Understanding the curves of a MOSFET
Question
What do the curves and the red dot represent in the following MOSFET Id vs Vds and Vgs characteristic graph?


Answer
Part A - Meaning of the curves and the operation point

The green (update: pale cyan) region is the &quot;saturation&quot; region.

The yellow region is the &quot;linear&quot;, or &quot;ohmic&quot;, or &quot;triode&quot; region.

In the saturation region, the thick horizontal (well, slightly tilting upwards) straight lines (well, OK, curves) represent the (connected) points in the region of a particular Vgs value.

So for example, the curve that the red dot sits represents the points of Vgs = 2.5V.

The vertical lines 0, 5, 10, 15, 20 mean the voltage across Drain and Source, Vds.

Now the red dot operating point says this: If (a) Vds = 10V, and (b) Vgs = 2.5V, then (c) Ids = approx 16A.



Part B - Meanings of &quot;Linear region&quot;, &quot;Saturated region&quot; and &quot;Linear mode&quot; and why the MOSFET can be &quot;operated in linear mode at the saturated region&quot;

(1) Meaning of &quot;linear region&quot;
When I first look at a curve in a two dimensional graph, I almost always look at the labels of the X and Y axis. For example, if (a) X axis is labelled &quot;voltage across a resistor, Vr&quot;, and (b) Y axis is labelled &quot;current through the resistor, Ir&quot;, and (c) The Ir vs Vr &quot;curve&quot;, is a straight line starting from origin and goes, say 30 degrees, upwards, then we can conclude that Ir is proportional to Vr, or in mathematical terms, Ir is a function  Vr, ie, Ir = f(Vr), where function f, the proportional constant, is a linear function. This is the mathematical definition of a linear function.
Now let us go back to National Semi's EE engineer Locher's Ir vs Vds graph (Fig 8) and focus only at the straight line labelled &quot;liner&quot; in yellow, we should conclude that the straight line should represent a linear function, Ir = f(Vds), or Ir = (1/R) * Vr, where R is a constant, the resistance value in Ohms, of course obeying Ohm's Law.
We might now ask ourselves: &quot;OK, the straight line represents a linear or &quot;Ohmic&quot;  function, but how come this linear &quot;straight line&quot; becomes a linear &quot;region&quot;?
Well, Prof Jaeger gives the answer with the following graph:

One thing to clarify is that the linear region shown above is a zoom in view of the left bottom corner of the big I-V characteristics.  It is only at the zoom in that we can see the linear curves separated. In the big picture, the curves are merged and becomes just one straight line.  Here, the y-axis shows current in order of 0.1mA, and voltage in 0.1V, so the resistance is approx 0.1mA / 0.1V or of the order of 1 milliOhm.
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References
(1) Microelectronic Circuit Design, 4th Ed (free eBook) - Richard C  Jaegar, Travis N Ballock, McGraw Hill 2011
(2) MOSFET Characteristic Curves (Ohmic, Triode &amp; Saturation Region) (25 min YouTube) - Dr Sunanda Manke, Barkatullah University
India 2020sep03
(3) Linear Mode Operation and Safe Operating Diagram of Power-MOSFETs - J Schoiswohl, Infenion, App Note V1.1 2017may
(4) AN-558 Introduction to Power MOSFETs and Their Applications, Doc No SNVA008 - Ralph Locher, National Semi, 1988dec (page 5 for the description of linear and saturation regions)

Appendices
Appendix A - Recommended reading list of the Jaeger book
Part 1 Solid State Electronics and Devices
Chapters

Chapter 4 Field-Effect Transistors page 145,

Chapter 5 Bipolr Junction Transistors page 217



Sections

Saturation of the I-V characteristics, Section 4.2.4, Page 154, Fig 4.8

Mathematical Model in the Saturation (Pinch-off) Region, Section 4.2.5, Page 155, Fig 4.10

NMOS Transistor Mathematical ModelSummary (Cutoff region, Triode region, Saturation region, Threshold voltage) Chapter 4, page 160.



Appendix B - Clarifying concepts and terms in MOSFET characteristics graph
Linear Mode Operation and Safe Operating Digram of Power-MOSFETs - J Schoiswohl, Infenion, App Note V1.1 2017may


Appendix C - Comparing and Constrasting between MOSFET and BJT
Introduction
MOSFET and BJT, by their structure and operation mode, cannot be easily compared, though can be more easily constrasted.  The following discussion is limited to NPN BJT and N-channel MOSFET, and are over simplified and therefore potentially misleading.
1.1 BJT is basically a &quot;current device&quot;.  So we talk about (a) current amplification gain Ic/Ib and (b) current switching.
1.2 MOSFET is basically a &quot;voltage device&quot;.  We change Vgs which causes a change in Rds and therefore Ids and Vload. So the amplification is more indirect.


Appendix D - Linear Region vs Saturation Region


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