporation into this project. it is not necessary. but I've found small step-down power transformers of 120/6 volt ratio to be perfectly adequate for the task.154 CHAPTER 4." with its primary and secondary windings represented by impedance values (1000 Ω : 8 Ω) instead of voltages. cheaper (especially when taken from an old thrift-store alarm clock radio). CROSS-REFERENCES Lessons In Electric Circuits. as you could spend hundreds of dollars on a pair of headphones to get the absolute best sensitivity! Take heart. using the 6-volt secondary winding tap) • Two 1N4001 rectifying diodes (Radio Shack catalog # 276-1101) • 1 kΩ resistor • 100 kΩ potentiometer (Radio Shack catalog # 271-092) • Two "banana" jack style binding posts. chapter 12: "AC Metering Circuits" LEARNING OBJECTIVES • Soldering practice • Use of a transformer for impedance matching . or other terminal hardware. A linear-taper potentiometer works quite well. you should try a few different headphone models at a high-quality audio store and "listen" for which ones produce an audible sound for the lowest volume setting on a radio or CD player. An audio transformer will work. the better. Volume 1. Volume 2.
I've found the series connection to work best. to produce the most sound from a small signal: . you may skip this experiment. just connect to those two contact points. If you only have a "mono" headphone set with a two-contact plug. SENSITIVE AUDIO DETECTOR • Detection of extremely small electrical signals 155 • Using diodes to "clip" voltage at some maximum level SCHEMATIC DIAGRAM headphones test lead 1 kΩ diodes transformer jack plug test lead ILLUSTRATION headphones resistor Binding posts diodes 120 V 6V transformer jack plug INSTRUCTIONS This experiment is identical in construction to the "Sensitive Voltage Detector" described in the DC experiments chapter. The headphones. If you've already built this detector. You will be connecting to only two of those three contact points.4.5. that is. most likely being stereo units (separate left and right speakers) will have a three-contact plug. You may either connect the two stereo speakers in series or in parallel.
potentiometric (null-balance) voltmeter circuits.156 CHAPTER 4. work together to "clip" the input voltage to a maximum of about 0.7 volts. once the detector components are mounted inside a box. It is also valuable in that it allows you to use a different bodily sense in interpreting the behavior of a circuit. This detector system is extremely sensitive. You may use ordinary multimeter probes. especially for the low-budget experimenter without an oscilloscope. This may be accomplished by connecting a voltage divider to the "front" of the circuit: SCHEMATIC DIAGRAM test lead 1 kΩ 100 kΩ test lead ILLUSTRATION . This does one thing and one thing only: limit the amount of sound the headphones can produce. Detectors are intended to be used for balancing bridge measurement circuits. The two diodes connected in parallel with the transformer's primary winding. The system will work without the diodes and resistor in place. the detector's extremely high sensitivity should be attenuated. along with the series-connected 1 kΩ resistor. AC CIRCUITS To transformer To transformer common right left Speakers in series common right left Speakers in parallel Solder all wire connections well. and any loose wire connections in the circuit will add unwanted noise to the sounds produced by the measured voltage signal. or make your own probes with alligator clips at the ends for secure connection to a circuit. but there will be no limit to sound volume in the circuit. and detect extremely low-amplitude AC ("alternating current") signals in the audio frequency range. It is a valuable piece of test equipment. and the resulting sound caused by accidently connecting the test leads across a substantial voltage source (like a battery) can be deafening! Binding posts provide points of connection for a pair of test probes with banana-style plugs. For connection across any non-trivial source of voltage (1 volt and greater).
respectively). but it is symbolized in equations by the capital letter "Z" rather than the capital letter "R". The voltage produced by metalto-electrolyte contact (called galvanic voltage) is very small. maximum sound power will be delivered by the headphone speakers when their impedance is "matched" to the impedance of the voltage source. by comparison. it might look something like this: .5. is a strictly measure of opposition to direct current (DC). With my cheap headphones. some much higher than the nominal 8 Ω of the headphone speakers. The transformer does this. I recommend building this detector in a permanent fashion (mounting all components inside of a box. You should still hear soft clicking sounds. SENSITIVE AUDIO DETECTOR 157 potentiometer Adjust the 100 kΩ voltage divider potentiometer to about mid-range when initially sensing a voltage signal of unknown magnitude. If the sound is too loud. a "click" being heard whenever the test leads make or break contact with the source under test. Constructed as such. Resistance. including alternating current (AC). and providing nice test lead wires) so it can be easily used in the future. We use the term "impedance" to describe the headphone's opposition to current because it is primarily AC signals that headphones are normally subjected to. Like resistance. Impedance is a measure of opposition to any and all forms of electric current. As the Maximum Power Transfer Theorem predicts.4. Most small signal sources have high internal impedances. A good demonstration of the detector's sensitivity is to touch both test leads to the end of your tongue. As with the low-voltage AC power supply experiment. Try unplugged the headphone plug from the jack (receptacle) and similarly touching it to the end of your tongue. This detector even senses DC and radio-frequency signals (frequencies below and above the audio range. but enough to produce soft "clicking" sounds every time the leads make and break contact on the wet skin of your tongue. thus "amplifying" the signal by magnetically storing up electrical energy and suddenly releasing it to the headphone speakers. but they will be much smaller in amplitude. Headphone speakers are "low impedance" devices: they require low voltage and "high" current to deliver substantial sound power. The transformer also helps aid the detection of small DC signals by producing inductive "kickback" every time the test lead circuit is broken. This is a technical way of saying that they are incapable of supplying substantial amounts of current. turn it up and try again. If too soft. I've been able to detect currents of less than 1/10 of a microamp (¡ 0.1 µA) DC. and similarly low-magnitude RF signals up to 2 MHz. turn the potentiometer down and try again. with the sensitivity adjustment set to maximum. not DC. impedance is measured in the unit of the Ohm (Ω).
AC CIRCUITS headphones Test leads Sensitivity plug .158 CHAPTER 4.
Sensing AC magnetic fields
PARTS AND MATERIALS • Audio detector with headphones • Electromagnet coil from relay or solenoid What is needed for an electromagnet coil is a coil with many turns of wire, so as to produce the most voltage possible from induction with stray magnetic fields. The coil taken from an old relay or solenoid works well for this purpose. CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 7: "Mixed-Frequency AC Signals" LEARNING OBJECTIVES • Effects of electromagnetic induction. • Electromagnetic shielding techniques. SCHEMATIC DIAGRAM
Audio detector circuit
sensing coil
1 kΩ 100 kΩ
Audio detector circuit sensing coil
INSTRUCTIONS Using the audio detector circuit explained earlier to detect AC voltage in the audio frequencies, a coil of wire may serve as sensor of AC magnetic fields. The voltages produced by the coil will be quite small, so it is advisable to adjust the detector's sensitivity control to "maximum." There are many sources of AC magnetic fields to be found in the average home. Try, for instance, holding the coil close to a television screen or circuit-breaker box. The coil's orientation is every bit as important as its proximity to the source, as you will soon discover on your own! If you want to listen to more interesting tones, try holding the coil close to the motherboard of an operating computer (be careful not to "short" any connections together on the computer's circuit board with any exposed metal parts on the sensing coil!), or to its hard drive while a read/write operation is taking place. One very strong source of AC magnetic fields is the home-made transformer project described earlier. Try experimenting with various degrees of "coupling" between the coils (the steel bars tightly fastened together, versus loosely fastened, versus dismantled). Another source is the variable inductor and lamp circuit described in another section of this chapter. Note that physical contact with a magnetic field source is unnecessary: magnetic fields extend through space quite easily. You may also want to try "shielding" the coil from a strong source using various materials. Try aluminum foil, paper, sheet steel, plastic, or whatever other materials you can think of. What materials work best? Why? What angles (orientations) of coil position minimize magnetic coupling (result in a minimum of detected signal)? What does this tell us regarding inductor positioning if inter-circuit interference from other inductors is a bad thing? Whether or not stray magnetic fields like these pose any health hazard to the human body is a hotly debated subject. One thing is clear: in today's modern society, low-level magnetic fields of all frequencies are easy to find!
Sensing AC electric fields
PARTS AND MATERIALS • Audio detector with headphones CROSS-REFERENCES Lessons In Electric Circuits, Volume 2, chapter 7: "Mixed-Frequency AC Signals" LEARNING OBJECTIVES • Effects of electrostatic (capacitive) coupling. • Electrostatic shielding techniques. SCHEMATIC DIAGRAM
sensing wire
Audio detector circuit
1 kΩ 100 kΩ
sensing wire
Audio detector circuit
connection to water pipe
INSTRUCTIONS "Ground" one lead of the detector to a metal object in contact with the earth (dirt). Most any water pipe or faucet in a house will suffice. Take the other lead and hold it close to an electrical appliance or lamp fixture. Do not try to make contact with the appliance or with any conductors within! Any AC electric fields produced by the appliance will be heard in the headphones as a buzzing tone. Try holding the wire in different positions next to a good, strong source of electric fields. Try using a piece of aluminum foil clipped to the wire's end to maximize capacitance (and therefore its ability to intercept an electric field). Try using different types of material to "shield" the wire from an electric field source. What material(s) work best? How does this compare with the AC magnetic field experiment? As with magnetic fields, there is controversy whether or not stray electric fields like these pose any health hazard to the human body.
Automotive alternator
PARTS AND MATERIALS • Automotive alternator (one required, but two recommended) Old alternators may be obtained for low prices at automobile wrecking yards. Many yards have alternators already removed from the automobile, for your convenience. I do not recommend paying full price for a new alternator, as used units cost far less money and function just as well for the purposes of this experiment. I highly recommend using a Delco-Remy brand of alternator. This is the type used on General Motors (GMC, Chevrolet, Cadillac, Buick, Oldsmobile) vehicles. One particular model has been produced by Delco-Remy since the early 1960's with little design change. It is a very common unit to locate in a wrecking yard, and very easy to work with. If you obtain two alternators, you may use one as a generator and the other as a motor. The steps needed to prepare an alternator as a three-phase generator and as a three-phase motor are the same. CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 14: "Magnetism and Electromagnetism" Lessons In Electric Circuits, Volume 2, chapter 10: "Polyphase AC Circuits" LEARNING OBJECTIVES • Effects of electromagnetism • Effects of electromagnetic induction • Construction of real electromagnetic machines • Construction and application of three-phase windings SCHEMATIC DIAGRAM
Typical alternator
"field" terminals
"battery" terminal
An automotive alternator is a three-phase generator with a built-in rectifier circuit consisting of six diodes. As the sheave (most people call it a "pulley") is rotated by a belt connected to
the automobile engine's crankshaft, a magnet is spun past a stationary set of three-phase windings (called the stator ), usually connected in a Y configuration. The spinning magnet is actually an electromagnet, not a permanent magnet. Alternators are designed this way so that the magnetic field strength can be controlled, in order that output voltage may be controlled independently of rotor speed. This rotor magnet coil (called the field coil, or simply field ) is energized by battery power, so that it takes a small amount of electrical power input to the alternator to get it to generate a lot of output power. Electrical power is conducted to the rotating field coil through a pair of copper "slip rings" mounted concentrically on the shaft, contacted by stationary carbon "brushes." The brushes are held in firm contact with the slip rings by spring pressure. Many modern alternators are equipped with built-in "regulator" circuits that automatically switch battery power on and off to the rotor coil to regulate output voltage. This circuit, if present in the alternator you choose for the experiment, is unnecessary and will only impede your study if left in place. Feel free to "surgically remove" it, just make sure you leave access to the brush terminals so that you can power the field coil with the alternator fully assembled. ILLUSTRATION
INSTRUCTIONS First, consult an automotive repair manual on the specific details of your alternator. The documentation provided in the book you're reading now is as general as possible to accommodate different brands of alternators. You may need more specific information, and a service manual is the best place to obtain it. For this experiment, you'll be connecting wires to the coils inside the alternator and extending them outside the alternator case, for easy connection to test equipment and circuits. Unfortunately, the connection terminals provided by the manufacturer won't suit our needs here, so you need to make your own connections. Disassemble the unit and locate terminals for connecting to the two carbon brushes. Solder a pair of wires to these terminals (at least 20 gauge in size) and extend these wires through vent holes in the alternator case, making sure they won't get snagged on the spinning rotor when the alternator is re-assembled and used. Locate the three-phase line connections coming from the stator windings and connect wires to them as well, extending these wires outside the alternator case through some vent holes. Use the largest gauge wire that is convenient to work with for these wires, as they may be carrying substantial current. As with the field wires, route them in such a way that the rotor will turn freely with the alternator reassembled. The stator winding line terminals are easy to locate: the three of them
connect to three terminals on the diode assembly, usually with "ring-lug" terminals soldered to the ends of the wires.
Interior view of alternator, rotor removed stator add these wires diodes brush
I recommend that you solder ring-lug terminals to your wires, and attach them underneath the terminal nuts along with the stator wire ends, so that each diode block terminal is securing two ring lugs. Re-assemble the alternator, taking care to secure the carbon brushes in a retracted position so that the rotor doesn't damage them upon re-insertion. On Delco-Remy alternators, a small hole is provided on the back case half, and also at the front of the brush holder assembly, through which a paper clip or thin-gauge wire may be inserted to hold the brushes back against their spring pressure. Consult the service manual for more details on alternator assembly. When the alternator has been assembled, try spinning the shaft and listen for any sounds indicative of colliding parts or snagged wires. If there is any such trouble, take it apart again and correct whatever is wrong. If and when it spins freely as it should, connect the two "field" wires to a 6-volt battery. Connect an voltmeter to any two of the three-phase line connections:
across the same battery terminals. If you have a second alternator. Connect the field wires of one alternator to a 6 volt battery. The voltmeter reading should alternate between positive and negative as the shaft it turned: a demonstration of very slow alternating voltage (AC voltage) being generated. switch the multimeter to the "AC volts" setting and try again. Try reversing any two of the three-phase line connections between the two units and spin the generator again. and the loads should function. respectively. connecting five of your own wires to the field brushes and stator line terminals. What you should notice is that the alternator shaft becomes more difficult to spin. Now. What difference(s) do you notice? Find some sort of polarity-insensitive 6 or 12 volts loads. If this test is successful. such as small incandescent lamps. AC voltmeter.166 CHAPTER 4. You can then use it as a three-phase motor. AC CIRCUITS With the multimeter set to the "DC volts" function. Wrap a thin rope or heavy string around the groove of the sheave ("pulley") and spin the alternator rapidly. This alternator will be the generator. Try spinning the shaft slow and fast. Wrap rope around the sheave in preparation to spin it. powered by the first alternator. slowly rotate the alternator shaft. if the battery is strong . try connecting 12 volts DC to the field wires. as mechanical energy is converted into electrical energy. modify it as you modified the first one. Repeat the DC voltmeter. Short-circuit any two of the three-phase line wires and try spinning the alternator. What is different this time? Connect the field wires of the motor unit to the a 6 volt battery (you may parallel-connect this field with the field of the generator unit. Connect each of the three-phase line wires of the first alternator to the respective wires of the second alternator. and connect them to the three-phase line wires. and short-circuit tests described above. comparing voltmeter readings between the two conditions. This alternator will be the motor: Motor Generator + - Spin the generator shaft while watching the motor shaft's rotation. The heavy electrical load you've created via the short circuit causes a heavy mechanical load on the alternator. Take the two field wires of the second alternator and short them together.
The generator hangs from a steel support structure (I used welded 2-inch square tubing. where the field wires were simple shorted together. This belt also supports the rear of the bicycle. A . In the first motor setup. If you are feeling particularly ambitious and are skilled in metal fabrication techniques. but it is reliable enough to be used as an exercise machine. In the second setup. the motor was functioning as an induction motor.8. which I use for a load when riding the bicycle as an exercise machine. but a frame could be made out of lumber). you may make your own high-power generator platform by connecting the modified alternator to a bicycle. Not only is this machine practical. it functioned as a synchronous motor. I've built an arrangement that looks like this: alternator The rear wheel drives the generator sheave with a long v-belt. AUTOMOTIVE ALTERNATOR 167 enough to deliver the several amps of current both coils will draw together).4. and it is inexpensive to make: You can see a bank of three 12-volt "RV" light bulbs behind the bicycle unit (in the lower-left corner of the photograph). where the motor's rotor was magnetized. This will magnetize the rotor of the motor. maintaining a constant tension when a rider is pedaling the bicycle. Try spinning the generator again and note any differences in operation.
where I can turn loads on and off while riding. By rectifying the three-phase AC power produced. it is possible to have the alternator power its own field coil with DC voltage. . However.168 CHAPTER 4. eliminating the need for a battery. some independent source of DC voltage will still be necessary for start-up. AC CIRCUITS set of three switches is mounted at the front of the bicycle. as the field coil must be energized before any AC power can be produced.
9 Phase shift PARTS AND MATERIALS • Low-voltage AC power supply • Two capacitors. 0. chapter 1: "Basic AC Theory" Lessons In Electric Circuits.1 µF each. because they are insensitive to polarity (non-polarized). as these will be destroyed when powered by AC! CROSS-REFERENCES Lessons In Electric Circuits. inexpensive. non-polarized (Radio Shack catalog # 272-135) • Two 27 kΩ resistors I recommend ceramic disk capacitors. Volume 2. Volume 2. chapter 4: "Reactance and Impedance – Capacitive" LEARNING OBJECTIVES • How out-of-phase AC voltages do not add algebraically.4. but according to vector (phasor) arithmetic SCHEMATIC DIAGRAM R1 R2 27 kΩ 27 kΩ 0. PHASE SHIFT 169 4. and durable.9. Avoid capacitors with any kind of polarity marking.1 µF 0.1 µF 12 V RMS C1 C2 ILLUSTRATION .
170 CHAPTER 4. since they add simply and directly. You will discover that the voltage drops do not add up to equal the total voltage. AC CIRCUITS Low-voltage AC power supply 12 6 6 C2 C1 R2 R1 INSTRUCTIONS Build the circuit and measure voltage drops across each component with an AC voltmeter. only amplitude. like the drop measured across the two resistors. This tells you that both the resistors' voltage drop waveforms are in-phase with each other. Z=E/I). this tells you that both the capacitors' voltage drop waveforms are in-phase with each other. This voltage drop. The polar magnitudes of the results should closely agree with your voltmeter readings. Measure total (supply) voltage with the same voltmeter. calculate impedances for all components and determine all voltage drops using Ohm's Law (E=IZ . Given that the power supply frequency is 60 Hz (household power frequency in the United States). I=E/Z . This is due to phase shifts in the circuit: voltage dropped across the capacitors is out-of-phase with voltage dropped across the resistors. Measure voltage dropped across both capacitors at once. Likewise. Taking phase angle into consideration. will equal the sum of the voltage drops measured across each capacitor separately. This voltage drop will equal the sum of the voltage drops measured across each resistor separately. Try measuring voltage dropped across both resistors at once. they do add up to equal the total. COMPUTER SIMULATION Schematic with SPICE node numbers: . and thus the voltage drop figures do not add up as one might expect. but a voltmeter doesn't provide phase angle measurements.
0) .9.print ac v(1. PHASE SHIFT 171 1 R1 R2 V1 3 Rbogus1 4 Rbogus2 0 0 C2 C1 1 27 kΩ 2 27 kΩ 3 0. This is a "fix" for one of SPICE's quirks.3) v(3.1u rbogus1 3 4 1e9 rbogus2 4 0 1e9 .end .1 µF 0 The two large-value resistors Rbogus1 and Rbogus1 are connected across the capacitors to provide a DC path to ground in order that SPICE will work.ac lin 1 60 60 * Voltage across each component: .print ac v(1.2) v(2. These two resistors are entirely unnecessary in the real circuit.1u c2 4 0 0.4.3) v(3. to avoid it from seeing the capacitors as open circuits in its analysis. Netlist (make a text file containing the following text. verbatim): phase shift v1 1 0 ac 12 sin r1 1 2 27k r2 2 3 27k c1 3 4 0.0) * Voltage across pairs of similar components .1 µF 4 0.4) v(4.
AC CIRCUITS 4.10 Sound cancellation PARTS AND MATERIALS • Low-voltage AC power supply • Two audio speakers • Two 220 Ω resistors Large. low-frequency ("woofer") speakers are most appropriate for this experiment. Volume 2.172 CHAPTER 4. the speakers should be identical and mounted in enclosures. chapter 1: "Basic AC Theory" LEARNING OBJECTIVES • How phase shift can cause waves to either reinforce or interfere with each other • The importance of speaker "phasing" in stereo systems SCHEMATIC DIAGRAM 220 Ω 220 Ω 12 V ILLUSTRATION . For optimum results. CROSS-REFERENCES Lessons In Electric Circuits.
So. In one mode. Such systems sample the waveform of the ambient noise. 60-Hertz tone should be heard from the speakers. Now. In the other mode. and even light waves! Multiple speakers in a stereo sound system must be properly "phased" so that their respective sound waves don't cancel each other. electrical signals (voltage "waves"). even in an AC system where there really is no such thing as constant "polarity. facing toward each other.4. If the tone sounds too loud. SOUND CANCELLATION 173 Low-voltage AC power supply 12 6 6 Speaker Speaker INSTRUCTIONS Connect each speaker to the low-voltage AC power supply through a 220 Ω resistor. A low-pitched." the sequence of wire connections may make a significant difference in system performance. Listen to the volume of the 60-Hertz tone. This principle of volume reduction by destructive interference may be exploited for noise cancellation. This phenomenon is common to all wave events: sound waves. the sound waves will destructively interfere. they cancel each other . comparing volume levels each way. With both speakers connected and producing sound. use higher-value resistors. When the two sound signals meet. What do you notice? By reversing wire connections to one speaker. waves in water. reverse the connections (the "polarity") of just one of the speakers and note the volume again. resulting in diminished volume. then produce an identical sound signal 180o out of phase with the noise. position them so that they are only a foot or two away.10. Try switching the polarity of one speaker back and forth from original to reversed. leaving less total sound level for the listener(s) to hear. The resistor limits the amount of power delivered to each speaker by the power supply. you are reversing the phase of that speaker's sound wave in reference to the other speaker. the sound waves will reinforce one another for a strong volume.
this is much easier accomplished with noise sources of steady frequency and amplitude.174 CHAPTER 4. as some sort of signal-processing circuit must sample the noise and generate precisely the right amount of cancellation sound at just the right time in order to be effective. ideally eliminating all the noise. . Cancellation of random. As one might guess. AC CIRCUITS out. broad-spectrum noise is very difficult.
One may be scavenged from a small. The primary winding is rated in ohms of impedance (1000 Ω). flute.) would be good. The "impedance matching transformer" is a small-size transformer easily obtained from an electronics supply store. junk radio: it connects between the speaker and the circuit board (amplifier). harp. and is usually center-tapped. the 1000 Ω winding will read more resistance than the 8 Ω winding.11. The "mono" plug will be plugged into the headphone jack of the musical keyboard. chapter 7: "Mixed-Frequency AC Signals" LEARNING OBJECTIVES • Difference between amplitude and frequency • Measuring AC voltage. If such a transformer cannot be obtained for the experiment. etc. chapter 1: "Basic AC Theory" Lessons In Electric Circuits. so get a plug that's the correct size for the keyboard. Volume 2.11 Musical keyboard as a signal generator PARTS AND MATERIALS • Electronic "keyboard" (musical) • "Mono" (not stereo) headphone-type plug • Impedance matching transformer (1k Ω to 8 Ω ratio. current with a meter • Transformer operation. a regular 120V/6V step-down power transformer works fairly well. You need not purchase an expensive keyboard for this – but one with at least a few dozen "voice" selections (piano.4. because it has more turns. MUSICAL KEYBOARD AS A SIGNAL GENERATOR 175 4. Volume 2. so don't expect to read 1000 Ω and 8 Ω with your ohmmeter – however. The secondary winding is 8 Ω and not center-tapped. Radio Shack catalog # 273-1380) • 10 kΩ resistor In this experiment. too. These impedance figures are not the same as DC resistance. you'll learn how to use an electronic musical keyboard as a source of variablefrequency AC voltage signals. CROSS-REFERENCES Lessons In Electric Circuits. so is easily identifiable by location. step-up SCHEMATIC DIAGRAM Keyboard plug 8Ω 1 kΩ 10 kΩ .
When you insert the plug into the jack. and the signal that used to power that speaker will be available at the plug wires. and provides features that most signal generators cannot match. An inexpensive electronic keyboard is a cheaper alternative to a regular signal generator. AC CIRCUITS V V OFF A A 1000 Ω 8Ω A COM plug "Voice" selection Volume INSTRUCTIONS Normally. a student of electronics in a school would have access to a device called a signal generator. In this . or function generator. such as producing mixed-frequency waves. used to make variable-frequency voltage waveforms to power AC circuits.176 ILLUSTRATION CHAPTER 4. you'll need to insert a plug into the headphone jack (sometimes just labeled "phone" on the keyboard) complete with two wires for connection to circuits of your own design. To "tap in" to the AC voltage produced by the keyboard. the normal speaker built in to the keyboard will be disconnected (assuming the keyboard is equipped with one).
or something close to it (flute. It should be the same as for the voltage for any given note (keyboard key). Make sure the keyboard is set to a mode where the note will be sustained as any key is held down – otherwise. If your multimeter has a frequency function.11. I recommend using the keyboard to power the 8 Ω side of an audio "output" transformer to step up voltage to a higher level. of integer-multiple frequency). then decaying rapidly to zero). for example). If your multimeter has a "frequency" function. write the frequencies in Hertz in black ink on the white keys. you can measure the frequency of this current as well. Being composed of just one frequency. MUSICAL KEYBOARD AS A SIGNAL GENERATOR 177 particular experiment. Using an AC voltmeter. so there is no shock hazard in this experiment. Try different notes on the keyboard and record their frequencies. and measure AC current with your multimeter. there should be no change in signal amplitude (voltage) as different frequencies (notes on the keyboard) are tried. Do you notice a pattern in frequency as you activate different notes. . especially keys that are similar to each other (notice the 12-key black-andwhite pattern repeated on the keyboard from left to right)? If you don't mind making marks on your keyboard. If using a power transformer instead of an audio output transformer. read the voltage as stepped up by the transformer. I have found that the "panflute" voice setting produces the truest sine-wave waveform. use it to measure the frequency of the waveform produced by the keyboard. If you adjust the volume up and down. Try connecting the keyboard output to a 10 kΩ load resistance (through the headphone plug). Amplitude and frequency are two completely independent aspects of an AC signal. is recommended to start experimenting with since it is relatively free of harmonics (many waveforms mixed together.4. noting the step ratio. Using an inexpensive Yamaha keyboard. it is a less complex waveform for your multimeter to measure. connect the keyboard to the low-voltage winding so that it operates as a step-up device. read the voltage direct from the headphone plug. you should discover that changes in amplitude should have little or no impact on frequency measurement. near the tops where fingers are less likely to rub the numbers off. Keyboards produce very low voltage signals. Then. Ideally. This waveform. the amplitude (voltage) of the waveform will be constantly changing (high when the key is first pressed.
12 PC Oscilloscope PARTS AND MATERIALS • IBM-compatible personal computer with sound card. for free personal and academic use. It plots waveforms on the computer screen in response to AC voltage signals interpreted by the sound card microphone input. Constantin Zeldovich. AC CIRCUITS 4. chapter 7: "Mixed-Frequency AC Signals" Lessons In Electric Circuits. Volume 2. called Oscope. CROSS-REFERENCES Lessons In Electric Circuits. running Windows 3. downloaded free from internet • Electronic "keyboard" (musical) • "Mono" (not stereo) headphone-type plug for keyboard • "Mono" (not stereo) headphone-type plug for computer sound card microphone input • 10 kΩ potentiometer The Winscope program I've used was written by Dr. If you don't have access to either software.178 CHAPTER 4.1 or better • Winscope software. is made for the Linux operating system. chapter 12: "AC Metering Circuits" LEARNING OBJECTIVES • Computer use • Basic oscilloscope function SCHEMATIC DIAGRAM Keyboard plug 10 kΩ plug Computer ILLUSTRATION . Volume 2. you may use the "sound recorder" utility that comes stock with most versions of Microsoft Windows to display crude waveshapes. A similar program.
commercial oscilloscopes tend to be expensive. No serious electronics lab should be without one (or two!). Unfortunately." Connect these test leads to the potentiometer: between the middle terminal (the wiper) and either of the outer terminals. but other voltage sources might be hazardous to your computer's health. Almost any waveshape will be "clipped" to look like a square wave if it exceeds the amplitude limit of the sound card. this becomes a viable alternative for the experimenter on a budget.4. Since most people either have a personal computer or can obtain one for less cost than an oscilloscope. you need to adjust the potentiometer for a lower-amplitude signal. Start the Winscope program and click on the "arrow" icon in the upper-left corner (it looks like the "play" arrow seen on tape player and CD player control buttons). One word of caution: you can cause significant hardware damage to your computer if signals of excessive voltage are connected to the sound card's microphone input! The AC voltages produced by a musical keyboard are too low to cause damage to your computer through the sound card. and it is almost impossible to design and build your own without another oscilloscope to troubleshoot it! However. If you press a key on the musical keyboard.12. connect the keyboard output to the outer terminals of a 10 kΩ potentiometer. the sound card of a personal computer is capable of "digitizing" low-voltage AC signals from a range of a few hundred Hertz to several thousand Hertz with respectable resolution. If the computer displays a waveform that looks kind of like a square wave. you should see some kind of waveform displayed on the screen. Solder two wires to the connection points on the sound card microphone input plug. PC OSCILLOSCOPE 179 Computer plug mic. Choose the "panflute" or some other flute-like voice on the musical keyboard for the best sine-wave shape. Use this "oscilloscope" at your own risk! Using the keyboard and plug arrangement described in the previous experiment. input plug "Voice" selection Volume Monitor INSTRUCTIONS The oscilloscope is an indispensable test instrument for the electronics student and professional. . so that you have a set of "test leads" for the "oscilloscope. and free software is available for displaying these signals in oscilloscope form on the computer screen.
catalog # 910-3914. AC CIRCUITS Test different instrument "voices" on the musical keyboard and note the different waveshapes. noting how they change the appearance of the waveform. It is very limited in the ranges of voltage and frequency it can display. Experiment with the different controls in the Winscope window. and they are typically sold at less cost than a complete stand-alone oscilloscope (around $400. As a test instrument. Also. Having a computer serve as the display medium brings many advantages. not the least of which is the ability to easily store waveform pictures as digital files. relegating it to the analysis of lowand mid-range audio tones. It has almost no capability to make precision measurements of voltage. Radio Shack sells one made by Velleman. although its frequency precision is surprisingly good. presumably because of its limited frequency response. compared to the panflute voice. year 2002)." Despite these shortcomings. this "oscilloscope" is quite poor.180 CHAPTER 4. there are several professional-quality oscilloscope adapter devices manufactured for personal computers whose performance is far beyond that of a sound card. and for initial explorations into waveform analysis for the beginning student of electronics. it is useful as a demonstration tool. the coupling capacitor found in sound card microphone input circuits prevents it from measuring DC voltage: it is as though the "AC coupling" feature of a normal oscilloscope were stuck "on. Note how complex some of the waveshapes are. . For those who are interested. I have had very little success getting the "oscilloscope" to display good square waves.
13. chapter 7: "Mixed-Frequency AC Signals" LEARNING OBJECTIVES • Understand the difference between time-domain and frequency-domain plots • Develop a qualitative sense of Fourier analysis SCHEMATIC DIAGRAM Keyboard plug 10 kΩ plug Computer ILLUSTRATION . WAVEFORM ANALYSIS 181 4. with wires for connecting to voltage sources • 10 kΩ potentiometer Parts and equipment for this experiment are identical to those required for the "PC oscilloscope" experiment. Volume 2.4.1 or better • Winscope software. CROSS-REFERENCES Lessons In Electric Circuits.13 Waveform analysis PARTS AND MATERIALS • IBM-compatible personal computer with sound card. downloaded free from internet • Electronic "keyboard" (musical) • "Mono" (not stereo) headphone-type plug for keyboard • "Mono" (not stereo) headphone-type plug for computer sound card microphone input. running Windows 3.
the plot should show two distinct peaks. Contrast this with normal oscilloscope (time-domain) plot by clicking once again on the "rainbow" icon. while nonsymmetrical waveforms contain even-numbered harmonics as well. Generate a sine-wave signal using the musical keyboard (panflute or flute voice). AC CIRCUITS Computer plug mic. correlating the timedomain plot with the frequency-domain plot. Use the cursor to locate the specific frequency of each peak on the plot. Experiment with different instrument "voices" on the musical keyboard. If two notes are activated on the musical keyboard.182 CHAPTER 4. which plots amplitude (vertical) over frequency (horizontal). However. and you should see a single "spike" on the display. or fundamental frequency). A musical chord displayed in time-domain format is a very complex waveform. If using Winscope. Moving the mouse cursor beneath the peak should result in the frequency being displayed numerically at the bottom of the screen. and a calculator to determine whether each peak is even. Waveforms that are symmetrical above and below their centerlines contain only odd-numbered harmonics (odd-integer multiples of the base. a frequency-domain plot is the best tool.or odd-numbered. when it is desirable to see the harmonic constituency of a complex wave. each one corresponding to a particular note (frequency). which is fine for displaying waveshape. and so on. An oscilloscope's "time-domain" display plots amplitude (vertical) over time (horizontal). corresponding to the amplitude of the single-frequency signal. but is quite simple to resolve into constituent notes (frequencies) on a frequency-domain display. Basic chords (three notes) produce three spikes on the frequency-domain plot. click on the "rainbow" icon to switch to frequency-domain mode. . input plug "Voice" selection Volume Monitor INSTRUCTIONS The Winscope program comes with another feature other than the typical "time-domain" oscilloscope display: "frequency-domain" display.
CROSS-REFERENCES Lessons In Electric Circuits. INDUCTOR-CAPACITOR "TANK" CIRCUIT 183 4.4. The unused winding should be left open. but such inductors are more difficult to obtain than power transformers. with only one winding connected. Volume 2. single-winding inductor (sometimes known as a choke) may also be used. A simple iron core.14 Inductor-capacitor "tank" circuit PARTS AND MATERIALS • Oscilloscope • Assortment of non-polarized capacitors (0.1 µF to 10 µF) • Step-down power transformer (120V / 6 V) • 10 kΩ resistors • Six-volt battery The power transformer is used simply as an inductor.14. chapter 6: "Resonance" LEARNING OBJECTIVES • How to build a resonant circuit • Effects of capacitor size on resonant frequency • How to produce antiresonance SCHEMATIC DIAGRAM L C ILLUSTRATION .
oscillations will decay in amplitude over the course of several cycles due to the resistive and magnetic losses of the inductor. Ideally. called the resonant frequency. due to capacitor size. of course. Inductors with a high "Q" rating will. This effect of resistance dampening tank circuit oscillation is . Important note: I recommend against using a PC/sound card as an oscilloscope for this experiment. oscillations will ensue as energy is exchanged from the capacitor to inductor and visa-versa. You might notice changes in the duration of oscillations as well. Since you know how to calculate resonant frequency from inductance and capacitance. Use this figure as a rough estimate of inductance for your circuit to calculate expected oscillation frequency. and then briefly energized by connection to a DC voltage source. according to the following equation: fresonant = 1 2π LC Many small power transformers have primary (120 volt) winding inductances of approximately 1 H. A tank circuit's natural frequency. and perhaps other portions of the computer as well.184 CHAPTER 4. Try changing capacitor values and noting the effect on oscillation frequency. Realistically. is determined by the size of the inductor and the size of the capacitor. can you figure out a way to calculate inductor inductance from known values of circuit capacitance (as measured by a capacitance meter) and resonant frequency (as measured by an oscilloscope)? Resistance may be intentionally added to the circuit – either in series or parallel – for the express purpose of dampening oscillations. These oscillations may be viewed with an oscilloscope connected in parallel with the inductor/capacitor circuit. These high voltages will surely damage the sound card's input. the oscillations produced by a tank circuit continue indefinitely. because very high voltages can be generated by the inductor when the battery is disconnected (inductive "kickback"). produce longer-lasting oscillations than low-Q inductors. Parallel inductor/capacitor circuits are commonly known as tank circuits. AC CIRCUITS + - touch clips together (transformer used as an inductor) INSTRUCTIONS If an inductor and a capacitor are connected in parallel with each other.
Netlist (make a text file containing the following text. A lower Rstray value causes longer-lived oscillations because less energy is dissipated.14. verbatim): tank circuit with loss l1 1 0 1 ic=0 rstray 1 2 1000 c1 2 0 0.end .plot tran v(1. INDUCTOR-CAPACITOR "TANK" CIRCUIT 185 known as antiresonance.1u ic=6 .4.1m 20m uic . It is analogous to the action of a shock absorber in dampening the bouncing of a car after striking a bump in the road. Eliminating this resistor from the circuit results in endless oscillation. COMPUTER SIMULATION Schematic with SPICE node numbers: 1 L1 0 Rstray 2 C1 0 Rstray is placed in the circuit to dampen oscillations and produce a more realistic simulation.tran 0.0) .
AC CIRCUITS 4. Volume 2. Any unshielded multiconductor cable will suffice for this experiment.15 Signal coupling PARTS AND MATERIALS • 6 volt battery • One capacitor.186 CHAPTER 4. Volume 2. 0. chapter 7: "Mixed-Frequency AC Signals" Lessons In Electric Circuits.22 µF (Radio Shack catalog # 272-1070 or equivalent) • One capacitor. 0.047 µF (Radio Shack catalog # 272-134 or equivalent) • Small "hobby" motor. permanent-magnet type (Radio Shack catalog # 273-223 or equivalent) • Audio detector with headphones • Length of telephone cable. Cables with thin conductors (telephone cable is typically 24-gauge) produce a more pronounced effect. CROSS-REFERENCES Lessons In Electric Circuits. chapter 8: "Filters" LEARNING OBJECTIVES • How to "couple" AC signals and block DC signals to a measuring instrument • How stray coupling happens in cables • Techniques to minimize inter-cable coupling SCHEMATIC DIAGRAM Telephone cable Mtr ILLUSTRATION . several feet long (Radio Shack catalog # 278-872) Telephone cable is also available from hardware stores.
The motor should run. with the 0.047 µF capacitor in series. as expected. Now. SIGNAL COUPLING 187 Motor + Telephone cable headphones plug Sensitivity INSTRUCTIONS Connect the motor to the battery using two of the telephone cable's four conductors. connect the audio signal detector across the motor terminals.4.15. like this: .
because the motor is connected directly in parallel with the battery. The purpose of the series capacitor is to act as a high-pass filter. representing the AC "noise" voltage produced by the motor as the brushes make and break contact with the rotating commutator bars. Since the motor's terminals are electrically common with the respective terminals of the battery. and the battery's nature is to maintain a constant DC voltage. AC CIRCUITS + - headphones plug Sensitivity You should be able to hear a "buzz" or "whine" in the headphones.188 CHAPTER 4. current pulses drawn by the motor produce oscillating voltage "dips" at the motor terminals. so that the detector only receives the AC voltage across the motor's terminals. one would expect nothing but pure DC voltage at the motor's terminals. right? Well. causing the AC "noise" heard by the detector: . not any DC voltage. Ideally. nothing but DC voltage should appear at the motor terminals. because of resistance internal to the battery and along the conductor lengths. This is precisely how oscilloscopes provide an "AC coupling" feature for measuring the AC content of a signal without any DC bias voltage: a capacitor is connected in series with one test probe.
SIGNAL COUPLING 189 Rwire Battery Motor Rwire Use the audio detector to measure "noise" voltage directly across the battery. the less noise voltage we should detect: + headphones Sensitivity plug You may also measure noise voltage dropped along either of the telephone cable conductors supplying power to the motor. by connecting the audio detector between both ends of a single cable conductor.4. Since the AC noise is produced in this circuit by pulsating voltage drops along stray resistances.15. the less resistance we measure across. The noise detected here originates from current pulses through the resistance of the wire: .
because there is no DC voltage between these points for the detector to detect anyway: + - headphones Sensitivity plug .190 CHAPTER 4. AC CIRCUITS + - headphones Sensitivity plug Now that we have established how AC noise is created and distributed in this circuit. The 0. let's explore how it is coupled to adjacent wires in the cable.047 µF capacitor is not needed in this exercise. Use the audio detector to measure voltage between one of the motor terminals and one of the unused wires in the telephone cable.
If the additional signal was a DC signal. Since the primary coupling phenomenon in this circuit is capacitive in nature. higher-frequency noise voltages are more strongly coupled than lower-frequency noise voltages. with no AC expected in it. To illustrate. So long as the decoupling capacitor value is significantly larger than the stray "coupling" capacitance between the cable's conductors. depending on how much noise was coupled between the two circuits and how sensitive one circuit was to the other's noise. This could be quite detrimental. whether it be intentional or unintentional.4. that signal would become tainted with noise voltage from the motor. as shown: + "decoupling" capacitor headphones Sensitivity plug The decoupling capacitor acts as a practical short-circuit to any AC noise voltage. If we were to try and conduct a voltage signal between one of the unused wires and a point common with the motor. the AC noise voltage will be held to a minimum.15.22 µF capacitor for this purpose. Use the 0. while not affecting DC voltage signals between those two points at all. we could mitigate the problem of coupled noise by "decoupling" the AC noise with a relatively large capacitor connected across the DC signal's conductors. Remember that no current actually goes through a capacitance. SIGNAL COUPLING 191 The noise voltage detected here is due to stray capacitance between adjacent cable conductors creating an AC current "path" between the wires. provides alternating current a pathway of sorts. but the alternate charging and discharging action of a capacitance. connect the audio detector between the two unused wires and listen for a noise signal: . Another way of minimizing coupled noise in a cable is to avoid having two circuits share a common conductor.
Thus.192 CHAPTER 4. . The reason for this drastic reduction in noise is that stray capacitance between cable conductors tends to couple the same noise voltage to both of the unused conductors in approximately equal proportions. AC CIRCUITS + - headphones Sensitivity plug There should be far less noise detected between any two of the unused conductors than between one unused conductor and one used in the motor circuit. the detector only "sees" the difference between two approximately identical noise signals. when measuring voltage between those two conductors.
oscillators. amplifiers. Just for fun. and many other circuits. there are still some applications for vacuum tubes. one circuit is included in this section using a vacuum tube for amplification instead of a semiconductor transistor. but are far more mobile than in an insulator. Thus. connected together on some kind of circuit board or terminal strip. or integrated circuits. Though now considered obsolete for most purposes.1 Introduction A semiconductor device is one made of silicon or any number of other specially prepared materials designed to exploit the unique properties of electrons in a crystal lattice. "vacuum tubes" were the workhorses of the electronics industry: used to make rectifiers. These circuits employ all the components and concepts explored in the previous chapters. Before the advent of transistors. A discrete device is one contained in its own package. where electrons are not as free to move as in a conductor. not built on a common semiconductor substrate with other components. 193 . and it can be fun building and operating circuits using these devices. "discrete semiconductor circuits" are circuits built out of individual semiconductor components.Chapter 5 DISCRETE SEMICONDUCTOR CIRCUITS 5. so a firm comprehension of DC and AC electricity is essential before embarking on these experiments. as is the case with ICs.
chapter 3: "Diodes and Rectifiers" LEARNING OBJECTIVES • Review inductive "kickback" • Learn how to suppress "kickback" using a diode SCHEMATIC DIAGRAM Switch #1 Switch #2 Diode Neon lamp Battery Inductor ILLUSTRATION . Volume 3. DISCRETE SEMICONDUCTOR CIRCUITS 5. even the home-made inductor or transformer from the AC experiments chapter! The diode need not be an exact model 1N4001. I recommend household light switches for their low cost and durability. 120VAC step-down to 12VAC (Radio Shack catalog # 273-1365. and they are quite easy to obtain.2 Commutating diode PARTS AND MATERIALS • 6 volt battery • Power transformer. Volume 1. Single-Throw") A power transformer is specified. SPST ("Single-Pole. CROSS-REFERENCES Lessons In Electric Circuits. but any iron-core inductor will suffice.194 CHAPTER 5. 273-1352. • One 1N4001 rectifying diode (Radio Shack catalog # 276-1101) • One neon lamp (Radio Shack catalog # 272-1102) • Two toggle switches. or 273-1511). chapter 16: "RC and L/R Time Constants" Lessons In Electric Circuits. Any of the "1N400X" series of rectifying diodes are suitable for the task.
noting the difference in circuit behavior. If switch #2 is closed (turned "on"). The cathode end of the diode (the end marked with a single band) must face the positive (+) side of the battery. Quickly close and open (turn "on" and then "off") switch #1. creating a short-circuit. and will give a greater lamp-flashing effect. This time. If the voltmeter registers only a small voltage with switch #1 "on. dissipating the inductor's stored energy harmlessly in the form of light and heat. the diode will now be a part of the circuit. COMMUTATING DIODE 195 Switch #1 + - 120 V Switch #2 12 V INSTRUCTIONS When assembling the circuit.2. When that switch is opened. Inductive kickback is detrimental to switch contacts. In this circuit." the diode is probably connected backward. causing undue arcing and shortened switch life. there is still a fairly high voltage dropped across the opening contacts of switch #1.5. However. the neon bulb will flash from the effect of inductive "kickback." Rapid current decrease caused by the switch's opening causes the inductor to create a large voltage drop as it attempts to keep current at the same magnitude and going in the same direction. be very careful of the diode's orientation. Connect a voltmeter across the inductor to verify that the inductor is still receiving full battery voltage with switch #1 closed. This disconnects the diode from the circuit so that it has no effect. as it causes excessive arcing whenever they are opened. Set switch #2 to the "off" position. The diode should be reverse-biased and nonconducting with switch #1 in the "on" position. Use the high-voltage (120 V) winding of the transformer for the inductor coil. . The primary winding of a step-down transformer has more inductance than the secondary winding. the neon lamp actually diminishes the effect by providing an alternate current path for the inductor's current when the switch opens. Quickly close and open switch #1 again. the neon lamp does not flash.
so use a greater-value capacitor value if you experience difficulty hearing the tone(s). CROSS-REFERENCES Lessons In Electric Circuits.3 Half-wave rectifier PARTS AND MATERIALS • Low-voltage AC power supply (6 volt output) • 6 volt battery • One 1N4001 rectifying diode (Radio Shack catalog # 276-1101) • Small "hobby" motor. If you haven't built one already. A 0. This capacitor's value is not critical. Any of the "1N400X" series of rectifying diodes are suitable for the task.196 CHAPTER 5.1 µF capacitor is specified for "coupling" the audio detector to the circuit. Lower capacitor values attenuate low-frequency signals to a greater degree. I've used capacitors ranging from 0. and they are quite easy to obtain. See the AC experiments chapter for detailed instructions on building the "audio detector" listed here. chapter 3: "Diodes and Rectifiers" LEARNING OBJECTIVES • Function of a diode as a rectifier • Permanent-magnet motor operation on AC versus DC power • Measuring "ripple" voltage with a voltmeter SCHEMATIC DIAGRAM Diode AC power supply Mtr (motor) ILLUSTRATION .1 µF capacitor (Radio Shack catalog # 272-135 or equivalent) The diode need not be an exact model 1N4001. you're missing a simple and valuable tool for experimentation.27 µF to 0. DISCRETE SEMICONDUCTOR CIRCUITS 5. resulting in less sound intensity from the headphones. so that only AC reaches the detector circuit. Volume 3. permanent-magnet type (Radio Shack catalog # 273-223 or equivalent) • Audio detector with headphones • 0.015 µF with success.
The diode only allows current to pass through during one half-cycle of a full positive-and-negative cycle of power supply voltage.5. albeit a pulsating current. Take a jumper wire and short past the diode momentarily. As a result. the motor only "sees" current in one direction.3. HALF-WAVE RECTIFIER 197 Low-voltage AC power supply 12 6 6 Diode Motor INSTRUCTIONS Connect the motor to the low-voltage AC power supply through the rectifying diode as shown. noting the effect on the motor's operation: . allowing it to spin in one direction. eliminating one half-cycle from ever reaching the motor.
Measure DC voltage across the motor like this: . DISCRETE SEMICONDUCTOR CIRCUITS Low-voltage AC power supply 12 6 6 Temporary jumper As you can see. Note the effect on the motor. permanent-magnet "DC" motors do not function well on alternating current. Remove the temporary jumper wire and reverse the diode's orientation in the circuit.198 CHAPTER 5.
3. measure AC voltage across the motor as well: V V OFF A A Low-voltage AC power supply 12 6 6 A COM . HALF-WAVE RECTIFIER 199 V V OFF A A Low-voltage AC power supply 12 6 6 A COM Then.5.
Ripple voltage is the varying portion of the voltage. interpreted as an AC quantity by measurement equipment although the voltage waveform never actually reverses polarity. Compare these measurements of DC and AC with voltage measurements taken across the motor while powered by a battery: V V OFF A A A COM + - Batteries give very "pure" DC power. and as a result there should be very little AC voltage measured across the motor in this circuit.200 CHAPTER 5. like this: . A qualitative assessment of ripple voltage may be obtained by using the sensitive audio detector described in the AC experiments chapter (the same device described as a "sensitive voltage detector" in the DC experiments chapter). and these two measurements show the DC average and AC "ripple" voltages. resulting in pulsating voltage "dips" at the motor terminals. Turn the detector's sensitivity down for low volume. and connect it across the motor terminals through a small (0. respectively of the power "seen" by the motor. Ripple may be envisioned as an AC signal superimposed on a steady DC "bias" or "offset" signal. This pulsating current causes pulsating voltages to be dropped across any stray resistances in the circuit. Whatever AC voltage is measured across the motor is due to the motor's pulsating current draw as the brushes make and break contact with the rotating commutator bars.1 µF) capacitor. DISCRETE SEMICONDUCTOR CIRCUITS Most digital multimeters do a good job of discriminating AC from DC voltage.
the ripple should sound like a highpitched "buzz" or "whine.5. "listening" with the detector to the low-pitched "buzz" of the half-wave rectified power: .3. With a battery powering the motor.1 µF Sensitivity plug + - The capacitor acts as a high-pass filter." where DC signals are blocked from viewing by a seriesconnected capacitor." Try replacing the battery with the AC power supply and rectifying diode. blocking DC voltage from reaching the detector and allowing easier "listening" of the remaining AC voltage. HALF-WAVE RECTIFIER headphones 201 Capacitor 0. This is the exact same technique used in oscilloscope circuitry for "AC coupling.
verbatim): Halfwave rectifier v1 1 0 sin(0 8.0) .tran .485 60 0 0) rload 2 0 10k d1 1 2 mod1 .202 CHAPTER 5.model mod1 d .0) v(2.end This simulation plots the input voltage as a sine wave and the output voltage as a series of "humps" corresponding to the positive half-cycles of the AC source voltage. unfortunately.plot tran v(1. The dynamics of a DC motor are far too complex to be simulated using SPICE. .5m 25m . DISCRETE SEMICONDUCTOR CIRCUITS headphones Low-voltage AC power supply 12 6 6 Sensitivity plug COMPUTER SIMULATION Schematic with SPICE node numbers: D1 1 V1 0 2 Rload 0 Netlist (make a text file containing the following text.
In simulations where the distinction between RMS and peak value isn't relevant. A 6 volt RMS sine-wave voltage is actually 8. but I discuss it here for your edification. the distinction is not terribly important in this simulation. I will not bother with an RMS-to-peak conversion like this.5. HALF-WAVE RECTIFIER 203 AC source voltage is specified as 8. . To be truthful.3.485 instead of 6 volts because SPICE understands AC voltage in terms of peak value only.485 volts peak.
The diodes need not be exact model 1N4001 units. Volume 3. permanent-magnet type (Radio Shack catalog # 273-223 or equivalent) • Audio detector with headphones • 0. A transformer with a non-tapped secondary winding simply will not work for this circuit.204 CHAPTER 5.4 Full-wave center-tap rectifier PARTS AND MATERIALS • Low-voltage AC power supply (6 volt output) • Two 1N4001 rectifying diodes (Radio Shack catalog # 276-1101) • Small "hobby" motor. Any of the "1N400X" series of rectifying diodes are suitable for the task. Single-Throw") It is essential for this experiment that the low-voltage AC power supply be equipped with a center tap. CROSS-REFERENCES Lessons In Electric Circuits. chapter 3: "Diodes and Rectifiers" LEARNING OBJECTIVES • Design of a center-tap rectifier circuit • Measuring "ripple" voltage with a voltmeter SCHEMATIC DIAGRAM Diode AC power supply Diode ILLUSTRATION Mtr (motor) . DISCRETE SEMICONDUCTOR CIRCUITS 5. and they are quite easy to obtain.1 µF capacitor • One toggle switch. SPST ("Single-Pole.
FULL-WAVE CENTER-TAP RECTIFIER 205 Low-voltage AC power supply 12 6 6 Terminal strip Motor INSTRUCTIONS This rectifier circuit is called full-wave because it makes use of the entire waveform. there is less "ripple" voltage seen at the load.5. you may add a switch in the circuit to open and close this connection at will: Mtr Switch (close for full-wave operation) . Use a voltmeter to measure both the DC and AC voltage delivered to the motor. both positive and negative half-cycles.4. The RMS (Root-Mean-Square) value of the rectifier's output is also greater for this circuit than for the half-wave rectifier. of the AC source voltage in powering the DC load. As a result. An experimental advantage of this circuit is the ease of which it may be "de-converted" to a half-wave rectifier: simply disconnect the short jumper wire connecting the two diodes' cathode ends together on the terminal strip. You should notice the advantages of the full-wave rectifier immediately by the greater DC and lower AC indications as compared to the last experiment. Better yet. for quick comparison between half and full-wave rectification.
206 CHAPTER 5. DISCRETE SEMICONDUCTOR CIRCUITS Low-voltage AC power supply 12 Switch 6 6 With the ability to quickly switch between half. Use the audio signal detector to "listen" to the ripple voltage present between the motor terminals for half-wave and full-wave rectification modes. noting both the intensity and the quality of the tone. you may easily perform qualitative comparisons between the two different operating modes.and full-wave rectification. Remember to use a coupling capacitor in series with the detector so that it only receives the AC "ripple" voltage and not DC voltage: .
4.485 60 0 0) v2 0 3 sin(0 8. verbatim): Fullwave center-tap rectifier v1 1 0 sin(0 8.1 µF Sensitivity plug Test "probes" COMPUTER SIMULATION Schematic with SPICE node numbers: 1 V1 0 V2 3 D1 2 2 Rload 0 D2 2 Netlist (make a text file containing the following text.5. FULL-WAVE CENTER-TAP RECTIFIER 207 headphones Capacitor 0.485 60 0 0) rload 2 0 10k d1 1 2 mod1 .
DISCRETE SEMICONDUCTOR CIRCUITS .208 d2 3 2 mod1 .tran .0) v(2.0) .model mod1 d .end CHAPTER 5.5m 25m .plot tran v(1.
compared to the center-tap circuit SCHEMATIC DIAGRAM AC power supply Mtr (motor) ILLUSTRATION Low-voltage AC power supply 12 6 6 Terminal strip Motor . chapter 3: "Diodes and Rectifiers" LEARNING OBJECTIVES • Design of a bridge rectifier circuit • Advantages and disadvantages of the bridge rectifier circuit.5. FULL-WAVE BRIDGE RECTIFIER 209 5.5. permanent-magnet type (Radio Shack catalog # 273-223 or equivalent) CROSS-REFERENCES Lessons In Electric Circuits. Volume 3.5 Full-wave bridge rectifier PARTS AND MATERIALS • Low-voltage AC power supply (6 volt output) • Four 1N4001 rectifying diodes (Radio Shack catalog # 276-1101) • Small "hobby" motor.
verbatim): Fullwave bridge rectifier v1 1 0 sin(0 8.model mod1 d . In applications where a center-tapped. DISCRETE SEMICONDUCTOR CIRCUITS INSTRUCTIONS This circuit provides full-wave rectification without the necessity of a center-tapped transformer.tran . this is the only practical method of full-wave rectification. Compare the DC voltage reading across the motor terminals with the reading obtained from the last experiment. In addition to requiring more diodes than the center-tap circuit.5m 25m .210 CHAPTER 5.0) v(2. source is unavailable. given the same AC power supply and the same motor. or split-phase.485 60 0 0) rload 2 3 10k d1 3 1 mod1 d2 1 2 mod1 d3 3 0 mod1 d4 0 2 mod1 .end . COMPUTER SIMULATION Schematic with SPICE node numbers: 1 D1 V1 3 D3 0 0 D 4 1 D2 2 2 Rload 3 Netlist (make a text file containing the following text.3) . this disadvantage is easily measured.plot tran v(1. the full-wave bridge suffers a slight performance disadvantage as well: the additional voltage drop caused by current having to go through two diodes in each half-cycle rather than through only one. With a low-voltage source such as the one you're using (6 volts RMS).
choose a capacitor with a working voltage rating at least twice the RMS AC voltage output of the low-voltage AC power supply. at least 25 WVDC (Radio Shack catalog # 272-1047 or equivalent) • Four "banana" jack style binding posts. so long as its working voltage is high enough.6 Rectifier/filter circuit PARTS AND MATERIALS • Low-voltage AC power supply • Bridge rectifier pack (Radio Shack catalog # 276-1185 or equivalent) • Electrolytic capacitor. chapter 8: "Filters" LEARNING OBJECTIVES • Capacitive filter function in an AC/DC power supply • Importance of heat sinks for power semiconductors SCHEMATIC DIAGRAM Rectifier AC in + DC out . 25 watt • Lamp socket A bridge rectifier "pack" is highly recommended over constructing a bridge rectifier circuit from individual diodes. High-wattage 12-volt lamps may be purchased from recreational vehicle (RV) and boating supply stores. A larger capacitor value is fine to use in this experiment. CROSS-REFERENCES Lessons In Electric Circuits. 1000 µF. This lamp will be used as a "heavy" load for the power supply. because such "packs" are made to bolt onto a metal heat sink. A metal box is recommended over a plastic box for its ability to function as a heat sink for the rectifier.6. RECTIFIER/FILTER CIRCUIT 211 5. Common sizes are 25 watt and 50 watt. To be safe. for connection to potentiometer circuit (Radio Shack catalog # 274-662 or equivalent) • Metal box • 12-volt light bulb. Volume 2. or other terminal hardware.5.
Rectifier units of this size are often equipped with "quick-disconnect" terminals. and plug. and they also allow for easy disconnection of wires without sacrificing connection durability. power cord. Terminal strips inherently provide test points for taking voltage measurements. self-contained 120VAC/DC power supply. you should build it to be maintained. It also means making "test points" accessible to meter probes throughout the circuit. more than enough for the output of the low-voltage AC power supply specified in the AC experiments chapter. so that troubleshooting may be executed with a minimum of inconvenience. but I recommend against direct soldering to any semiconductor component for two reasons: possible heat damage during soldering. among other things. The bridge rectifier unit should be rated for a current at least as high as the transformer's secondary winding is rated for. .212 ILLUSTRATION CHAPTER 5. This is the preferred method of terminal connection. DC power suitable as a replacement for a battery in battery-powered experiments. plus an additional safety margin). The Radio Shack rectifier specified in the parts list is rated for 25 amps and 50 volts. you may add all the componentry of the low-voltage AC supply to the "AC in" side of this circuit: a transformer. With this device. and so if you have any intent of making a circuit permanent. Semiconductor devices are more prone to failure than most of the components covered in these experiments thus far. making all delicate components replaceable. Complementary "quick-disconnect" lugs are sold that crimp onto the bare ends of wire. You may solder wires directly to the lugs of the rectifier. Even if you don't choose to do this. you will have a source of low-voltage. I recommend using a metal box larger than necessary to provide room for additional voltage regulation circuitry you might choose to add to this project later. and difficulty of replacing the component in the event of failure. and for a voltage at least twice as high as the RMS voltage of the transformer's output (this allows for peak voltage. If you would like to make this device its own. "Maintainable construction" involves. DISCRETE SEMICONDUCTOR CIRCUITS Rectifier AC in AC Capacitor + AC - - DC out INSTRUCTIONS This experiment involves constructing a rectifier and filter circuit for attachment to the lowvoltage AC power supply constructed earlier.
It should read substantially higher than the RMS voltage of the AC input measured before. In this circuit especially. it is sensitive to damage by polarity reversal. A capacitor is included in the circuit to act as a filter to reduce ripple voltage. where the internal resistance of the transformer and rectifier are low and the short-circuit current consequently is high. Any metal radiator surface designed to lower the operating temperature of an electronic component is called a heat sink. Semiconductor devices in general are prone to damage from overheating. switch your multimeter to the DC voltage function and measure the DC voltage output by the rectifier/filter circuit. so that the polarities match. so providing a path for heat transfer from the device(s) to the ambient air is very important when the circuit in question may handle large amounts of power. Make sure that you connect the capacitor properly across the DC output terminals of the rectifier. This voltage measurement is the RMS voltage of the AC power supply. RECTIFIER/FILTER CIRCUIT 213 Bolt the rectifier unit to the inside of the metal box. The filtering action of the capacitor provides a DC output voltage equal to the peak AC voltage. The box's surface area will act as a radiator. Your meter should indicate approximately 6 volts if the circuit is connected as shown. Being an electrolytic capacitor.5. Now. the potential for damage is great.6. Warning: a failed capacitor in this circuit will likely explode with alarming force! After the rectifier/filter circuit is built. keeping the rectifier unit cool as it passes high currents. connect it to the low-voltage AC power supply like this: Low-voltage AC power supply 12 6 6 Rectifier AC in AC Capacitor + AC - - DC out Measure the AC voltage output by the low-voltage power supply. hence the greater voltage indication: .
with filtering Time Measure the AC ripple voltage magnitude with a digital voltmeter set to AC volts (or AC millivolts). connect the 25 watt light bulb to the output of the rectifier/filter circuit like this: Low-voltage AC power supply 12 6 6 Rectifier AC in AC Capacitor + AC - - DC out Re-measure the ripple voltage present between the rectifier/filter unit's "DC out" terminals. resulting in greater ripple than before: .214 CHAPTER 5. As usual. but only the AC ripple. rectified DC voltage. Feel free to use your audio detector to "listen" to the AC ripple voltage output by the rectifier/filter unit. After taking unloaded AC ripple voltage measurements. Very little sound should be heard. the filter capacitor becomes discharged between rectified voltage peaks. DISCRETE SEMICONDUCTOR CIRCUITS Full-wave. With a heavy load. connect a small "coupling" capacitor in series with the detector so that it does not respond to the DC voltage. rectified DC voltage Time Full-wave. You should notice a much smaller ripple voltage in this circuit than what was measured in any of the unfiltered rectifier circuits previously built.
5. be sure to use an iron-core inductor for maximum inductance. Leave the primary (120 volt) winding open: Leave these wires disconnected! DC out COMPUTER SIMULATION Schematic with SPICE node numbers: 1 D1 V1 3 D3 0 1 D2 2 0 D C1 4 2 Rload 3 .6. and one with thick enough wire to safely handle the full rated current of power supply. If a suitable choke cannot be obtained. because they "choke" AC ripple voltage from getting to the load. or a more complex filter circuit may be built using two capacitors and an inductor: DC out If you choose to build such a filter circuit. a larger capacitor may be used. filtered DC voltage under heavy load Time If less ripple is desired under heavy-load conditions. Inductors used for the purpose of filtering are sometimes referred to as chokes. RECTIFIER/FILTER CIRCUIT 215 Full-wave. the secondary winding of a step-down power transformer like the type used to step 120 volts AC down to 12 or 6 volts AC in the low-voltage power supply may be used.
tran .216 CHAPTER 5. As it is with a 10 kΩ load resistor.485 60 0 0) rload 2 3 10k c1 2 3 1000u ic=0 d1 3 1 mod1 d2 1 2 mod1 d3 3 0 mod1 d4 0 2 mod1 . verbatim): Fullwave bridge rectifier v1 1 0 sin(0 8.5m 25m . .end You may decrease the value of Rload in the simulation from 10 kΩ to some lower value to explore the effects of loading on ripple voltage.0) v(2.plot tran v(1. DISCRETE SEMICONDUCTOR CIRCUITS Netlist (make a text file containing the following text.3) . the ripple is undetectable on the waveform plotted by SPICE.model mod1 d .
I highly recommend one with a zener voltage rating greater than the voltage of a single battery. for maximum learning experience. Whatever diode model you choose. CROSS-REFERENCES Lessons In Electric Circuits. chapter 3: "Diodes and Rectifiers" LEARNING OBJECTIVES • Zener diode function SCHEMATIC DIAGRAM 10 kΩ Zener diode ILLUSTRATION + - . It is important that you see how a zener diode functions when exposed to a voltage less than its breakdown rating. 12 volt – type 1N4742 (Radio Shack catalog # 276-563 or equivalent) • One 10 kΩ resistor Any low-voltage zener diode is appropriate for this experiment.5.7. The 1N4742 model listed here (zener voltage = 12 volts) is but one suggestion. VOLTAGE REGULATOR 217 5.7 Voltage regulator PARTS AND MATERIALS • Four 6 volt batteries • Zener diode. Volume 3.
Record this voltage drop for future reference. forming an 18 volt and 24 volt power source. this 12-volt zener diode does not drop 12 volts when the power source is only 6 volts strong. as well as the resistor's voltage drop. DISCRETE SEMICONDUCTOR CIRCUITS INSTRUCTIONS Build this simple circuit. because they act to clamp the voltage drop across themselves at a predetermined level. It is helpful to think of a zener diode as a voltage limiter : establishing a maximum voltage drop. Whatever excess voltage is supplied by the power source becomes dropped across the series resistor.218 CHAPTER 5. for 12 volts total power source voltage. Also. respectively. and measure the voltage across the diode with one battery as a power source. then four 6-volt batteries together in series. Re-measure the diode's voltage drop. measure and record the voltage drop across the 10 kΩ resistor. COMPUTER SIMULATION . with a voltmeter: V V OFF A A A COM + - + - Connect three. it is important to note that a zener diode cannot make up for a deficiency in source voltage. Modify the circuit by connecting two 6-volt batteries in series. For instance. What do you notice about the diode's voltage drop for these four different source voltages? Do you see how the diode voltage never exceeds a level of 12 volts? What do you notice about the resistor's voltage drop for these four different source voltage levels? Zener diodes are frequently used as voltage regulating devices. but not a minimum voltage drop. However. being sure to connect the diode in "reverse-bias" fashion (cathode positive and anode negative). Measure and record the diode's and resistor's voltage drops for each new power supply voltage.
.dc v1 18 18 1 .0) .7.end A zener diode may be simulated in SPICE with a normal diode. the reverse breakdown parameter (bv=12) set to the desired zener breakdown voltage. VOLTAGE REGULATOR Schematic with SPICE node numbers: 219 1 10 kΩ 2 Zener diode 0 0 Netlist (make a text file containing the following text. verbatim): Zener diode v1 1 0 r1 1 2 10k d1 0 2 mod1 .model mod1 d bv=12 .5.print dc v(2.
8 Transistor as a switch PARTS AND MATERIALS • Two 6-volt batteries • One NPN transistor – models 2N2222 or 2N3403 recommended (Radio Shack catalog # 2761617 is a package of fifteen NPN transistors ideal for this and other experiments) • One 100 kΩ resistor • One 560 Ω resistor • One light-emitting diode (Radio Shack catalog # 276-026 or equivalent) Resistor values are not critical for this experiment. DISCRETE SEMICONDUCTOR CIRCUITS 5. Neither is the particular light emitting diode (LED) selected. CROSS-REFERENCES Lessons In Electric Circuits.220 CHAPTER 5. chapter 4: "Bipolar Junction Transistors" LEARNING OBJECTIVES • Current amplification of a bipolar junction transistor SCHEMATIC DIAGRAM 560 Ω 6V 6V 100 kΩ Q1 ILLUSTRATION . Volume 3.
12 mA. because the 100 kΩ resistor to which the loose wire is attached restricts current through it to a far lesser value than 20 mA. the LED should light up. TRANSISTOR AS A SWITCH 221 CBE + - + - INSTRUCTIONS The red wire shown in the diagram (the one terminating in an arrowhead. like this: .8. or 120 µA! The connection made by your touching the wire to a positive point in the circuit conducts far less current than 1 mA. connected to one end of the 100 kΩ resistor) is intended to remain loose. so this behavior should strike you as interesting. such as the positive side of the DC power source. so that you may touch it momentarily to other points in the circuit. At most. It takes 20 mA to fully illuminate a standard LED. a total voltage of 12 volts across a 100 kΩ resistance yields a current of only 0. yet through the amplifying action of the transistor. Try using an ammeter to connect the loose wire to the positive side of the power source.5. is able to control a much greater current through the LED. If you touch the end of the loose wire to any point in the circuit more positive than it.
try measuring the LED's current (the controlled current) and compare magnitudes. switching current on and off to the LED at the command of a much smaller current signal conducted through its base terminal. DISCRETE SEMICONDUCTOR CIRCUITS CBE + - + - V V OFF A A A COM You may have to select the most sensitive current range on the meter to measure this small flow. To further illustrate just how miniscule the controlling current is. the transistor is acting as a kind of electrically-controlled switch. remove the loose wire from the circuit and try "bridging" the unconnected end of the 100 kΩ resistor to the power source's positive pole with two fingers of one hand. You may need to wet the ends of those fingers to maximize conductivity: .222 CHAPTER 5. After measuring this controlling current. Don't be surprised if you find a ratio in excess of 200 (the controlled current 200 times as great as the controlling current)! As you can see.
Try varying the contact pressure of your fingers with these two points in the circuit to vary the amount of resistance in the controlling current's path. i. as a variable COMPUTER SIMULATION Schematic with SPICE node numbers: 1 1 560 Ω 1 R2 3 D1 100 kΩ 4 Q1 0 V1 1 0 R1 2 Netlist (make a text file containing the following text.5.8. verbatim): Transistor as a switch v1 1 0 r1 1 2 100k r2 1 3 560 d1 3 4 mod2 . to conduct a small current to the transistor's base. TRANSISTOR AS A SWITCH 223 CBE + - + - Bridge the two points identified by arrows with two fingers of one hand. Can you vary the brightness of the LED by doing so? What does this indicate about the transistor's ability to act as more than just a switch.e.
R1 's voltage drop (voltage between nodes 1 and 2) ends up being 11. .15 volts.224 q1 4 2 .32 mA by Ohm's Law (I=E/R).print .5 µA.3) v(3.0) v(4.0) v(1.26 volts. the is=1e-28 parameter in the diode's . a very small current is exerting control over a much larger current in this circuit.4) In this simulation.model line is there to make the diode act more like an LED with a higher forward voltage drop.end CHAPTER 5.model . indicating a LED current of 18.dc v1 . Obviously. DISCRETE SEMICONDUCTOR CIRCUITS 0 mod1 mod1 npn bf=200 mod2 d is=1e-28 12 12 1 dc v(2. which across 100 kΩ gives a current of only 111.2) v(1.model . In case you were wondering. the voltage drop across the 560 Ω resistor v(1.3) turns out to be 10.
STATIC ELECTRICITY SENSOR 225 5. models 2N3819 or J309 recommended (Radio Shack catalog # 276-2035 is the model 2N3819) • One 6 volt battery • One 100 kΩ resistor • One light-emitting diode (Radio Shack catalog # 276-026 or equivalent) • Plastic comb The particular junction field-effect transistor. so be sure to check the manufacturer's specifications (component datasheet). Beware that it is possible for the transistor's package and even the manufacturer's datasheet to show incorrect terminal identification diagrams! Double-checking pin identities with your multimeter's "diode check" function is highly recommended. P-channel JFETs are also okay to use. Volume 3. CROSS-REFERENCES Lessons In Electric Circuits. consult chapter 5 of the Semiconductor volume (volume III) of this book series. or JFET. chapter 5: "Junction Field-Effect Transistors" LEARNING OBJECTIVES • How the JFET is used as an on/off switch • How JFET current gain differs from a bipolar transistor SCHEMATIC DIAGRAM 6V 100 kΩ Q1 . This will dictate how you connect the transistors together and to other components. Beware that not all transistors share the same terminal designations.5. or pinouts. For details on how to identify junction field-effect transistor terminals using a multimeter. but are not as popular as N-channel transistors. model used in this experiment is not critical.9 Static electricity sensor PARTS AND MATERIALS • One N-channel junction field-effect transistor. even if they share the same physical appearance. easily obtained from the manufacturer's website.9.
the mere presence of static electricity can turn it on and off at a distance. a much more "solid" connection between the transistor's gate terminal and a source of voltage was needed to turn it on. watching the effect on the LED. connected to the 100 kΩ resistor) with your hand. The action of combing your hair with a plastic object creates a high static voltage between the comb and your body. For a more controlled test. In fact. a junction field-effect transistor is used instead. giving dramatically improved sensitivity.226 ILLUSTRATION CHAPTER 5. there is no need for a dropping resistor to limit circuit current: the JFET does it intrinsically. for example. touch the wire with one hand and alternately touch the positive (+) and negative (-) terminals of the battery with one finger of your other hand. has a typical saturated drain current (I DSS ) of 10 mA and a maximum of 20 mA. Your body acts as a conductor (albeit a poor one). brush your hair with the plastic comb and then wave the comb near the transistor. Build this circuit and touch the loose wire end (the wire shown in red on the schematic diagram and in the illustration. as evidenced by full on-and-off control simply by conduction of a control current through your body. demonstrates how great of a current gain it has. The fact that a JFET is turned on and off so easily (requiring so little control current). Not so with the JFET. The strong electric field produced between these two objects should be detectable by this circuit from a significant distance! In case you're wondering why there is no 560 Ω "dropping" resistor to limit current through the LED. The model 2N3819. . connecting the gate terminal of the JFET to either terminal of the battery as you touch them. This circuit makes a fine sensor of static electricity! Try scuffing your feet on a carpet and then touching the wire end if no effect on the light is seen yet. To further experiment with the effects of static electricity on this circuit. With the BJT "switch" experiment. many small-signal JFETs tend to self-limit their controlled current to a level acceptable by LEDs. Try to relate this behavior with what you've read about JFETs in chapter 5 of the Semiconductor volume. Make note which terminal makes the LED turn on and which makes the LED turn off. In this experiment. Simply touching this wire will likely have an effect on the LED's status. Since most LEDs are rated at a forward current of 20 mA. DISCRETE SEMICONDUCTOR CIRCUITS SGD + - INSTRUCTIONS This experiment is very similar to the previous experiment using a bipolar junction transistor (BJT) as a switching device to control current through an LED.
you can use a nice set of audio headphones (closed-cup style.10. Connect these portions of the headphone stereo plug to the transformer's secondary (6 volt) winding: To transformer To transformer common right left Speakers in series common right left Speakers in parallel Try both the series and the parallel connection schemes for the loudest sound. just for this experiment. Volume 3. you really should – it is a valuable piece of test equipment for your collection.10 Pulsed-light sensor PARTS AND MATERIALS • Two 6-volt batteries • One NPN transistor – models 2N2222 or 2N3403 recommended (Radio Shack catalog # 2761617 is a package of fifteen NPN transistors ideal for this and other experiments) • One light-emitting diode (Radio Shack catalog # 276-026 or equivalent) • Audio detector with headphones If you don't have an audio detector already constructed. CROSS-REFERENCES Lessons In Electric Circuits. that completely covers your ears) and a 120V/6V step-down transformer to build a sensitive audio detector without volume control or overvoltage protection. If you haven't made an audio detector as outlined in both the DC and AC experiments chapters.5. PULSED-LIGHT SENSOR 227 5. chapter 4: "Bipolar Junction Transistors" LEARNING OBJECTIVES • How to use a transistor as a crude common-emitter amplifier • How to use an LED as a light sensor SCHEMATIC DIAGRAM .
LEDs have the little-known ability to produce .228 CHAPTER 5. DISCRETE SEMICONDUCTOR CIRCUITS 6V ILLUSTRATION CBE + - headphones Sensitivity plug INSTRUCTIONS This circuit detects pulses of light striking the LED and converts them into relatively strong audio signals to be heard through the headphones.
10. PULSED-LIGHT SENSOR 229 voltage when exposed to light. so a transistor is used to amplify the LED's signals. in a manner not unlike a semiconductor solar cell. . Sources of light suitable for this experiment include fluorescent and neon lamps. the "receiver" circuit shown here would convert those light pulses back into audio signals. With a little imagination.5. By itself. If the LED is exposed to a pulsing source of light. which blink rapidly with the 60 Hz AC power energizing them. a tone will be heard in the headphones. it is not difficult to grasp the concept of transmitting audio information – such as music or speech – over a beam of pulsing light. The rapidly passing shadows will cause the LED to generate pulses of voltage. then waving your fingers in front of the LED. Given a suitable "transmitter" circuit to pulse an LED on and off with the positive and negative crests of an audio waveform from a microphone. You may also try using bright sunlight for a steady light source. the LED does not produce enough electrical power to drive the audio detector circuit. creating a brief "buzzing" sound in the headphones.
or pinouts. Volume 3. chapter 4: "Bipolar Junction Transistors" LEARNING OBJECTIVES • Purpose of circuit "ground" when there is no actual connection to earth ground • Using a shunt resistor to measure current with a voltmeter • Measure amplifier voltage gain • Measure amplifier current gain • Amplifier impedance transformation SCHEMATIC DIAGRAM 6V 10 kΩ 6V Rbase Q1 1 kΩ Rload 1 kΩ . consult chapter 4 of the Semiconductor volume (volume III) of this book series.230 CHAPTER 5. even if they share the same physical appearance. Beware that it is possible for the transistor's package and even the manufacturer's datasheet to show incorrect terminal identification diagrams! Double-checking pin identities with your multimeter's "diode check" function is highly recommended. CROSS-REFERENCES Lessons In Electric Circuits. so be sure to check the manufacturer's specifications (component datasheet). easily obtained from the manufacturer's website.11 Voltage follower PARTS AND MATERIALS • One NPN transistor – models 2N2222 or 2N3403 recommended (Radio Shack catalog # 2761617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two 6-volt batteries • Two 1 kΩ resistors • One 10 kΩ potentiometer. DISCRETE SEMICONDUCTOR CIRCUITS 5. single-turn. This will dictate how you connect the transistors together and to other components. linear taper (Radio Shack catalog # 271-1715) Beware that not all transistors share the same terminal designations. For details on how to identify bipolar transistor terminals using a multimeter.
The voltage follower is the safest and easiest transistor amplifier circuit to build. This does not necessarily represent a connection to the actual earth. With bipolar junction transistors. not even for all NPN-type transistors! As usual. Its purpose is to provide approximately the same voltage to a load as what is input to the amplifier.11. What it means is that this point in the circuit – and all points electrically common to it – constitute the default reference point for all voltage measurements in the circuit. This is correct for the model 2N2222 transistor and some others. but at a much greater current.5. Base. but it does have current gain. Note that the negative (-) side of the power supply is shown in the schematic diagram to be connected to ground. a "common" point of reference designated in a circuit gives us the ability to speak meaningfully of voltage at particular. beware that the transistor you select for this experiment may not have the same terminal designations shown here. single points in that circuit. check with the manufacturer for details on the particular component(s) you choose for a project. VOLTAGE FOLLOWER ILLUSTRATION 231 CBE + - + - INSTRUCTIONS Again. . it has no voltage gain. as indicated by the symbol in the lower-left corner of the diagram. it is easy enough to verify terminal assignments with a multimeter. and so the breadboard layout shown in the illustration may not be correct for you. from left to right. and Emitter. In my illustrations. Since voltage is by necessity a quantity relative between two points. In other words. but not for all . I show all TO-92 package transistors with terminals labeled "CBE": Collector.
Input voltage is the voltage at the potentiometer's wiper (voltage between the wiper and circuit ground). Using Ohm's Law.6 volts or so?). while output voltage is the load resistor voltage (voltage across the load resistor. Not very impressive. and measure output voltage versus input voltage for several different potentiometer settings. is it? Now measure current through the base of the transistor (input current) versus current through the load resistor (output current). current through each resistor may be easily calculated: divide the measured voltage by the known resistance . consider an alternative method: measure voltage across the base and load resistors. but having an implicit reference point for voltage measurements makes such statements meaningful: 6V 10 kΩ 6V Rbase Q1 1 kΩ Rload + 1 kΩ Voltmeter measuring base voltage (VB) V - Build this circuit.232 CHAPTER 5. or emitter voltage: between emitter and circuit ground). whose resistance values are known. DISCRETE SEMICONDUCTOR CIRCUITS 6V 10 kΩ 6V Rbase Q1 1 kΩ Rload 1 kΩ These points are all considered "ground" For example. it is nonsense to speak of voltage at a single point. You should see a close correlation between these two voltages: one is just a little bit greater than the other (about 0. we say that the AC voltage gain of this amplifier is nearly 1. with the red probe touching the base terminal and the black probe touching ground. but a change in the input voltage gives almost equal change in the output voltage. Normally. if I were to speak of voltage at the base of the transistor (VB ). Because the relationship between input change and output change is almost 1:1. Before you break the circuit and insert your ammeter to take these measurements. I would mean the voltage measured between the transistor's base terminal and the negative side of the power supply (ground).
print dc v(2.937 volts and an output voltage of 5.3) .5. The output side of this amplifier delivers the same voltage. with an input current of 25. You should expect to find huge differences between input and output currents for this amplifier circuit. The input side of this amplifier accepts a voltage signal without drawing much current.0) v(2.11. they are often referred to as shunt resistors. it shows an input voltage of 5. Another way of thinking of this circuit's function is in terms of impedance. Cast in terms of impedance.095 volts. but it really doesn't matter much for the purposes of this experiment. When resistors are used to take current measurements by "translating" a current into a corresponding voltage. For best precision. you may measure the resistance of each resistor rather than assume an exact value of 1 kΩ.dc v1 12 12 1 . This calculation is particularly easy with resistors of 1 kΩ value: there will be 1 milliamp of current for every volt of drop across them. VOLTAGE FOLLOWER 233 (I=E/R).0) v(4.35 µA (2. This is the primary purpose of a voltage follower circuit: to boost the current capacity of a "weak" signal without altering its voltage. we could say that this amplifier has a high input impedance (voltage dropped with very little current drawn) and a low output impedance (voltage dropped with almost unlimited current-sourcing capacity). COMPUTER SIMULATION Schematic with SPICE node numbers: 1 Rpot1 V1 2 Rpot2 0 1 5 kΩ Rbase 3 1 kΩ 5 kΩ 0 Rload 1 Q1 4 1 kΩ 0 Netlist (make a text file containing the following text.end When this simulation is run through the SPICE program. verbatim): Voltage follower v1 1 0 rpot1 1 2 5k rpot2 2 0 5k rbase 2 3 1k rload 4 0 1k q1 1 3 4 mod1 . In fact. it is not uncommon to experience current gains well in excess of 200 for a small-signal transistor operating at low current levels. but at a current limited only by load resistance and the current-handling ability of the transistor.model mod1 npn bf=200 .535E-02 volts .
. inferred from the output voltage of 5.095 mA. You may change the "potentiometer" setting in this circuit by adjusting the values of Rpot1 and Rpot2 .095 volts dropped across a load resistance of exactly 1 kΩ.234 CHAPTER 5. 5. always keeping their sum at 10 kΩ. of course. DISCRETE SEMICONDUCTOR CIRCUITS dropped across the 1 kΩ Rbase resistor). Output current is.
chapter 4: "Bipolar Junction Transistors" LEARNING OBJECTIVES • Design of a simple common-emitter amplifier circuit • How to measure amplifier voltage gain • The difference between an inverting and a noninverting amplifier • Ways to introduce negative feedback in an amplifier circuit SCHEMATIC DIAGRAM 10 kΩ 6V 100 kΩ 10 kΩ 6V Vin Q1 Vout ILLUSTRATION .12. linear taper (Radio Shack catalog # 271-1715) • One 1 MΩ resistor • One 100 kΩ resistor • One 10 kΩ resistor • One 1.12 Common-emitter amplifier PARTS AND MATERIALS • One NPN transistor – model 2N2222 or 2N3403 recommended (Radio Shack catalog # 2761617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two 6-volt batteries • One 10 kΩ potentiometer. Volume 3. single-turn.5 kΩ resistor CROSS-REFERENCES Lessons In Electric Circuits. COMMON-EMITTER AMPLIFIER 235 5.5.
7 volts (high). or 6 divided by 0. 9 volts. Secondly. that the input-to-output effect is "reversed. For example. This effect is known as signal inversion. choose several voltage levels between those limits (1 volt. if an input voltage of 1. Try leaving the potentiometer in one position and heating the transistor by grasping it firmly with your hand or heating it with some other source of heat such as an electric hair dryer (WARNING: be careful not to get it so hot that your plastic breadboard melts!). 7 volts.0 volt. Measuring the output voltage with a meter. 5 volts. For example.1 volts (low) to 11.50. but they are rarely used in as crude a form as this." that is. DISCRETE SEMICONDUCTOR CIRCUITS CBE + - + - INSTRUCTIONS Build this circuit and measure output voltage (voltage measured between the transistor's collector terminal and ground) and input voltage (voltage measured between the potentiometer's wiper terminal and ground) for several position settings of the potentiometer. then choosing several voltages spanning that output range to take measurements at. Then. the amplifier's voltage gain is (7. . Common-emitter amplifiers are widely used due to their high voltage gain.5).0 . Take any two pairs of voltage figures and calculate voltage gain by dividing the difference in output voltages by the difference in input voltages. if full rotation on the potentiometer drives the amplifier circuit's output voltage from 0.66 1. In the end. 3 volts. noting the exact figure for later reference. Although this amplifier circuit works to demonstrate the basic concept.1.0)/(1.0 volts and an input voltage of 1. I recommend determining the output voltage range as the potentiometer is adjusted through its entire range of motion. and record that voltage figure as well. adjust the potentiometer to obtain each of these predetermined voltages at the output. You should immediately notice two characteristics while taking these voltage measurements: first. You may also explore temperature effects by cooling the transistor: touch an ice cube to its surface and note the change in output voltage. which had a voltage gain of about 1.236 CHAPTER 5.5 volts gives me an output voltage of 7.66 volts gives me an output voltage of 1. you should have a table of numbers representing several different output voltages along with their corresponding input voltages. this amplifier exhibits a very strong voltage gain: a small change in input voltage results in a large change in output voltage. and this kind of amplifier as an inverting amplifier. it is very susceptible to changes in temperature.16: a gain ratio of 37. and 11 volts). This should stand in stark contrast to the "voltage follower" amplifier circuit discussed earlier. measure the exact input voltage producing that output voltage. an increasing input voltage results in a decreasing output voltage.
whereby a portion of the output voltage is "fed back" to the amplifier's input so as to have a negative.12. This in turn alters the controlled current through the collector terminal. or canceling.5. COMMON-EMITTER AMPLIFIER 237 When the transistor's temperature changes.5 kΩ CBE + - + - Repeat the same voltage measurement and recording exercise with the 1. but practical nonetheless. Try altering the transistor's temperature again and noting the output voltage for a steady input voltage. Stability is improved at the expense of voltage gain.5 kΩ resistor? Another method of introducing negative feedback to this amplifier circuit is to "couple" the output to the input through a high-value resistor. a compromise solution. Such changes may be minimized through the use of signal feedback. thus affecting output voltage. calculating the new (reduced) voltage gain.5 kΩ resistor installed. resulting in different amounts of base current for the same input voltage. Connecting a 1 MΩ resistor between the transistor's collector and base terminals works well: . effect on voltage gain. so that the input voltage becomes divided between the base-emitter PN junction and the voltage drop across the new resistance: 10 kΩ 6V 100 kΩ 10 kΩ 6V Vin Q1 Vout 1. its base-emitter diode characteristics change. Does it change more or less than without the 1. Perhaps the simplest way to add negative feedback to a common-emitter amplifier is to add some resistance between the emitter terminal and ground.
Note the range of possible output voltages with each feedback scheme (the low and high voltage values obtained with a full sweep of the input voltage potentiometer). and how this differs between the two circuits. COMPUTER SIMULATION Schematic with SPICE node numbers: . the two feedback circuits will not behave identically.238 CHAPTER 5. DISCRETE SEMICONDUCTOR CIRCUITS 10 kΩ 1 MΩ 6V 100 kΩ 10 kΩ 6V Vin Q1 Vout CBE + - + - Although this different method of feedback accomplishes the same goal of increased stability by diminishing gain.
with a steep change in the middle where the transistor is in its active mode of operation. verbatim): Common-emitter amplifier vsupply 1 0 dc 12 vin 3 0 rc 1 2 10k rb 3 4 100k q1 2 4 0 mod1 .0) ." from 0 to 2 volts in 0.5.model mod1 npn bf=200 .end This SPICE simulation sets up a circuit with a variable DC voltage source (vin) as the input signal.05 . Results are shown on a plot. COMMON-EMITTER AMPLIFIER 239 1 Rc 2 Vsupply Vin 0 3 100 kΩ Rb 4 1 10 kΩ Vout Q1 0 0 Netlist (make a text file containing the following text. The input voltage is varied.dc vin 0 2 0. with the input voltage appearing as a straight line and the output voltage as a "step" figure where the voltage begins and ends level.05 volt increments. .0) v(3. and measures the corresponding output voltage between nodes 2 and 0.plot dc v(2.12. or "swept.
Volume 3. chapter 4: "Bipolar Junction Transistors" LEARNING OBJECTIVES • Design of a multi-stage. linear taper (Radio Shack catalog # 271-1715) • One 1 MΩ resistor • Three 100 kΩ resistors • Three 10 kΩ resistors CROSS-REFERENCES Lessons In Electric Circuits. direct-coupled common-emitter amplifier circuit • Effect of negative feedback in an amplifier circuit SCHEMATIC DIAGRAM 1 MΩ 10 kΩ Vin 10 kΩ 100 kΩ 100 kΩ 10 kΩ 10 kΩ Vout 6V 6V 100 kΩ ILLUSTRATION . single-turn.240 CHAPTER 5.13 Multi-stage amplifier PARTS AND MATERIALS • Three NPN transistors – model 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two 6-volt batteries • One 10 kΩ potentiometer. DISCRETE SEMICONDUCTOR CIRCUITS 5.
I recommend building this circuit without the 1 MΩ feedback resistor to begin with. Even if you can't adjust the input voltage fine enough to stabilize the output voltage in the active range of the last transistor.5. the output tends to drive to a high voltage when the input goes low. You may find it impossible to adjust the potentiometer for a stable output voltage (that isn't saturated at full supply voltage or zero). that is. You should notice the reduction in gain immediately by the decreased sensitivity of the output signal on input signal changes (changes in potentiometer position). MULTI-STAGE AMPLIFIER 241 CBE CBE CBE + - + - INSTRUCTIONS By connecting three common-emitter amplifier circuit together – the collector terminal of the previous transistor to the base (resistor) of the next transistor – the voltage gains of each stage compound to give a very high overall voltage gain. noting whether or not the output voltage increases or decreases with an increase in input voltage. As with the simple common-emitter amplifier discussed in an earlier experiment. Since any one of the common-emitter "stages" is inverting in itself. because it is far easier to manufacture . an even number of staged common-emitter amplifiers gives noninverting response. to see for yourself just how high the unrestricted voltage gain is. This is good. it is a good idea here to make a table of input versus output voltage figures with which you may calculate voltage gain. and visa-versa. the feedback signal provided through the 1 MΩ resistor from the output of the last transistor to the input of the first should be negative in nature. the amplifier isn't nearly as "touchy" as it was without the feedback resistor in place. while an odd number of stages gives inverting. it will act to stabilize the amplifier's response and minimize the voltage gain. Connect the 1 MΩ feedback resistor into the circuit. Experiment with different values of feedback resistance. Simply put. coupling the collector of the last transistor to the base of the first. Since the overall response of this three-stage amplifier is inverting. the gain being so high.13. You may experience these relationships by measuring the collector-to-ground voltage at each transistor while adjusting the input voltage potentiometer. As such. you should be able to tell that the output-to-input relationship is inverting. What effect do you think a decrease in feedback resistance have on voltage gain? What about an increase in feedback resistance? Try it and find out! An advantage of using negative feedback to "tame" a high-gain amplifier circuit is that the resulting voltage gain becomes more dependent upon the resistor values and less dependent upon the characteristics of the constituent transistors.
verbatim): Multi-stage amplifier vsupply 1 0 dc 12 vin 2 0 r1 2 3 100k r2 1 4 10k q1 4 3 0 mod1 r3 4 7 100k r4 1 5 10k q2 5 7 0 mod1 r5 5 8 100k r6 1 6 10k q3 6 8 0 mod1 rf 3 6 1meg . This amplifier circuit is a bit simplified from what you will normally encounter in practical multi-stage circuits.end . Rarely is a pure common-emitter configuration (i.0) v(2. DISCRETE SEMICONDUCTOR CIRCUITS consistent resistors than consistent transistors.242 CHAPTER 5. it is easier to design an amplifier with predictable gain by building a staged network of transistors with an arbitrarily high voltage gain.5 0. COMPUTER SIMULATION Schematic with SPICE node numbers: 3 1 MΩ 6 1 R2 2 R1 3 Vin 0 100 kΩ Q1 4 10 kΩ 10 kΩ 5 R3 7 100 kΩ Rf 1 R4 R6 10 kΩ 6 R5 8 1 1 Vout Vsupply Q3 0 Q2 100 kΩ 0 0 0 Netlist (make a text file containing the following text.0) . and if the amplifier's service is for AC signals.1 .dc vin 0 2.e. with no emitter-to-ground resistor) used. Radio-frequency amplifier circuits are often transformer-coupled. then mitigate that gain precisely through negative feedback.plot dc v(6.model mod1 npn bf=200 . with capacitors connected in parallel with the transformer windings for resonant tuning. the inter-stage coupling is often capacitive with voltage divider networks connected to each transistor base for proper biasing of each stage. It is this same principle that is used to make operational amplifier circuits behave so predictably. Thus.
You may calculate voltage gain by taking any two analysis points and dividing the difference in output voltages by the difference in input voltages. MULTI-STAGE AMPLIFIER 243 This simulation plots output voltage against input voltage.5. just like you do for the real circuit. and allows comparison between those variables in numerical form: a list of voltage figures printed to the left of the plot.13. Experiment with different feedback resistance values (rf) and see the impact on overall voltage gain. without reference to any other circuit component! . Do you notice a pattern? Here's a hint: the overall voltage gain may be closely approximated by using the resistance figures of r1 and rf.
linear taper (Radio Shack catalog # 271-1715) • Two 10 kΩ resistors • Four 1. or pinouts.14 Current mirror PARTS AND MATERIALS • Two NPN transistors – models 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two 6-volt batteries • One 10 kΩ potentiometer. DISCRETE SEMICONDUCTOR CIRCUITS 5. This will dictate how you connect the transistors together and to other components. However. any pair of identical NPN transistors may be used to build a current mirror. chapter 4: "Bipolar Junction Transistors" LEARNING OBJECTIVES • How to build a current mirror circuit • Current limitations of a current mirror circuit • Temperature dependence of BJTs • Experience a controlled "thermal runaway" situation SCHEMATIC DIAGRAM . Beware that not all transistors share the same terminal designations.244 CHAPTER 5. CROSS-REFERENCES Lessons In Electric Circuits.5 kΩ resistors Small signal transistors are recommended so as to be able to experience "thermal runaway" in the latter portion of the experiment. single-turn. even if they share the same physical appearance. easily obtained from the manufacturer's website. so be sure to check the manufacturer's specifications (component datasheet). consult chapter 4 of the Semiconductor volume (volume III) of this book series. Larger "power" transistors may not exhibit the same behavior at these low current levels. Beware that it is possible for the transistor's package and even the manufacturer's datasheet to show incorrect terminal identification diagrams! Double-checking pin identities with your multimeter's "diode check" function is highly recommended. For details on how to identify bipolar transistor terminals using a multimeter. Volume 3.
14. Rlimit.5. and Radjust are 10 kΩ each Q1 Q2 ILLUSTRATION V V OFF A A A COM TP5 TP4 TP3 TP2 TP1 CBE CBE + - + - .5 kΩ each Rload4. CURRENT MIRROR 245 + A - TP5 Rload4 TP4 6V Radjust 6V Rlimit Rload3 TP3 Rload2 TP2 Rload1 TP1 Rload1 through Rload3 are 1.
Q2 . Well. but one that finds wide use due to its simplicity. DISCRETE SEMICONDUCTOR CIRCUITS INSTRUCTIONS A current mirror may be thought of as an adjustable current regulator.246 CHAPTER 5. In other words. The practical result of all this is Q2 's collector current mimicking whatever current magnitude has been established through the collector of Q1 by the potentiometer. you will get the opportunity to build one of these circuits. explore its current-regulating properties. This transistor is connected to act as a simple diode: just a PN junction. you should see a nearly unchanged amount of current. that is how it is supposed to work. for easy current measurement. I've marked five test points. touch the test probe to TP4 and adjust the potentiometer through its range of travel. Voltage dropped across the base-emitter junction of Q 1 is impressed across the base-emitter junction of the other transistor. Since voltage across the two transistors' base-emitter junctions is the same – the two junction pairs being connected in parallel with each other – so should the current be through their base terminals. You will be using it in the last part of this experiment. TP1 through TP5. Matched transistors should have the same β ratios. without regard to load resistance. This allows you to quickly and effortlessly change load resistance: touching the probe to TP1 results in practically no load resistance. changing current indicated by your ammeter as you move the potentiometer mechanism: no more than a few milliamps. Changes in load resistance (resistance connecting the collector of Q2 to the positive side of the battery) have no effect on Q1 's current. then TP1. as well. causing it to turn "on" and likewise conduct current. With a constant base current and a nearly constant β ratio. the current mirror circuit acts to regulate current at a value set by the potentiometer. so equal base currents means equal collector currents. This demonstrates the current regulating behavior of this circuit. and consequently have no effect upon the base-emitter voltage or base current of Q2 . Again. It is a rather crude current regulator circuit. Move the probe to TP2. while touching it to TP5 results in approximately 14.5 kΩ fixed-value resistor from the parts specified in the parts list. . Reality isn't quite so simple. You will have one extra 1. there is some variation over this range. In this experiment. Try adjusting the potentiometer to another position.5 kΩ of load resistance. noting the stability of the current indications as you change load resistance. Rather than solidly connect the ammeter's black probe to a definite point in the circuit. current through Q2 mirrors the current through Q1 . To begin the experiment. Build the circuit as shown in the schematic and illustration. assuming identical junction characteristics and identical junction temperatures.5 kΩ. and also experience some of its practical limitations firsthand. for you to touch the black test probe to while measuring current. Leave the potentiometer set to a position giving a round number of milliamps and move the meter's black test probe to TP3. giving a different current indication. You should note that the current regulation isn't perfect. Q2 will drop as much or as little collector-emitter voltage as necessary to hold its collector (load) current constant. In the circuit diagram shown. as you are about to see. anyway. Why use a transistor instead of a regular diode? Because it is important to match the junction characteristics of these two transistors when using them in a current mirror circuit. The potentiometer sets the amount of current through transistor Q1 . the load circuit of Q2 is completed to the positive side of the battery through an ammeter. The current indication should be very nearly the same as before. the current limit being easily set by a single resistance. Thus. You should see a small. Despite regulating the current at nearly the value for load resistances between 0 and 4. and touch the meter's black probe to test points TP1 through TP4.
while Q1 is cool. to maintain the same amount of current with this great a load resistance as with lesser load resistances. as any current regulator circuit capable of supplying a constant amount of current through any load resistance imaginable would require an unlimited source of voltage to do it! Ohm's Law (E=IR) dictates the amount of voltage needed to push a given amount of current through a given amount of resistance. and finally TP5. An important caveat for current mirror circuits in general is that of equal temperature between the two transistors. the more current it will pass for a given amount of voltage drop. without further potentiometer motion! Break the circuit by removing the meter probe from TP1 when the current exceeds 30 mA. and the circuit will no longer "mirror" current as expected. This phenomenon is common to all current-regulator circuits: there is a limited amount of resistance a current regulator can handle before it saturates. you should notice Q 2 is warm.14. To illustrate this dependence on equal temperature. Why is this? Because too much load resistance has been inserted into Q2 's circuit. noting the meter's indication at each connection point. The hotter a PN junction is. The current "mirroring" taking place between the two transistors' collector circuits depends on the base-emitter junctions of those two transistors having the exact same properties. then TP3. Grasp the other transistor between your fingers to heat it up. There. Place the ammeter's black probe on TP1 and observe the current indication. When building a real current mirror circuit using discrete transistors. replace the 10 kΩ Rlimit resistor with a 1. it may become very hot! You can receive a bad burn on your fingertip by touching an overheated semiconductor component. for all they can really do is limit current to some maximum value. Move the potentiometer in the direction of increasing current until you read about 10 mA through the ammeter. Q2 cannot "turn on" any more than it already has. Leaving the potentiometer at that position. as indicated with the ammeter test probe connected to TP1. this procedure should be conducted no longer than is necessary to observe load current begin to "run away. Try adjusting the potentiometer so that maximum current is obtained. a finite limit of load current and load resistance definitely exists for this circuit. You will notice current begin to increase all on its own. try grasping one transistor between your fingers to heat it up.5. then TP4. TP5. to avoid damaging transistor Q 2 . it will pass more collector current than the other. and consequently through Q2 as well. If you carefully touch both transistors with a finger. the voltage/current relationship for a PN junction strongly depends on junction temperature. For this reason. we will intentionally allow one of the transistors to overheat and note the effects. Simply put. If one transistor should become hotter than the other. stop moving the potentiometer and just observe the current. the two transistors should be epoxy-glued together (back-to-back) so that they remain at approximately the same temperature. What happens to the current through the load resistors as the transistor's temperature increases? Now. and with only 12 volts of power supply voltage at our disposal. The current should be regulated at a nearly constant value until the meter probe is moved to the last test point. This stands to reason.5 kΩ resistor. let go of the transistor and blow on it to cool it down to ambient temperature. it may be helpful to think of current regulator circuits as being current limiter circuits. CURRENT MIRROR 247 The regulation may be much worse if load resistance is allowed to rise too high. At that point. As the "diode equation" describes. Warning: if Q2 's current has been allowed to "run away" too far or for too long a time. To avoid damaging a transistor. move the meter probe to TP2. Next. the current indication will be substantially lower than at the other test points. What does the load current do now? In this next phase of the experiment. This will allow a higher current to pass through Q1 . so be careful here! . adjust the potentiometer for minimum current." To begin.
print dc i(vammeter) . .model mod1 npn bf=100 . all load resistance was removed. not just current mirrors. This gross imbalance of power dissipation caused Q2 to heat more than Q1 . This caused it to heat up even faster. As the temperature increased.end Vammeter is nothing more than a zero-volt DC battery strategically placed to intercept load current.248 CHAPTER 5. as no dedicated "ammeter" component exists in the SPICE language. so Q2 had to drop full battery voltage between collector and emitter as it regulated current. so its power dissipation was far less than that of Q 2 . DISCRETE SEMICONDUCTOR CIRCUITS What just happened to make Q2 overheat and lose current control? By connecting the ammeter to TP1. COMPUTER SIMULATION Schematic with SPICE node numbers: 1 1 Vammeter 3 0V Rlimit V1 12 V 2 2 Q1 0 0 Rload 4 Q2 0 Netlist (make a text file containing the following text.dc v1 12 12 1 . as it was passing more collector current while still dropping the full 12 volts between collector and emitter. The effect is known as thermal runaway. verbatim): Current mirror v1 1 0 vammeter 1 3 dc 0 rlimit 1 2 10k rload 3 4 3k q1 2 2 0 mod1 q2 4 2 0 mod1 . Transistor Q1 at least had the 1.5 kΩ resistance of Rlimit in place to drop most of the battery voltage. and it is possible in many bipolar junction transistor circuits. This is nothing more than a trick to measure current in a SPICE simulation. Q2 began to pass more current for the same amount of base-emitter voltage drop.
Something to bear in mind when altering the netlist or programming your own SPICE simulation! You will have to experiment with different resistance values of Rload in this simulation to appreciate the current-regulating nature of the circuit.14.1 mA. the regulated current through Rload will be 1. even this simulation shows the load current suffering a decrease as in real life. With Rlimit set to 10 kΩ and a power supply voltage of 12 volts. but if we were to incorporate more than one currentmeasuring voltage source in the circuit and name them "vammeter1" and "vammeter2".1 mA for a wide range of load resistances. SPICE would see them as being two instances of the same component "vammeter" (seeing only the first eight characters) and halt with an error. CURRENT MIRROR 249 It is important to remember that SPICE only recognizes the first eight characters of a component's name. if the load resistance is increased beyond 10 kΩ. SPICE shows the regulation to be perfect (isn't the virtual world of computer simulation so nice?). However.5. the load current remaining at 1. . respectively. The name "vammeter" is okay.
chapter 3: "Diodes and Rectifiers" LEARNING OBJECTIVES • How to use a JFET as a current regulator • How the JFET is relatively immune to changes in temperature SCHEMATIC DIAGRAM . easily obtained from the manufacturer's website. Volume 3. single-turn. even if they share the same physical appearance. models 2N3819 or J309 recommended (Radio Shack catalog # 276-2035 is the model 2N3819) • Two 6-volt batteries • One 10 kΩ potentiometer.5 kΩ resistors For this experiment you will need an N-channel JFET. CROSS-REFERENCES Lessons In Electric Circuits. not a P-channel! Beware that not all transistors share the same terminal designations. For details on how to identify junction field-effect transistor terminals using a multimeter. Volume 3. This will dictate how you connect the transistors together and to other components.250 CHAPTER 5. Beware that it is possible for the transistor's package and even the manufacturer's datasheet to show incorrect terminal identification diagrams! Double-checking pin identities with your multimeter's "diode check" function is highly recommended. or pinouts. chapter 5: "Junction Field-Effect Transistors" Lessons In Electric Circuits. linear taper (Radio Shack catalog # 271-1715) • One 1 kΩ resistor • One 10 kΩ resistor • Three 1. DISCRETE SEMICONDUCTOR CIRCUITS 5. so be sure to check the manufacturer's specifications (component datasheet). consult chapter 5 of the Semiconductor volume (volume III) of this book series.15 JFET current regulator PARTS AND MATERIALS • One N-channel junction field-effect transistor.
5 kΩ each Rload4 and Radjust are 10 kΩ each Rlimit is 1 kΩ 6V Radjust Q1 Rlimit ILLUSTRATION V V OFF A A A COM TP5 TP4 TP3 TP2 TP1 + - + - SGD . JFET CURRENT REGULATOR 251 A + TP5 Rload4 TP4 Rload3 TP3 Rload2 TP2 6V Rload1 TP1 Rload1 through Rload3 are 1.15.5.
touch the black test probe to TP2. the current will remain approximately constant. However. then TP3. Why? Because at this level of load resistance. but the thermal effects are all but eliminated as well due to the relative thermal immunity of the field-effect transistor. Now. Instead. then TP4. Connecting the black test probe of your ammeter to that test point gives a combined load resistance of 14. Try cooling it down afterward by blowing on it. a decided advantage over bipolar junction transistors. With this circuit. then TP4. at the end of a 10 kΩ resistor. Move the probe to TP2. For all these test point positions. To begin the experiment. transistor temperature is almost irrelevant. this diode isn't really a PN junction device at all. and touch the meter's black probe to test points TP1 through TP4. An important caveat with the BJT current mirror circuit is that both transistors must be at equal temperature for the two currents to be equal. Move the black test probe back to TP1 and adjust the potentiometer for minimum current.5 kΩ. Now. Try adjusting the potentiometer to another position. and finally TP5. What do you notice about the current indication at all these points? When the current regulation point is adjusted to a lesser value. In other words. however. touch the black test probe to TP1 and adjust the potentiometer for maximum current. Try grasping the transistor between your fingers to heat it up. giving a different current indication. then TP3. TP5. DISCRETE SEMICONDUCTOR CIRCUITS Previously in this chapter.252 INSTRUCTIONS CHAPTER 5. noting the stability of the current indications as you change load resistance. An interesting application of this current-regulator circuit is the so-called constant-current diode. the current will fall dramatically. but uses a single junction field-effect transistor (JFET) instead of two BJTs. the transistor is able to maintain regulation over a much larger range of load resistance. Not only is the requirement of transistor matching eliminated (due to the use of just one transistor). the other's current level being established by a variable resistance. The current indication should be very nearly the same as before. changing current indicated by your ammeter as you move the potentiometer mechanism: no more than a few milliamps. which will be too much resistance for the transistor to maintain maximum regulated current through. the transistor will be saturated as it attempts to provide more current than the circuit resistance will allow. To experience what I'm describing here. This demonstrates the current regulating behavior of this circuit. you should see a nearly unchanged amount of current. is provided for introducing a large change in load resistance. Described in the "Diodes and Rectifiers" chapter of volume III. while the load resistors and the test points between them serve only to demonstrate constant current despite changes in load resistance. when you touch the black probe to TP5. Again. then TP1. there is insufficient voltage drop across the transistor to maintain regulation. touch the test probe to TP4 and adjust the potentiometer through its range of travel. Leave the potentiometer set to a position giving a round number of milliamps and move the meter's black test probe to TP3. The two series resistors Radjust and Rlimit set the current regulation point. noting the load current with your ammeter. This circuit performs the same task of regulating current. whereby one transistor would try to maintain the same current through it as through the other. move the black test probe to TP2. You should see a small. it is a JFET with a fixed resistance connected between the gate and source terminals: . you saw how a pair of bipolar junction transistors (BJTs) could be used to form a current mirror. This behavior also makes field-effect transistors immune to thermal runaway.
COMPUTER SIMULATION Schematic with SPICE node numbers: 1 Rload 1 4. verbatim): JFET current regulator vsource 1 0 rload 1 2 4.5k j1 2 0 3 mod1 rlimit 3 0 1k .plot dc i(vsource) .5.model mod1 njf .dc vsource 6 12 0. JFET CURRENT REGULATOR 253 Constant-current diode Anode Symbol Anode Actual device Cathode Cathode A normal PN-junction diode is included in series with the JFET to protect the transistor against damage from reverse-bias voltage.15.1 .5 kΩ 2 Vsource 0 J1 3 Rlimit 1 kΩ 0 0 0 Netlist (make a text file containing the following text. but otherwise the current-regulating facility of this device is entirely provided by the field-effect transistor.
254 . Many manufacturers give SPICE model parameters for their transistors. you can set rload to different resistance values and verify that the circuit current remains constant.1 volt steps.8 µA. so to demonstrate the current regulation of this circuit over a wide range of conditions. With an rlimit value of 1 kΩ. DISCRETE SEMICONDUCTOR CIRCUITS SPICE does not allow for "sweeping" resistance values. This current figure will most likely not be the same as your actual circuit current. I've elected to sweep the source voltage from 6 to 12 volts in 0. .end CHAPTER 5. If you wish.model line of the netlist for a more accurate circuit simulation. which may be typed in the . due to differences in JFET parameters. the regulated current will be 291.
• Working definitions of differential and common-mode voltages SCHEMATIC DIAGRAM 22 kΩ 6V 10 kΩ (noninv) 6V 10 kΩ 100 kΩ Q1 Q2 22 kΩ 10 kΩ Vout 10 kΩ (inv) 1. DIFFERENTIAL AMPLIFIER 255 5. but have been chosen to provide high voltage gain for a "comparator-like" differential amplifier behavior.16. chapter 8: "Operational Amplifiers" LEARNING OBJECTIVES • Basic design of a differential amplifier circuit.5. Volume 3.16 Differential amplifier PARTS AND MATERIALS • Two 6-volt batteries • Two NPN transistors – models 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two 10 kΩ potentiometers.5 kΩ . chapter 4: "Bipolar Junction Transistors" Lessons In Electric Circuits. linear taper (Radio Shack catalog # 271-1715) • Two 22 kΩ resistors • Two 10 kΩ resistors • One 100 kΩ resistor • One 1. Volume 3. CROSS-REFERENCES Lessons In Electric Circuits.5 kΩ resistor Resistor values are not especially critical in this experiment. single-turn.
2. the differential voltage will be 0. which is whatever level of voltage common to both inputs.5) but the common-mode voltage will be 2.5 and 3 volts. respectively (0. this condition should produce the same output signal voltage as if the inputs were set at 3.5 volts.5 volts.5 kΩ). . Ideally. allowing full 0 to 12 volt adjustment range from each potentiometer. Do not worry about building up excessive heat while adjusting potentiometers in this circuit! Unlike the current mirror circuit. quite nonlinear and unsymmetrical with regard to output voltage versus input voltage(s). Measure the output voltage (voltage at the collector of Q2 with respect to ground) as the input voltages are varied. its behavior could be worse. This is the essential nature of a differential amplifier : two complementary inputs. In the form shown here.5 volts (3 .5 volts differential. Note how the input signal potentiometers have been limited by 22 kΩ resistors to an adjustable range of approximately 0 to 4 volts. However. though. DISCRETE SEMICONDUCTOR CIRCUITS + - CBE CBE Noninverting + Inverting INSTRUCTIONS This circuit forms the heart of most operational amplifier circuits: the differential pair. this circuit is protected from thermal runaway by the emitter resistor (1. If you'd like to see how this circuit behaves without any input signal limiting. Note how the two potentiometers have different effects on the output voltage: one input tends to drive the output voltage in the same direction (noninverting). its output voltage depends on both the differential voltage and the common-mode voltage. it acts primarily as a comparator: the output voltage rapidly changing value as the two input voltage signals approach equality. For example. With a high voltage gain created by a large collector/emitter resistor ratio (100 kΩ/1. This circuit falls considerably short of the ideal. given a power supply voltage of 12 volts. as even a cursory test will reveal. since that is the lowest input signal level.5 kΩ). An ideal differential amplifier ignores all common-mode voltage. Ideally. with contrary effects on the output signal. As imperfect as this differential amplifier is. it is a rather crude differential amplifier. the output voltage of such an amplifier is strictly a function of the difference between the two input signals. In other words.256 ILLUSTRATION CHAPTER 5. just bypass the 22 kΩ resistors with jumper wires. which doesn't allow enough transistor current to cause any problem. with a 3 volt common-mode voltage). this circuit does not give the same result for the two different input signal scenarios. while the other tends to drive the output voltage in the opposite direction (inverting). if the inverting input is at 3 volts and the noninverting input at 2.
Volume 3.17 Simple op-amp PARTS AND MATERIALS • Two 6-volt batteries • Four NPN transistors – models 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two PNP transistors – models 2N2907 or 2N3906 recommended (Radio Shack catalog # 2761604 is a package of fifteen PNP transistors ideal for this and other experiments) • Two 10 kΩ potentiometers. linear taper (Radio Shack catalog # 271-1715) • One 270 kΩ resistor • Three 100 kΩ resistors • One 10 kΩ resistor CROSS-REFERENCES Lessons In Electric Circuits. single-turn. SCHEMATIC DIAGRAM 100 kΩ 6V 10 kΩ (noninv) 6V Q5 Rprg Q1 Q2 Vout Q3 Q4 10 kΩ (inv) Q6 . chapter 4: "Bipolar Junction Transistors" Lessons In Electric Circuits. • Effects of negative feedback on a high-gain differential amplifier. Volume 3. chapter 8: "Operational Amplifiers" LEARNING OBJECTIVES • Design of a differential amplifier circuit using current mirrors. SIMPLE OP-AMP 257 5.5.17.
Rather than use resistors to drop voltage in the differential pair circuit. or op-amp. To make a voltage follower circuit. PNP transistors Q1 and Q2 form a current mirror which tries to keep current split equally through the two differential pair transistors Q3 and Q4 . Measure the output voltage (voltage at the collector of Q4 with respect to ground) as the input voltages are varied. this circuit is able to function as a working operational amplifier.258 ILLUSTRATION CHAPTER 5. so understanding the internal workings of an operational amplifier is important. the result being higher voltage gain and more predictable performance. while the other tends to drive the output voltage in the opposite direction (inverting). you are ready to use this circuit as a real op-amp. Once the circuit's differential response has been proven (the output voltage sharply transitioning from one extreme level to another when one input is adjusted above and below the other input's voltage level). This means connecting the collector and base terminals of Q4 together. Op-amps form the basis of a great many modern analog semiconductor circuits. With a higher voltage gain. and discarding the "inverting" potentiometer: . Note how the two potentiometers have different effects on the output voltage: one input tends to drive the output voltage in the same direction (noninverting). a set of current mirrors is used instead. setting the total differential pair current at a level predetermined by resistor R prg . You will notice that the output voltage is most responsive to changes in the input when the two input signals are nearly equal to each other. NPN transistors Q5 and Q6 form another current mirror. DISCRETE SEMICONDUCTOR CIRCUITS + - CBE CBE CBE CBE Noninverting CBE CBE + Inverting INSTRUCTIONS This circuit design improves on the differential amplifier shown previously. A simple op-amp circuit called a voltage follower is a good configuration to try first. directly connect the output of the amplifier to its inverting input.
respectively. SIMPLE OP-AMP 259 100 kΩ 6V 10 kΩ Vin 6V Q5 Rprg Q1 Q2 Vout Q3 Q4 Q6 Op-amp diagram − Vin + Vout + - CBE CBE CBE CBE Noninverting CBE CBE + - Note the triangular symbol of the op-amp shown in the lower schematic diagram. deviating no more than a few hundredths of a volt.5. The inverting and noninverting inputs are designated with (-) and (+) symbols. described in an earlier experiment! . As a voltage follower. The feedback wire connecting output to inverting input is shown in red in the above diagrams. This is a much more precise follower circuit than that of a single common-collector transistor. the output voltage should "follow" the input voltage very closely. with the output terminal at the right apex.17.
and it uses a pair of resistors in the feedback loop to "feed back" a fraction of the output voltage to the inverting input. causing the amplifier to output a voltage equal to some multiple of the voltage at the noninverting input. we have a voltage amplifier with a precise gain of 2: 100 kΩ 6V 10 kΩ Vin 6V Q5 Rprg Q1 Q2 Vout Q3 Q4 100 kΩ 100 kΩ Q6 Op-amp diagram − Vin + Vout + - CBE CBE CBE CBE Noninverting CBE CBE + - . If we use two equal-value resistors. causing the output voltage to become twice the voltage impressed at the noninverting input. the feedback voltage will be 1/2 the output voltage. DISCRETE SEMICONDUCTOR CIRCUITS A more complex op-amp circuit is called the noninverting amplifier.260 CHAPTER 5. Thus.
and may be greatly diminished if we add more amplification stages to increase the differential voltage gain. trimmed to precise value at the factory. Do not use a resistance less than 10 kΩ. you may notice slight discrepancies between the output and input voltages. However. SIMPLE OP-AMP 261 As you test this noninverting amplifier circuit. and are called programmable op-amps. According to the feedback resistor values. Most opamps are not programmable. the voltage gain should be exactly 2. These deviations are due to imperfections of the differential amplifier circuit. However. This resistor sets the lower current mirror's control point. . and have their internal current mirror control points fixed by an internal resistance. ranging from 10 kΩ to 1 MΩ. you may notice deviations in the order of several hundredths of a volt between what the output voltage is and what it should be. Try substituting difference resistance values." Some operational amplifiers available in prepackaged units provide a way for the user to similarly "program" the differential pair's current mirror. one way we can maximize the precision of the existing circuit is to change the resistance of Rprg . and in so doing influences many performance parameters of the op-amp.17.5. or else the current mirror transistors may begin to overheat and thermally "run away.
18 Audio oscillator PARTS AND MATERIALS • Two 6-volt batteries • Three NPN transistors – models 2N2222 or 2N3403 recommended (Radio Shack catalog # 276-1617 is a package of fifteen NPN transistors ideal for this and other experiments) • Two 0.1 µF 100 kΩ Probe 6V 6V 1 kΩ ILLUSTRATION . DISCRETE SEMICONDUCTOR CIRCUITS 5.262 CHAPTER 5. chapter 4: "Bipolar Junction Transistors" Lessons In Electric Circuits.1 µF 0. two 1 kΩ) • One light-emitting diode (Radio Shack catalog # 276-026 or equivalent) • Audio detector with headphones CROSS-REFERENCES Lessons In Electric Circuits. Volume 3. less than 100 kΩ (ex: two 10 kΩ. chapter 10: "Multivibrators" LEARNING OBJECTIVES • How to build an astable multivibrator circuit using discrete transistors SCHEMATIC DIAGRAM 100 kΩ 0. Volume 4.1 µF capacitors (Radio Shack catalog # 272-135 or equivalent) • One 1 MΩ resistor • Two 100 kΩ resistors • One 1 kΩ resistor • Assortment of resistor pairs. two 5 kΩ.
Unfortunately. free-running oscillator circuit timed by the sizes of the resistors.18. AUDIO OSCILLATOR 263 CBE CBE CBE + - + - INSTRUCTIONS The proper name for this circuit is "astable multivibrator ". With a 12 volt supply. distortion doesn't matter much. its output waveform is very distorted. I recommend placing a 1 MΩ resistor in series with the audio detector to minimize both circuit loading effects and headphone loudness: CBE CBE CBE + - + - headphones 1 MΩ Use resistor lead as test probe for audio detector plug Sensitivity . It is a simple. however. neither sine wave nor square. and power supply voltage.5.1 µF capacitors. For the simple purpose of making an audio tone. 100 kΩ resistors. the oscillation frequency will be in the low audio range. and 0. You may listen to this signal with the audio detector connected with one test probe to ground and the other to one of the transistor's collector terminals. capacitors.
try different components (same values. Why is this? The LED's common-collector transistor amplifier is a voltage follower. This circuit is no exception. it will not glow. Since the forward-biased base-emitter junction of an active transistor drops only about 0. The third transistor shown in the schematic and illustration is there for driving the LED. One shortcoming of many oscillator circuits is its dependence on a minimum amount of power supply voltage. The audio detector. Given the low oscillating frequency of this multivibrator circuit. as well as experience the effect supply voltage change has on oscillation frequency. Too little voltage and the circuit ceases to oscillate. but different units) in the circuit. to be used as a visual indicator of oscillator action. Feel free to substitute lower-value resistors in place of the two 100 kΩ units shown. You may notice that the LED fails to blink with its probe wire touching the base of either multivibrator transistor. being extraordinarily sensitive. One shortcoming specific to this circuit is the dependence on mismatched components for successful starting. In order for the circuit to begin oscillating. if the voltage under test is less than the minimum required by the LED to light up. DISCRETE SEMICONDUCTOR CIRCUITS The multivibrator itself is just two transistors. What happens to the oscillation frequency when you do so? I recommend using resistors at least 1 kΩ in size to prevent excessive transistor current. Thus. you should be able to see the LED blink rapidly with the probe wire connected to the collector terminal of either multivibrator transistor. Usually. there is insufficient voltage at either transistor base to energize the LED. one transistor must turn on before the other one. meaning that it doesn't amplify voltage. If this happens. but it is possible for the circuit to "freeze" and fail to oscillate at power-up. though. Use the probe wire connected to the base of this commonemitter amplifier to detect voltage at different parts of the circuit with respect to ground. You might want to experiment with lower supply voltages and determine the minimum voltage necessary for oscillation.7 volts. two resistors. yet the audio detector tells you there is an oscillating voltage there. there is enough mismatch in the various component values to enable this to happen. and two cross-connecting capacitors. detects this low voltage signal easily. .264 CHAPTER 5.
250 WVDC capacitors. each rated at 50 WVDC. and may be found in old "tubed" electronic test equipment (oscilloscopes. so you need not rely on "New-Old-Stock" (NOS) components left over from defunct American manufacturers. 120VAC step-down to 12VAC (Radio Shack catalog # 273-1365. • Bridge rectifier module (Radio Shack catalog # 276-1173) • Electrolytic capacitor. However. or other source of audio voltage signal Where can you obtain a 12AX7 tube.19 Vacuum tube audio amplifier PARTS AND MATERIALS • One 12AX7 dual triode vacuum tube • Two power transformers. tape player. with a working voltage of at least 200 volts DC. Go to any good music store and you will find them available for a modest price ($12 US or less). I strongly recommend choosing a capacitor with a voltage rating well in excess of the expected operating voltage. VACUUM TUBE AUDIO AMPLIFIER 265 5. If you are not as fortunate. or 273-1511). at least 47 µF. musical keyboard. • Automotive ignition coil • Audio speaker. SPST ("Single-Pole. 273-1352. you may build this circuit using five capacitors.1 µF capacitor. so as to handle unexpected voltage surges or any other event that may tax the capacitor. It is important to select an electrolytic capacitor with sufficient working voltage (WVDC) to withstand the output of this amplifier's power supply circuit (about 170 volts).5.19. I purchased the Radio Shack electrolytic capacitor assortment (catalog # 272-802). This model of tube was very popular in its day. 8 Ω impedance • Two 100 kΩ resistors • One 0. you ask? These tubes are very popular for use in the "preamplifier" stages of many professional electric guitar amplifiers. oscillators). 250 WVDC (Radio Shack catalog # 272-1053) • "Low-voltage AC power supply" as shown in AC Experiments chapter • One toggle switch. to substitute for one 250 WVDC unit: . and it happened to contain two 47 µF. if you happen to have access to such equipment. A Russian manufacturer named Sovtek makes these tubes new. Single-Throw") • Radio. I strongly suggest buying a tube new rather than taking chances with tubes salvaged from antique equipment.
Here is a photograph of the coil I used for this experiment: . DISCRETE SEMICONDUCTOR CIRCUITS 22 kΩ 22 kΩ (Each capacitor rated for 50 volts DC) 22 kΩ 22 kΩ 250 WVDC 22 kΩ 110 kΩ equivalent to Bear in mind that the total capacitance for this five-capacitor network will be 1/5. it is used (very unconventionally. of each capacitor's value.266 CHAPTER 5. be sure all capacitor values (in µF) and all resistor values are identical. The specific choice of "coil" is not critical. so long as it is in good operating condition. to ensure even charging of capacitors in the network. or 20%. I might add!) as an impedance-matching transformer between the vacuum tube and an 8 Ω audio speaker. An automotive ignition coil is a special-purpose high-voltage transformer used in car engines to produce tens of thousands of volts to "fire" the spark plugs. In this experiment. Also.
as well as a large (100 watt) 3-way stereo speaker for this experiment. Since obviously placing wires on your head with high voltage to ground would be very hazardous. Do not use a set of headphones under any circumstances. as the ignition coil does not provide electrical isolation between the 170 volts DC of the "plate" power supply and the speaker. Volume 3. with an appropriate cable plugged into the "headphone" or "audio out" jack to convey the signal to your amplifier. I recommend a small battery-powered radio or musical keyboard. Volume 3. I've used small "bookshelf" speakers. thus elevating the speaker connections to that voltage with respect to ground. automotive (6"x9") speakers. chapter 3: "Diodes and Rectifiers" Lessons In Electric Circuits. VACUUM TUBE AUDIO AMPLIFIER 267 The audio speaker need not be extravagant. chapter 13: "Electron Tubes" Lessons In Electric Circuits.5. and they all work fine. CROSS-REFERENCES Lessons In Electric Circuits.19. Volume 2. chapter 9: "Transformers" LEARNING OBJECTIVES • Using a vacuum tube (triode) as an audio amplifier • Using transformers in both step-down and step-up operation • How to build a high-voltage DC power supply . please do not use headphones! You will need some source of audio-frequency AC as an input signal to this amplifier circuit.
DISCRETE SEMICONDUCTOR CIRCUITS • Using a transformer to match impedances SCHEMATIC DIAGRAM B+ (100 to 300 volts DC) Class-A single-ended tube audio amplifier .268 CHAPTER 5.+ Automotive ignition "coil" 8 Ω speaker 0.1 µF 12AX7 "hi-mu" dual triode tube Audio input 100 kΩ to filament power (12 volts AC) .
5. VACUUM TUBE AUDIO AMPLIFIER 269 High-voltage "plate" DC power supply Switch Fuse Plug (optional) 12 volt AC to filaments Low-voltage AC power supply Transformer 120/12 ratio Plate supply switch DANGER! High voltage!! ≈ 170 volts B+ 47 µF 250 WVDC 100 kΩ 12/120 ratio Transformer ILLUSTRATION .19.
DISCRETE SEMICONDUCTOR CIRCUITS - "Plate supply" switch 12 volt side + Filament power 120 volt side Power supply Amplifier Ground B+ + Audio input 5 4 6 - 3 7 2 8 1 9 12AX7 tube Speaker INSTRUCTIONS Welcome to the world of vacuum tube electronics! While not exactly an application of semiconductor technology (power supply rectifier excepted). electronics technicians. If testing circuit voltages with the power on. or engineers) if attempting to build this amplifier. as 170 volts DC is capable of electrocuting you!! It is recommended that beginners seek qualified assistance (experienced electricians. turn off the "plate" power supply switch and wait for the filter capacitor to discharge below 30 volts before touching any part of the circuit. this circuit is useful as an introduction to vacuum tube technology. It should be noted that building and operating this circuit involves work with lethal voltages! You must exhibit the utmost care while working with this circuit. and an interesting application for impedance-matching transformers. Building the high-voltage power supply . use only one hand if possible to avoid the possibility of an arm-to-arm electric shock.270 Low-voltage AC power supply 12 6 6 CHAPTER 5. WARNING: do not touch any wires or terminals while the amplifier circuit is energized! If you must make contact with the circuit at any point.
and then rectify that into 170 volts DC?" The answer to this is twofold: first. running power through two transformers inherently limits the amount of current that may be sent into an accidental short-circuit on the plate-side of the amplifier circuit." posing an additional shock hazard . I've operated this amplifier on as high as 235 volts DC. Note the toggle switch connected between the 12-volt windings of the two transformers. the power output will be miniscule and the sound quality poor. Tubes require power applied to a small filament (sometimes called a heater ) in order to function. it is a good habit to wait for the tube to reach full operating temperature before applying plate voltage. and discovered that both sound quality and intensity improved slightly. and the "filament" power. when shutting off one main switch would accomplish the same thing? The answer lies in proper vacuum tube operation: like incandescent light bulbs. as it provides the capacitor a path for discharge when the AC power is turned off.5. As always. but not enough in my estimation to warrant the additional hazard to experimenters. there will be a piece of wire connecting these two "ground" points together. thereby controlling plate voltage to the amplifier circuit. so having this additional switch in the circuit allows you to shut off the DC high voltage (for safety when modifying or adjusting the circuit) without having to shut off the filament. Without this "bleeder" resistor in the circuit. the capacitor would likely retain a dangerous charge for a long time after "power-down. The "ground" terminal shown on the DC output of the power supply circuit need not connect to earth ground. so our power supply of 170 volts DC specified here is well within that maximum limit. which is only 12 volts AC. Also. it is merely a symbol showing a common connection with a corresponding ground terminal symbol in the amplifier circuit. In the circuit you build. as the cathode must be hot enough to thermally emit electrons. The power supply actually has two different power outputs: the "B+" DC output for plate power. You might be wondering. Rather. continuously providing indication of the power supply voltage. If we were to rectify wall-socket power with a diode bridge. "why step the voltage back up to 120 volts with another transformer? Why not just tap off the wall socket plug to obtain 120 volt AC power directly. Although it is possible to operate the amplifier circuit described in this experiment on as low as 24 volts DC. This meter will show you when the filter capacitor has discharged below the shock-hazard limit (30 volts) when you turn off the "Plate supply switch" to service the amplifier circuit. Second.19. The 12AX7 triode is rated at a maximum "plate voltage" (voltage applied between plate and cathode terminals) of 330 volts. vacuum tubes "wear" when their filaments are powered up and down repeatedly. you should have a voltmeter connected to the "B+" output of the power supply (between the B+ terminal and ground). and that doesn't happen at room temperature! Using one power transformer to step household 120 volt AC power down to 12 volts AC provides low-voltage for the filaments. and this second switch allows you to delay the application of plate voltage until the tube has had time to reach operating temperature. During operation. the designation of certain common points in a circuit by means of a shared symbol is standard practice in electronic schematics. This resistor is quite necessary. it electrically isolates the plate circuit from the wiring system of your house. VACUUM TUBE AUDIO AMPLIFIER 271 Vacuum tubes require fairly high DC voltage applied between plate and cathode terminals in order to function efficiently. and another transformer connected in step-up fashion brings the voltage back up to 120 volts. labeled "Plate supply switch. thereby increasing the shock hazard. it would make both DC terminals (+ and -) elevated in voltage from the safety ground connection of your house's electrical system. Why not just use the main power switch connected to the 120 volt plug? Why have a second switch to shut off the DC high voltage." This switch controls power to the step-up transformer. You will note that the schematic diagram shows a 100 kΩ resistor in parallel with the filter capacitor.
no matter how well it may be designed and built. then build the circuit you intend to power with it. In the circuit I built – with a 47 µF capacitor and a 100 kΩ bleeder resistor – the time constant of this RC circuit was a brief 4. showing the 12AX7 in an inverted position (pin-side-up). most "tubed" electronic devices used sockets for mounting the tubes. do we build circuits with tubes. if we might not be able to obtain sockets for them to plug in to? For small tubes. Here is a photograph of my tube amplifier. thus enabling you to "plug" the tube into a solderless breadboard.272 CHAPTER 5. Given the limited lifetime of most "receiver" tubes (a few years). Be sure you have the power supply safely constructed and working reliably before attempting to power the amplifier circuit with it. If you happen to find a larger filter capacitor value (good for minimizing unwanted power supply "hum" in the speaker).7 seconds. since most "pin connection diagrams" for tubes are shown from a bottom view: . you will need to use a correspondingly smaller value of bleeder resistor. the sockets they plug into are considerably scarcer – your local Radio Shack will not have them in stock! How. One benefit of mounting the tube in this position is ease of pin identification. Building the amplifier One of the problems with building vacuum tube circuits in the 21st century is that sockets for these components can be difficult to find. Though tubes may still be obtained (from music supply stores) with relative ease. then. as these are leftover components from a digital circuit experiment assembled previously on my breadboard. then neither will the powered circuit. If the power supply does not function as it should. so that they could be easily removed and replaced. DISCRETE SEMICONDUCTOR CIRCUITS to you. This is good circuit-building practice in general: build and troubleshoot the power supply first. Please disregard the 10-segment LED bargraph to the left and the 8-position DIP switch assembly to the right in the photograph. or wait longer for the voltage to bleed off each time you turn the "Plate supply" switch off. this problem may be circumvented by directly soldering short lengths of 22gauge solid copper wire to the pins of the tube.
and later the output of a compact disk (CD) player. The 0. You may use just one of the triodes. bias circuits are used to keep the grid slightly negative with respect to ground. but it is not necessary for demonstrating basic operation.) to the tube's grid(s). if you wish. musical keyboard. but for this purpose a bias circuit would introduce more complexity than it's worth. I was able to easily send the amplifier audio signals of varying amplitude to test its performance over a wide range of conditions: . grid connected to grid. Typically. Using a "mono"-to-"phono" connector extension cord plugged into the headphone jack of the receiver/CD player. etc. for simplicity. and cathode connected to cathode.1 µF capacitor shown on the schematic "couples" the audio signal source (radio. and cannot "float" to some high level. VACUUM TUBE AUDIO AMPLIFIER 273 12AX7 dual triode tube Filament 1 Filament 2 4 5 6 Plate 1 Grid 1 Cathode 2 3 7 Grid 2 2 8 Cathode 1 Plate 2 Filament tap (view from bottom) 1 9 You will notice on the amplifier schematic that both triode elements inside the 12AX7's glass envelope are being used.5. as the audio signal source. in parallel: plate connected to plate. I used the output of a radio receiver.19. The 100 kΩ resistor ensures that the average DC voltage between grid and cathode is zero. When I tested my amplifier circuit. and alligator clip jumper wires connecting the "mono" tip of the cord to the input terminals of the tube amplifier. allowing AC to pass but blocking DC. This is done to maximize power output from the tube.
274 CHAPTER 5. though. Now. This means that the speaker wires will be at a high DC voltage with respect to circuit ground. there will be no problem. apply power to the filaments of the tube and wait about 30 seconds for it to reach operating temperature. orange glow. increase the .. the transformer would provide complete isolation as well as impedance matching. we will need a transformer with an impedance ratio of about 10. So long as we know this. we're looking for a transformer with a turns ratio of about 100:1. and the speaker only has about 8 ohms impedance. making it well suited for this application. low-current source to the low-voltage. Since the impedance ratio of a transformer is the square of its turns ratio (or voltage ratio). high current load. low-current device. A typical automotive ignition coil has approximately this turns ratio. Turn the volume control of your radio/CD player/musical keyboard signal source to minimum. To successfully match the high-voltage. Since the vacuum tube is a high-voltage. then turn on the plate supply switch. visible from both the top and bottom views of the tube.000:1. make all connections in the circuit with the power turned off ! After checking connections visually and with an ohmmeter to ensure that the circuit is built as per the schematic diagram. since the device is actually an autotransformer. and most speakers are low-voltage. we must use a step-down transformer. Remember. phones "Phono" plug "Mono" headphone plug A transformer is essential at the output of the amplifier circuit for "matching" the impedances of vacuum tube and speaker. ... Ideally. high-current devices. The voltmeter you have connected between the power supply's B+ output terminal and "ground" should register full voltage (about 170 volts). The only bad aspect of using an ignition coil is that it provides no electrical isolation between primary and secondary windings. and avoid touching those wires during operation. and it is also rated for extremely high voltage on the high-voltage winding. DISCRETE SEMICONDUCTOR CIRCUITS Amplifier circuit Radio Audio input . The both filaments should emit a soft.. the mismatch between them would result in very audio low power output if they were directly connected. with each winding sharing a common terminal at one end. Since the vacuum tube circuit's Thevenin resistance ranges in the tens of thousands of ohms. and the speaker wires would be perfectly safe to touch during use.
Bear in mind that most AC voltmeters will register a transient voltage when initially connected across a source of DC voltage. Connect a 0. then connect one of the test leads to ground. If all is well.19.. VACUUM TUBE AUDIO AMPLIFIER 275 volume control on the signal source and listen to the speaker.1 µF headphones Amplifier circuit . then at the plate of the tube. Troubleshooting this circuit is best done with the sensitive audio detector described in the DC and AC chapters of this Experiments volume. Using two coupling capacitors instead of just one adds an additional degree of safety.. To discharge this voltage. so don't be surprised to see a "spike" (a strong. just its mere presence. especially if you built your detector using a 120 volt power transformer (rather than an "audio output" transformer) as suggested. you should hear the correct sounds clearly through the speaker. though. If you would rather use a voltmeter to test for the presence of audio signal. Being capacitively coupled. briefly touch the free test lead to the grounded test lead. and may need additional filter capacitance. doesn't tell you anything about the quality of the signal. until the problem is found. Use capacitors with a high voltage rating. After testing a point in the amplifier circuit with large DC voltage to ground. Even without the extra capacitor. setting it to a sensitive AC voltage range. not loud.1 µF capacitor in series with each test lead to block DC from the detector. while using the other test lead to check for audio signal at various points in the circuit. momentary voltage indication) at the very moment contact is made with the meter's probes to the circuit.. the power supply is not filtered adequately enough. etc. If it is loud. the detector is also able to test for excessive power supply "hum:" touch the free test lead to the supply's B+ terminal and listen for a loud 60 Hz humming noise.1 µF Sensitivity plug "ground" . you may do so. then at the grid pin(s) of the tube. Use it to test for a good signal at the input. the detector's internal transformer should provide sufficient electrical isolation for your safety in using it to test for signals in a high-voltage circuit like this.. The indication you get from a voltmeter. though. Test leads 0. in helping to isolate the unit from any (high) DC voltage.5. like the one used on the input of the amplifier circuit: B+ Using the sensitive audio detector as a troubleshooting instrument for the amplifier 0. A "pop" sound should be heard in the headphones as the coupling capacitors discharge. the coupling capacitors on the detector may build up substantial voltage. rapidly decreasing to the true AC signal . The noise should be very soft.
the circuit is quite crude and sacrifices quality for simplicity and parts availability. negative feedback. You may be pleasantly surprised at the quality and depth of tone from this little amplifier circuit. Advanced hobbyists and students may wish to experiment with biasing networks. especially given its low power output: less than 1 watt of audio power. but it serves to demonstrate the basic principle of vacuum tube amplification. illustrating what can be done when care and craftsmanship are applied to a project like this. Here is a photo of a very similar amplifier circuit. .276 CHAPTER 5. to obtain more power and/or better sound quality. DISCRETE SEMICONDUCTOR CIRCUITS value. different output transformers. Of course. built by the husband-and-wife team of Terry and Cheryl Goetz. and even different tubes. different power supply voltages.
discrete-component circuit construction is favored only when power dissipation levels are too high for integrated circuits to handle. As you will see in this chapter. The circuits in this chapter make use of IC. many so-called "linear" circuits are quite nonlinear in their behavior. Most integrated circuits provide the same functionality as "discrete" semiconductor circuits at higher levels of reliability and at a fraction of the cost. benefitting students. or integrated circuit. Essentially nothing more than a differential amplifier with very high voltage gain. 277 . either by necessity of physics or by design. Perhaps the most versatile and important analog integrated circuit for the student to master is the operational amplifier. which almost exclusively employ "all or nothing" signals: voltages restricted to values of zero and full supply voltage. Integrated circuits providing a multitude of pre-engineered functions are available at very low cost. a wide variety of behaviors may be obtained from this single device. op-amps are the workhorse of the analog design world. Analog circuits are often referred to as linear circuits to emphasize the valid continuity of signal range forbidden in digital circuits. Many different models of op-amp are available at low cost. Usually. components. but this label is unfortunately misleading. with no valid state in between those extreme limits. hobbyists and professional circuit designers alike. or op-amp.1 Introduction Analog circuits are circuits dealing with signals free to vary from zero to full power supply voltage.Chapter 6 ANALOG INTEGRATED CIRCUITS 6. This stands in contrast to digital circuits. By cleverly applying feedback from the output of an op-amp to one or more of its inputs. but circuits described in this chapter will incorporate only commonly available op-amp models. Just because a voltage or current signal is allowed to vary smoothly between the extremes of zero and full power supply limits does not necessarily mean that all mathematical relationships between these signals are linear in the "straight-line" or "proportional" sense of the word. Such components are actually networks of interconnected components manufactured on a single wafer of semiconducting material.
Volume 3. respectively) • Three 6 volt batteries • Two 10 kΩ potentiometers. I recommend that you purchase and use "dual" op-amps over "single" op-amps even if a project only requires one. with two complete amplifier circuits housed in the same 8-pin DIP package. CROSS-REFERENCES Lessons In Electric Circuits. this makes sense. ANALOG INTEGRATED CIRCUITS 6. linear taper (Radio Shack catalog # 271-1715) • One light-emitting diode (Radio Shack catalog # 276-026 or equivalent) • One 330 Ω resistor • One 470 Ω resistor This experiment only requires a single operational amplifier.2 Voltage comparator PARTS AND MATERIALS • Operational amplifier. model 1458 or 353 recommended (Radio Shack catalog # 276-038 and 900-6298. because they are more versatile (the same op-amp unit can function in projects requiring only one amplifier as well as in projects requiring two).278 CHAPTER 6. In the interest of purchasing and stocking the least number of components for your home laboratory. The model 1458 and 353 are both "dual" op-amp units. chapter 8: "Operational Amplifiers" LEARNING OBJECTIVES • How to use an op-amp as a comparator SCHEMATIC DIAGRAM 6V − 1 330 Ω 470 Ω 6V 6V + /2 1458 ILLUSTRATION .
all voltages measured with respect to ground. This behavior is much easier understood by experimenting with a comparator circuit than it is by reading someone's verbal description of it. The result of this comparison is indicated by the output voltage: if the op-amp's output is saturated in the positive direction. VOLTAGE COMPARATOR 279 + - + 1458 + - INSTRUCTIONS A comparator circuit compares two voltage signals and determines which one is greater. 0 volts. For greater insight into this circuit's operation.2. one can easily comprehend the function of a comparator circuit. it means the inverting input (-) has a greater voltage applied to it than the noninverting input (+). voltage than the inverting input (-). two potentiometers supply variable voltages to be compared by the op-amp. you might want to connect a pair of voltmeters to the op-amp input terminals (both voltmeters referenced to ground) so that both input voltages may be numerically compared with each other. If the op-amp's voltage is near the negative supply voltage (in this case. the noninverting input (+) is a greater. In this experiment. or more positive.6. these meter indications compared to the LED status: . or ground potential). The output status of the op-amp is indicated visually by the LED. By adjusting the two potentiometers and observing the LED.
that wind speed signal could be compared with a "set-point" voltage and compared by an op-amp to drive a high wind speed alarm: 6V − 1 330 Ω 470 Ω 6V 6V + Gen - + /2 1458 LED lights up when wind speed exceeds "set-point" limit established by the potentiometer position. if a small generator were attached to an anemometer wheel to produce a voltage proportional to wind speed.280 CHAPTER 6. ANALOG INTEGRATED CIRCUITS + - + 1458 + - VΩ A COM A VΩ COM Comparator circuits are widely used to compare physical measurements. . For instance. provided those physical variables can be translated into voltage signals.
3. model 1458 or 353 recommended (Radio Shack catalog # 276-038 and 900-6298. PRECISION VOLTAGE FOLLOWER 281 6.3 Precision voltage follower PARTS AND MATERIALS • Operational amplifier. chapter 8: "Operational Amplifiers" LEARNING OBJECTIVES • How to use an op-amp as a voltage follower • Purpose of negative feedback • Troubleshooting strategy SCHEMATIC DIAGRAM 6V − 1 6V 6V Vinput + /2 1458 Voutput ILLUSTRATION .6. Volume 3. linear taper (Radio Shack catalog # 271-1715) CROSS-REFERENCES Lessons In Electric Circuits. respectively) • Three 6 volt batteries • One 10 kΩ potentiometer.
resulting in the output voltage saturating for virtually any amount of differential voltage applied between the two input terminals. As such. This is good if we desire comparator operation. but if we want the op-amp to behave as a true amplifier. without any feedback from output to input. Watch the op-amp's output voltage follow the input voltage as you adjust the potentiometer through its range. this is not a disadvantage as one might think. the output voltage will precisely "follow" the noninverting input's voltage. the full voltage gain of the operational amplifier was available. we are limited to external connections and componentry. and the output voltage between the op-amp's output terminal and circuit ground. which approximated the input voltage to within several tenths of a volt. between output and input voltages by connecting the voltmeter between the op-amp's two input terminals. Actually. Unlike the voltage follower circuit made from a single transistor (see chapter 5: Discrete Semiconductor Circuits). You may directly measure the difference. the output voltage will seek whatever level is necessary to balance the inverting input's voltage with that applied to the noninverting (+) input. the amplifier was used in "open-loop" mode. If this feedback connection is direct. that is. Throughout most of the poten- . as in a straight piece of wire. this voltage follower circuit will output a voltage accurate to within mere microvolts of the input voltage! Measure the input voltage of this circuit with a voltmeter connected between the op-amp's noninverting (+) input terminal and circuit ground (the negative side of the power supply).282 CHAPTER 6. If we connect the output of an op-amp to its inverting (-) input. or error. ANALOG INTEGRATED CIRCUITS + - + 1458 + - INSTRUCTIONS In the previous op-amp experiment. we need it to exhibit a manageable voltage gain. much easier than if we were to exercise the option of modifying its internal circuitry. because the combination of extremely high open-loop voltage gain coupled with feedback allows us to use the op-amp for a much wider variety of purposes. Since we do not have the luxury of disassembling the integrated circuitry of the op-amp and changing resistor values to give a lesser voltage gain.
the specified models included. its output voltage is unable to exactly reach these high and low limits.0) v(2.0) v(1. Try moving the potentiometer to one of its extreme positions.print dc v(1. this error voltage should be almost zero. respectively. Voltage follower circuits have another important use for circuit builders: they allow for simple linear testing of an op-amp. An op-amp that fails to work as a voltage follower certainly won't work as anything more complex! COMPUTER SIMULATION Schematic with SPICE node numbers: 2 1 Vinput − + E1 2 Rload Rbogus 0 0 Netlist (make a text file containing the following text. You may find that it can only go within a volt or two of the power supply "rails. If full "rail-to-rail" output voltage swing is required in a circuit design. If one of those op-amps seems to be causing a problem and you suspect it may be faulty.dc vinput 5 5 1 . Measure error voltage." This is a very important limitation to understand when designing circuits using operational amplifiers. Precision voltage follower circuits are useful if the voltage signal to be amplified cannot tolerate "loading. but rather with amplifying a signal's capacity to deliver current to a load. verbatim): Voltage follower vinput 1 0 rbogus 1 0 1meg e1 2 0 1 2 999meg rload 2 0 10k ." that is. Due to limitations in the 1458's internal circuitry. you should measure a substantial error voltage. far clockwise or far counterclockwise. if it has a high source impedance. PRECISION VOLTAGE FOLLOWER 283 tiometer's range. the "rail" voltages are +18 volts and 0 volts. cannot "swing" their output voltage exactly to full power supply ("rail") voltage levels.3. In this case. Do you notice anything unusual? If you are using the model 1458 or model 353 op-amp for this experiment. its purpose has nothing to do with amplifying voltage. or compare output voltage against input voltage.2) . or difference between output and input. try re-connecting it as a simple voltage follower and see if it functions in that capacity. The model 3130 is one such op-amp.end . Since a voltage follower by definition has a voltage gain of 1.6. Suppose that you are building a circuit using one or more op-amps to perform some advanced function. other op-amp models may be selected which offer this capability. Many op-amps. One of the troubleshooting techniques I recommend is to simplify and rebuild.
ANALOG INTEGRATED CIRCUITS An ideal operational amplifier may be simulated in SPICE using a dependent voltage source (e1 in the netlist). Such "bogus" resistances should be arbitrarily large. non-inverting input first (1 2). The output nodes are specified first (2 0). then the two input nodes. This is the purpose of R bogus : to provide DC path to ground for the Vinput voltage source. As you can see. Open-loop gain is specified last (999meg) in the dependent voltage source line. some finite amount of resistance must be included to avoid an analysis error. In this simulation I chose 1 MΩ for an Rbogus value. SPICE doesn't like open circuits! .284 CHAPTER 6. A load resistor is included in the circuit for much the same reason: to provide a DC path for current at the output of the dependent voltage source. Because SPICE views the input impedance of a dependent source as infinite.
linear taper (Radio Shack catalog # 271-1715) CROSS-REFERENCES Lessons In Electric Circuits.6.4 Noninverting amplifier PARTS AND MATERIALS • Operational amplifier. NONINVERTING AMPLIFIER 285 6. respectively) • Three 6 volt batteries • Two 10 kΩ potentiometers.4. negative feedback SCHEMATIC DIAGRAM R2 6V − 1 6V 6V R1 Vinput + /2 1458 Voutput ILLUSTRATION . model 1458 or 353 recommended (Radio Shack catalog # 276-038 and 900-6298. chapter 8: "Operational Amplifiers" LEARNING OBJECTIVES • How to use an op-amp as a single-ended amplifier • Using divided. Volume 3.
What is the lowest voltage gain attainable with this amplifier configuration? Why do you think this is? COMPUTER SIMULATION Schematic with SPICE node numbers: . Because the output voltage increases in a positive direction for a positive increase of the input voltage. positive increasing input voltage results in positive decreasing or negative increasing output). Measure both input and output voltage for several positions of the input potentiometer R 1 . With only a fraction of the output voltage fed back to the inverting input. If the output and input voltages were related to one another in an inverse fashion (i. this amplifier is referred to as noninverting. In other words. then the amplifier would be known as an inverting type. that gain being established by the position of the feedback potentiometer (R2 ). the op-amp will now function as an amplifier with a controllable voltage gain. Try adjusting R2 for maximum and minimum voltage gain. Set R2 to approximately mid-position. This should give a voltage gain of about 2. The ability to leverage an op-amp in this fashion to create an amplifier with controllable voltage gain makes this circuit an extremely useful one. ANALOG INTEGRATED CIRCUITS + - + 1458 + - INSTRUCTIONS This circuit differs from the voltage follower in only one respect: output voltage is "fed back" to the inverting (-) input through a voltage-dividing potentiometer rather than being directly connected. For any given R2 position.e. the ratio between output and input voltage should be the same. It would take quite a bit more design and troubleshooting effort to produce a similar circuit using discrete transistors. You will also notice that the input and output voltages are always positive with respect to ground. Move R2 to a different position and re-take voltage measurements for several positions of R1 . the op-amp will output a corresponding multiple of the voltage sensed at the noninverting (+) input in keeping the input differential voltage near zero.286 CHAPTER 6.
0) v(3. To simulate the potentiometer at the 75% position. set R 2 to 7.6.4.dc vinput 5 5 1 .5 kΩ and R1 to 2.5 kΩ. .end With R1 and R2 set equally to 5 kΩ in the simulation.print dc v(1. NONINVERTING AMPLIFIER 287 R1 0 2 1 Vinput 0 2 − + Rbogus R2 3 E1 3 Rload 0 Netlist (make a text file containing the following text.0) . it mimics the feedback potentiometer of the real circuit at mid-position (50%). verbatim): Noninverting amplifier vinput 1 0 r2 3 2 5k r1 2 0 5k rbogus 1 0 1meg e1 3 0 1 2 999meg rload 3 0 10k .
model TL082 recommended (Radio Shack catalog # 276-1715) • Operational amplifier. but is actually a 1 mA movement sold with a 15 kΩ +/. chapter 8: "Operational Amplifiers" LEARNING OBJECTIVES • Voltmeter loading: its causes and its solution • How to make a high-impedance voltmeter using an op-amp • What op-amp "latch-up" is and how to avoid it SCHEMATIC DIAGRAM . CROSS-REFERENCES Lessons In Electric Circuits. This meter experiment is based on a JFET-input op-amp such as the TL082. ANALOG INTEGRATED CIRCUITS 6.1% tolerance multiplier resistor. The other op-amp (model 1458) is used in this experiment to demonstrate the absence of latch-up: a problem inherent to the TL082. Any very high resistance resistors will suffice. You don't need 1 MΩ resistors. If you get this Radio Shack meter movement. you can use the included 15 kΩ resistor for the resistor specified in the parts list. exactly. model LM1458 recommended (Radio Shack catalog # 276-038) • Four 6 volt batteries • One meter movement. Volume 3.288 CHAPTER 6. 1 mA full-scale deflection (Radio Shack catalog #22-410) • 15 kΩ precision resistor • Four 1 MΩ resistors The 1 mA meter movement sold by Radio Shack is advertised as a 0-15 VDC meter.5 High-impedance voltmeter PARTS AND MATERIALS • Operational amplifier.
6. there will be no "impact" on the circuit as the voltage is being measured. .5. meaning that it draws zero current from the circuit under test. This way. HIGH-IMPEDANCE VOLTMETER 289 6V 6V 6V 6V 15 kΩ − - 0-1 mA + 1 MΩ TP3 1 MΩ TP2 TL082 + Test probe 1 MΩ TP1 1 MΩ ILLUSTRATION + - TP3 TP2 TP1 + - TL082 + - + - 0 to 1 mA meter movement + INSTRUCTIONS An ideal voltmeter has infinite input impedance.
ANALOG INTEGRATED CIRCUITS The more current a voltmeter draws from the circuit under test. After you've proven this circuit to work. This loading is more pronounced on circuits of high resistance. This entails removing the center-tap ground connection between the 2nd and 3rd batteries. or TP3 (with respect to ground). TP2. Does the meter read falsely high or falsely low? Why do you think this is? If we were to increase the meter's input impedance. The meter's range is set by the resistor connecting the inverting (-) input to ground. and 9 volts. and TP3. Note that the meter movement is part of the op-amp's feedback loop from output to inverting input. the meter should read exactly 0 volts. and try to use this voltmeter to measure the voltages at TP1. we would diminish its current draw or "load" on the circuit under test and consequently improve its measurement accuracy. respectively). you'd encounter severe measurement errors induced by meter "impact:" 6V 6V TP3 should be 9 volts TP2 should be 6 volts TP1 should be 3 volts 15 kΩ 0-1 mA + 1 MΩ TP3 1 MΩ TP2 1 MΩ However. shown in the schematic diagram. If you were to build a simple 0-15 volt range voltmeter by connecting the 1 mA meter movement in series with the 15 kΩ precision resistor. Notice how you can drive the needle upward on the scale simply by measuring battery voltage through your body resistance: an impossible feat with the original. with the meter movement accurately measuring these voltages (approximately 3. unamplified voltmeter circuit. the more the measured voltage will "sag" under the loading effect of the meter. Build the op-amp meter circuit as shown and re-take voltage measurements at TP1. . An op-amp with highimpedance inputs (using a JFET transistor input stage rather than a BJT input stage) works well for this application. You should enjoy far better success this time. the more the tire's pressure will be impacted in the act of measurement. TP2. You may witness the extreme sensitivity of this voltmeter by touching the test probe with one hand and the most positive battery terminal with the other. like the voltage divider made of 1 MΩ resistors. not from the circuit under test through the test probe. the requisite current supplied directly from the batteries through the op-amp's power supply pins. If you touch the test probe to ground. like a tire-pressure gauge releasing air out of the tire being measured: the more air released from the tire.290 CHAPTER 6. 6. the meter will fail to measure these voltages correctly due to the meter's "loading" effect! TP1 1 MΩ Try using the meter movement and 15 kΩ resistor as shown to measure these three voltages. modify it by changing the power supply from dual to split. This circuit drives the meter movement with a current proportional to the voltage impressed at the noninverting (+) input.
With a 15 kΩ range resistor and a 1 mA meter movement. although you may still get incorrect meter readings with the measured voltage exactly equal to the negative power supply rail.5. and TP3 to 6. rather than a "single" +24 volt supply). 12. so grounding the test probe brings the noninverting (+) input exactly to that rail voltage. When the op-amp ran on a "dual" supply (+12/-12 volts. so grounding the test probe didn't violate the op-amp's common-mode voltage limit. measuring 18 volts will gently "peg" the meter. the op-amp's negative power rail is at ground potential (0 volts). However. respectively. HIGH-IMPEDANCE VOLTMETER and grounding the far negative battery terminal instead: 291 6V 6V 6V 6V 15 kΩ − - 0-1 mA + 1 MΩ TP3 1 MΩ TP2 TL082 + 1 MΩ TP1 1 MΩ This alteration in the power supply increases the voltages at TP1. based on how op-amps are supposed to function. TP2. As a general rule. we have a problem. In this case. With a single supply. the negative power supply rail was 12 volts away from ground (0 volts). This is bad for a JFET op-amp. neither input should be allowed to come close to either power supply rail voltage. as with many JFET-input op-amps. Note that some op-amps do not "latch-up" the way the model TL082 does. with the "single" +24 volt supply. but it will not! What is happening here is an op-amp phenomenon called latch-up: where the op-amp output drives to a positive voltage when the input common-mode voltage exceeds the allowable limit. and 18 volts. which is pin-for-pin compatible (no breadboard wiring changes needed). You may replace the TL082 with an LM1458 op-amp. .6. The model 1458 will not "latch-up" when the test probe is grounded. This should drive the meter needle to exactly 0 volts as before. but you should be able to measure the 6 and 12 volt test points just fine. you should always be sure the op-amp's power supply rail voltages exceed the expected input voltages. Try touching the meter's test probe to ground. even though it doesn't seem like it should. and drives the output strongly positive.
CROSS-REFERENCES Lessons In Electric Circuits. However. but I'm specifying the model 1458 over the 353 because the 1458 has much higher input bias currents. high input bias current is a bad characteristic for an op-amp to have in a precision DC amplifier circuit (and especially an integrator circuit!). Normally.1 µF each. model 1458 recommended (Radio Shack catalog # 276-038) • One 10 kΩ potentiometer.1 µF + 1 MΩ /2 1458 Voutput . ANALOG INTEGRATED CIRCUITS 6. linear taper (Radio Shack catalog # 271-1715) • Two capacitors.292 CHAPTER 6. non-polarized (Radio Shack catalog # 272-135) • Two 100 kΩ resistors • Three 1 MΩ resistors Just about any operational amplifier model will work fine for this integrator experiment. I want the bias current to be high in order that its bad effects may be exaggerated.6 Integrator PARTS AND MATERIALS • Four 6 volt batteries • Operational amplifier. and so that you will learn one method of counteracting its effects. 0. chapter 8: "Operational Amplifiers" LEARNING OBJECTIVES • Method for limiting the span of a potentiometer • Purpose of an integrator circuit • How to compensate for op-amp bias current SCHEMATIC DIAGRAM 6V 6V 6V 6V 100 kΩ 10 kΩ 100 kΩ 1 MΩ − 1 0. Volume 3.
a voltage of about -0. This is precisely the opposite of differentiation. To use calculus terms. That is. the wiper voltage should measure zero volts. At the other extreme of motion.5 volt will be produced. If you have two voltmeters. Slowly move the potentiometer control while monitoring the output voltage.6. the input voltage level establishes the output voltage rate of change over time. so that full movement produces a fairly small range of input voltages for the op-amp to operate on. we would say that the output voltage represents the integral (with respect to time) of the input voltage function. Connect a voltmeter between the op-amp's output terminal and the circuit ground point. INTEGRATOR ILLUSTRATION 293 + - + - 1458 + - + - INSTRUCTIONS As you can see from the schematic diagram. This is to limit the span of the potentiometer. The output voltage should be changing at a rate established by the potentiometer's deviation from zero (center) position.5 volt (with respect the the ground point in the middle of the series battery string) will be produced at the potentiometer wiper. At one extreme of the potentiometer's motion. where the derivative of a signal or function is its instantaneous rate of change. one on each end. When the potentiometer is positioned dead-center. the potentiometer is connected to the "rails" of the power source through 100 kΩ resistors. a voltage of about 0. you may readily see this relationship between input voltage and output voltage rate of change by measuring the wiper voltage (between the potentiometer wiper and .6.
1 µF + /2 1458 1 MΩ Voutput Connect integrator input directly to ground . the faster its output voltage will change. engineers used analog computers to simulate such processes as machinery vibration. like this: 6V 6V 6V 6V 100 kΩ 10 kΩ 100 kΩ 1 MΩ − 1 0. and potentiometers (dividers). Because differential equations describe so many physical processes. Adjusting the potentiometer to give zero volts should result in the slowest output voltage rate-of-change. Conversely. Move the potentiometer until the op-amp's output voltage is as close to zero as you can get it. almost any differential equation could be modeled. summers. rocket trajectory. ANALOG INTEGRATED CIRCUITS ground) with one meter and the output voltage (between the op-amp output terminal and ground) with the other. analog computers are useful as simulators. Disconnect the integrator input from the potentiometer wiper terminal and connect it instead to ground. Even though analog computers are considered obsolete by modern standards. and solutions obtained by measuring voltages produced at various points in the network of circuits. the more voltage input to this circuit. and control system response. This will halve the integrator's input resistance." Try connecting the second 0.294 CHAPTER 6. their constituent components still work well as learning tools for calculus concepts. This will double the amount of capacitance in the op-amp's feedback loop. and moving as slowly as you can make it. By connecting integrator circuits with amplifiers.1 µF capacitor in parallel with the first. or "ramp. What affect does this have on the circuit's integration rate for any given potentiometer position? Try connecting another 1 MΩ resistor in parallel with the input resistor (the resistor connecting the potentiometer wiper to the inverting terminal of the op-amp). What affect does this have on the circuit's integration rate? Integrator circuits are one of the fundamental "building-block" functions of an analog computer. Before the advent of modern digital computers.
Connect integrator input directly to ground
Applying exactly zero voltage to the input of an integrator circuit should, ideally, cause the output voltage rate-of-change to be zero. When you make this change to the circuit, you should notice the output voltage remaining at a constant level or changing very slowly.
With the integrator input still shorted to ground, short past the 1 MΩ resistor connecting the op-amp's noninverting (+) input to ground. There should be no need for this resistor in an ideal op-amp circuit, so by shorting past it we will see what function it provides in this very real op-amp circuit:
100 kΩ 10 kΩ 100 kΩ
0.1 µF
/2 1458
Connect integrator input directly to ground Short past the "grounding" resistor -
Connect integrator input directly to ground Short past the "grounding" resistor
As soon as the "grounding" resistor is shorted with a jumper wire, the op-amp's output voltage will start to change, or drift. Ideally, this should not happen, because the integrator circuit still
has an input signal of zero volts. However, real operational amplifiers have a very small amount of current entering each input terminal called the bias current. These bias currents will drop voltage across any resistance in their path. Since the 1 MΩ input resistor conducts some amount of bias current regardless of input signal magnitude, it will drop voltage across its terminals due to bias current, thus "offsetting" the amount of signal voltage seen at the inverting terminal of the op-amp. If the other (noninverting) input is connected directly to ground as we have done here, this "offset" voltage incurred by voltage drop generated by bias current will cause the integrator circuit to slowly "integrate" as though it were receiving a very small input signal. The "grounding" resistor is better known as a compensating resistor, because it acts to compensate for voltage errors created by bias current. Since the bias currents through each op-amp input terminal are approximately equal to each other, an equal amount of resistance placed in the path of each bias current will produce approximately the same voltage drop. Equal voltage drops seen at the complementary inputs of an op-amp cancel each other out, thus nulling the error otherwise induced by bias current. Remove the jumper wire shorting past the compensating resistor and notice how the op-amp output returns to a relatively stable state. It may still drift some, most likely due to bias voltage error in the op-amp itself, but that is another subject altogether! COMPUTER SIMULATION Schematic with SPICE node numbers:
2 −
0.1 µF 3
Netlist (make a text file containing the following text, verbatim): DC integrator vinput 1 0 dc 0.05 r1 1 2 1meg c1 2 3 0.1u ic=0 e1 3 0 0 2 999k .tran 1 30 uic .plot tran v(1,0) v(3,0) .end
555 audio oscillator
PARTS AND MATERIALS • Two 6 volt batteries • One capacitor, 0.1 µF, non-polarized (Radio Shack catalog # 272-135) • One 555 timer IC (Radio Shack catalog # 276-1723) • Two light-emitting diodes (Radio Shack catalog # 276-026 or equivalent) • One 1 MΩ resistor • One 100 kΩ resistor • Two 510 Ω resistors • Audio detector with headphones • Oscilloscope (recommended, but not necessary) A oscilloscope would be useful in analyzing the waveforms produced by this circuit, but it is not essential. An audio detector is a very useful piece of test equipment for this experiment, especially if you don't have an oscilloscope. CROSS-REFERENCES Lessons In Electric Circuits, Volume 4, chapter 10: "Multivibrators" LEARNING OBJECTIVES • How to use the 555 timer as an astable multivibrator • Working knowledge of duty cycle SCHEMATIC DIAGRAM
510 Ω 1 MΩ Vcc 555 Disch 100 kΩ Thresh Trig 0.1 µF Gnd Ctrl 510 Ω 6V Out RST 6V
555 + -
INSTRUCTIONS The "555" integrated circuit is a general-purpose timer useful for a variety of functions. In this experiment, we explore its use as an astable multivibrator, or oscillator. Connected to a capacitor and two resistors as shown, it will oscillate freely, driving the LEDs on and off with a square-wave output voltage. This circuit works on the principle of alternately charging and discharging a capacitor. The 555 begins to discharge the capacitor by grounding the Disch terminal when the voltage detected by the Thresh terminal exceeds 2/3 the power supply voltage (Vcc ). It stops discharging the capacitor when the voltage detected by the Trig terminal falls below 1/3 the power supply voltage. Thus, when both Thresh and Trig terminals are connected to the capacitor's positive terminal, the capacitor voltage will cycle between 1/3 and 2/3 power supply voltage in a "sawtooth" pattern. During the charging cycle, the capacitor receives charging current through the series combination of the 1 MΩ and 100 kΩ resistors. As soon as the Disch terminal on the 555 timer goes to ground potential (a transistor inside the 555 connected between that terminal and ground turns on), the capacitor's discharging current only has to go through the 100 kΩ resistor. The result is an RC time constant that is much longer for charging than for discharging, resulting in a charging time greatly exceeding the discharging time. The 555's Out terminal produces a square-wave voltage signal that is "high" (nearly V cc ) when the capacitor is charging, and "low" (nearly 0 volts) when the capacitor is discharging. This alternating high/low voltage signal drives the two LEDs in opposite modes: when one is on, the other will be off. Because the capacitor's charging and discharging times are unequal, the "high" and "low" times of the output's square-wave waveform will be unequal as well. This can be seen in the relative brightness of the two LEDs: one will be much brighter than the other, because it is on for a longer period of time during each cycle. The equality or inequality between "high" and "low" times of a square wave is expressed as that wave's duty cycle. A square wave with a 50% duty cycle is perfectly symmetrical: its "high" time is precisely equal to its "low" time. A square wave that is "high" 10% of the time and "low" 90% of the time is said to have a 10% duty cycle. In this circuit, the output waveform has a "high" time
exceeding the "low" time, resulting in a duty cycle greater than 50%. Use the audio detector (or an oscilloscope) to investigate the different voltage waveforms produced by this circuit. Try different resistor values and/or capacitor values to see what effects they have on output frequency or charge/discharge times.
555 ramp generator
PARTS AND MATERIALS • Two 6 volt batteries • One capacitor, 470 µF electrolytic, 35 WVDC (Radio Shack catalog # 272-1030 or equivalent) • One capacitor, 0.1 µF, non-polarized (Radio Shack catalog # 272-135) • One 555 timer IC (Radio Shack catalog # 276-1723) • Two PNP transistors – models 2N2907 or 2N3906 recommended (Radio Shack catalog # 2761604 is a package of fifteen PNP transistors ideal for this and other experiments) • Two light-emitting diodes (Radio Shack catalog # 276-026 or equivalent) • One 100 kΩ resistor • One 47 kΩ resistor • Two 510 Ω resistors • Audio detector with headphones The voltage rating on the 470 µF capacitor is not critical, so long as it generously exceeds the maximum power supply voltage. In this particular circuit, that maximum voltage is 12 volts. Be sure you connect this capacitor in the circuit properly, respecting polarity! CROSS-REFERENCES Lessons In Electric Circuits, Volume 1, chapter 13: "Capacitors" Lessons In Electric Circuits, Volume 4, chapter 10: "Multivibrators" LEARNING OBJECTIVES • How to use the 555 timer as an astable multivibrator • A practical use for a current mirror circuit • Understanding the relationship between capacitor current and capacitor voltage rate-of-change
we will compare its operation in two different capacitor-charging modes: traditional RC and constant-current. just as you would expect from an RC charging circuit. Measure voltage directly across the capacitor again. we are using a 555 timer IC as an astable multivibrator. then taper off as it builds up to 2/3 supply voltage. however. The charging cycle begins again at this point. - . This allows the capacitor to charge through a 47 kΩ resistor. It should rise quickly at first. This allows the capacitor to be charged through the controlled-current leg of a current mirror circuit formed by the two PNP transistors. Measure voltage directly across the capacitor with a voltmeter (a digital voltmeter is preferred). Remove the jumper wire from TP3. and note the rate of capacitor charging over time.302 CHAPTER 6. Connecting test point #1 (TP1) to test point #3 (TP3) using a jumper wire. ANALOG INTEGRATED CIRCUITS 510 Ω 47 kΩ TP2 TP3 Vcc 555 Disch Thresh RST 6V Out Ctrl Gnd 6V + A 100 kΩ TP1 Trig 510 Ω 470 µF ILLUSTRATION + TP3 TP2 CBE CBE 555 TP1 + - INSTRUCTIONS Again. noting the difference in charging rate over time as compared to the last circuit configuration. When the capacitor has reached 2/3 supply voltage. the 555 timer switches to "discharge" mode and discharges the capacitor to a level of 1/3 supply voltage almost immediately. and re-connect it to TP2. or oscillator. This time.
8. This circuit works just as well at high frequencies as it does at low frequencies. It is an interesting experiment at this point to change the temperature of either current mirror transistor by touching it with your finger. as described by the equation i = C(de/dt). so will be its rate-of-change of voltage over time. the capacitor receives a nearly constant charging current. As the transistor warms. the current decreases. Measure both DC microamps and AC microamps. If the capacitor's current is constant. Record these current figures on paper. it will conduct more collector current for the same base-emitter voltage. Now.1 µF capacitor. however. With the ammeter connected between TP1 and TP3 (RC mode). connect the ammeter between TP1 and TP2 (constant-current mode). Replace the 470 µF capacitor with a 0. Connected between TP1 and TP2. you should see a current that starts at a relatively high value at the beginning of the charging cycle. The detector should produce an audio tone that is easy to hear. 555 RAMP GENERATOR 303 By connecting TP1 to TP2.6. The result is a "ramp" waveform rather than a "sawtooth" waveform: Sawtooth waveform (RC circuit) Ramp waveform (constant current) The capacitor's charging current may be directly measured by substituting an ammeter in place of the jumper wire. The capacitor's voltage will now be changing much too fast to view with a voltmeter in the DC mode. Connected between TP1 and TP3. Measuring AC current in addition to DC current is an easy way to determine which circuit configuration gives the most stable charging current. If the controlling transistor (the one connected to the 100 kΩ resistor) is touched. but we can still measure capacitor current with an ammeter. noting any differences in current readings between this circuit configuration and the last one. and use an audio detector to sense the voltage waveform at the 555's output terminal. For the most stable current mirror operation. the two transistors should be cemented together so that their temperatures never differ by any substantial amount. measure both DC microamps and AC microamps. the current increases. If the controlled transistor is touched. . Constant capacitor charging current yields a voltage curve that is linear. The ammeter will need to be set to measure a current in the range of hundreds of microamps (tenths of a milliamp). the current will be much more stable. and tapers off toward the end. If the current mirror circuit were perfect – the capacitor charging current absolutely constant – there would be zero AC current measured by the meter.
0. model 1458 recommended (Radio Shack catalog # 276-038) • One NPN power transistor – (Radio Shack catalog # 276-2041 or equivalent) • Three 1N4001 rectifying diodes (Radio Shack catalog # 276-1101) • One 10 kΩ potentiometer. ANALOG INTEGRATED CIRCUITS 6. linear taper (Radio Shack catalog # 271-1715) • One 33 kΩ resistor • 12 volt automotive tail-light lamp • Audio detector with headphones CROSS-REFERENCES Lessons In Electric Circuits.9 PWM power controller PARTS AND MATERIALS • Four 6 volt batteries • One capacitor. 35 WVDC (Radio Shack catalog # 272-1028 or equivalent) • One capacitor. 100 µF electrolytic.1 µF Gnd Ctrl Out + RST 1 − + 1 33 kΩ /2 1458 Load 6V 6V /2 1458 − Power transistor 6V 6V . Volume 3.1 µF. chapter 8: "Operational Amplifiers" Lessons In Electric Circuits. non-polarized (Radio Shack catalog # 272-135) • One 555 timer IC (Radio Shack catalog # 276-1723) • Dual operational amplifier. Volume 2. chapter 7: "Mixed-Frequency AC Signals" LEARNING OBJECTIVES • How to use the 555 timer as an astable multivibrator • How to use an op-amp as a comparator • How to use diodes to drop unwanted DC voltage • How to control power to a load by pulse-width modulation SCHEMATIC DIAGRAM Vcc 555 Disch Thresh Trig 0.304 CHAPTER 6.
varying in duty cycle according to the potentiometer's position. . or pulse width. The comparison of these two voltage signals produces a square-wave output from the op-amp. The 555's oscillation frequency is much higher than the lamp filament's ability to thermally cycle (heat and cool).6.9. This variable duty cycle signal then drives the base of a power transistor. so any variation in duty cycle. PWM POWER CONTROLLER ILLUSTRATION 305 E B C + - + - 555 + + - 1458 INSTRUCTIONS This circuit uses a 555 timer to generate a sawtooth voltage waveform across a capacitor. switching current and and off through the load. using an op-amp as a comparator. has the effect of controlling the total power dissipated by the load over time. then compares that signal against a steady voltage provided by a potentiometer.
is known as pulse-width modulation. you will notice two operational amplifiers connected in parallel. This should only be done if the op-amps in question are overload-protected. When the transistor is saturated. the lamp will turn on and off at regular intervals. the load power will not be proportioned as before. so an alternative method is to slow the 555 oscillator down enough that the three voltages may be compared with a simple DC voltmeter. ANALOG INTEGRATED CIRCUITS EC Output (low power to load) Control voltage EC Output (high power to load) Controlling electrical power through a load by means of quickly switching it on and off. Replace the 0. which the 1458 series of op-amps are. . The inherent short-circuit protection offered by the 1458 allows for direct driving of the power transistor base without any need for a current-limiting resistor. its power dissipation is zero because there is no current through it. However. and varying the "on" time. enabling you to measure the capacitor voltage slowly rise over time. This will slow the oscillation frequency down by a factor of at least a thousand. It is a very efficient means of controlling electrical power because the controlling element (the power transistor) dissipates comparatively little power in switching on and off. Feel free to experiment with other capacitor or resistor values to speed up the oscillations enough so the lamp never fully turns on or off. and op-amp output waveforms all on one (tripletrace) oscilloscope to see how they relate to one another. When you examine the schematic. it is possible (though unlikely) that one op-amp could turn on before the other. PWM is a concept easier understood through experimentation than reading.306 CHAPTER 6. its dissipation is very low because there is little voltage dropped between collector and emitter while it is conducting current. and to the load power. much less any oscilloscope at all. With such a slow oscillation frequency. so two op-amps are used in tandem. and damage result from the two outputs short-circuiting each other (one driving "high" and the other driving "low" simultaneously). and the op-amp output transition from "high" to "low" when the capacitor voltage becomes greater than the potentiometer voltage. but is "throttled" by quick on-and-off pulsing of the transistor. especially if compared to the wasted power dissipated of a rheostat in a similar situation. Rather. or PWM. This is done to provide maximum current output to the base terminal of the power transistor. most of us have no access to a triple-trace oscilloscope. Otherwise. potentiometer voltage. A single op-amp (one-half of a 1458 IC) may not be able to provide sufficient output current to drive the transistor into saturation.1 µF capacitor with one that is 100 µF or larger. It would be nice to view the capacitor voltage. When the transistor is in cutoff.
which makes the tone sound different. Adjusting the potentiometer has no effect on signal frequency. versus a kind of similarity in sound just above or below 50% duty cycle." It is interesting to listen to the op-amp output signal through an audio detector as the potentiometer is adjusted through its full range of motion. only odd-numbered.1 volts (0. and there will be even-numbered harmonics. Note the difference in tone quality." Because the 1458 op-amp cannot swing its output voltage all the way down to ground potential. as some of them correspond to octaves of the fundamental frequency and thus "fit" more naturally into the tone scheme. Any waveform that is symmetrical above and below its centerline. . PWM POWER CONTROLLER 307 The three diodes in series connecting the op-amps' outputs to the transistor's base are there to drop voltage and ensure the transistor falls into cutoff when the op-amp outputs go "low. Varying the duty cycle has the effect of changing the harmonic content of the waveform.6. If the duty cycle is below or above 50%. or timbre. This is due to the absence or presence of even-numbered harmonics. the waveform will not exhibit this symmetry.7 volts times 3) to ensure there is minimal voltage at the transistor's base when the op-amp outputs go "low.9. but only to within about 2 volts of ground. You might notice a particular uniqueness to the sound heard through the detector headphones when the potentiometer is in center position (50% duty cycle – 50% load power). such as a square wave with a 50% duty cycle. The presence of these even-numbered harmonic frequencies can be detected by the human ear. as the potentiometer varies the duty cycle from 0% to 50% to 100%. but it greatly affects duty cycle. Adding three silicon diodes in series drops approximately 2. a direct connection from the op-amp to the transistor would mean the transistor would never fully turn off. contains no even-numbered harmonics.
model TL082 recommended (Radio Shack catalog # 276-1715) • One NPN power transistor in a TO-220 package – (Radio Shack catalog # 276-2020 or equivalent) • One PNP power transistor in a TO-220 package – (Radio Shack catalog # 276-2027 or equivalent) • One 1N914 switching diode (Radio Shack catalog # 276-1620) • One capacitor. TO-3 case) power transistors. Volume 3. which are closely matched NPN and PNP power transistors with dissipation ratings of 65 watts each. linear taper (Radio Shack catalog # 271-1715) Be sure to use an op-amp that has a high slew rate. chapter 8: "Operational Amplifiers" LEARNING OBJECTIVES • How to build a "push-pull" class B amplifier using complementary bipolar transistors • The effects of "crossover distortion" in a push-pull amplifier circuit • Using negative feedback via an op-amp to correct circuit nonlinearities SCHEMATIC DIAGRAM . Volume 3.22 µF. try to obtain TIP41 and TIP42 transistors.e. CROSS-REFERENCES Lessons In Electric Circuits. the TIP3055 (available from Radio Shack) is a good substitute. the better. Avoid the LM741 or LM1458 for this reason. chapter 4: "Bipolar Junction Transistors" Lessons In Electric Circuits. as the op-amp may have trouble driving enough current to their bases for good operation.308 CHAPTER 6. The closer matched the two transistors are. If possible. non-polarized (Radio Shack catalog # 272-1070) • One 10 kΩ potentiometer. Do not use very large (i. ANALOG INTEGRATED CIRCUITS 6. 35 WVDC (Radio Shack catalog # 272-1015 or equivalent) • Two capacitors. 47 µF electrolytic. 0.10 Class B audio amplifier PARTS AND MATERIALS • Four 6 volt batteries • Dual operational amplifier. If you cannot get a TIP41 NPN transistor.
or any other source of audio signals. tape player. For stereo operation.22 µF 1 MΩ -V +V 6V 6V 6V 6V -V − 1 309 Volume 10 kΩ /2 TL082 Audio signal in + − 1 +V 0. two identical .22 µF /2 TL082 TIP41 or TIP3055 8Ω speaker TIP42 + -V 47 µF 1N914 10 kΩ -V Power supply ILLUSTRATION + Volume control NPN + B CE PNP B CE TL082 + - - + Audio input Speaker INSTRUCTIONS This project is an audio amplifier suitable for amplifying the output signal from a small radio.6.10. CLASS B AUDIO AMPLIFIER +V +V 0. CD player.
as the power dissipation varies according to the type of speaker used). but leads to a distinct type of nonlinearity known as "crossover distortion." push-pull circuit.310 CHAPTER 6. neither transistor remains "on" for the entire cycle. distortion may cause unpleasant tones to be superimposed on the true sound. This makes for a power-efficient amplifier circuit. This particular circuit is called a "class B.. equivalent to a constant audio tone of constant volume: . . and may be run without heat sinks on the transistors (though you should experiment with it a bit before deciding to forego heat sinks.. In this scheme. There are many different configurations of audio amplifier circuitry. one for the left channel and other for the right channel. modular stereo components. The goal of any amplifier circuit is to reproduce the input waveshape as accurately as possible. Most audio "power" amplifiers use a class B configuration." Shown here is a sine-wave shape. where one transistor provides power to the load during one-half of the waveform cycle (it pushes) and a second transistor provides power to the load for the other half of the cycle (it pulls). of course. It provides a surprising amount of sound power when played through a large speaker. giving each one a time to "rest" and cool during the waveform cycle. and any differences between the output and input waveshapes is known as distortion. phones "Phono" plug "Mono" headphone plug This amplifier circuit also works well in amplifying "line-level" audio signals from high-quality. each with its own advantages and disadvantages. just connect it to the output of a radio or other audio device like this: Amplifier circuit Radio Audio input .. Perfect reproduction is impossible.. ANALOG INTEGRATED CIRCUITS amplifiers must be built. In an audio amplifier. To obtain an input signal for this amplifier to amplify.
but is merely being "shorted" from one power supply rail to the other (from -V to +V). but it dissipates more heat energy in the transistors. though. The first (leftmost) op-amp shown in the schematic diagram is nothing more than a buffer. This saves energy and decreases heat dissipation.). so that both transistors are in a state of conduction for a brief moment during the crossover period: Transistor #1 both Transistor #1 both both Transistor #1 both both Transistor #2 Transistor #2 Transistor #2 This form of amplification is technically known as class AB rather than class B. they are never conducting at the same time. because each transistor is "on" for more than 50% of the time during a complete waveform cycle. which has been placed in . etc. junction resistances. though. but lends itself to crossover distortion.10. This type of distortion. because during the moments of time where both transistors are conducting. the transistors operate in pure class B mode. The disadvantage to doing this. their characteristics change (Vbe forward voltage drop. making proper biasing difficult. One common method of mitigating crossover distortion is to bias the transistors so that their turnon/turn-off points actually overlap.6. the two transistors take turns amplifying the alternate half-cycles of the waveform like this: Transistor #1 Transistor #1 Transistor #1 Transistor #2 Transistor #2 Transistor #2 If the "hand-off" between the two transistors is not precisely synchronized. In this experiment. is called crossover distortion. where the waveform "flattens" at the crossover point between positive and negative half-cycles. That is. The solution taken in this circuit is to use an op-amp with negative feedback to quickly drive the transistors through the "dead" zone producing crossover distortion and reduce the amount of "flattening" of the waveform during crossover. When transistors increase in temperature. distortion results from the fact that there is a delay between the time one transistor turns off and the other transistor turns on. the amplifier's output waveform may look something like this instead of a pure sine wave: Transistor #1 Transistor #1 Transistor #1 Transistor #2 Transistor #2 Transistor #2 Here. β. Not only is this a waste of energy. is increased power consumption of the amplifier circuit. there is current conducted through the transistors that is not going through the load. CLASS B AUDIO AMPLIFIER 311 In a push-pull amplifier circuit. A buffer helps to reduce the loading of the input capacitor/resistor network.
Thus. Usually. because there would be a "dead" zone in the transistors' operation as the base voltage went from + 0. and accentuates the high-frequency ("treble"). preventing any DC voltage from becoming amplified by the circuit and sent to the speaker where it might cause damage.7 volts Bottom transistor doesn't turn on until Vbe drops below -0.4 volts span of base voltage swing.7 volts 8Ω speaker -V If you have already constructed the amplifier circuit in its final form.7 volts to . but it will sound horrible! The reason for the crossover distortion is that when the op-amp output signal is between + 0.312 CHAPTER 6.7 volts. there is a "zone" in the .7 volts: Output +V Audio signal in − 1 +V /2 TL082 Vbe + -V Top transistor doesn't turn on until Vbe exceeds +0. the capacitor/resistor filtering circuit reduces the low-frequency ("bass") response of the amplifier. though.0. It will amplify an audio signal. we would experience significant crossover distortion. Without the buffer op-amp. you may simplify it to this form and listen to the difference in sound quality. The second op-amp functions as an inverting amplifier whose gain is controlled by the 10 kΩ potentiometer. the schematic diagram shown above would be a good starting point. This does nothing more than provide a volume control for the amplifier. neither transistor will be conducting. ANALOG INTEGRATED CIRCUITS the circuit to filter out any DC bias voltage out of the input signal.7 volts and . If you have not yet begun construction of the circuit. inverting op-amp circuits have their feedback resistor(s) connected directly from the op-amp output terminal to the inverting input terminal like this: Input +V − + -V If we were to use the resulting output signal to drive the base terminals of the push-pull transistor pair. and the output voltage to the speaker will be 0 volts for the entire 1.0.
such as 0.4 volts.6 volts or 0. where both transistors will be in a state of conduction part of the time. Usually. CLASS B AUDIO AMPLIFIER 313 input signal range where no change in speaker output voltage will occur.4 volt "gap" in transistor input signal response.4 volts Input signal 8Ω speaker -V The two series-connected diodes will drop approximately 1. resulting in a scenario where each transistor is just on the verge of turning on when the input signal is zero volts. Thus. their Vbe forward voltage drops will decrease from 0. equivalent to the combined Vbe forward voltage drops of the two transistors. This. will not experience the same change in forward voltage drop. though. A common solution to this problem is the insertion of temperature-compensation "feedback" resistors in the emitter legs of the push-pull transistor circuit: . eliminating the 1. exacerbating the problem of forward voltage drop change.5 volts. The diodes. this solution is not perfect: as the transistors heat up from conducting power to the load.4 volt "dead" signal zone that existed before.4 volt bias voltage even though the transistors require less bias voltage due to heating. the diodes will continue to provide the same 1.7 volts to something less.6. which are not subject to the same heating effect because they do not conduct any substantial current. Unfortunately.10. The result will be that the circuit drifts into class AB operation. will result in more heat dissipation through the transistors. something like this is done: +V + 1. of course. Here is where intricate biasing techniques are usually introduced to the circuit to reduce this 1.
7 volt bias voltage for the push-pull pair. I use one diode to provide a 0. It also has the unfortunate effect of inserting resistance in the load current path. ANALOG INTEGRATED CIRCUITS +V Rfeedback Rfeedback Input signal 8Ω speaker -V This solution doesn't prevent simultaneous turn-on of the two transistors. The solution I opted for in this experiment is one that capitalizes on the principle of op-amp negative feedback to overcome the inherent limitations of the push-pull transistor output circuit. but merely reduces the severity of the problem and prevents thermal runaway. limiting the output current of the amplifier. but it reduces it by at least 50%: +V Audio signal in − 1 +V /2 TL082 + -V 8Ω speaker -V .314 CHAPTER 6. This is not enough to eliminate the "dead" signal zone.
Slower op-amps such as the LM741 or LM1458 may not be able to keep up with the high dv/dt (voltage rate-of-change over time.7 volt bias voltage constant despite large voltage swings in the op-amp's output. the op-amp has the ability to sense any "dead" zone where neither transistor is conducting. CLASS B AUDIO AMPLIFIER 315 Since the voltage drop of a single diode will always be less than the combined voltage drops of the two transistors' base-emitter junctions. and output an appropriate voltage signal to the bases of the transistors to quickly drive them into conduction again to "keep up" with the input signal waveform. thereby preventing class AB operation.10.22 µF capacitor connected between the base and emitter of the NPN transistor helps reduce crossover distortion at low volume settings: . the feedback signal of the op-amp is taken from the output terminal of the amplifier (the transistors' emitter terminals) like this: +V Audio signal in − 1 +V /2 TL082 + -V 8Ω speaker -V The op-amp's function is to output whatever voltage signal it has to in order to keep its two input terminals at the same voltage (0 volts differential). Only a couple of capacitors are added to this circuit to bring it into its final form: a 47 µF capacitor connected in parallel with the diode helps to keep the 0. also known as de/dt) necessary for low-distortion operation. to help get rid of the remaining crossover distortion. while a 0.6. This requires an op-amp with a high slew rate (the ability to produce a fast-rising or fast-falling output voltage). By connecting the feedback wire to the emitter terminals of the push-pull transistors. the transistors can never turn on simultaneously. which is why the TL082 op-amp was specified for this circuit. Next.
316 +V CHAPTER 6.22 µF 1 MΩ -V +V 6V 6V 6V 6V -V − 1 Volume 10 kΩ /2 TL082 Audio signal in + − 1 +V 0.22 µF /2 TL082 TIP41 or TIP3055 8Ω speaker TIP42 + -V 47 µF 1N914 10 kΩ -V Power supply . ANALOG INTEGRATED CIRCUITS +V 0.
or frequently touching a grounded object). Circuits using TTL technology require a regulated power supply voltage of 5 volts. and it will be expected that you realize its unique power supply requirements. Most integrated circuits provide the same functionality as "discrete" semiconductor circuits at higher levels of reliability and at a fraction of the cost.Chapter 7 DIGITAL INTEGRATED CIRCUITS 7. These are sets of holes in the breadboard that are electrically common along the entire length of the board. Though CMOS circuitry is susceptible to damage from static electricity (high voltages will puncture the insulating barriers in the MOSFET transistors). and will not tolerate any substantial deviation from this voltage level.1 Introduction Digital circuits are circuits dealing with signals restricted to the extreme limits of zero and some full amount. Circuits in this chapter will primarily use CMOS technology. Integrated circuits providing a multitude of pre-engineered functions are available at very low cost. Proper handling of CMOS involves the use of anti-static foam for storage and transport of IC's. These circuits find use in "true/false" logical operations and digital computation. and measures to prevent static charge from building up on your body (use of a grounding wrist strap. When building digital circuits using integrated circuit "chips. benefitting students. hobbyists and professional circuit designers alike. in which signals are free to vary continuously between the limits imposed by power supply voltage and circuit resistances. Such components are actually networks of interconnected components manufactured on a single wafer of semiconducting material. modern CMOS ICs are far more tolerant of electrostatic discharge than the CMOS ICs of the past. This stands in contrast to analog circuits. Connect one to the positive terminal of a battery. or integrated circuit. and the other to the negative terminal. reducing the risk of chip failure by mishandling. components. and DC power will be 317 . Any TTL circuits in this chapter will be adequately labeled as such. as this form of IC design allows for a broad range of power supply voltage while maintaining generally low power consumption levels." it is highly recommended that you use a breadboard with power supply "rail" connections along the length. The circuits in this chapter make use of IC.
Up until this point. making this feature more than just a convenience. not to mention the V DD (or VCC ) and ground power terminals which require connection to the power supply.318 CHAPTER 7. digital circuits seem to require more connections to the power supply than other types of breadboard circuits. but some do not. having both terminals of the power supply readily available for connection at any point along the board's length is very useful." and "disable" terminals needing to be maintained in a "high" or "low" state. . However." "enable. I've been illustrating circuits using a breadboard lacking this feature. DIGITAL INTEGRATED CIRCUITS available to any area of the breadboard via connection through short jumper wires: These points electrically common + - These points electrically common With so many of these integrated circuits having "reset. Most breadboards that I have seen have these power supply "rail" holes. just to show how it isn't absolutely necessary.
2.7.2 Basic gate function PARTS AND MATERIALS • 4011 quad NAND gate (Radio Shack catalog # 276-2411) • Eight-position DIP switch (Radio Shack catalog # 275-1301) • Ten-segment bargraph LED (Radio Shack catalog # 276-081) • One 6 volt battery • Two 10 kΩ resistors • Three 470 Ω resistors Caution! The 4011 IC is CMOS. and therefore sensitive to static electricity! CROSS-REFERENCES Lessons In Electric Circuits. Volume 4. chapter 3: "Logic Gates" LEARNING OBJECTIVES • Purpose of a "pulldown" resistor • How to experimentally determine the truth table of a gate • How to connect logic gates together • How to create different logical functions by using NAND gates SCHEMATIC DIAGRAM 1 /4 4011 6V 10 kΩ 10 kΩ 470 Ω ILLUSTRATION . BASIC GATE FUNCTION 319 7.
but it means the same thing. . when connecting IC terminals to other circuit elements. However. It is highly recommended that you have a datasheet for the 4011 chip available when you build your circuit. The datasheet's connection diagram is an essential piece of information to have. Pin #'s 14 and 7 conduct DC power to all four gate circuits inside the IC chip. especially "pinout" diagrams. since only two switches and one LED are needed to show the operation of a single NAND gate. I've shown the circuit built using the lower-left NAND gate: pin #'s 1 and 2 are the inputs.320 CHAPTER 7. Shown here is my own rendition of what any 4011 datasheet shows: "Pinout. DIGITAL INTEGRATED CIRCUITS + 4011 INSTRUCTIONS To begin. Sometimes the negative power supply terminal will be labeled "VSS " instead of "Gnd" on a datasheet. the use of an 8-position switch and a 10-segment LED bargraph may seem excessive. connect a single NAND gate to two input switches and one LED. as shown. At first. and help make the circuit layout both clean and compact. and pin #3 is the output. the presence of those extra switches and LEDs make it very convenient to expand the circuit. or ground. Don't just follow the illustration shown above! It is important that you develop the skill of reading datasheets. and "Gnd" representing the negative side of the power supply (-V)." or "connection" diagram for the 4011 quad NAND gate VDD 14 13 12 11 10 9 8 1 2 3 4 5 6 7 Gnd In the breadboard illustration. "VDD " representing the positive side of the power supply (+V).
If I were to speak of a "high" signal being present on a certain pin of the chip. I show all the top inputs connected to V DD . Since the 4011 is a CMOS integrated circuit. ground is still the implicit point of reference for all voltage measurements. This would very likely damage the gate! Gate output terminals. It matters little if we choose to connect these unused gate inputs "high" (VDD ) or "low" (ground). though. this would be true if any of its inputs were "low"). I may be forcing a gate to assume the opposite output state that it's trying to achieve. In the breadboard illustration. this could lead to damage of the chip." the gates' internal transistors may begin to turn on in such a way as to draw excessive current. The two 10 kΩ resistors are placed in the circuit to avoid floating input conditions on the used gate. With the NAND gate connected to the two switches and one LED as shown. the respective input will be directly connected to V DD and therefore be "high. Draw a truth table on a piece of paper like this: A 0 0 1 1 B Output 0 1 0 1 . BASIC GATE FUNCTION 321 Digital logic circuitry does not make use of split power supplies as op-amps do. its upper (P-channel) output transistor would be turned on in vain.2. At worst. the input will not be susceptible to stray static voltages. you are ready to develop a "truth table" for the NAND gate. With a switch closed. if static voltage signals appear at the gate inputs that are not fully "high" or fully "low. which is a complicated way of saying that I would have created a short-circuit. but an act of intentional design. by their very nature. I would mean that there was full voltage between that pin and the negative side of the power supply (ground). and CMOS circuit inputs left unconnected (floating) can assume any voltage level merely from intercepting a static electric charge from a nearby object. the 10 kΩ "pulldown" resistor provides a resistive connection to ground. ensuring a secure "low" state at the gate's input terminal. This way. If such a gate were to have its output terminal directly connected to ground. Note how all inputs of the unused gates inside the 4011 chip are connected either to V DD or ground. and for good reason! If I were to do that. Why is this undesirable. if we aren't using those gates? Who cares what signals they receive. This is not a mistake. At best it means excessive power consumption. sourcing maximum current to a nonexistent load. Instead. so long as we connect them to one of those two places. Imagine a gate that is supposed to output a "high" logic level (for a NAND gate. generate their own logic levels and never "float" in the same way that CMOS gate inputs do." With a switch open. and all the bottom inputs (of the unused gates) connected to ground.7. Even if you already know what a NAND gate truth table looks like. it could never reach a "high" state (being made electrically common to ground through the jumper wire connection). if we are not doing anything with their outputs? The problem is. This was done merely because those power supply rail holes were closer and did not require long jumper wires! Please note that none of the unused gate outputs have been connected to V DD or ground. leaving inputs floating means that those unused gates may receive any random combinations of "high" and "low" signals. this is a good exercise in experimentation: discovering a circuit's behavioral principles by induction. Like op-amp circuits.
and has the further benefit of indicating if a switch fails to close (or open) by showing the true input signal to the gate. is represented by the LED: whether it is lit (1) or unlit (0). as ensured by its pulldown resistor. in addition to the one LED assigned to indicate the output. its state is "low. When the switch is on. this breadboard circuit is not limited to testing NAND gates." or 0. two pulldown resistors. rather than forcing you to infer input status from switch position: + 4011 . As you can imagine. Any gate type may be tested with two switches.322 CHAPTER 7. DIGITAL INTEGRATED CIRCUITS The "A" and "B" columns represent the two input switches. of course. When the switch is off. compare the resulting truth table with what a NAND gate's truth table should be. After placing the switches in every possible combination of states and recording the LED's status. This makes operation a little more interesting to observe. its state is "high" or 1. Not all "quad" gate chips have the same pin assignments! An improvement you might want to make to this circuit is to assign a couple of LEDs to indicate input status. and an LED to indicate output status. Just be sure to double-check the chip's "pinout" diagram before substituting it pin-for-pin in place of the 4011. The gate's output. respectively.
3. chapter 10: "Multivibrators" LEARNING OBJECTIVES • The effects of positive feedback in a digital circuit • What is meant by the "invalid" state of a latch circuit • What a race condition is in a digital circuit • The importance of valid "high" CMOS signal voltage levels SCHEMATIC DIAGRAM 1 /4 4001 6V 10 kΩ 1 /4 4001 470 Ω ILLUSTRATION . chapter 3: "Logic Gates" Lessons In Electric Circuits. and therefore sensitive to static electricity! CROSS-REFERENCES Lessons In Electric Circuits.7. NOR GATE S-R LATCH 323 7.3 NOR gate S-R latch PARTS AND MATERIALS • 4001 quad NOR gate (Radio Shack catalog # 276-2401) • Eight-position DIP switch (Radio Shack catalog # 275-1301) • Ten-segment bargraph LED (Radio Shack catalog # 276-081) • One 6 volt battery • Two 10 kΩ resistors • Two 470 Ω resistors • Two 100 Ω resistors Caution! The 4001 IC is CMOS. Volume 4. Volume 4.
the circuit's Q and Q-not outputs will remain in their last states." In fact. . "remembering" their prior settings. positive feedback creates hysteresis. there will be positive feedback from output to input." This is known as the reset state of the circuit." the left LED will be the "Q" output and the right LED the "Q-not" output." diagram is as such: "Pinout." or "connection." Q will go "high" and Q-not will go "low. the output signal tends to maintain the gate in its last output state. With the Set input "high" (switch on) and the Reset input "low. This is known as the latched state of the circuit. there are solid-state computer memory technologies based on circuitry like this! If we designate the left switch as the "Set" input and the right switch as the "Reset. identical in input. If both inputs are placed into the "low" state. Its "pinout. Just as in op-amp circuits. and power supply pin assignments to the 4011 quad NAND gate. That is. output." This is known as the set state of the circuit. This tendency for the circuit to remain in its last output state gives it a sort of "memory.324 CHAPTER 7. Making the Reset input "high" and the Set input "low" reverses the latch circuit's output state: Q "low" and Q-not "high." or "connection" diagram for the 4001 quad NOR gate VDD 14 13 12 11 10 9 8 1 2 3 4 5 6 7 Gnd When two NOR gates are cross-connected as shown in the schematic diagram. DIGITAL INTEGRATED CIRCUITS + 4001 INSTRUCTIONS The 4001 integrated circuit is a CMOS quad NOR gate.
due to a defect in the chip." and the race is won by the faster gate. Thus. noting the status of the two LEDs as the circuit is powered up again and again: make and break contact! + 4011 When a latch circuit such as this is powered up into its "latched" state. the circuit will be very predictable on power-up with both inputs "low. with no previous state to hold.3. not because something has gone wrong. as this experiment shows. but because the outputs have failed to meet the expectations established by their labels. Since the "latched" state is a hysteretic condition whereby the last output states are "remembered. If one of the gates reaches its "high" output state before the other. where one of the two NOR gates was exceptionally slow-acting.7. both gates try to output "high" signals. but if race conditions are present." one might wonder what will happen if the circuit powers up this way. NOR GATE S-R LATCH 325 Because the outputs have been designated "Q" and "Q-not. place both switches in their off positions. the gates race against each other for control. To experiment. Invariably. Normal circuit behavior is not supposed to change when a component is replaced. for instance. However." it is implied that their states will always be complementary (opposite). making both Set and Reset inputs low. we would be inclined to call that mode of the circuit "invalid." This is exactly what will happen if we make both Set and Reset inputs "high:" both Q and Q-not outputs will be forced to the same "low" logic state." However. Imagine a scenario. due to internal variations between gates in the chip. This is known as the invalid or illegal state of the circuit. What this usually means is that the circuit tends to power up in the same mode. and/or external resistances and capacitances that act to delay one gate more than the other. suppose that the unusual chip were to be replaced by one with more evenly matched gates. because of the unpredictability they create. then disconnect one of the battery wires from the breadboard. you should see at least a few times where the latch circuit powers up latched in the opposite state from normal. as they lead to unpredictable operation. This handicap would cause the other gate to win the power-up race every time. over and over again. or by a chip where the other NOR gate were consistently slower. Then. if you are persistent in your powering/unpowering cycles. In other words. if something were to happen that forced both outputs to the same state. Given the "low" inputs. a change of components may very well do just that. one gate wins the race. They can be particularly troublesome to locate. Race conditions are generally undesirable in any kind of system. . that "high" state will be fed back to the other gate's input to force its output "low. quickly make and break contact between that battery wire and its proper connection point on the breadboard.
and measure the output voltage of the other gate when its output is "high. This is one reason I favor the use of a voltmeter as a logic "probe" for determining digital signal levels. can only be found with test equipment providing quantitative measurements of signal level. but rather use external means to "force" the race so that the desired gate always "wins. which depends on a solid "high" signal fed back from the output of one gate to the input of the other. The obvious effect of this alteration will be increased LED brightness. The one loaded down by the "heavier" load (100 Ω resistor) will be much less: so much less that this voltage will not be interpreted by the other NOR gate's input as a "high" signal at all as it is fed back! All logic gates have permissible "high" and "low" input signal voltage ranges. it might not be properly interpreted by the receiving gate. In a latch circuit such as this. Try replacing one of the 470 Ω resistors with a 100 Ω resistor. such as 100 Ω. a "weak" signal will not be able to maintain the positive feedback necessary to keep the circuit latched in one of its states. for example). but only in the other state. and if the voltage of a digital signal falls outside this permissible range. one should not design a circuit with the expectation of a consistent power-up state. and operate the input signal switches through all four possible setting combinations. as more current is allowed through. whereas a voltmeter definitely will by means of its quantitative indication. A logic probe may not indicate the presence of a "weak" signal. This type of problem. rather than an actual logic probe with "high" and "low" lights. and it is this effect which holds great learning value. when the input switches are both set "low" (the "latch" mode)." Note the difference between the two gate output voltage levels. . You should note that the circuit refuses to latch in one of its states (either Set or Reset). one gate loaded by an LED with a 470 Ω resistor. DIGITAL INTEGRATED CIRCUITS Due to the inherent race tendency of an S-R latch. and the other loaded by an LED with a 100 Ω resistor. Why is this? Take a voltmeter and measure the output voltage of the gate whose output is "high" when both inputs are "low." Note this voltage indication.326 CHAPTER 7. noting the behavior of the circuit. then set the input switches in such a way that the other state (either Reset or Set) is forced." An interesting modification to try in this circuit is to replace one of the 470 Ω LED "dropping" resistors with a lower-value unit. A not-so-obvious effect will also result. common in circuits where different "families" of integrated circuits are mixed (TTL and CMOS.
Volume 4. NAND GATE S-R ENABLED LATCH 327 7.4 NAND gate S-R enabled latch PARTS AND MATERIALS • 4011 quad NAND gate (Radio Shack catalog # 276-2411) • Eight-position DIP switch (Radio Shack catalog # 275-1301) • Ten-segment bargraph LED (Radio Shack catalog # 276-081) • One 6 volt battery • Three 10 kΩ resistors • Two 470 Ω resistors Caution! The 4011 IC is CMOS. chapter 10: "Multivibrators" LEARNING OBJECTIVES • Principle and function of an enabled latch circuit SCHEMATIC DIAGRAM Set Enable Reset (power connections to gates not shown for simplicity) Q 1 Q /4 4011 1 /4 4011 6V 1 /4 4011 10 kΩ 10 kΩ 1 /4 4011 470 Ω ILLUSTRATION . and therefore sensitive to static electricity! CROSS-REFERENCES Lessons In Electric Circuits. chapter 3: "Logic Gates" Lessons In Electric Circuits.4.7. Volume 4.
When the Enable input is "high. leaving the circuit in its latched state. When the Enable input is "low. R Q E Q S E 0 0 0 0 1 1 1 1 S 0 0 1 1 0 0 1 1 R 0 1 0 1 0 1 0 1 Q latch latch latch latch latch 0 1 0 Q latch latch latch latch latch 1 0 0 . The purpose of the Enable input is to enable or disable the Set and Reset inputs from having effect over the circuit's output status. but the NAND gate design is easier to build since it makes use of all four gates in a single integrated circuit. DIGITAL INTEGRATED CIRCUITS + 4011 INSTRUCTIONS Although this circuit uses NAND gates instead of NOR gates." the Set and Reset inputs are disabled and have no effect whatsoever on the outputs. except for the presence of a third input: the Enable." and a "high" Reset input drives Q-not "high"). This kind of latch circuit (also called a gated S-R latch).328 CHAPTER 7." the circuit acts just like the NOR gate S-R latch. may be constructed from two NOR gates and two AND gates. its behavior is identical to that of the NOR gate S-R latch (a "high" Set input drives Q "high.
chapter 10: "Multivibrators" LEARNING OBJECTIVES • The difference between a gated latch and a flip-flop • How to build a "pulse detector" circuit • Learn the effects of switch contact "bounce" on digital circuits SCHEMATIC DIAGRAM .5 NAND gate S-R flip-flop PARTS AND MATERIALS • 4011 quad NAND gate (Radio Shack catalog # 276-2411) • 4001 quad NOR gate (Radio Shack catalog # 276-2401) • Eight-position DIP switch (Radio Shack catalog # 275-1301) • Ten-segment bargraph LED (Radio Shack catalog # 276-081) • One 6 volt battery • Three 10 kΩ resistors • Two 470 Ω resistors Caution! The 4011 IC is CMOS. and as shown in prior latch circuits. feel free to use the bargraph as called for in the parts list.5. two integrated circuits. This is due to lack of room on my breadboard to mount the switch assembly. CROSS-REFERENCES Lessons In Electric Circuits. NAND GATE S-R FLIP-FLOP 329 7. Volume 4. and the bargraph. the illustration shows two individual LEDs being used instead. If you have room on your breadboard. chapter 3: "Logic Gates" Lessons In Electric Circuits. and therefore sensitive to static electricity! Although the parts list calls for a ten-segment LED unit. Volume 4.7.
330 CHAPTER 7. so that the edge of a clock pulse generates a brief "high" Enable pulse: . Converting an enabled latch into a flip-flop simply requires that a "pulse detector" circuit be added to the Enable input. DIGITAL INTEGRATED CIRCUITS (power connections to gates not shown for simplicity) Q 1 Set Clock Reset Q /4 4011 1 /4 4011 6V 1 /4 4011 10 kΩ 10 kΩ 1 /4 4011 470 Ω 1 /4 4001 1 /4 4001 1 /4 4001 1 /4 4001 ILLUSTRATION + 4001 4011 INSTRUCTIONS The only difference between a gated (or enabled ) latch and a flip-flop is that a flip-flop is enabled only on the rising or falling edge of a "clock" signal. rather than for the entire duration of a "high" enable signal.
thus using all four NOR gates of a 4001 integrated circuit: Pulse detector circuit Input 1 1 /4 4001 Output /4 4001 1 /4 4001 1 /4 4001 Normally. The first high-to-low transition caused by bouncing will trigger the pulse detector circuit. contact bounce is a very common problem for digital gate circuits operated by switch inputs." When you build this circuit. In this experiment. and so I parallel the NOR inputs to make inverters rather than use the more conventional method. Here. of course.7. This means that the flip-flop circuit should be responsive to the Set and Reset input states only when the middle switch is moved from "on" to "off." not from "off" to "on. Ideally. making it responsive to the Set and Reset inputs. I use three NOR gates with paralleled inputs to create three inverters. and must be understood . though. when using a NOR gate as an inverter. cascaded gates. there will most likely be several low-high-low "cycles" as the contact pads "bounce" upon off-to-on actuation. to minimize input capacitance and increase speed. not just when it is switched from a "high" state to a "low" state. Instead of the Clock switch producing a single. though. switches are perfect and bounce-free. due to the elastic collision of the metal contact pads. one input would be grounded while the other acts as the inverter input.5. NAND GATE S-R FLIP-FLOP 331 Input Output Delayed input Input Delayed input Output Brief period of time when both inputs of the NOR gate are low The single NOR gate and three inverter gates create this effect by exploiting the propagation delay time of multiple. slow response is desired. you may discover that the outputs respond to Set and Reset input signals during both transitions of the Clock input. Please note that this particular pulse detector circuit produces a "high" output pulse at every falling edge of the clock (input) signal. clean low-to-high signal transition when closed. In the real world. enabling the S-R latch for that moment in time. however. The reason for this is contact bounce: the effect of a mechanical switch rapidly making-and-breaking when its contacts are first closed.
DIGITAL INTEGRATED CIRCUITS . CHAPTER 7.332 well if it is to be overcome.
6. LED SEQUENCER 333 7.047 to 0. The audio detector will be used to assess signal frequency. Volume 4. chapter 4: "Switches" Lessons In Electric Circuits. single-throw switch is adequate. Volume 4. 0.6 LED sequencer PARTS AND MATERIALS • 4017 decade counter/divider (Radio Shack catalog # 276-2417) • 555 timer IC (Radio Shack catalog # 276-1723) • Ten-segment bargraph LED (Radio Shack catalog # 276-081) • One SPST switch • One 6 volt battery • 10 kΩ resistor • 1 MΩ resistor • 0. the audio detector is unnecessary. Volume 4.7. and is readily available at any hardware store. and therefore sensitive to static electricity! Any single-pole. chapter 3: "Logic Gates" Lessons In Electric Circuits. A household light switch will work fine.001 µF • Ten 470 Ω resistors • Audio detector with headphones Caution! The 4017 IC is CMOS.1 µF capacitor (Radio Shack catalog # 272-135 or equivalent) • Coupling capacitor. chapter 11: "Counters" LEARNING OBJECTIVES • Use of a 555 timer circuit to produce "clock" pulses (astable multivibrator) • Use of a 4017 decade counter/divider circuit to produce a sequence of pulses • Use of a 4017 decade counter/divider circuit for frequency division • Using a frequency divider and timepiece (watch) to measure frequency • Purpose of a "pulldown" resistor • Learn the effects of switch contact "bounce" on digital circuits • Use of a 555 timer circuit to "debounce" a mechanical switch (monostable multivibrator) . If you have access to an oscilloscope. CROSS-REFERENCES Lessons In Electric Circuits.
and hold its end in your hand. If low-to-high voltage pulses are applied to the "clock" (Clk) terminal of the 4017. it will increment its count. Try disconnecting the jumper wire leading from the 4017's "Clock" terminal (pin #14) to the 555's "Output" terminal (pin #3) where it connects to the 555 timer chip." the chip will stop responding to the clock signal and pause in its counting sequence. forcing the next output into a "high" state. and "recycling" back to the first LED. "Reset" and "Clock Enable. . If the "Clock Enable" is made "high." the 4017's output will be reset back to 0 (pin #3 "high. Feel free to experiment with resistor and capacitor values on the 555 timer to create different flash rates. If the "Reset" terminal is made "high.334 SCHEMATIC DIAGRAM CHAPTER 7. one at a time. One of these ten terminals will be in a "high" state at any given time. DIGITAL INTEGRATED CIRCUITS Clk ClkEn Rst Carry Vcc 1 MΩ Disch 6V Thresh Trig 0. This is necessary if the chip is to count freely. The result is a visually pleasing sequence of flashing lights." giving a "oneof-ten" output sequence." all other output pins "low"). Two terminals on the 4017 chip.1 µF Gnd Ctrl Ten-segment LED bargraph 470 Ω each 555 Out RST VDD 4017 0123456789 Gnd ILLUSTRATION + 555 4017 INSTRUCTIONS The model 4017 integrated circuit is a CMOS counter with ten output terminals." are maintained in a "low" state by means of a connection to the negative side of the battery (ground). With a 555 timer connected as an astable multivibrator (oscillator) of low frequency. the 4017 will cycle through its ten-count sequence. the 4017 will detect it as a fast clock signal. If there is sufficient 60 Hz power-line "noise" around you. causing the LEDs to blink very rapidly. with all others being "low. lighting up each LED.
ten-step count). if the clock signal from the 555 timer is 200 Hz. With the 4017 "Reset" terminal grounded. or truncated. corresponding to 1/10 of the 555's actual output frequency: . giving a full. to take a clock signal and produce a pulse occurring at some integer factor of the clock frequency. and the 4017 is configured for a full-count sequence (the "Reset" terminal connected to ground. through a very small capacitor (0. then connecting a long jumper wire to the "Reset" terminal for easy connection to the outputs at the ten-segment LED bargraph. The capacitor is used for "coupling" AC signals only. and you will hear a "click" in the headphones every time the "0" LED lights up. a signal with a period ten times as long (20 Hz) will be present at any of the 4017's output terminals. Notice how many (or how few) LEDs light up with the "Reset" connected to any one of the outputs: touch end of long jumper wire to an LED terminal disconnect + 555 4017 Counters such as the 4017 may be used as digital frequency dividers. connect your audio detector between output 0 (pin #3) of the 4017 and ground. LED SEQUENCER 335 If the 4017's "Reset" terminal is connected to one of its ten output terminals. For example. to that you may audibly detect pulses without placing a DC (resistive) load on the counter chip output. you will have a fullcount sequence.6. To experiment with this principle. its counting sequence will be cut short. In other words.047 µF to 0.7.001 µF). You may experiment with this by disconnecting the "Reset" terminal from ground. each output terminal will cycle once for every ten cycles of the clock signal: a frequency ten times as slow.
This final figure is the clock frequency in Hz.1 µF capacitor in the 555 timing circuit. Using a 1 MΩ resistor and 0. Multiply the number of pulses counted at the "0" output by 10 to obtain the number of cycles produced by the 555 timer during that same time (my circuit: 79 x 10 = 790 cycles). The buzzing you hear is the undivided clock frequency: . leaving one test probe of the audio detector connected to ground. Now. count the number of clicks heard in one full minute while connected to the 4017's "0" output. I counted 79 clicks in one minute from my circuit.336 CHAPTER 7.17). Your circuit may produce slightly different results. DIGITAL INTEGRATED CIRCUITS + 555 4017 headphones Sensitivity plug In fact. and a power supply voltage of 13 volts (instead of 6). take the other test probe (the one with the coupling capacitor connected in series) and connect it to pin #3 of the 555 timer. Using a stopwatch or other timepiece. Divide this number by 60 to obtain the number of timer cycles elapsed in each second (my circuit: 790/60 = 13. knowing this mathematical relationship between clicks heard in the headphone and the clock frequency allows us to measure the clock frequency to a fair degree of precision.
1/3. this means the output frequency will be a different factor of the clock frequency: 1/9.6. 1/4. Re-connect the audio detector test probe to output "0" of the 4017 (pin #3). This should produce a 1/5 frequency division ratio: . 1/5. LED SEQUENCER 337 + 555 4017 headphones Sensitivity plug By connecting the 4017's "Reset" terminal to one of the output terminals. 1/7. If we are using the 4017 as a frequency divider. depending on which output terminal we connect the "Reset" jumper wire to. 1/8. 1/6.7. or 1/2. a truncated sequence will result. and connect the "Reset" terminal jumper to the sixth LED from the left on the bargraph.
you will need a switch to provide clock signals to the 4017 chip. Octaves are readily distinguished from other divided frequencies by their similar pitches to the original tone." For this. See if you can produce octaves by dividing the original frequency by 2. such as 10 kΩ. you should obtain a number approximately twice as large as what was counted with the 4017 configured for a 1/10 ratio. instead of the 555 timer. Try replacing the 1 MΩ timing resistor in the 555 circuit with one of greatly lesser value. and connect this assembly to the 4017 "Clock" input as shown: . and then by 8 (each descending octave represents one-half the previous frequency). DIGITAL INTEGRATED CIRCUITS + 555 4017 headphones 4017 output frequency is 1/5 of input (clock) frequency Sensitivity plug Counting the number of clicks heard in one minute again. If you do not obtain a count that is exactly twice what you obtained before. This will increase the clock frequency driving the 4017 chip. because 1/5 is twice as large a ratio as 1/10.338 CHAPTER 7. Re-connect the "Reset" jumper wire to ground to enable a full ten-step count sequence. Use the audio detector to listen to the divided frequency at pin #3 of the 4017. and disconnect the 555's output from the 4017's "Clock" input terminal. then by 4. Connect a switch in series with a 10 kΩ pulldown resistor. noting the different tones produced as you move the "Reset" jumper wire to different outputs. creating different frequency division ratios. it is because of error inherent to the method of counting cycles: coordinating your sense of hearing with the display of a stopwatch or other time-keeping device. A final lesson that may be learned from this circuit is that of switch contact "bounce.
there will be an elastic collision. the 4017 should increment once in its count. However. leaving it susceptible to interference from stray static voltages or electrical "noise.7. LED SEQUENCER 339 Clk ClkEn Rst Carry VDD 4017 0123456789 6V Ten-segment LED bargraph 10 kΩ 470 Ω each Gnd + 555 4017 The purpose of a "pulldown" resistor is to provide a definite "low" logic state when the switch contact opens. Why is this? It is due to very rapid. the 4017's "Clock" input will have a definite. Without this resistor in place. providing a stable "low" logic state that precludes any interference from static electricity or "noise" coupled from nearby AC circuit wiring. With the pulldown resistor in place. albeit resistive. the 4017's "Clock" input wire would be floating whenever the switch contact was opened. Actuate the switch on and off.6. you may notice some strange behavior: sometimes. but in a digital circuit such as this where the counter chip is able to respond to very quick clock pulses. mechanical "bouncing" of the switch contacts. This collision results in the contacts making and breaking very rapidly as they "bounce" off one another." either one capable of making the 4017 count randomly. this "bouncing" is much to rapid for you to see its effects. Normally. noting the action of the LEDs. co nn connect ec t co nn ec t disconnect . connection to ground. When two metallic contacts are brought together rapidly as does happen inside most switches. With each off-to-on switch transition. the LED sequence will "skip" one or even several steps with a single switch closure.
Actuate the switch again and note the counting behavior of the 4017. and the count incremented accordingly. The 555 timer circuit is capable of functioning as a debouncer. DIGITAL INTEGRATED CIRCUITS these "bounces" are interpreted as distinct clock signals. we must re-connect pin #3 of the 555 chip to pin #14 of the 4017 chip! Also. One way to combat this problem is to use a timing circuit to produce a single pulse for any number of input pulse signals received within a short amount of time. you should return to the original 1 MΩ and 0. crisp pulse for every on-to-off actuation (notice the inversion of operation here!) of the switch.340 CHAPTER 7. It is important that the timing of the 555 circuit be appropriate: the time to charge the capacitor should be longer than the . if you have altered the values of the resistor or capacitor in the 555 timer circuit. because the 555 timer outputs a single. and any technique eliminating the false pulses caused by switch contact "bounce" is called debouncing.1 µF Gnd 10 kΩ Ctrl 555 Out RST VDD 4017 0123456789 Gnd + 555 4017 Please note that since we are using the 555 once again to provide a clock signal to the 4017.1 µF components. The circuit is called a monostable multivibrator. if the "Trigger" input is connected to the switch as such: Using the 555 timer to "debounce" the switch Clk ClkEn Rst Carry Vcc 1 MΩ Disch 6V Thresh Trig 0. There should be no more "skipped" counts as there were before.
LED SEQUENCER 341 "settling" period of the switch (the time required for the contacts to stop bouncing). . if they were to occur.6. but not so long that the timer would "miss" a rapid sequence of switch actuations.7.
and therefore sensitive to static electricity! This experiment may be built using only one 8-position DIP switch. one switch acts to hold the correct code for unlocking the lock. For extra effect. The idea is. but the concept is easier to understand if two switch assemblies are used. DIGITAL INTEGRATED CIRCUITS 7. if you understand this concept clearly. which means it must be physically located elsewhere from where the data entry switch assembly is. choose different colors of LED: green for "Go" and red for "No go. you may build a working circuit with only one 8-position switch. using the left four switches for data entry and the right four switches to hold the "key" code. of course. However. eight-position DIP switches (Radio Shack catalog # 275-1301) • Two light-emitting diodes (Radio Shack catalog # 276-026 or equivalent) • Four 1N914 "switching" diodes (Radio Shack catalog # 276-1122) • Ten 10 kΩ resistors • Two 470 Ω resistors • Pushbutton switch. In real life. This requires two switch assemblies." CROSS-REFERENCES Lessons In Electric Circuits.342 CHAPTER 7. Volume 4. the switch assembly with the "key" code set on it must be hidden from the sight of the person opening the lock. chapter 3: "Logic Gates" LEARNING OBJECTIVES • Using XOR gates as bit comparators • How to build simple gate functions with diodes and a pullup/down resistor • Using NOR gates as controlled inverters SCHEMATIC DIAGRAM . while the other switch serves as a data entry point for the person trying to open the lock. normally open (Radio Shack catalog # 275-1556) • Two 6 volt batteries Caution! Both the 4001 and 4070 ICs are CMOS.7 Simple combination lock PARTS AND MATERIALS • 4001 quad NOR gate (Radio Shack catalog # 276-2401) • 4070 quad XOR gate (Radio Shack catalog # 900-6906) • Two.
If the two numbers do not exactly match. the red "No go" LED will light up when the "Enter" pushbutton is pressed.7. . each number "entered" into the circuit via a set of switches.7. If the two numbers match. Four of these XOR gates compare the respective bits of two 4-bit binary numbers. the green "Go" LED will light up when the "Enter" pushbutton switch is pressed. bit for bit. SIMPLE COMBINATION LOCK Vdd "Key code" 343 switch No go 470 Ω 470 Ω Vdd 10 kΩ (all) Go 10 kΩ Enter Vdd Data entry switch 10 kΩ 10 kΩ (all) ILLUSTRATION Data entry + - Enter + - 4070 "Key" code 4001 INSTRUCTIONS This circuit illustrates the use of XOR (Exclusive-OR) gates as bit comparators.
" and the pull-down resistor connected to the common sides of the diodes will provide a "low" signal state to the NOR logic. The NOR gate logic performs a simple task: prevent either of the LEDs from turning on if the "Enter" pushbutton is not pressed. DIGITAL INTEGRATED CIRCUITS Because four bits provides a mere sixteen possible combinations. If it were used in a real application such as a home security system. Again. and the key code switch assembly behind the door with the rest of the circuitry. If this were part of a real security system. but it is entirely possible to build the circuit using just a single (8-position) DIP switch assembly. In other words. I do not describe how to work this circuit into a real security system or lock mechanism. so that the entry of an incorrect code would deter an unauthorized person from attempting another code entry. there should be some sort of penalty for entering an incorrect code. this lock circuit is not very sophisticated. The "key" code that must be matched at the data entry switch array should be hidden from view. the "No go" output would have to be connected to some kind of siren or other alarming device." the "No go" LED will light up. The four XOR gates' output terminals are connected through a diode network which functions as a four-input OR gate: if any of the four XOR gates outputs a "high" signal – indicating that the entered code and the key code are not identical – then a "high" signal will be passed on to the NOR gate logic. If the Enter switch is pressed and any of the XOR outputs are "high. if this were a real security system. In this experiment." the "Go" LED will light up.344 CHAPTER 7. It is the nature of an XOR gate to output a "high" (1) signal if the input signals are not the same logic state. Only when this pushbutton is pressed can either of the LEDs energize. indicating that an incorrect code has been entered. but only how to make it recognize a pre-entered code. Let your imagination guide your design of this detail! . but merely to introduce you to the principle of XOR gate code comparison. the purpose of the experiment is not to make a real security system. If the Enter switch is pressed and the XOR outputs are all "low. you will likely locate the two switch assemblies on two different breadboards. then none of the XOR gate outputs will be "high. indicating that the correct code has been entered. the data entry switch assembly would be located outside the door. If the two 4-bit codes are identical. Again. Otherwise. of course. it would not take much time to try all combinations (0000 through 1111) until the correct one was found! In this experiment. it would be wise to have the "No go" output do something that deters an unauthorized person from discovering the correct code by trial-and-error.
8 3-bit binary counter PARTS AND MATERIALS • 555 timer IC (Radio Shack catalog # 276-1723) • One 1N914 "switching" diode (Radio Shack catalog # 276-1122) • Two 10 kΩ resistors • One 100 µF capacitor (Radio Shack catalog # 272-1028) • 4027 dual J-K flip-flop (Radio Shack catalog # 900-4394) • Ten-segment bargraph LED (Radio Shack catalog # 276-081) • Three 470 Ω resistors • One 6 volt battery Caution! The 4027 IC is CMOS.8. chapter 11: "Counters" LEARNING OBJECTIVES • Using the 555 timer as a square-wave oscillator • How to make an asynchronous counter using J-K flip-flops SCHEMATIC DIAGRAM 10 kΩ 10 kΩ 6V Vcc 555 Disch Thresh Trig RST J Out Ctrl Gnd C K S Q J C Q R K S Q Q R 0. and therefore sensitive to static electricity! CROSS-REFERENCES Lessons In Electric Circuits. chapter 10: "Multivibrators" Lessons In Electric Circuits. Volume 4. 3-BIT BINARY COUNTER 345 7.1 µF (LSB) 470 Ω 470 Ω (MSB) 470 Ω . Volume 4.7.
DIGITAL INTEGRATED CIRCUITS + 555 4027 INSTRUCTIONS In a sense. square-wave oscillator with a duty cycle of approximately 50 percent. Remember that a small amount of extra attention paid to detail near the beginning of a project is worth an enormous amount of troubleshooting work near the end! Students who make the mistake of not testing circuit portions before attempting to operate the entire circuit often (falsely) think that the time it would take to test those sections is not worth it. this circuit "cheats" by using only two J-K flip-flops to make a three-bit binary counter. before even plugging the 4027 IC into the breadboard. and that it is a reliable signal (no erratic behavior. It is highly recommended. its count sequence goes from 111 to 110 to 101 to 100 to 011 to 010 to 001 to 000 and then back to 111.346 ILLUSTRATION CHAPTER 7. Ordinarily. testing each one and verifying its performance before building the next. so that the charging time constant is only RC and not 2RC as it would be without the diode in place. Make sure that the output oscillates in a slow. proceed to plug the 4027 IC into the breadboard and complete the rest of the necessary connections between it. That is. If the 555 timer is not working properly. no unexplained pauses). and then spend days trying to figure out what the problem(s) might be with their experiment. and the LED assembly. squarewave pattern (LED is "lit" for about as long as it is "off" in a cycle). While it is possible to construct an "up" counter using J-K flip-flops. to build the circuit in stages: identify portions of the circuit with specific functions. three flip-flops would be used – one for each binary bit – but in this case we can use the clock pulse (555 timer output) as a bit of its own. this would require additional components and introduce more complexity into the circuit. and then be faced with the possibility of several problems simultaneously when it comes time to finally apply power to it. A very common mistake of new electronics students is to build an entire circuit at once without testing sections of it during the construction process. in this experiment as in all experiments. the 555 timer circuit. Connect the 555's output (pin #3) to the "Least Significant Bit" (LSB) LED. build the 555 timer circuit first. neither will the rest of the counter circuit! Once the timer circuit has been proven good. you will find that it is a "down" counter. Following this philosophy. The 555 timer operates as a slow. and build those portions one at a time. This duty cycle is made possible by the use of a diode to "bypass" the lower resistor during the capacitor's charging cycle. so that you have visual indication of its status. . When you build this circuit.
7.9 7-segment display PARTS AND MATERIALS • 4511 BCD-to-7seg latch/decoder/driver (Radio Shack catalog # 900-4437) • Common-cathode 7-segment LED display (Radio Shack catalog # 276-075) • Eight-position DIP switch (Radio Shack catalog # 275-1301) • Four 10 kΩ resistors • Seven 470 Ω resistors • One 6 volt battery Caution! The 4511 IC is CMOS. 7-SEGMENT DISPLAY 347 7. chapter 9: "Combinational Logic Functions" LEARNING OBJECTIVES • How to use the 4511 7-segment decoder/display driver IC • Gain familiarity with the BCD code • How to use 7-segment LED assemblies to create decimal digit displays • How to identify and use both "active-low" and "active-high" logic inputs SCHEMATIC DIAGRAM (LSB) (MSB) 6V 10 kΩ each VDD LT BI 4511 a A b B c C d D e f g LE Gnd 470 Ω each f e a g d b c Cathode .9. and therefore sensitive to static electricity! CROSS-REFERENCES Lessons In Electric Circuits. Volume 4.
All LEDs inside the display unit are made common to each other on one side. DIGITAL INTEGRATED CIRCUITS + 4511 INSTRUCTIONS This experiment is more of an introduction to the 4511 decoder/display driver IC than it is a lesson in how to "build up" a digital function from lower-level components. remove the short jumpers connecting them to either power supply rail (one at a time!). e. 1101. Most 7-segment displays also provide for a decimal point (sometimes two!). and output (or not output!) accordingly. and energize the proper output lines to form the corresponding decimal digit on the 7-segment LED display." To learn what these inputs do. it is good to be familiar with the "driving" circuits behind them. c. For example. there is no real meaning for 1010. and so on through 1001 (decimal "9"). and D in order from least-significant to most-significant. The BCD inputs are designated A. These are binary values beyond the range of a single decimal digit. each letter corresponding to a standardized segment designation for 7-segment displays. The 4511 IC is built to recognize this. remove the short jumper connecting the "Latch Enable" input (pin #5) to ground. and replace it with a long jumper wire that can reach all the way to the Vdd power supply rail. Since 7-segment displays are very common components of digital devices. and so that is what is used here. and g. d. Outputs are labeled a.348 ILLUSTRATION CHAPTER 7. b." observing the results on the 7-segment display as you alter the BCD code with the four input switches. 1011. After building the circuit and applying power. and the 4511 is a good example of a typical driver IC. since each LED segment requires its own dropping resistor. connect it to the . What happens for the binary numbers 1010 (10) through 1111 (15)? Read the datasheet on the 4511 IC and see what the manufacturer specifies for operation above an input value of 9. and so have no function in a BCD system. and replace the short jumper with a longer one that can reach the other power supply rail. 1100. Of course. C. A 0000 input should result in a decimal "0" display. 1110. a 0001 input should result in a decimal "1" display." "Blanking Input. B." and "Latch Enable. we must use seven 470 Ω resistors placed in series between the 4511's output terminals and the corresponding terminals of the display unit. operate the four switches in a binary counting sequence (0000 to 1111). a separate LED and terminal designated for its operation. or 1111. In the BCD code. After you've learned what the input's function is. Its operating principle is to input a four-bit BCD (Binary-Coded Decimal) value. Experiment with making this input "high" and "low. f. noting the 7-segment display. either cathode or anode. The 4511 display driver IC requires a common-cathode 7-segment display unit. Three inputs on the 4511 chip have been permanently connected to either V dd or ground: the "Lamp Test.
and correspondingly it is shown connected to ground ("low") in the schematic so as to not invoke that function. and proceed to experiment with the next input (either "Lamp Test" or "Blanking Input"). . Note that the "Lamp Test" (LT) and "Blanking Input" (BI) input labels are written with boolean complementation bars over the abbreviations. Once again. which means it must be made "high" (connected to Vdd ) in order to invoke its function. 7-SEGMENT DISPLAY 349 power supply rail enabling normal operation. Bar symbols designate these inputs as active-low.7.9. the "Latch Enable" (LE) input has no complementation bar written over its abbreviation. Making an active-low input "high" places that particular input into a "passive" state where its function will not be invoked. the manufacturer's datasheet will be informative as to the purpose of each of these three inputs. meaning that you must make each one "low" in order to invoke its particular function. The "Latch Enable" input is an active-high input. Conversely.
having spent much time at home struggling to comprehend the material within. Sure. I had experienced the benefit of receiving free instruction and encouragement in my pursuit of learning electronics from many people. but a secondary goal was to make the book as affordable as possible. My students were daily frustrated with the many typographical errors and obscure explanations in this book. but the really good books seemed a bit too heavy on the math and the less intimidating books omitted a lot of information I felt was important. that adage is true. Over the years. The goal was to copyright the text – so as to protect my authorship – but expressly allow anyone to distribute and/or modify the text to suit their own needs with a minimum of legal encumbrance. and I resolved to find an alternative text. I decided to make it "open. Adding insult to injury was the $100+ price. This willful and formal revoking of standard distribution limitations 351 . and the Linux operating system. Worse yet were the many incorrect answers in the back of the book to selected problems. My request to review the draft for the next edition of their book was met with disinterest on their part. So.Chapter 8 ABOUT THIS BOOK 8. Some of the best books were out of print. At least in the case of this book. including several teachers of mine in elementary and high school. whose fame is growing even as I write). Finding a suitable alternative was more difficult than I had imagined. . paving the way for a rewarding career and fascinating hobby. As an industrial electronics instructor. Their selfless assistance played a key role in my own studies." following the same development model used in the making of free software (most notably the various UNIX utilities released by the Free Software Foundation. Even though the particular text I was using had been in print and in popular use for a couple of years. It was out of frustration that I compiled Lessons in Electric Circuits from notes and ideas I had been collecting for years. My primary goal was to put readable. high-quality information into the hands of my students. and those that were still being printed were quite expensive.1 Purpose They say that necessity is the mother of invention. I was forced to use a sub-standard textbook during my first year of teaching. there were plenty of texts in print. If only I could extend the gift of their help by giving to other people what they gave to me . More than that. they claimed my complaint was the first they'd ever heard. Contacting the publisher proved to be an exercise in futility. . I decided to make the book freely available.
you must give credit where credit is due (to me. then apply those principles to specific instances that the student may or may not be able to explore by themselves. I strongly encourage experimentation on the part of the reader. etc. I guaranteed that no instructor would be limited by a text insufficient for their needs. adding or editing to your heart's content. however. its wording is not as clear as it could be for that application. Electricity maims and kills without provocation. fire.2 The use of SPICE One of the best ways to learn how things work is to follow the inductive approach: to observe specific instances of things working and derive general conclusions from those observations.352 CHAPTER 8. I discovered this when I started to learn a . and deserves the utmost respect. High-power electric circuits should be left to the care of trained professionals! The Design Science License clearly states that neither I nor any contributors to this book bear any liability for what is done with its contents. For the instructor or electronics professional. but anyone has the freedom to change it. if you pass it on to someone else. The only "catch" is this: if you plan to distribute your modified version of this text. but several Licenses already exist. editing it as you feel necessary if you come across a useful piece of information. I'm sure this book in its initial form will not satisfy everyone. Although electronic components are typically inexpensive. explosion. Most textbooks seem to approach the task of education from a deductive perspective: tell the student how things are supposed to work. and you must ensure that whoever you give the text to is aware of their freedom to similarly share and edit the text. as useful as it is. In science education. not everyone has the means or opportunity to set up a laboratory in their own homes. learn what you can from this book. I appreciate the sense of frustration students may have in teaching themselves from books. Then. labwork is the traditionally accepted venue for this type of learning. In "copylefting" this text. The inductive approach. although in many cases labs are designed by educators to reinforce principles previously learned through lecture or textbook reading. I chose one of them (the Design Science License. and anyone else whose modifications are contained in your version). and although its introductory language is broad enough to cover works of text. you will be giving them something better than what you received. is hard to find in the pages of a book. covering the fine legal points in great detail. textbooks don't have to be this way. ABOUT THIS BOOK under copyright is whimsically termed copyleft. the subject matter is broad and harbors many potential dangers. For the beginning student of electronics. The first such License I applied to my work was the GPL – General Public License – of the Free Software Foundation (GNU). Having taught myself most of the electronics that I know. 8. rather than to allow the student to learn on their own through a truly exploratory process. as I had been with error-ridden textbooks from major publishers. and when things go wrong there's no one to ask for help. The GPL. leveraging my efforts to suit variant and individual requirements. less specific copyleft Licenses began appearing within the free software community. the original author. The next chapter covers this process in more detail. is intended to copyleft works of computer software. Anyone can "copyleft" their creative work simply by appending a notice to that effect on their work. feel free to use this as a reference manual. or DSL) as the official notice for my project. When other. However. but only with circuits powered by small batteries where there is no risk of electric shock. It must be mentioned that although I strive to maintain technical accuracy in all of this book's content.
There may be more flashy (graphic) circuit simulation programs in existence. frequency. the reader can immediately see for themselves that what the author describes is indeed true. and a host of others too numerous to mention.8. ACKNOWLEDGEMENTS 353 computer program called SPICE. Another advantage to including computer analyses in a textbook is the empirical verification it adds to the concepts presented. With demonstrations. I made a discovery: SPICE could be used within a textbook to present circuit simulations to allow students to "observe" the phenomena for themselves. are liable to err and/or communicate poorly. It is a text-based piece of software intended to model circuits and provide analyses of voltage. Although nothing is quite as good as building real circuits to gain knowledge in electronics.3. Furthermore. in seeing SPICE used over and over again. and hopefully in a gentle enough way that it doesn't create confusion.3 Acknowledgements First. however. and the respective programmers: • GNU/Linux Operating System – Linus Torvalds. I wish to thank my wife. • Texinfo document formatting system – Free Software Foundation. • Gimp image manipulation program – too many contributors to mention. Richard Stallman. • Xcircuit drafting program – Tim Edwards. . In learning how to use this powerful tool. like all human beings. A • L TEX document formatting system – Leslie Lamport and others. providing a perfectly safe means of experimentation on their own computers with circuit simulations of their own design. • Vim text editor – Bram Moolenaar and others. The problem with faith. Demonstrations also serve to clarify the meaning of the text with concrete examples. SPICE is introduced early in volume I (DC) of this book series. they should be able to understand how to use it themselves. but SPICE is free. I also wish to thank those whose open-source software development efforts have made this endeavor all the more affordable and pleasurable. computer simulation is an excellent alternative. a virtue complementing the charitable philosophy of this book very nicely. Authors. current. is that it is only as good as the authority in which it is placed and the accuracy of interpretation through which it is understood. the readers could learn the concepts inductively (by interpreting SPICE's output) as well as deductively (by interpreting my explanations). a chapter in this volume (volume V) contains an overview of SPICE with many example circuits. trusting that what has been written is indeed accurate. For those wishing to learn more. whose patience during those many and long evenings (and weekends!) of typing has been extraordinary. of course. • TEX text processing system – Donald Knuth and others. Without demonstrations. etc. • SPICE circuit simulation program – too many contributors to mention. This way. 8. The following is a list of various free computer software used to make this book. the reader is left to take the author's statements on faith.
and a wider audience for the online version of this book. whose first edition of Introductory Circuit Analysis taught me more about electric circuits than any other book. many thanks to my parents and those teachers of mine who saw in me a desire to learn about electricity. and to Richard Stallman for pioneering the concept of copyleft. and who kindled that flame into a passion for discovery and intellectual adventure.com)) for providing encouragement. Tony Kuphaldt.lightandmatter. and to make the first effort in contributing to its form and content. Thanks to the staff of the Bellingham Antique Radio Museum.) Appreciation is also extended to Robert L. Boylestad. I honor you by helping others as you have helped me.andamooka. ABOUT THIS BOOK • Winscope signal analysis software – Dr. Last but certainly not least. Thanks also to David Sweet (website: (http://www. July 2001 "A candle loses nothing of its light when lighting another" Kahlil Gibran . Thanks to Michael Stutz for drafting his Design Science License. Bernard Grob's second edition of Introduction to Electronics I. (Free for personal and academic use. Constantin Zeldovich.354 CHAPTER 8. I wish to specifically thank Jeffrey Elkner and all those at Yorktown High School for being willing to host my book as part of their Open Book Project. who were generous enough to let me terrorize their establishment with my camera and flash unit.org)) and Ben Crowell (website: (http://www. Other important texts in my electronics studies include the 1939 edition of The "Radio" Handbook. constructive criticism. and Forrest Mims' original Engineer's Notebook.
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short. 70 Drift. 142. 277.Index β ratio. switch contact. 116. 247 Diode. calculus. 28 Divider. 184 Astable multivibrator. 317 Analog computer. 154 Autoranging meter. 258 Differentiation. 302. calibration. 233 Amplifier. 201 Active-high input. 15 Diode. 183 363 Choke. operational. 256. 293 Detector. 299. 123 Differential amplifier. 145 Alternator. null. 163 Amp. 299 Audio taper potentiometer. current. 293 Capacitor. 18 Beta ratio. 299 E. constant-current. 132. 296 Binding posts. 305 AC. 252. 31 Common-mode voltage. oscilloscope. 339 Breadboard. filter. 331. electrical. 59 Debouncing. 145 AC coupling. 43 . definition. symbol for voltage. 252 Direct current. decoupling. 252 Contact bounce. voltage. 28 Circuit. 256 Commonality. 35 DC. 286 Amplifier. 25 Diode equation. 142 Constant-current diode. 132. 339 Continuity. 263. 293 Digital. 142. 349 Active-low input. 191 Derivative. calculus. 177 Analog. 142 Analog multimeter. 142. 258 Differential pair. 188. 98 Bounce. 23 Computer simulation. 18 Alternating current. 349 Alligator clip. 15 Antiresonance. 35 Amplifier circuit. 331. 35 Ampere. 277. 236. op-amp. 59 Discontinuity. noninverting. 23 Current divider. inverting. 106 Duty cycle. 76 Computer. 286 Amplifier. 83 Current mirror. 241 Amplitude. 246 Current. 21 Calculus. 86. 83 Divider. 256. 317 Digital multimeter. 98 Battery. 17 Banana plugs and jacks. 302 Current regulator. commonality. analog. 340 Decoupling capacitor. 21 Continuity vs. switch. 246 Bias current. 191 Choke. 133 Amplifier impedance. 246 555 timer. 215 Circuit.
172 Experiment: Static electricity sensor. 244 Experiment: Differential amplifier. 64 Electromagnetic induction. 60 Experiment: Signal coupling. 108 Experiment: Transformer. 56 Electromagnetism. 235 Experiment: Commutating diode. diode. 116 Experiment: Voltage divider. 178 Experiment: Parallel batteries. 47 Experiment: Precision potentiometer. 292 Experiment: JFET current regulator. 63 Experiment: Phase shift. 41 Experiment: Ohmmeter usage. 150 Experiment: Vacuum tube audio amplifier. 152 Experiment: Voltage averager. 54 Experiment: Electrostatic field sensor. 255 Experiment: Electromagnetic field sensor. 220 Experiment: Bridge rectifier. 211 Experiment: Rheostat range limiting. 323 Experiment: Ohm's Law. 141 Experiment: Rectifier/filter. AC. 204 Experiment: Class B audio amplifier. 25 Electrically common points. 109 Electrical continuity. 181 . 281 Experiment: Pulsed-light sensor. 21 Electrical shock hazard. 130 Experiment: Voltage comparator. 44 Experiment: NOR gate S-R latch. 298 Experiment: 555 ramp generator. 27 Experiment: Simple combination lock. 92 Experiment: Potentiometer as voltage divider. 347 Experiment: AC power supply. 225 Experiment: Switch in circuit. 230 Experiment: Voltage regulator. 227 Experiment: PWM power controller. AC. 135 Experiment: Potentiometer as rheostat. 217 Experiment: Voltmeter usage. 55 Equation. 301 Experiment: 7-segment display. 98 Experiment: Precision voltage follower. sensitive. 15 Experiment: Waveform analysis. 126 Experiment: 555 audio oscillator. 137 Experiment: Center-tap rectifier. 257 Experiment: Sound cancellation. 319 Experiment: BJT switch. 52 Experiment: Tank circuit. 329 Experiment: Noninverting amplifier. 240 Experiment: Multimeter. 304 Experiment: Rate-of-change indicator. 308 Experiment: Common-emitter amplifier. 345 Experiment: 4-wire resistance measurement. 342 Experiment: Simple op-amp. 175 Experiment: LED sequencer. 163 Experiment: Ammeter usage. 146 Experiment: Alternator. 262 Experiment: Basic gate function. 196 Experiment: High-impedance voltmeter. homemade. 186 Experiment: Simple circuit. 333 Experiment: Multi-stage amplifier. 247 Experiment: 3-bit binary counter. 183 Experiment: Thermoelectricity. 23. 169 Experiment: Potato battery. 20 Experiment: Oscilloscope. 77 Experiment: Current mirror. 154 Experiment: Audio oscillator. 265 Experiment: Variable inductor. 278 Experiment: Voltage detector. 159 Experiment: Electromagnetic induction. 161 Experiment: Half-wave rectifier. 250 Experiment: Keyboard as signal generator. 67 Experiment: Voltage follower. 111 INDEX Experiment: NAND gate S-R enabled latch. 194 Experiment: Current divider. PC. 34 Experiment: Audio detector. 101 Experiment: Series batteries. 121 Experiment: Power dissipation. 285 Experiment: Nonlinear resistance. 327 Experiment: NAND gate S-R flip-flop. 86 Experiment: Potentiometric voltmeter. 209 Experiment: Capacitor charging and discharging.364 Effect. 56 Experiment: Electromagnetism. Seebeck. 288 Experiment: Integrator.
167 Motor. 324 Inverting amplifier. 324 Impedance matching. 86 Potentiometric voltmeter. 277. 277. AC signal. 317 Illegal state. 277. 277 Operational amplifier. 324 LED. 64. symbol for current. 50 Programmable op-amp. 25 Polarity. 237 Noninverting amplifier. 179 Oscilloscope coupling. 119. 241. audio taper. 182 Fuse. 182 Full-wave rectification. 43 Ohm's Law. 299 Multivibrator. 176 Half-wave rectification. 233 Impedance. 24. 339 Frequency. alternator. 43 IC. 123 Power supply. 157 Induction. 177 Frequency domain. 157 Impedance. definition. 256. 163 Filter. slow-blow. 188. 197 Harmonics. 18. 340 Negative feedback. 100 Invalid state. 340 Motor. 70 Latch-up. 317 Integration. 154 365 Magnet wire. definition. 111 Meter overrange. induction. 119. 215 Floating input. 54. meter. 256. 19. 163 Generator. calculus. 263. 123 Ohm. 86. 212 Hysteresis. 86 Potentiometer as rheostat. 236. monostable. 70 KVL. 177 Hazard. 116. electrical shock. 18 Light-Emitting Diode. 37 Monostable multivibrator. programmable. 237 Field winding. 50 Jumper wire. 321. 170 Op-amp. 36 Fuse. 193. 30 Potentiometer. 261 Oscilloscope. synchronous. 193. 111 Multimeter. 167 Movement. 15 Multivibrator. AC version. 213 Filter choke. 18 Linear taper potentiometer. 83 Kirchhoff's Current Law. 150 Maximum Power Transfer Theorem. 145 Power. 123 Null-balance voltmeter. linear vs. 21 Ohm's Law. 286 Joule's Law. 286 Null detector. 258 Operational amplifier. 104 Permeability. 157 Megger. 256. electromagnetic. 83 Kirchhoff's Voltage Law. 170 Photocell. 176 Fundamental frequency. 258 Parallel. 146 Generator. 116 Heat sink. 291 Latched state. negative. 293 Interactive adjustment. 119. 205 Function generator. 201 Overrange. 258. 17 Pair. amplifier. 17 Metric prefix. differential. 153 Phase shift. 324 I.INDEX Feedback. defined. meter. 56 Integrated circuit. 127 Meter movement. 18 KCL. 282 Feedback. 261 . 25 Headphone. 93 Potentiometer.
Unit. definition. 157 Zero calibration. 340 Tank circuit. 226 Unit. computer. 33 Switch. 338 Resistor. 109 Time constant. 52 Switch debouncing. ampere. 258. 31 Shunt resistor. 324 Shielding. 66 Set state. 43 Race condition. pulldown. 324 Resistance. 184 Rheostat. 184 Resonant frequency. polarity. 17 Voltage divider. 95 Transistor. 21 Resistor color code. 176 Simulation. 23 Resistor. magnet. 25 Regulator. 232 Signal generator. symbol for resistance. 25 Short circuit. 193 Series. 61. 17 Voltage. 252 Thermocouple. shunt. 119. 256 Voltage. 17 watt. 147 Span calibration. 151 Reset state. 50 Wire. 325 Rail voltage. 197 Rectifying diode. 76 Split phase. 109 Semiconductor. 30 Voltage. 70 Voltage follower. magnetic. 93 Ring-lug terminal. 163 Strip. 213 Watt. 205 Rectification. 338 Pulse-width modulation. 283 Rectification. definition. 306 R. 199. 232 Resonance. 116.366 Pulldown resistor. 104 SPICE. 103 Series-parallel. 164 Ripple voltage. full-wave. 164 Thermal runaway. 160. 104 . alternator. 21 volt. junction field-effect. 33 Terminal. Unit. common-mode. Unit. 19. 306 PWM power control. current. terminal. 182 Transformer. half-wave. 213 Seebeck effect. 76 Slip ring. ring lug. 184 Terminal strip. 50 INDEX Volt. 282 Voltage. 54 Z. 210 Stator winding. 139 Time domain. 247. 246 Reluctance. ripple. alternator. 199. 162 Shock hazard. 164 Soldering. symbol for impedance. 145 Transistor. 231. 35 ohm.
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