text:
Systems and methods are described for transmitting a waveform having a controllable attenuation and propagation velocity. An exemplary method comprises: generating an exponential waveform, the exponential waveform (a) being characterized by the equation Vin=De−A
1-41. (canceled)
42. A method comprising:
determining a length of an electrical cable using a time-domain reflectometry (TDR) technique, wherein said determining the length of the electrical cable using the TDR technique includes:
sending an electrical pulse into the electrical cable, and
detecting a reflected signal in response to the electrical pulse due to presence of an impedance discontinuity at an end of the electrical cable, wherein the electrical pulse is an exponential waveform.
43. The method of
44. The method of
45. The method of
determining a time-of-flight associated with said sending and said detecting; and
computing the length of the electrical cable using the time-of-flight.
46. The method of
determining a time t1 when the electrical pulse crosses a threshold signal level;
determining a time t2 when the reflected signal crosses the threshold signal level; and
computing a difference between t2 and t1.
47. The method of
48. The method of
capturing the electrical pulse and the reflected signal into a memory buffer;
repeatedly scanning the memory buffer to determine corresponding time-of-flight values; and
averaging the time-of-flight values;
wherein each of said scans of the memory buffer includes:
determining a time t1 when the captured electrical pulse crosses a threshold signal level;
determining a time t2 when the captured reflected signal crosses the threshold signal level; and
computing a difference between t2 and t1;
wherein each of said scans uses a different value of the threshold signal level.
49. A system comprising:
a signal generator configured to generate an input waveform for stimulating a transmission medium, wherein the input waveform includes an exponential leading-edge portion; and
a receiver configured to: (a) capture a response waveform from the transmission medium, (b) determine a first time-of-flight between said generation and said capture using the captured response waveform, and (c) compute a length of the transmission medium using the first time-of-flight.
50. The system of
determining a time t1 when the input waveform crosses a threshold signal level;
determining a time t2 when the response waveform crosses the threshold signal level; and
computing a difference between t2 and t1.
51. The system of
52. The system of
computing a number of time-of-flight values; and
computing the first time-of-flight by averaging the time-of-flight values;
wherein each of said time-of-flight values is computed by:
determining a time t1 when the captured input waveform crosses a threshold signal level;
determining a time t2 when the captured response waveform crosses the threshold signal level; and
computing a difference between t2 and t1;
wherein the computation of each of the time-of-flight values uses a different value of the threshold signal level.
53. The system of
54. The system of
55. The system of
56. The system of
57. A measurement device for measuring a length of a transmission medium, the measurement device comprising:
a signal generator configured to generate an input signal for stimulating the transmission medium, wherein the input signal includes a leading-edge portion that has an exponential shape; and
a receiver configured to: (a) capture a response signal from the transmission medium, (b) determine a first time-of-flight between said generation and said capture using the captured response signal, and (c) compute a length of the transmission medium using the first time-of-flight.
58. The measurement device of
determining a time t1 when the input signal crosses a threshold signal level;
determining a time t2 when the response signal crosses the threshold signal level; and
computing a difference between t2 and t1.
59. The measurement device of
60. The measurement device of
computing a number of time-of-flight values; and
computing the first time-of-flight by averaging the time-of-flight values;
wherein each of said time-of-flight values is computed by:
determining a time t1 when the input signal samples cross a threshold signal level;
determining a time t2 when the response signal samples cross the threshold signal level; and
computing a difference between t2 and t1;
wherein each of the time-of-flight values is computed using a different value of the threshold signal level.
61. The measurement device of
62. A method comprising:
transmitting an input pulse into a transmission medium;
capturing the input signal that is transmitted into the transmission medium;
capturing an output signal from the transmission medium;
determining a transfer function for the transmission medium using the captured input signal and the captured output signal;
computing a simulated response signal using the transfer function and a simulated input signal, wherein the simulated input signal has an exponential leading-edge portion;
determining a time delay between the simulated input signal and the simulated response signal;
computing a length value using the time delay, wherein the length value represents an estimate of a length of the transmission medium.
63. The method of
64. The method of
computing a time t1 when the simulated input signal crosses a threshold signal level;
computing a time t2 when the simulated response signal crosses the threshold signal level; and
computing a difference between t2 and t1.
65. The method of
This application is a continuation-in-part of, and claims priority to, U.S. patent application Ser. No. 10/224,541 filed Aug. 20, 2002 which is a continuation-in-part of U.S. patent application Ser. No. 09/519,922, filed Mar. 7, 2000, now U.S. Pat. No. 6,441,695. The entire text of each of the above related applications is incorporated by reference in its entirety.
1. Field of the Invention
The invention relates generally to the field of signal transmission. More particularly, a representative embodiment of the invention relates to transmission line testing and communication.
2. Discussion of the Related Art
Transmission lines, with their characteristic loss of signal as well as inherent time delay, may create problems in designing systems that employ a plurality of signals, which may be subject to delay and distortion. Typical signals used to generate inputs to transmission lines generally exhibit delay or propagation times that are not easily determinable. The propagation velocity of these waves is also variable with displacement along the transmission line.
A Time Domain Reflectometer (TDR) is a test instrument used to find faults in transmission lines and to empirically estimate transmission line lengths and other parameters characterizing the line, such as: inductance per unit length, capacitance per unit length, resistance per unit length and conductance per unit length.
An important measurement in TDR test technology is the time-of-flight (TOF) of a test pulse generated by the instrument and applied to the line. The time-of-flight may be measured by timing the passage of the pulse detected at two locations along the line. Along with a value of the propagation speed of the pulse, time-of-flight measurements can allow one to obtain the distance between measurement points or, in the case of a reflected wave, the distance from the pulse launch point to the location of the impedance change causing the pulse to be reflected and returned.
A fundamental limitation in TDR technology is the poor accuracy of TOF measurements in lossy, dispersive transmission lines. The relatively high TDR accuracy of TOF values obtainable in short low loss, low dispersion transmissions lines is possible only because the propagating test pulses keep their shape and amplitude in tact over the distances they travel during TOF measurements. By contrast, in dispersive, lossy long transmission lines the test pulses used in the art change shape, amplitude, and speed as they travel.
Further, it is difficult to provide high-speed communications in a lossy, frequency dependent transmission media. It would be advantageous to have a method to increase data transmission rates in such transmission lines.
Until now, the requirements of providing a method and/or apparatus for accurately measuring times-of-flight, estimating line lengths and other parameters characterizing lossy, dispersive transmission lines, and providing high-speed communications via such transmission media have not been met. What is needed is a solution that addresses these requirements.
Shortcomings are reduced or eliminated by the techniques disclosed here. In one respect, the disclosure involves a method for transmitting an exponential waveform. The exponential waveform, which can be characterized by the equation VSD=De−A
In another respect, the disclosure involves transmitting a waveform including a speedy delivery signal envelope modulated with a sinusoidal signal on a media. The waveform can be characterize by the equation V(z,s)=B(s)e−zγ(s) and having a substantially constant shape during transmission on the media. In some embodiments, an exponential waveform can include a truncated speedy delivery signal envelope modulated with a sinusoidal carrier signal, in which the media can be a resistance-capacitance-inductance transmission line. In other embodiments, an electromagnetic plane waveform can include a truncated speedy delivery signal envelope modulated with a sinusoidal electromagnetic plane wave on a media, such as a dispersive plasma media.
In other respects, the disclosure involves a method for determining a temperature of a media. The method includes generating an exponential waveform on the media and determining the delay of the exponential waveform. The delay can be characterized by the equation
Where the temperature is proportional to the length of travel of the exponential waveform on the media.
In another respect, a method is provided for measuring a temperature of a media. The method includes generating a speedy delivery (SD) signal on a media and determining the delay of the SD signal characterized by the equation ΔSD=l(T)�√{square root over (L(T)C(T))}{square root over (L(T)C(T))}�√{square root over (1+τ/(L(T)/R(T)))}{square root over (1+τ/(L(T)/R(T)))}. The method also includes determining the temperature of the media which can be proportional to the delay.
In yet another respect, the disclosure involves a method for reducing interconnect delays. A signal is generated on an interconnect and the delay of the signal can be characterized by a line model and the equation δSD=√{square root over (LC)}√{square root over (1+τ(L/R))}. In one embodiment, the method includes reducing the delay by decreasing τ. In another embodiment, the method includes inserting a repeater on the interconnect.
In other respects, the disclosure involves a method including steps for generating an exponential waveform having an essentially constant shape during transmission on a media at a first location. A plurality of exponentials can be encoded on a leading edge of the exponential waveform, where the encoded exponential waveform is transmitted to a second location. The method also includes decoding the encoded exponential waveform at the second location.
The disclosure also involves a method for determining a length of an interconnect for a desired delay. A signal can be generated and a length of the interconnect can be characterized by the equation
where L is the inductance per unit length of the interconnect, R resistance per unit length of the interconnect, C is the capacitance per unit length of the interconnect, and ΔSD is the desired delay.
A thermometer is also presented. The thermometer includes a signal generator configured to generate a truncated exponential waveform characterized by the equation VSD=De−A
In another respect, the present disclosure includes a time domain reflectometer. The time domain reflectometer includes a signal generator configured to generate a truncated exponential waveform on a media. Using the generated truncated exponential media, the time domain reflectometer is configured to determine the length of the media. In another embodiment, the time domain reflectometer is configured to detect the locations of possible faults.
These, and other, embodiments of the invention will be better appreciated and understood when considered in conjunction with the following description and the accompanying drawings. It should be understood, however, that the following description, while indicating various embodiments of the invention and numerous specific details thereof, is given by way of illustration and not of limitation. Many substitutions, modifications, additions and/or rearrangements may be made within the scope of the invention without departing from the spirit thereof, and the invention includes all such substitutions, modifications, additions and/or rearrangements.
The drawings accompanying and forming part of this specification are included to depict certain aspects of the invention. A clearer conception of the invention, and of the components and operation of systems provided with the invention, will become more readily apparent by referring to the exemplary, and therefore nonlimiting, embodiments illustrated in the drawings, wherein like reference numerals (if they occur in more than one view) designate the same or similar elements. The invention may be better understood by reference to one or more of these drawings in combination with the description presented herein. It should be noted that the features illustrated in the drawings are not necessarily drawn to scale.
representing an embodiment of the invention.
The invention and the various features and advantageous details thereof are explained more fully with reference to the nonlimiting embodiments that are illustrated in the accompanying drawings and detailed in the following description. Descriptions of well known starting materials, processing techniques, components and equipment are omitted so as not to unnecessarily obscure the invention in detail. It should be understood, however, that the detailed description and the specific examples, while indicating specific embodiments of the invention, are given by way of illustration only and not by way of limitation. Various substitutions, modifications, additions and/or rearrangements within the spirit and/or scope of the underlying inventive concept will become apparent to those skilled in the art from this disclosure.
Within this application several publications are referenced by Arabic numerals within parentheses or brackets. Full citations for these, and other, publications may be found at the end of the specification immediately preceding the claims after the section heading References. The disclosures of all these publications in their entireties are hereby expressly incorporated by reference herein for the purpose of indicating the background of the invention and illustrating the state of the art.
In general, the context of the invention can include signal transmission. The context of the invention can include a method and/or apparatus for measuring and estimating transmission line parameters. The context of the invention can also include a method and/or apparatus for performing high-speed communication over a lossy, dispersive transmission line.
A practical application of the invention that has value within the technological arts is in time domain reflectometry. Further, the invention is useful in conjunction with lossy transmission lines. The invention is also useful in conjunction with frequency dependent transmission lines. Another practical application of the invention that has value within the technological arts is high-speed communications. There are virtually innumerable other uses for the invention. In fact, any application involving the transmission of a signal may benefit.
A method for transmitting a waveform having a controllable attenuation and propagation velocity, representing an embodiment of the invention, can be cost effective and advantageous. The invention improves quality and/or reduces costs compared to previous approaches.
The invention includes a method and/or apparatus for utilizing a truncated waveform, coined a Speedy Delivery (SD) waveform by the inventors. An analysis of SD propagation in coupled lossy transmission lines is presented and practical considerations associated with truncating the SD waveforms are addressed. Parameters used to describe the propagation of the SD waveform are defined and techniques for determining their values are presented. These parameters include the Speedy Delivery propagation velocity, vSD, the Speedy Delivery attenuation coefficient, ASD, and the Speedy Delivery impedance, ZSD. These parameters may depend on properties of a transmission media as well as an exponential coefficient α (SD input signal parameter).
The invention describes SD signal propagation in coupled transmission lines. An embodiment involving two transmission lines is illustrated. More complex configurations that include a larger number of coupled lines may be readily developed by one of ordinary skill in the art in light of this disclosure. Additionally, the behavior of the propagation of a slowly varying envelope of an optical pulse containing a truncated SD signal in a single mode communication fiber is described.
The invention teaches a method for using SD test pulses to obtain empirical estimates of the SD signal propagation parameters, ASD and vSD, in lossy transmission lines, including those with frequency dependent parameters. Once the value of vSD is determined for a calibration cable length, constant threshold time of flight measurements can be used to measure distances to discontinuities in similar cables. The calibration procedure can be repeated experimentally for each exponential coefficient α.
The invention provides a method for utilizing a wideband, non-SD waveform in order to develop an empirical transfer function for a calibration length of a given transmission media. This transfer function may be used to simulate the transmission of SD waveforms with a wide range of values for the exponential coefficient α. The SD parameters ASD(α) and vSD(α) can be determined from these simulated waveforms. The inclusion of a simulation step in the calibration process can significantly reduce the experimental measurements needed to determine the values of ASD(α) and vSD(α) for a variety of values for α. The SD behavior of a media can then be determined by simulation, without the need for an SD waveform generator.
The invention teaches a method for determining the SD impedance of a transmission line. It also illustrates the predicable variation of ZSD as a function of α. This predictability can allow a designer to control the transmission line SD impedance by appropriately selecting the parameter α.
The invention also describes an alternate precision distance measurement method using truncated SD test pulses with high loss, long lines. As the test pulses travel down these lines, the attenuation can be so extensive that their amplitudes are too small for common threshold crossing time of flight measurements to be feasible. The invention includes a method for predicting an attenuation and overcoming this difficulty, extracting accurate length measurements for long lossy lines.
The invention demonstrates the utility of the SD test waveform in accurately determining distances to impedance discontinuities. Examples show how to use SD wave propagation as the basis for an accurate time domain reflectometry (TDR) unit. This unit may include an SD waveform generator, a means of coupling with the transmission media, a means of measuring the applied and reflected waveforms, a display, memory storage, and computational ability to analyze and interpret the SD waveforms. The invention can also include a computer. The invention can include a method which can be applied to modify currently available TDR units to increase their accuracy. This modification may be a TDR software modification resulting in a nonrecurring unit manufacturing cost. A standard TDR waveform may be used to determine an empirical transfer function for the line under test, and this transfer function may then be used to simulate the propagation of the SD waveform. This process allows all the advantages of SD to be incorporated into currently available units with only a modification of existing computational algorithms, creating a virtual SD TDR unit.
The truncated SD test pulse approach can also be applied to the propagation of acoustic waves in sonar and geophysical applications. Reflected acoustic signals can be used to accurately determine the location of underwater objects and to determine locations of geophysical strata boundaries. Empirical transfer functions can be determined and used to simulate SD pulse propagation eliminating the need to physically generate complex acoustic pulses.
The invention provides an SD waveform that has several propagation properties in lossy, frequency dependent transmission media, which make it suitable for enhancing a data transmission scheme.
The invention provides a method to increase the number of bits transmitted per pulse by varying the value of α to encode data on truncated SD waveforms. The example provided utilizes SD pulses with four different α's sequentially transmitted on a 2 kft cable. These SD pulses are received at the end of the cable with the exponential constants undistorted. The four pulses may be transmitted as positive or negative signals resulting in eight possible states. Therefore, each pulse represents three bits of transmitted information in each symbol period. This strategy can be used with short, low loss transmission lines.
The invention also teaches the use of SD propagation properties to generate a set of pulses consisting of linear combinations of truncated SD waveforms that are orthogonal at the receiver. Data can be encoded on these pulses by varying their amplitude, and these amplitude-modulated pulses may be transmitted simultaneously on a transmission line. The individual pulse amplitudes are computed at the receiver taking advantage of their orthogonality. This method provides improved noise immunity, and can be used with longer, higher loss transmission lines.
The invention also teaches the use of SD waveforms in digital circuits, specifically, on-chip clock circuits. It provides a method for utilizing truncated SD clock waveforms to reduce clock skew.
The propagation of a Speedy Delivery (SD) waveform in a transmission line can be described by the equation V(x,t)=De−
For the case of two balanced twisted wire pair transmission lines, the differential voltage can be equally divided between the two wires and the current on each wire in the pair is equal in magnitude but opposite in direction. In this case, the telegrapher's equations can be written:
This analysis includes the net cross capacitance, Cij, and the net cross inductances, Mij. The cross resistance and conductance terms are neglected. These equations are then Laplace transformed into the complex frequency domain.
Taking the partial derivative of the top equation with respect to x, and substituting the bottom equation for the
term, gives the result:
This system of equations has the solution:
Applying the boundary conditions for a semi-infinite pair of transmission lines, V(x=0,s) at x=0, and V(x→∞,s)=0 gives:
For the case where the applied boundary conditions at x=0 are SD waveforms, V1(x=0,t)=D1eα
where P(αi) is a real matrix.
If we designate P−1 as Q, we can write:
The real constants associated with the eigenvector matrix, P, its inverse, P−1=Q, and the SD parameters D can be written:
The signals on transmission lines will be:
Thus, there are SD attenuations and velocities associated with each eigenvalue, γi, of the product
Because positive exponential waveforms continually increase, practical considerations may create the need to truncate or limit the waveform at some level determined by the specific application. Truncation may be accomplished by several methods, as is known in the art.
The result of this truncation of the input of a transmission media is that the propagating exponential (SD) signal is also limited in magnitude as it travels in the media, and in lossy media, this maximum amplitude decreases with distance traveled exhibiting an attenuating behavior.
The propagating (SD) signal is described in the coordinate frame, (x, t), by V(x,t)=De−A
Referring to
In the case of a four parameter (LCRG) transmission line, we have the expressions
The attenuation of the traveling SD wave may be viewed from the perspective of a moving reference frame traveling at the speed 1/√{square root over (LC)}.
Introducing the new coordinates:
If we view the traveling wave after traveling a distance, x=x′=l, in the transmission media, then
Setting t′=ti, yields the maximum value of the truncated SD waveform at x=l, and for any value 0≦tj≦ti, the value of the signal at the associated point tj in the moving reference frame at x=l is:
Referring to
This attenuation of the signal at a point tj of a truncated SD waveform traveling in a transmission line with frequency dependent parameters whose Laplace transforms are
Furthermore, in this transmission media with frequency dependent parameters, if the input exponential pulse is rapidly closed when the exponential amplitude truncation limit is reached, then the end of the exponential region of the leading edge of the transmitted pulse is further reduced in amplitude and rounded by the chromatic dispersion.
Coupled transmission lines can be treated in a similar fashion. The equations governing SD propagation on one of two coupled transmission lines is:
Applying the substitution: t′=t−x√{square root over (
Which can be written:
Another example includes of the evolution of a slowly varying envelope, E(x,t), of an optical pulse in a single mode communication fiber. The Schr�dinger partial differential equation [3],
describes the evolution of the shape of the propagating pulse envelope undergoing chromatic dispersion in fiber. Chromatic dispersion occurs because the mode-propagation constant, β(ω), is a nonlinear function of the angular frequency ω, where
and ωo is the frequency of the light being modulated in the fiber.
ωo/βo is the phase velocity of the pulse. 1/β1 is the group velocity, β2 is the group velocity dispersion (GVD) parameter which causes the pulse to broaden as it propagates in the fiber. β3 is the third-order dispersion (TOD) parameter [4]
The higher order derivatives of β with respect to ω are assumed negligible. However, they may be added in these analyses by anyone familiar with the art. The fiber attenuation is represented by the parameter γ.
The SD solution of the linear Schr�dinger equation with loss (γ≠0) is:
The boundary condition at the input to the fiber at x 0 is
The receiver detector in a fiber optic communication network responds to the square of the magnitude |E(x,t)|2 of the propagating pulse envelope. In this case
where the velocity of propagation of a truncated SD leading edge of the envelope is
Transforming to a moving reference frame traveling at the group velocity 1/β1,
The SD propagation speed in this moving reference frame is
The attenuation of the truncated SD portion of the leading edge of the pulse envelope is
This result implies that if To can be made small enough, this attenuation may be reduced. Higher order terms of β(ω), which were not included is this particular analysis, may become more significant as To become smaller.
Specific embodiments of the invention will now be further described by the following, nonlimiting examples which will serve to illustrate in some detail various features. The following examples are included to facilitate an understanding of ways in which the invention may be practiced. It should be appreciated that the examples which follow represent embodiments discovered to function well in the practice of the invention, and thus can be considered to constitute preferred modes for the practice of the invention. However, it should be appreciated that many changes can be made in the exemplary embodiments which are disclosed while still obtaining like or similar result without departing from the spirit and scope of the invention. Accordingly, the examples should not be construed as limiting the scope of the invention.
This example teaches how SD test pulses may be used to obtain empirical estimates of the transmission line parameters, ASD and vSD, that describe the propagation of SD waveforms in lossy, dispersive lines, including those with frequency dependent parameters. The numerical values of ASD and vSD as a function of α can be determined empirically.
Referring to
The values of D, α and the duration of the SD signal were chosen to prevent the occurrence of reflections at the measurement point, d, during the initial time of flight of the SD signal propagating in the test line. The additional length of transmission line also ensures that all reflections occurring in the test line are delayed until well after the propagating SD waveform measurement at d is complete.
The SD signal time of flight can be directly measured by timing the propagating SD waveform crossing of constant voltage thresholds (
The SD attenuation coefficient, ASD, can be calculated from α and vsd using the relationship ASD�vSD=α. The calculated ASD obtained from the waveforms shown in
Once this velocity is known for a calibrated length of the cable, this type of threshold crossing TOF measurement can be used to determine the unknown length of another sample of the same transmission line.
Referring to
The high accuracy of this method results from the use of an average of TOF measurements taken over a range of signal threshold amplitudes. It is feasible to use the average of these values to improve the accuracy of the measurement of TOF since all points on the leading SD edge of the waveform travel at the same speed. This is in contrast with the current time domain reflectometry art in which a measurement of the time of emergence of the dispersing test pulse is attempted. This is equivalent to attempting to accurately measure the threshold crossing time of the pulse at a zero threshold level when the slope of the pulse is also nearly zero.
The method described in example 1 can be limiting in that it should be experimentally repeated for each exponential coefficient α. This may require a lengthy laboratory calibration time for each cable type. Simulation can be included in the calibration process to significantly reduce the experimental measurements needed to determine the values of ASD and vSD. The use of simulation in this process requires a transfer function that describes the response of the specific type of cable. The α's analyzed for the T1 cable range from 1�105 sec−1 to 1�107 sec−1. This range of a's corresponds to the frequency band of 16 kHz to 1.6 MHz, so the transfer function must be accurate for this range. The transfer function of the cable may available from the manufacturer or can be determined empirically by applying a known pulse and measuring the applied cable input waveform and the response waveform at a known (calibration) distance along the cable. The transfer function is then calculated from the ratio of the fast Fourier transforms (FFT) of the input-output pulses:
Once the transfer function is determined, the propagation of SD waveforms with a series of different values for α can be simulated and the times of flight and SD parameters, ASD and vSD, determined.
This method can be demonstrated for the T1 cable used in example 1. The end of the total 2004 length has been terminated with a 100-Ohm resistor (Rt in
Once the transfer function is known, a waveform with any α in the indicated range of interest can be simulated and the value of ASD and vSD determined. The values of ASD and vSD of the measured SD waveforms of section three provide a test of the transfer function for an α of 3�106 sec−1.
This process is performed for the range of a's by simulating the initial SD waveforms and using the transfer function to predict the waveforms at 1002 ft. In all cases, the simulated initial waveforms were closed with a 1 μsec ramp to reduce their high frequency components.
The SD line impedance, ZSD(α), is a real number which may be determined for the α's of interest. If the Laplace transform of the frequency dependent transmission line parameters
The SD line impedance, ZSD(α), may also be experimentally determined for a test transmission line by measuring the SD portion of the voltage waveform across various known termination impedances and computing the value ZSD(α) from the measurements. The measured SD waveform at a termination, vSD(Rt), consists of the sum of the incident SD waveform, VSD +, and a reflected SD wave. The reflected wave is the product of the SD reflection coefficient, Γ, and the incident wave. The measured SD signal at the termination will be
Note that all lumped and distributed impedance values are real for SD signals.
The experimental setup used to determine ZSD from line measurements is shown in
with known terminations and the incident waveform gives a direct measurement of the reflection coefficient, Γt, for each termination resistance,
Using the two finite values for Rt, 98.6Ω and 49.5Ω, yields two estimates for Zsd:
for this T1 cable.
This process was repeated for α's from 5�105 sec−1 to 10�106 sec−1 and the results are shown in
This example describes an alternate precision TOF measurement method of SD test pulses for higher loss, longer lines whose attenuation of the test pulses is so extensive that their amplitudes become too small as they travel down the line for a common threshold crossing measurement to be feasible.
The time of flight measured at a constant voltage threshold becomes more difficult to estimate as the waveform is attenuated. This can be seen by examining the voltage traces along an approximately 6-kft, 24 AWG, fifty twisted wire pair, telephone cable (See
Even though the signal was detectable at much greater distances than 6 kft, the constant threshold time of flight could not be measured.
The first step in precisely measuring highly attenuated SD pulse time of flight is to detect the SD region of the propagating pulse, V(t), measured and recorded at the distance #along the cable. This is done by computing the ratio
of the measured pulse waveform. In the SD region of the pulse, this ratio is α. The end of the SD region is then found by detecting the time that this ratio diverges from α. The ratio
can also be used to detect the end of the SD region. In the SD region, this ratio is also α. The later ratio of the second and first derivative responds more quickly, but is also more susceptible to noise than the ratio of the first derivative and the signal. These ratios as a function of time are plotted in
for any positive n will have this property. Additionally, the ratio of the signal and its integral can be used to locate the SD region. In the SD region, we have the relationship:
Thus, the ratio will converge on α as time progresses. This ratio diverges at the end of the SD region. In a lossy transmission medium with constant transmission line parameters, the end of the estimated SD region can provide a good marker to determine the speed of light in the medium. The truncated SD leading edge of the pulse does not disperse, even with frequency dependent parameters. The high frequency components of the closing pulse, however, do undergo dispersion. These fast, high frequency components tend to erode the end of the truncated SD region as the pulse propagates. At long distances, these high frequency components are also more highly attenuated so the amount of SD region erosion is not proportional to the distance traveled. In this case, the detected end of the SD region serves as an initial estimate of the pulse time of flight or the distance the wave has traveled and serves to define the region examined for more precise time of flight measurements in the next step.
The attenuation of the truncated SD signal propagating a distance d was shown to be e−A
Once the initial TOF estimate of end of the SD region in the leading edge of the propagating pulse is obtained at the distance l, the input waveform is attenuated and time shifted assuming the end of the SD region of the traveling wave corresponds to the point of truncation of the initial SD waveform, (
This process was repeated eight times giving average distances of 6,113 ft, 12,216 ft, and 18,327 ft for the best-fit shift locations of the attenuated input waveform to the measured waveforms. The standard deviations of the three lengths were 1 ft, 1 ft, and 5 ft respectively. The fits associated with one of these data sets are shown in
A Time Domain Reflectometer (TDR) is a test instrument used to find faults in transmission lines and to empirically estimate transmission line lengths and other parameters characterizing the line such as inductance per unit length, capacitance per unit length, resistance per unit length and conductance per unit length. A fundamental measurement in TDR test technology is the time of flight (TOF) of a test pulse generated by the instrument and applied to the line. This time of flight may be measured by timing the passage of the pulse detected at two locations along the line, referred to as Time Domain Transmission measurements (TDT). Or by Time Domain Reflection measurements which estimate the launch time of a pulse at one position and the subsequent return time of the pulse back to the same location after the pulse has been reflected from a fault or other impedance change some distance along the line. These measured TOF values, along with a value of the propagation speed of the pulse, allows one to obtain the distance between measurement points or in the case of the reflected wave, the distance from the pulse launch point to the location of the impedance change causing the pulse to be reflected and returned to the launch point.
A fundamental limitation in TDR technology is the poor accuracy of these TOF measurements in lossy, dispersive transmission lines. The relatively high TDR accuracy of TOF values obtainable in short low loss, low dispersion transmissions lines is possible only because the propagating test pulses keep their shape and amplitude in tact over the distances they travel during TOF measurements. By contrast, in dispersive, lossy long transmission lines the test pulses used in the art change shape, change amplitude any speed as they travel. The TOF measurements used in the art under these circumstances focus on estimating the emergence time of the leading profile of the test pulses. This part of the signature of test pulses used in the art has characteristically a low signal level and low signal slope making an accurate pulse emergence time measurement difficult to obtain.
Several advantages can be obtained in TDR technology for lossy, dispersive transmission lines by using a test pulse that contains a truncated SD signal in its leading edge. This truncated SD leading edge travels at a constant speed along these transmission lines without changing shape. The speed of propagation of this SD edge is a function of the line parameters and the SD signal parameter alpha and is controllable by changing alpha. The truncated SD leading edge of the test pulse will be attenuated as it travels along a lossy line. However, this rate of attenuation is also a function of the line parameters and the SD signal parameter alpha and is controllable by changing alpha.
The same principles used for TDR can be applied to waveforms other than electromagnetic waves in a transmission line. The reflections of acoustic waves in SONAR or geophysical applications can be analyzed using the techniques discussed in this section to provide accurate time of flight and distance estimates as well as be used to characterize the transmission media.
The accuracy of the SD test waveform in a TDR application can be demonstrated by an example using the T1 cable, as discussed in examples 1 and 2. The two twisted wire pairs inside the T1 cable are connected in series to form a 2004 ft cable and the truncated SD signal is applied to the input. The voltage trace is measured at the splice of the two lines at 1002 ft. This can eliminate the need to correct for any line impedance mismatch at the point of measurement. The exponential coefficient α of the applied wave is 6.7�106 sec−1. The SD parameters, ASD and vSD, are obtained from the empirical transfer function analysis presented in example 2. Interpolating from the data of table I gives an ASD of 10.703�10−3 ft−1 and a vSD of 6.276�108 ft/sec for this α.
The first demonstration terminates the cable with an open circuit. The reflected coefficient of an open circuit is +1, which results in a positive reflection.
The next demonstration terminates the second twisted wire pair with a short circuit. The reflected coefficient at a short circuit is −1, which results in a negative reflection.
The utility of the SD waveform to the TDR process can be increased by using an empirical transfer function obtained with the use of a non-SD pulse applied to the line in a way similar to the process discussed in example 2. As an example with this cable, an experimental voltage pulse is generated by an arbitrary function generator connected to a single unterminated twisted wire pair from the T1 cable. This waveform is shown in
This function, shown in
As a test of this process, a SD pulse with an α equal to the α used in the previous two experiments was simulated. The transfer function determined for the open terminated T1 cable, (
No actual SD signal was experimentally applied to the twisted wire pair to obtain these results. The test signal applied to the line (
The SD waveform has several properties that make it suitable as the basis for a data transmission scheme. For example: the exponential shape is maintained as it propagates at constant speed in a uniform cable; the attenuation of the SD waveform is adjustable by changing the exponential waveform parameter α; the propagating speed of the SD waveform is adjustable by changing the exponential waveform parameter α; and the SD waveforms with different α's are linearly independent.
This example teaches using the first property as the basis for a method of transmitting data using SD waveforms. The signals are transmitted 2004 ft along a transmission line consisting of the two twisted wire pairs in a 1002 ft T1 cable connected in series. The second twisted wire pair is terminated with a 100-ohm resistor. The data is encoded on four SD waveforms, each having a distinct α. Each waveform can be transmitted with a positive or a negative D, resulting in eight total states for three bits per symbol. One symbol is transmitted every three microseconds, giving a data rate of 1 Mbps. As one of ordinary skill in the art will recognize with the benefit of this disclosure, several other communication schemes can be readily derived from the teachings contained herein.
The symbols can consist of a two-microsecond truncated SD leading edge period followed by a one-microsecond recovery period. This recovery period includes a variable width half-sine compensating pulse adjusted to shorten the time required for the transmission line to return to a zero voltage. The need for this recovery period and compensating pulse is illustrated in
This example discusses using the fourth SD waveform property, that SD waveforms with different α's are linearly independent. This property can be utilized to generate an orthogonal set of pulses. Data can be encoded on these pulses by varying their amplitude. These amplitude-modulated orthogonal pulses are transmitted simultaneously on the transmission line. At the receiver, the individual pulse amplitudes are computed by taking advantage of their orthogonality. The basic pulses derived from the SD waveforms must be orthogonal at the receiver for this scheme to work.
The repetitive transmission of data may require closed pulses. As shown in example 6, that the SD portion of the leading edge of a closed propagating pulse maintains its shape, while the shape used to close the pulse will disperse as it propagates. The attenuation and propagation speed of the truncated SD leading region of the pulse is a function of the SD parameter α. Therefore, the orthogonality of a set of these pulses with a variety of α values will be reduced as the pulses propagate. Fortunately, the pulses only have to be orthogonal at the receiver. Techniques can be used to generate a set of orthogonal pulses from linearly independent component pulses. The effect of the transmission line on these component pulses can be determined empirically. These transmitted component waveforms, measured at the receiver, will be linearly independent. Linear combinations of these measured, linearly independent component pulses are used to generate a set of pulses that are orthogonal at the receiver. The constants determined by the orthogonalization process are supplied to the transmitter and used to generate transmitted pulses that will be orthogonal at the receiver. An example of this procedure follows. The process of generating and transmitting the orthogonal pulses is simulated for an 8 kft, 26 AWG twisted wire pair transmission line terminated with 100 Ohms resistance.
The example orthogonalization process can begin by using a set of SD waveforms Xm(t)=e(α
and t=0 . . . 7�10−6 sec. The five waveforms are shown for a seven-microsecond interval in
The set, Y, is orthonormal in that the inner product
The sharp waveform transitions at zero and seven microseconds have high frequency content that would disperse during transmission and contribute to inter-symbol interference. This effect is reduced by multiplying this orthonormal set by sin(ω�t), with
This has the effect of changing the SD waveform to X′, where
for m=1 . . . 5.
Although the SD waveforms, X′, are still linearly independent, the previous linear combination of these waveforms, Y′=Ā�X′, is no longer orthogonal. The waveforms, Y′, are shown in
delayed one microsecond after the start of the symbol period, see
The multiplication by the sine pulse, the adding of the compensating pulse, and the transmission in the channel, have all reduced the orthogonality of the initial five pulses. Initially the angles between the pulses in
The orthonormal set S is orthogonal and normalized at the receiver. The process accounts for the effects of the channel and allows the transmitter input waveforms to be easily constructed as a linear combination of defined components prior to transmission. This set S can be used as the basis functions for an orthogonal pulse amplitude modulation data transmission scheme. This process is depicted in
The data can be encoded by amplitude modulation with five bits on each of the four orthonormal pulses, S. Five bits requires thirty-two states. Each state corresponds to one amplitude level, ai, on each orthogonal pulse, Si. For this example the amplitude levels were �0.5, �1.5, . . . �15.5. These four modulated orthogonal pulses are summed to generate a symbol, Q=a1S1+a2S2+a3S3+a4S4.
The symbol is transmitted and decoded at the receiver by using the orthogonality of the pulses. For example, the applied signal on orthogonal pulse one can be found by taking the inner product of the symbol, Q, with the pulse one signal, S1. This is done by multiplying the received symbol by the known orthogonal pulse, integrating over the symbol period, and normalizing the result.
This example teaches the use of SD waveforms in digital circuits, specifically, in on-chip clock circuits. On-chip clock circuits may behave like transmission lines with the increased clock rates.
A major design advantage of the SD waveforms when used as clock signals is that the delay in an RC line (√{square root over (RC/α)}�l) is linear with length, l, instead of quadratic with length as it is with the commonly assumed step signal. Linear delay with length
is also true for the SD signal in an RLC line. In contrast, the delay in RLC transmission lines excited by a conventional signal exhibit an exponentially growing increase in delay with length [8].
The fact that the SD signal delay increases as a linear function of length for all types of clock lines can simplify the clock line layout design process. This linear relationship holds for the entire range of clock line behaviors, from the very lossy clock lines that behave like RC transmission lines to low loss clock lines that behave like RLC transmission lines. This simple linear relationship between line length and SD clock signal delay provides a basis for implementing software CAD tools that may enhance accuracy while reducing design computational requirements.
Time Skew Clock control is a major issue limiting system performance. A solution to this problem includes equalizing conductor lengths to the various locations on the chip where the clock signal is needed. Several geometrical patterns are commonly used (H, etc.) to equalize the signal path lengths, thereby equalizing signal delays. This requires equalizing the path lengths along the traces delivering the clock signal to pin locations that are physically close to the master chip clock driver with those clock signal path lengths to pin locations at the longest distances from the master driver. Small adjustments to equalize the delays may be accomplished by adjusting the line widths to modify the line parameters and thereby the delay per unit length and alternatively by active means such as varying the delay of delayed-locked loops embedded in the clock lines.
The invention provides a method and/or apparatus for utilizing truncated SD clock waveforms to reduce the clock skew. An advantage of the invention is that the delay per unit length can be adjusted with the exponential coefficient, α, chosen in the clock line driver design. This controllable delay per unit length has been demonstrated for a 100-ft coaxial cable in the initial patent application. The minimum coaxial cable delay measured was increased by a factor of 1.8.
The large increases in the clock signal delay per unit length achieved by varying the exponential coefficient α allows lines to the pins close to the clock driver to be shortened to more closely approximate the minimum physical distance between the driver and pin while maintaining a path delay equal to the delay of the longest clock lines on the chip. The shorter clock distribution lines may utilize less physical space on the chip and reduce the total clock line capacitance. This reduction in clock line capacitance reduces the total power consumption required by the chip for a given clock frequency. In one embodiment, an SD waveform driver may also be made to create an SD clock signal with adjustable delay by including a mechanism for adjusting the exponential coefficient α in the clock generator. This adjustable delay of the SD clock signal may provide a larger delay adjustment range than the delayed-locked loops utilized in the current technology.
The propagation of signals in a no-loss non-dispersive media is ideal because there is no distortion.[9] However, pulse shapes that propagate along lossy, dispersive transmission lines are commonly dispersive, i.e., change shape[10]. This property can lead to inaccuracy of measurements and mischaracterizations of propagation behaviors.
As noted in Example 4 and Example 5 and illustrated in
where L, C, R, and G are the transmission line parameters[12].
The SD solution of Eq. 1 in the time domain with boundary conditions v(x=0,t)=Deαt and v(x→∞,t)=0 is
which, when rewritten in the form F(vt−x) yields,
where γ2(s)=LCs2+(LG+RC)s+RG and
Thus, the SD wave does not change shape as it propagates with constant velocity on this dispersive lossy transmission line. The SD solution's propagation velocity depends on the SD boundary condition waveform parameter α and the principal line parameters L, C, R, and G (the dependence on α is removed if R=0 and G=0, in which case v=1/√{square root over (LC)}, the standard result for the ideal transmission line).
If the principal transmission line parameters are frequency dependent, the SD steady state solution is still valid, where the signal propagation velocity becomes
Any application of the SD signal in a circuit can require that the exponential signal be truncated at some maximum amplitude. The result of truncating the amplitude of the SD signal at the line input is that the responses measured at different locations along the transmission line are also truncated SD signals having the same shape, but whose peak amplitudes decline with distance. Formulas for this attenuation in the truncated SD signal amplitude and the propagation velocity of the truncated SD signal are contained in references for various types of transmission lines and other DLM. It is also noted that using a truncated SD signal as the forward edge of a closed pulse and closing the pulse with a non-SD waveform results in dispersion of the pulse wave form as a whole, with only the leading SD edge retaining the shape of the waveform as it propagates in DLM.
In this example, an electrical signal which includes a truncated SD signal envelope modulated with a sinusoidal carrier signal can propagate on a lossy dispersive RLC transmission line without distortion is demonstrated. Similarly, electromagnetic plane waves which can include a truncated SD signal envelope modulated by a sinusoidal electromagnetic plane wave propagating through a dispersive plasma media (e.g., an ionosphere) is also demonstrated. Furthermore, the example illustrates that the propagation speed and attenuation of the envelope can be controlled.
1. Steady State Response of a Lossy Dispersive Resistance-Capacitance-Inductance Transmission Line to a Truncated SD Signal Envelope Modulated by a Sinusoidal Carrier.
The propagation transfer function for a resistance-capacitance-inductance (RLC) transmission line is[12]
where[12] γ2(s)=LCs2+RCs and the SD boundary condition is b(t)=V(t,z=0)=Deαt sin ω0t. Note that the boundary condition is a SD envelope modulated with a carrier of frequency ω0 that is understood to be truncated in time. As such, the steady state solution in time domain is
Defining P(α,ω0)=LCα2−LCω0 2+RCα>0 if LCα2+RCα>LCω0 2 and Q(α,ω0)=2LCαω0+RCω0>0, then Eq. 6 becomes
Thus, the envelope of the carrier is
which has the form of a function F(vt−z) which propagates with a controllable velocity v and controllable attenuation of a truncated SD envelope without changing shape[12]. Therefore, the propagation velocity of the envelope is:
2. One Dimensional Electromagnetic Plane Wave Propagation in a Dispersive Media[3]
Assuming the electromagnetic field components are only a function of z and assuming the E-field is polarized in the x-direction, the electromagnetic field components are as follows:
If ωp 2(z,t)=ωp 2 (i.e., assuming no variations in the plasma frequency in z direction or time), then
Taking the Laplace Transform of the Eq. 14 of the E-field yields:
Then the propagation transfer function for the E-field, in terms of the electromagnetic boundary condition at the edge of the plasma, B(s), is e−γ(s)z where
and the SD boundary condition
It is noted that the boundary condition is a SD envelope modulated with a carrier of frequency ω0 that is understood to be truncated in time.
As such, the steady state solution in the time domain is
Defining P(α,ω0)≡α2+ωp 2−ω0 2>0 if α2+ωp 2>ω0 2 and Q(α,ω0)=2ω0α>0 if α>0 and ω0>0, then
Thus, the envelope of the carrier is
which has the form of a function F(vzt−z) which propagates with a controllable velocity vz and controllable attenuation of a truncated SD envelope without changing shape[12]. The propagation velocity of the envelope is:
Note a similar results hold for {dot over (H)}y in Eq. 15.
It is noted that the types of media discussed above (e.g., RLC transmission lines and ionospheres) are merely examples. A waveform which may include a speedy delivery signal envelope modulated with a sinusoidal signal may travel on other types of media without distortion such as, but not limited to travel of any energy wave including a signal envelope traveling on a lossy dispersive media.
The temperature of a cable can influence the electrical SD signal delay in a media, especially metal wire line cables, such as RG-58/U coaxial cable. The effect can be predicted by the SD signal delay theory for wire line cable where the relation between the delay of a cable delay and a temperature of a cable can be useful in creating a new type of precision temperature measuring instrument.
1. Temperature Measurements
An RLC transmission line model can be used to model a metal line wire, e.g., a RG-58/U cable, at signal frequencies where the dielectric loss in the cable is small. The SD signal delay per unit length, (δSD=1/velocity) of an RLC transmission line is
where the SD signal input voltage applied to the cable is Deαt and
The coaxial cable transmission line parameter, R(T), in Eq. 22 is the combined resistance per unit length of the center conductor and the shield of the metal line wire. As such, the resistance of the coaxial center conductor and shield decreases with increasing temperature. The inductance and capacitance can also change with temperature due to the changes in the cross sectional dimensions of the cable due to the temperature coefficient of expansion of the insulation (PE-Polyethylene). Therefore, the length of the conductor can also increase slightly with increasing temperature (17 ppm/C.�) resulting in a small increase in the two way travel time of the TDR SD test pulse.
2. Calibration Mode
If the cable temperature can be controlled from one isothermal temperature to another and delay measurements performed on the cable at each temperature, then the calibrated relation between temperature and cable delay can be used to monitor the unknown cable temperature by periodically measuring the cable delay. In one example, time domain reflectometer delay measurements of the two way travel of SD pulses were performed on an un-terminated 300 ft. RG-58/U cable while the cable was held at a series of measured constant temperatures. Un-terminated, as defined herein, is a media terminated by any impedance other than the characteristics impedance of the media. Referring to
The inductance per unit length of coaxial cable is
and the capacitance per unit length is
Thus, √{square root over (LC(T))}=√{square root over (μ∈(T))}. The resulting SD signal delay (e.g., the time of flight, TOF) during propagation from cable input to un-terminated cable end and reflection back to the cable input is a
The two measurements in
The RG 58/U cable parameters are R(20� C.)=15.5 mΩ/ft, L(20� C.)=0.0801 μH/ft, C(20� C.)=28.5 pF/ft. The coefficient of thermal expansion of the polyethylene dielectric is 1,500-3,000�10−7/� C. Follow from Eq. 23 and the above parameters,
The measurement signal delay ratio is
which equates to
indicating the increasing the dielectric constant when the cable is cooled.
As the above equations show, if the cable length is accurately known at a given temperature (e.g. room temperature), and the nominal dimensions of the cable as well as the metal and dielectric coefficients of expansion are also known, then the relation between SD signal cable delay and cable temperature may be used to estimate the cable dielectric constant at various temperatures.
3. Non-Negligible Dielectric Loss
In general cases, signals with higher signal frequency and dielectric loss in the cable are non-negligible. As such, when all four of the principal transmission line parameters are dependant on frequency as well as temperature, T, then the SD signal propagation velocity becomes
Metal cable temperature measuring instruments that analyze reflected electrical signal delay in a cable to estimate the temperature profile along the length of the cable are feasible.
4. Thermometer
In one embodiment, an apparatus may be used to measure the temperature of the media. Referring to
It is noted in the above examples that the delay is inversely proportional to the temperature. However, it will be apparent to those skilled in the art that depending on the characteristics of the media, for example the dielectric constants, the delay may be proportional to the temperature.
The delay of interconnects on high performance chips have been estimated from lossy transmission line theory using an approximation which is based on a distributed RC model of the transmission line which, until recently, have neglected inductive effects. New methods[14] now employ an RLC transmission line approximation for interconnects because inductive affects can no longer be neglected in integrated circuits designed to operate with high speed clocks (e.g., gigahertz clocks). Using the SD signal in these interconnects permits the employment of either the RC or RLC line models within the same theoretical framework for accurately analyzing circuit delay. For example, the RLC transmission model using the telegrapher's equation as described in Eq. 1 of Example 9 can be obtained by setting G to 0 which yields:
The SD signal delay per unit interconnect length, (δSD=1/velocity, τ=1/α), is
Note that if the SD signal waveform parameter τ equals (L/R), then the signal delay/unit distance traveled is √{square root over (2)} larger than √{square root over (LC)} (the minimum delay/unit length of the ideal no loss line). And if τ is reduced to approximately (0.1)(L/R), then the SD signal delay/unit length is also reduced becoming only about 5% smaller than √{square root over (LC)}.
Reducing τ to obtain smaller line delay with the SD signal, is also accompanied by an increase in the propagation attenuation vs. travel length of the truncated SD signal. However, the attenuation of this truncated signal on an RLC line at length l is bounded, being no worse than a limiting maximum value of
as τ→0.
1. SD Repeater Insertion
Repeater insertion is generally required in long lossy on chip interconnect lines[15] because of signal attenuation. As such, SD repeater insertion methods can be employed in long lines to reduce interconnect delay while maintaining signal amplitude constraints for adequate input signal integrity at the repeaters. In one embodiment, repeaters having a SD waveform output can be implemented in CMOS where the high speed latched comparator circuits in CMOS contain a middle stage (unstable feedback loop) that can produce the positive exponential waveform[16] [17].
A repeater insertion design for a 1 cm line using line parameters R=40.74 Ohm/mm, L=1.52 nH/mm, and C=228.5 fF/mm, and considering a target clock frequency of 10 GHz for a 0.07 μm CMOS technology is demonstrated. First, a cadence simulation of a 0.18 μm CMOS process technology of a re-settable latch with inverters as output buffers was performed and yielded a SD signal output with τ=60 ps. For the 0.07 μm CMOS technology, the estimated SD signal is scaled such that τ is approximately 23 ps. For a 10 GHz clock, τ can be assumed to be reduced by a factor 10 (τ is approximately 3 ps).
Choosing a maximum allowed attenuation of approximately 0.7 for each line segment length allows a maximum of 1.46 mm per segment. Assuming six segments over the total 10 mm length (the total 10 mm wire delay, excluding the repeater delays is 10�19.4 ps/mm=194 ps/mm), and a repeater delay, TR, of 3τ to 6τ. In this example, the repeater delay is approximately 10 ps which yields a total delay of the segmented line equal to 264 ps ((7�10 ps)+194 ps). This is approximately three clock periods for a 10 GHz clock. The minimum delay of an un-segmented (no repeaters) ideal no loss line of 10 mm length (10 mm�18.6 ps/mm) is 186 ps or approximately two clock periods at 10 GHz. The ratio (%) of the no loss 10 mm line delay (186 ps) to the total delay of SD repeater solution for the lossy 10 mm line (264 ps) is 70%.
By using the SD repeater insertion, any performance limiting interconnect delay larger than l√{square root over (LC)} over long paths of length l can be reduced by making the repeater delay and parameter τ of the SD repeater output signal smaller.
As noted above, the SD waveform and accompanying propagation properties can be incorporated into the signal waveforms of digital and communication systems. In communication systems, the coding modalities unique to the SD waveform can be utilized that complement current communication waveform coding techniques. For example, since the SD waveform does not change shape during propagation in dispersive and lossy media, the SD shape parameter α (exponential coefficient) maybe varied from one transmitted SD pulse to another with the pattern of change in a detected at the receiver. In this manner, the value of α may be coded to convey information transmission in the channel.
Additionally, the process of encoding also allows multiple distinct values of α to be simultaneously incorporated into SD portions of the leading edge of a pulse. An example is illustrated in the figures that follow.
These two pulses with composite SD shapes in their leading edge, together with two pulses with distinct single SD shapes corresponding to either α1 or α2 in their leading edge, together provide a modulation scheme capable of conveying two bits information in the channel. The standard pulse amplitude modulation process may be combined with this modulation of SD shapes creating a composite modulation technique to enhance data rate by two bits per symbol period with essentially no increase in bandwidth of the transmitted symbols. The values of α in the SD sections of these pulses may be detected (e.g., decoded) as discussed in Example 7.
The leading edge of a SD signal, in particular, a truncated SD signal, that is transmitted on a media has an exponential shape. However, the transmission of this signal may have a slow transient condition. The transient condition may be a bias resulting from a long, slow, decaying tail. This bias may be added to the exponential waveform, and thus may skew the waveform. This example demonstrates an algorithm for removing the bias.
1. Algorithm A: Compensation Algorithm for a Known or an Unknown a Value of Applied Signal
Referring to
A. Compensation Algorithm for a Known α Value of Applied Signal
Referring to
Referring to
As stated above, the unknown bias must be removed in order to obtain accurate threshold time of flight, TOF, values. In one embodiment, the unknown bias B can reflected in the slope of the natural log plot of the exponential waveform plus bias in the SD threshold overlap region. As such, the unknown bias can be estimated and removed. In this bias removal, the error tolerance of residual bias of both the applied and reflected signals is chosen to be 1 μV.
i. Applied Signal
In this experiment, the applied signal is be a pulled-down signal with a voltage value such that the measured signal graph becomes that of an exponential waveform with an unknown negative bias. In one embodiment, the voltage of the applied signal may be approximately 0.01 V. First, the graph is lifted gradually with an added incremental voltage value which is initially chosen to be +0.001 volts at the beginning (0.01/10 volts) and is incremented until the slope of natural log of the signal versus the time is lower than the known α value of the applied signal. Next, the process is continued by adding one incremental negative bias voltage level (−0.001 V). Then the previous process of incrementally adding positive voltage level (+0.001/10 volts) +0.0001 V is performed until the natural log plot has a positive bias again as indicated by the slope of the log plot of the SD threshold region being less than α. At this point, the waveform becomes an exponential with a positive additive voltage bias. The previous process is again repeated by subtracting +0.0001 V from the waveform resulting a negative bias again. The positive incremental bias level 0.00001 V is added to the signal repeating the process describe above. Then the whole process repeated one more time with a new incremental voltage level, e.g., 1 μV (+0.00001/10 volts). At this point the bias adjustment process is concluded. This process is separately used to reduce the residual bias to less than 1 μV for both the applied and reflected signals. The natural log of both signals with the bias less than 1 μV versus time plot is shown in
Once the biases of both signals have been reduced, the final results obtained in this manner will be used to calculate the constant threshold TOF values in each of a series of incremental threshold voltages.
B. Compensation for Unknown α Value of Applied Signal
Referring to
2. Algorithm B: Compensating Algorithm Using the Difference Between the Adjusted Applied Signal and the Reflected Signal
For the algorithm described above (e.g., algorithm for a known or an unknown α value of applied signal), adjusts both the applied and the reflected signals, which are termed as Bias1 and Bias2, respectively. A calibration program can be applied to a series of measured constant threshold TOF values for both Bias1 and Bias2 on the same length of the media, as shown in
In this example, the standard deviation of measured constant threshold TDR TOF values can be drastically reduced. For example, let
Comparison of the measured constant threshold TDR TOF values and histograms of employing the A algorithm and the B algorithm (
All of the methods and apparatuses disclosed and claimed can be made and executed without undue experimentation in light of the present disclosure. While the apparatus and methods of this invention have been described in terms of embodiments, it will be apparent to those of skill in the art that variations may be applied to the methods and in the steps or in the sequence of steps of the method described without departing from the concept, spirit and scope of the invention. In addition, modifications may be made to the disclosed apparatus and components may be eliminated or substituted for the components described where the same or similar results would be achieved. All such similar substitutes and modifications apparent to those skilled in the art are deemed to be within the spirit, scope and concept of the invention as defined by the appended claims.
The terms a or an, as used herein, are defined as one or more than one. The term plurality, as used herein, is defined as two or more than two. The term another, as used herein, is defined as at least a second or more. The terms including and/or having, as used herein, are defined as comprising (i.e., open language). The term coupled, as used herein, is defined as connected, although not necessarily directly, and not necessarily mechanically. The term approximately, as used herein, is defined as at least close to a given value (e.g., preferably within 10% of, more preferably within 1% of, and most preferably within 0.1% of). The term substantially, as used herein, is defined as at least approaching a given state (e.g., preferably within 10% of, more preferably within 1% of, and most preferably within 0.1% of). The term means, as used herein, is defined as hardware, firmware and/or software for achieving a result. The term program or phrase computer program, as used herein, is defined as a sequence of instructions designed for execution on a computer system. A program, or computer program, may include a subroutine, a function, a procedure, an object method, an object implementation, an executable application, an applet, a servlet, a source code, an object code, a shared library/dynamic load library and/or other sequence of instructions designed for execution on a computer system.
The appended claims are not to be interpreted as including means-plus-function limitations, unless such a limitation is explicitly recited in a given claim using the phrase(s) "means for" and/or "step for". Subgeneric embodiments of the invention are delineated by the appended independent claims and their equivalents. Specific embodiments of the invention are differentiated by the appended dependent claims and their equivalents.
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Secretary of State and State Librarian Jesse White recently announced that the Melrose Park Public Library was awarded a Fiscal Year 2014 "Another Opportunity for Back 2 Books" grant for the MPPL project titled Citizenship and Beyond. Grant funds will be used to purchase adult and juvenile titles in English, Spanish, and Polish to help immigrants achieve US Citizenship and get started as new Americans. All these materials are available in the new Everyday Life Collection at the Melrose Park Public Library.
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We come to New York City for 5 years in a row. Always stayed at a hotel. Never again. Breathtaking views from every window! You will never get tired of it. The door man was courteous and knowledgeable. He helped is with restaurants and travel. There is an awesome grocery store right across the street and a 24 hour drug... more
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Courtney Reagan is CNBC's Retail Reporter. In 2011, Reagan was named general assignment reporter for CNBC's Business Day programming. She also contributes to NBC's "TODAY," NBC's "Nightly News with Brian Williams" and "Nightly Business Report" on public television. Reagan also regularly contributes to CNBC.com.
Previously, Reagan anchored the daily business headline reports for CNBC, the NBC affiliate stations, MSNBC and CNBC world. She also worked on CNBC's planning team and was a segment producer for CNBC's "On the Money," where she pitched, wrote and produced feature and news stories and packages for the program. Reagan began her career at CNBC in 2006 on the News Desk.
Prior to CNBC, Reagan participated in the NBC Page program, where she held positions at "Dateline NBC" and "Weekend Today," and also worked in guest relations for the network. Reagan also held positions at ESPN Networks and Merrill Lynch.
She holds bachelor's degrees in finance and mass communication from Miami University in Oxford, Ohio. Reagan graduated with distinction from NYU's Stern School of Business with a MBA with specializations in economics, luxury marketing and entertainment/media/technology. She was her class recipient of the "Excellence in Economics" for academic achievement in economics while at NYU.
Follow Courtney Reagan on Twitter @CourtReagan.
Gap store closures will take place over the next several years and the company will also cut 250 jobs at headquarters in FY 2015. CNBC's Courtney Reagan reports.
The search continues for two inmates in New York State overnight; South Korea reports its 10th death from the Mers virus; and Former Florida Governor, Jeb Bush, continues his tour of Europe, reports CNBC's Courtney Reagan.
JC Penney CEO designee Marvin Ellison spoke with CNBC's Courtney Reagan.
Online sales are growing at a faster rate than in-store sales but around 90 percent of all purchases are still made in stores. CNBC's Courtney Reagan reports.
CNBC's Courtney Reagan reports Wal-Mart elected a new chairman of its board at its annual shareholder meeting.
Walmart's CEO is hosting the media on its wage hikes and free shipping tests. Details, with CNBC's Courtney Reagan.
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Pinterests new buy button let you purchase items directly in the app, reports CNBC's Courtney Reagan.
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CNBC's Courtney Reagan takes a look at how some malls are using innovation to entice traffic and provide a shopping experience that online retailers can't deliver.
July 4 celebrations mean some serious food and retail spending, according to a study by the National Retail Federation.
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Talk:Raid on Dunkirk (1800)
From Wikipedia, the free encyclopedia
|This is the talk page for discussing improvements to the Raid on Dunkirk (1800) article.
Article policies
|Raid on Dunkirk (1800) has been listed as one of the Warfare good articles under the good article criteria. If you can improve it further, please do so. If it no longer meets these criteria, you can reassess it.
The given coordinates, 51°02′85″N 02°21′09″E have a seconds number that is out of bounds, being greater than 60. It should be
51°02.85′N 02°21.09′E / 51.04750°N 2.35150°E, or possibly
—WWoods (talk) 23:36, 11 August 2009 (UTC)
GA Review[edit]
- This review is transcluded from Talk:Raid on Dunkirk (1800)/GA1. The edit link for this section can be used to add comments to the review.
Reviewer: Auntieruth55 (talk) 21:32, 24 November 2009 (UTC) I've suggested a minor revision of the lead to better summarize the article.??? Part of the issue is that it assumed a lot of preliminary info about why, who, and how. See if this reads better, okay?
- You've used a lot of passive voice and indirect voice. For example "....it was decided that an attack by a squadron of smaller vessels on the frigates stood a chance of success and a number of ships were instructed to gather off the coast." Who? The Admiralty decided?
- Other examples: By the late French Revolutionary Wars (1793–1802), a string of victories at sea had ensured that the Royal Navy was dominant. // By the late..., a string, insured the Royal Navy's dominance.
- The French Navy in particular had suffered heavy losses, and in Northern European waters had been forced back into its own harbours by British blockade squadrons. // In particular, the Navy had inflicted heavy losses on the French and the English Channel and the North Sea, had forced the French into blockaded harbours.
- Although large ports were watched by fleets of ships of the line, small ports had their own blockade squadrons too, including the shallow French ports on the English Channel. // Squadrons of ships of the line watched the large ports and squadrons of frigates, sloops, and brigs watched the shallow ports. These smaller ports could not accommodate the deep-drafted ships of the line, but were well situated for shallower drafted ships, which continued to break through blockade and attack shipping in British waters.
- One such port was Dunkirk in French Flanders, which contained a squadron of four French frigates: the 44-gun Poursuivante under Commodore Jean-Joseph Castagnier, the 40-gun Carmagnole and the 36-gun Désirée and Incorruptible. //Dunkirk, one such port in French Flanders, contained a squadron of four French frigates: ....
- This one is just complicated, and unless the shoals were man-made, a bit misleading. Dunkirk was well defended, with gun batteries, gunboats and complicated coastal shoals into which the frigates could retreat if attacked. Dunkirk was well-defended, with gun batteries and gunboats, and natural defenses that included complicated coastal shoals into which the French could retreat.
- It is reasonably well written.
- a (prose): b (MoS):
- c comment: see above/I made a few additional tweaks for clarity and easier reading, after you went through the background. If this is to go further, the sentence about deciding to do the mission needs some work -- who decided (right now, "it" was decided.
- It is factually accurate and verifiable.
- a (references): b (citations to reliable sources): c (OR):
- It is broad in its coverage.
- a (major aspects): b (focused):
- It follows the neutral point of view policy.
- Fair representation without bias:
- It is stable.
- No edit wars, etc.:
- It is illustrated by images, where possible and appropriate.
- a (images are tagged and non-free images have fair use rationales): b (appropriate use with suitable captions):
- Overall:
- Pass/Fail:
- 7com: Nice article. I like the inclusion of details, and also the fact that this isn't in the standard text books/source books about the war.
- Wikipedia good articles
- Wikipedia CD Selection-GAs
- Warfare good articles
- GA-Class maritime warfare articles
- Maritime warfare task force articles
- GA-Class British military history articles
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- GA-Class French military history articles
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- Napoleonic era task force articles
- GA-Class military history articles


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19th Annual Kendall-Jackson Heirloom Tomato Festival
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Red Wine Tasting Lab
Friday, May 6, 2011 from 11:00 AM to 1:00 PM (PDT)
Welcome to the Wine Tasting Lab!
Lab coats aren't boring. In this class, we'll explore the roles of acidity, alcohol, oak and tannin by tasting wines that have been doctored. Then, we'll work in teams to identify aromatics of several wines that we've tinker with in the lab. In addition to this sensory exploration of wine, we'll also taste plenty of amazing, undoctored wines as well as we sharpen palates and tighten vocabulary by looking more closely at color, aromatics, flavor and body. It's fun and provides you with a toolbox full of information to break any wine down to nuts, bolts and sub atomic particles.
Each Crushpad seminar explores a different varietal, region or wine making style - all designed to hone your palate and broaden your wine appreciation. While many wine classes simply focus on tasting, these tasting seminars explore how winemaking decisions shape the flavors in your glass. You'll learn to taste from a winemaker's perspective as we unlock the secrets of flavor and texture by tracing each wine from the bottle, back to the barrel, fermentation bin and into the vineyard.
Crushpad provides grapes from top California and Bordeaux vineyards, an industry-acclaimed wine making team, and a state-of-the-art winery 100% focused on making wine in small lots. No matter where you live, you can now make your own wine.
In order to purchase these tickets in installments, you'll need an Eventbrite account. Log in or sign up for a free account to continue.


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Helena Christensen Defends Kim Kardashian, Calls Fat-Shaming 'Despicable'
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- Prev
As a supermodel and former Victoria's Secret Angel, Helena Christensen is used to people talking about her body. But that doesn't mean she likes it. In fact, she's more sensitive to other women's body-image struggles because of it. The public shaming of one woman, in particular -- reality star and mom-to-be Kim Kardashian -- has the 44-year-old Danish beauty all riled up.
In an open letter posted on Huffington Post, Christensen defends Kardashian against criticism of her weight and slams the recent bullying over her changing body as "sacrilegious." (As reported in the April 1 issue of Us Weekly, the five-months-pregnant 32-year-old has been compared to Shamu and called "huge" and "fat.")
"It is disgusting and despicable the way that certain media constantly harass the pregnant Kim Kardashian," Christensen writes. "It's enough that they persistently project a negative focus on women's physical shapes; but a public bullying and attacking of a pregnant woman because of her growing shape is just lower than low."
The model -- who played Chris Isaak's mesmerizing girlfriend in the 1991 music video "Wicked Game" and is now a successful photographer and clothing designer -- knows firsthand what pregnancy does to a woman's body. She has a 13-year-old son, Mingus Lucien, with ex-boyfriend Norman Reedus (currently starring as Daryl Dixon on "The Walking Dead").
"There should be some moral compass," she continues. "It doesn't matter who the woman is or what she does. No one should ever be publicly judged for their body, but to attack an expecting mother is sacrilegious and just plain wrong. A pregnant woman should not be criticized for her shape, period!!"
Kardashian's boyfriend, rapper Kanye West, agrees -- and happens to love the mom-to-be's new curves. "Kanye thinks Kim is gorgeous," a source told Us. "He just wants her to be happy in her own skin."
Added the mom-to-be herself in a recent interview with E! News: "He loves [my body] and just embraces it. And he's helped me to really feel sexy and embrace it."
Kim has a new baby name idea: Easton West
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Vehicle registration plates of Azerbaijan
Vehicle registration plates of Azerbaijan are usually composed of two numbers (identifying the vehicle registration department), a hyphen, two letters, a hyphen and three numbers (e.g. 10-JA-234), the plates are coloured black font on a white background. The plates are the same size as European plates and usually have an Azerbaijan flag and the initials 'AZ' on the left side.
According to Olavsplates, new style plates with a rectangular flag and a microchip are being introduced, but pictures of such plates are missing and very hard to find on the web.
Since January 2011 the Azerbaijan License Plate incorporates an RFiD TAG/chip, the RFiD TAG is placed on the lower left corner of the LP below the Azerbaijan national flag, in most plates the TAG has the "AZ" letters printed on. The TAG may move to the top right corner and lose the "AZ" printing on some of the more squared LP formats. The colour of the LP still varies depending on the vehicles usage and ownership.
The Portuguese company Porta Saber, Lda is supplying the License Plate RFiD TAG and the License Plate RFiD Reading System and Software.
Car designations[edit]
As with Turkish plates (which in turn adopted a reversed version of the former French license plate system), in Azeri plates the first two digits of the license plate represent the department, followed by a progressive 2-letter and 3-number system (progression starting with AA-001 and ending with ZZ-999). Below is a list of digits and relevant departments:
Types of Plates[edit]
Private vehicles[edit]
- Government Officials - Composed XX-AA-XXX
- Presidential Administration - Composed XX-PA-XXX
- President's Secret Service - Composed XX-PM-XXX
- Trailers - Composed the same way as usual Azerbaijan plates, but with no hyphen.
- Foreign series - Composed of a letter, three numbers a space and three more numbers.
See also[edit]
External links[edit]
Media related to License plates of Azerbaijan at Wikimedia Commons


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AOTA met with long-term-care facility leaders about productivity pressures.
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Web Letter
I happen to be an ex-Marine and served my county without hesitation, and when I read things like this it is the perfect example of weakness and how terrorist feed off it, what I suggest is that you get out of America if you can't handle the fact that as soon as the exstremist can nuke or get us that they will and no matter what you think that we can live in a peaceful world with them you are out of your mind.
One thing I know is that actions speak louder than words when it comes to dealing with them. So please don't insult me or my country anymore by sitting at your little safe desk and whining about it!
Alex Holder
Venice , VFL
Feb 24 2007 - 4:37pm