NATL INST OF STAND & TECH

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* NBS SPECIAL PUBLICATION 634

U.S. DEPARTMENT OF COMMERCE/National Bureau of Standards

Proceedings

of the

Waveform Recorder

Seminar
NATIONAL BUREAU OF STANDARDS

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Proceedings of the Waveform Recorder

Seminar

Proceedings of the Seminar on Waveform Recorder Measurement

Needs and Techniques for Evaluation/Calibration,

held'in Boulder, CO, Oct. 15, 1981.

Edited by

Robert A. Lawton

Electromagnetic Technology Division

National Bureau of Standards

Boulder, CO 80303

NATIONAL «JUAU

OF STANDARDS

LI BRART

JUL 1 9 1982

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

Issued June 1982
Library of Congress Catalog Card Number: 82-600552

National Bureau of Standards Special Publication 634

Nat. Bur. Stand. (U.S.), Spec. Publ. 634, 97 pages (June 1982)

CODEN: XNBSAV

U.S. GOVERNMENT PRINTING OFFICE

WASHINGTON: 1982
CONTENTS

Page

Background and Objective of Seminar v Seminar on Waveform Recorder Measurement Needs - Program vii

Workshop on Measurement Techniques for Characterizing Waveform Recorder Parameters, etc.,. . ix

Waveform Recorder Standards Steering Committee Organizational Meeting xiii

Recommendations on Direction of Emphasis for Standards Committee xv Comments on Seminar xv

Some Generic Waveform Recorder Problems 1 Steady State Tests of Waveform Recorders . 7 Characterizing the Dynamic Performance of Waveform Digitizers 23

Measurement of the Transient Versus Steady-State Response of Waveform Recorders 27 Calibration Techniques for a Large Computerized Waveform Recording System 35 Sampling-Rate Drift Problems in Transfer Function Analysis of Electrical Power Cables .... 47 Automatic Pulse Parameter Determination with the Computer Augmented Oscilloscope System ... 55 Status of Reference Waveform Standards Development at NBS 69

iii

BACKGROUND AND OBJECTIVE OF SEMINAR

Robert A. Lawton

In the past, for the most part, precision electromagnetic measurements were concerned with the

measurement of parameters for sinusoidal (or steady state) excitation and response, e.g., magnitude,

phase, and power. One reason for the popularity of frequency domain measurement was that in this

domain only one complete data point need be recorded to constitute a useful measurement. Recording

a thousand data points as required for precision time domain waveform measurements simply was not

feasible. Today such frequency domain measurements are still important but now share their

importance with transient pulse time domain measurements. With the emergence of integrated circuit

components for (1) sampling or analog to digital conversion, (2) storage, and (3) control, real time

digital waveform recording is now practical and widespread in usage. Furthermore, by coupling

waveform recording components to minicomputers and microprocessors integrated circuitry it is now

possible to record single events using compact systems (instruments) which acquire, record, process,

and analyze transient signals. In fact, the incorporation of digital computation integrated

circuitry appears to be a major driving force in expanding the role of waveform measurements in the

academic, industrial and scientific communities.

We at the National Bureau of Standards are charged with the responsibility of encouraging the

orderly development of consistent standards and measurement techniques. We have been actively

engaged in waveform standards development for some time now and the papers in these proceedings

will give a sample of what NBS and others in the waveform community have done already. The

afternoon session consisted of a workshop which addressed the questions: Where do we go from

here? and Why?, culminating in the selection of a steering committee for the development of

standards for waveform recorders.

Key words: converters; electromagnetics; encoders; pulse; waveform generation;

waveform measurements; waveform recorder; standards.

Papers by non-NBS authors have not been reviewed or

of Standards accepts no responsibility for comments

edited by NBS. Therefore, the National

or recommendations contained therein.

Bureau

SEMINAR ON WAVEFORM RECORDER MEASUREMENT NEEDS AND TECHNIQUES

FOR EVALUATION/ CALIBRATION

October 15, 1981

PROGRAM

8:30 A.M.

8:35 A.M.

8:45 A.M.

8:55 A.M.

9:20 A.M.

9:45 A.M.

10:10 A.M.

10:30 A.M.

10:55 A.M.

11:20 A.K.

Session: N. S. Nahman, Session Chairman

Welcoming Remarks. R. A. Kamper, Chief, Electromagnetic Technology Division, NBS,

724.00, Boulder, CO

Background and Objective of the Seminar, R. A. Lawton, Group Leader, Electromagnetic

Waveform Metrology Group, NBS, 724.04, Boulder, CO

"Some generic waveform recorder problems," N. S. Nahman, Senior Scientist, Electromagnetic Waveform Metrology Group, NBS, 724.04, Boulder, CO

"Steady-state tests of waveform recorders," D. R. Flach, Physicist, Electrosystems

Division, 722, NBS, Washington, DC

"Characterizing dynamic performance of waveform digitizers," Phil Crosby, TV Products

Engineering, Tektronix, Inc. , Beaverton, OR

"Measurement of transient versus steady state response of waveform recorders,"

T. M. Souders, Physicist, Division 722, NBS, Washington, DC

Coffee Break

"Calibration techniques for a large computerized waveform recording system,"

W. A. Boyer, Pulsed Power Engineering Division -4251, Sandia National Laboratories,

Albuquerque, NM

"Sampling-rate drift problems in transfer function analysis of electrical power

cables," J. D. Ramboz, Electrosystems Division, NBS, Washington, DC, A. R. Ondrejka,

Electromagnetic Technology Division, NBS, Boulder, CO, and W. E. Anderson, also of

the NBS Electrosystems Division.

"Automatic pulse parameter determination with the computer augmented oscilloscope

system," A. A. Guido, L. Fulkerson, and P. E. Stuckert, Technical Staff, IBM Watson

Research Center, Yorktown Heights, NY

vii
11:45 A.M. "Status of reference waveform standards development at NBS," J. R. Andrews,

N. S. Nahman, and B. A. Bell. J. R. Andrews, Picosecond Pulse Labs., Lafayette, CO formerly with NBS 724.04; N. S. Nahman, 724.04; B. A. Bell, NBS, 722 on assignment to NBS 724.04

12:10 P.M. Lunch

II. Afternoon Session: Workshop Leader, B. A. Bell

1:30-3:00 P.M. Workshop on measurement techniques for characterizing waveform recorder

parameters and properties, and waveform recorder standards development.

3:00 P.M. Coffee Break

3:30-5:00 P.M. Workshop continues

5:00 P.M. Adjournment

viii
Workshop on Measurement Techniques for Characterizing Waveform Recorder Parameters, Etc.

The following are official notes recorded at the workshop and consist of lists of problems

presently encountered in waveform recorder evaluation and why proper evaluation of these recorders

is important as suggested by the workshop attendees.

Don Flach, NBS Difficulty in obtaining effective number of bits (every time). Need stable

answers. Instruments are hard to use.

Mike Souders, NBS Difficulty in specifying a few significant figures of merit for dynamic range

(converters)

.

Bill Boyer, Sandia Serial correlation in samples.

John Ramboz, NBS Time base or sample time interval drift (change in waveform shape) for realtime and equivalent time.

Paul Stuckert, IBM Terminology and definiton of terms for waveform recorders.

J. R. Andrews, Pico- Characterizing the leading edge (H.F.) properties of waveform recorders,

second Pulse Labs.

Gordon DeWitte, EG&G

Los Alamos

Terms and Definitions

Reliable, readily available, inexpensive pulse standards,

David Hutton, EG&G

Los Alamos

A major problem is the lack of methods and tools for accuracy measurements

that can be translated into overall performance specs., i.e., one has to be

able to predict performance for any input from a small (presumably) number of

test measurements.

Bob Billings, LeCroy

Research Systems

Separation of stimulus/measurement artifacts from the device under test. Availability of measurement standards (hardware) at rational cost.

Nelson Cochrane,

EG&G, Las Vegas

There is a real need to develop various methods of characterization that will

allow someone to make measurements on his waveform recorder and know the

methods are valid.

Example: Is sinewave response calibration valid for making pulse measurements ?

Chuck McConaghy

Lawrence Livermore

National Lab.

Comparison of analog (scopes) and waveform digitizers. Is there some standard that will characterize both so that they can be compared?

Figure of merit for transient recorders to compare one against another.

Bits vs. frequency for example.

ix
Sedki M. Riad,

Virginia Polytech.

& State University

I believe that the time base drift problem is the most important one. One

can deal to a certain extent with almost all of the others on the list

except the time drift one.

Second in priority in my opinion is characterizing the leading edge HF

properties of the recorder. Characterizing the recorders distortion to the

waveform is more or less the same kind of thing.

Serial correlation in samples.

Terminology and definitions.

Pete Schuller, Real time and equivalent time samplers give rise to both amplitude and time

Tektronix time base distortion. Amplitude distortion is particularly severe for real

time scopes since they are usually used with large amplitude signals which

result in more serious thermal effects. Resonances due to more complicated

triggering arrangements also cause problems. Equivalent time samplers also

generate amplitude distortion. This is particularly true for random samplers

with large voltage excursions between adjacent sample points.

Lee Sandoval, EG&G, Environmental Specifications - our diagnostic instrumentation systems are Las Vegas housed in mobile trailers. Instrumentation real estate is very valuable

and we try to put as many recording instruments as we can into a trailer.

We have limited power and air conditioning available. We need specifications

on environmental specs which are meaningful and valid. We also need these

specs in determining what we need to do to operate these instruments in a field environment.

Repeatability We are recording diagnostic data from underground

Accuracy \ nuclear tests. Since we cannot rep-rate a nuclear

Reliability ' test, repeatability, accuracy and reliability are very important to us. We have but one chance to record this data.

M. D. Carlisle, EG&G, In addition to standardizing many of the common characteristics of waveform

Las Vegas recorders, a need exists for a formal definition of the environmental conditions relative to device performance. Associated with this is a need for

standardizing a- procedure for the determination of MTBF under REAL

conditions

As an end-user of various waveform recorders, and responsible for the

commitment of a large amount of Government capital dollars, these are factors

of great importance in large systems. NBS could provide a valuable service

in helping to establish these standards.

A major factor in the ultimate cost of a data acquisition system is the

maintenance of the equipment and the peripheral equipment required to

x
M. C. Carlisle, Cont. provide proper temperature, airflow, etc.

Fernando Herrera,

Kelly AFB, San

Antonio, Texas

Repeatability; My most current needs are in the area of ATE calibration.

Presently, I am working closely with AGMC Newark AFS, Ohio in developing

a PATEC (Portable Automatic Test Equipment Calibrator) package for 3 systems (consisting of 5 testers).

Tommy Thompson,

EG&G. Las Vegas

In order of importance:

o Difficulty in repeatility

o Environmental affects to the specifications

o Identifying errors that can be corrected

o Drift time and amplitude

o Absolute accuracy

Tommy Thompson,

EG&G, Las Vegas

In my particular application, data collection at Nevada Test Site,

reliability is of major importance. Some means of anticipating failure

modes would be of great help.

Another thought - calibration of the digital system (7912 AD's) consumes

about $100K of equipment and 90% of our software time. System calibration

is expensive and time consuming, anything that would decrease the cost and

time would be helpful.

Jim Sorden, HP

Santa Clara, CA.

Objective measures are needed that will help skilled and nonskilled (users,

workers) in comparing instruments.

Bill Boyer, Sandia People will come and say the scope is broken and one has to prove that it is O.K. and to do that I want reliable information about the measurements.

Mike Carlisle, EG&G A device doesn't exist which can evaluate high speed diagnostic equipment.

Tommy Thompson, EG&G Applying the same source waveform to digital (such as 7912 's) and analog

instruments (such as oscilloscopes) gives different results. The average

difference is 5 to 7%. We calibrate to a system accuracy of 3%. The

discrepancy is probably not due to the plugin.

Mike Souders, NBS

Dave Hutton, EG&G

What is really required is bits per speed (conversion time).

Need to be able to evaluate recorders with 1 Gigasample per second, 200 MHz analog band width capability. The characterization must be inexpensive and

capable of 8 bits absolute accuracy. Seven bits of absolute accuracy can be

shown to yield useful physical data related to weapon yield. Other experiments require 10 gigasamples per second with less absolute accuracy.

Jim Sorden, HP The spectrum should be extended to D.C. There are medical diagnostic sonar, electromechanical and other applications on this end of the spectrum.

xi
Jim Sorden, Cont. Measurement evaluation techniques should be designed with not only skilled,

but also nonskilled operators in mind.

Bruce Peetz, HP One needs to have some idea how much worse than ideal any given instrument

is and how polluted the measured waveform is. These requirements are specifically different than simply determining whether the instrument is in

the failure mode. .

Some Specific Tests and Other Developments Needed.

Dave Hutton, EG&G o Differential linearity, ramp function, random trigger, histograph of

values

.

o Asynchronous techniques can be used to generate statistics. The result

should be flat. If it is not, look for a malfunction.

o Use a video A/D and record a sine wave. Perform the FFT and look at the

power outside the fundamental. This can be used to throw away bad A/D

recorders

.

Steve Hessel, HP o Look at the time evolution of error after transition. The current need is

-80 dB after 4 nanoseconds. The projected need is -80 dB after 500 picoseconds .

Barry Bell, NBS As with waveform recorders, sampling techniques are used in the measurement channels of modern ATE. Therefore, valid methods and standards are required for characterizing/calibrating multichannel ATE systems.

John Ramboz, NBS o A better time base.

A vigorous theoretical analysis with a variety of analytic functions to relate time base drift to the resulting error in the frequency domain and

determine the feasibility of applying corrections.

xii
1. Is the timing right? Consensus = "yes".

2. What should be the charter? Consensus = "Develop standard way of characterizing both analog

and digital waveform recorders for both real and equivalent time sampling.

3. Where and how often should the committee meet? Consensus = hold committee meetings and continue

the seminars in connection with other conferences such as the Fast A/D converter conference and

the Conference on Precision Electromagnetic Measurements (CPEM) . The first steering committee

meeting will be held in conjunction with the next Fast A/D Converter meeting February 15, 1982

in Santa Clara, California. The next Seminar will be held in conjunction with the next CPEM

meeting June 28-July 1, 1982 in Boulder, Colorado.

4. Suggested sponsors? Instrumentation and Measurement Society of IEEE; Power Engineering Society

Subcommittee on Digital Techniques; and International Electrotechnical Commission.

5. Who will be on the committee?

1. William B. Boyer

Sandia National Laboratories

Division 4251

Albuquerque, NM 87185

2. Mr. Don Campbell

Lawrence Livermore National Laboratory, L-473

P. 0. Box 5508

Livermore, CA 94550

3. Gordon DeWitte, Eng. Spec.

EG&G, Inc.

P. 0. Box 809

Los Alamos, NM 87544

4. David George

Naval Research Lab.

Orlando, FL

5. Fernando Herrera, Jr. Electronics Engineer

SA-ALC MATTE

Kelly Air Force Base, TX 78241

xiii
6. J. David Hutton

Scientific Specialist

EG & G, Inc.

P. 0. Box 809

Los Alamos, NM 87544

7 . Roydn Jones

Tektronix Mail Station 50-383

P. 0. Box 500

Beaverton, OR 97077

8. Mr. Louis Navarro

Tektronix Mail Station 39-133

P. 0. Box 500

Beaverton, OR 97077

9. Bruce Peetz

Hewlett Packard Co. 5301 Stevens Creek Blvd.

Santa Clara, CA 95050

10. R. Clayton Smith

Electronics Reaction History Group

Los Alamos Scientific Laboratory

University of California MS 410

Los Alamos, NM 87545

11. Christian E. Somers

Product Manager

Gould, Inc. 4600 Old Ironsides Drive

Santa Clara, CA 95050

12. James L. Sorden

R&D Section Manager

Hewlett Packard

5301 Stevens Creek Blvd.

Santa Clara, CA 95050

12 . Mike Souders

National Bureau of Standards

Division 72^

Metrology A-165

Washington, DC 20234

xiv
13. Paul E. Stuckert

Research Staff Member

IBM Research Center

Box 218

Yorktown Heights, NY 10598

Recommendations on Direction of Emphasis for the Standards Committee

Bill Boyer o I think standards should be oriented towards defining figures of merit and

test methods as independent as possible of the recording technique.

Sedki Riad o I would like to see both real time and equivalent time devices included

and I feel that the problem of analog vs. digital outputs is not a very

critical issue. However, I am leaning to support the digital output since

there is not much you can do with an analog one.

Comments on Seminar

Bill Boyer I would like to see more talks on new recording techniques and specific test methods

.

Fernando Herrera This seminar was very well presented. Overall, I have learned some aspects

which are applicable in my area of concern.

Lee Sandoval The seminar was useful. I would like to see more papers presented.

Tommy Thompson In general I felt the seminar was useful and informative.

xv

Some Generic Waveform Recorder Problems

N . S . Nahman

Electromagnetic Technology Division

National Bureau of Standards

Boulder, Colorado 80303

Because of physical limitations the waveform displayed by a waveform

recorder is not an exact replica of the signal or pulse applied to its input.

The term physical limitations pertains to the network and electronic-device

effects which can slow down and/or otherwise distort the shape of an applied

pulse or transient signal. The limiting factors can be roughly grouped into two categories (1) bandwidth or signal distortion limitation and (2) analog to digital conversion limitations. A brief discussion of these limitations is

given to provide some insight into the technical topics to be discussed by the

remaining seminar speakers.

Key Words: Errors; pulse measurements; time domain measurements; waveform

measurements; waveform recorders.

The basic reason for having this seminar is that the term pulse is not synonomous with the term

waveform. The IEEE and IEC Pulse Standards, "Glossary of Pulse Terms and Definitions" defines Pulse

as the physical modifications of state, and Waveform is the observed or measured shape of the pulse

[1-4]. Clearly, the physical entity, the pulse, always does differ to some degree from the

observable entity, the waveform.

The question that this seminar inherently poses is "How do we characterize the ability of a waveform recorder to provide an output that is a replica of a single-shot (or single-occurrance)

time varying signal applied to its input?" The term single shot specifies that the recorder

acquires the signal in real time as opposed to equivalent-time as encountered in sampling

oscilloscopes

There are many factors that must be considered in order to answer this question in any given

case. The speakers following me will present various aspects and methods for characterizing such

recorders - of course, what is presented here today will not be all inclusive, but will present some

of the techniques that have proved to be useful in specific cases.

The purpose of the present paper is to provide a perspective or framework for relating the

various ideas discussed by the other speakers. First of all, here is my definition of a waveform

recorder

A WAVEFORM RECORDER is a time domain

measurement instrument that is capable

of recording in real-time a physical Pulse

or Transient and steady-state signals,

and provides a Stored (Digital)

Electronic output.

1
Notice that the word digital appears in parentheses; from my perspective, the stored electronic

output could be an analog one even though today's fashion requires a digital output. Furthermore,

my guess is that most of you think in terms of a stored digital electronic output.

To emphasize the fact that the recorded information is never exactly identical to the input

signal, the term PULSE is used for the input analog signal while WAVEFORM is used for the stored

electronic output, Figure 1. These definitions are those required by the IEEE/IEC Standards [1-4].

Pulse or Transient

Analog Input

Stored. Electronic Output

(shown as digital)

Waveform

Recorder

IEEE PULSE IEEE WAVEFORM

Figure 1. The physical PULSE and its observed WAVEFORM

The output WAVEFORM is not identical to the input PULSE because:

1. a finite set of discrete points can not exactly represent an analog

transient signal.

2. the set of WAVEFORM discrete points overlays a distorted version

of the input PULSE.

At best we could have the discrete points exactly overlayed on the PULSE, Figure 2.

Figure 2. The discrete waveform points are exactly overlayed on the pulse.

2
However, in an actual case we always have error, Figure 3. To some degree, the discrete waveform

points are approximately overlayed on a distorted version of the PULSE.

Error Bars

Figure 3. To some degree, the discrete waveform points are approximately overlayed on a distorted

version of the pulse.

Consequently, it is possible to say at least in a qualitative sense that there are two generic

problems or categories underlying waveform recorder errors:

1. Distortion

2. Digitizing Errors

Distortion has its roots in analog processes and their time and frequency domain properties.

On the other hand, digitizing errors, i.e., incorrect output digital value for a given sample,

result from a mixture of digital and analog circuit errors. Note that here the term

digitizing-errors includes more effects than the usual definition based upon digital round-off

errors. At first glance, the cause appears to be an analog one in the sample and hold circuitry,

but a little thought brings one to the conclusion that that digital errors due to digital conversion

speed are also limited by analog processes in the digital circuitry. Figure 4 is an attempt to diagram where DISTORTION and DIGITIZING ERRORS occur in a waveform recorder, and to catalog the

processes and symptoms relevant to distortion and digitizing errors. In Figure 4, the notation T and/or F in parentheses following each item under distortion denotes that time-domain distortion

and/or frequency-domain distortion results from the specified effects. In the case of sampling rate

effects, only the frequency domain properties are affected when the time domain samples exactly lie

upon the PULSE, Figure 2. With all samples exactly overlayed on the PULSE, the time domain

distortion is zero; however, the number or density of points affects the Fourier transform or frequency domain properties as compared to the frequency domain properties of the analog PULSE.

In summary, a waveform recorder definition has been presented along with the IEEE Standard

terms PULSE and WAVEFORM which specify the input and output signals, respectively, of the waveform

recorder. The output WAVEFORM is not an exact replica of the input PULSE due to physical

3
s

W

CO5

w

CO

4
limitations in the waveform recorder passive and active circuitry. The errors or circuit problems

have been divided into two generic classifications: (1) DISTORTION and (2) DIGITIZING ERRORS. A

waveform recorder block diagram was given to provide a structure for illustrating the areas where

distortion and digitizing errors occur.

REFERENCES

1. "IEEE Pulse Measurement and Analysis, General Considerations", IEEE Standard 181-1977, The

Institute of Electrical and Electronic Engineers, N.Y., N.Y. July 22, 1977.

2. "IEEE Glossary of Pulse Terms and Definitions", IEEE Standard 194-1977, The Institute of

Electrical and Electronics Engineers, N.Y., N.Y., July 26, 1977.

3. "IEC, Pulse Techniques and Apparatus, Part I: Pulse Terms and Definitions, Publication No. 469-1, First Ed., International Electro-technical Commission, Geneva, Switzerland, 1974.

4. "IEC, Pulse Techniques and Apparatus, Part II: Pulse Measurement and Analysis General

Considerations", Publication No. 469-2, First Ed., 1974, International Electro-technical

Commission, Geneva, Switzerland, 1974.

5

Steady State Tests of Waveform Recorders

D. R. Flach

National Bureau of Standards

Washington, D.C. 20234

Sinusoidal stimuli are often used for the dynamic testing of waveform recorders and

fast analog-to-digital converters. This approach has the advantages that sinewaves are well-defined signals, and are easily generated over a wide frequency range with parameters

that are readily measureable. Two methods are presented for analyzing the data from such

tests, and two resulting figures of merit, the rms signal-to-noise ratio (S/N ratio) and the

effective number of bits, are discussed. In the frequency domain, the S/N ratio is obtained

from the magnitude spectrum, which is calculated by performing a Fast Fourier Transform on a set of m code words weighted with a Hanning window. In the time domain, a sinewave is fitted

to the set of data words, using a nonlinear least squares computation. The fitted curve is

then compared with the original digitized data to calculate the S/N ratio. The results of

sinewave tests on different types of waveform recorders are presented, along with a comparison

of time domain and frequency domain analysis of the data. The influence of two specific

types of analog-to-digital errors on the resulting S/N ratio are computed and presented as examples.

Key words: analog-to-digital converter; digitizer; dynamic testing; effective number of

bits; frequency domain; quantizing error; signal-to-noise ratio; time domain; transient

recorder.

1. Introduction

One method for the dynamic testing of waveform recorders and fast analog-to-digital

converters is to apply a periodic waveform to the input and analyze the performance of the test unit

by using digital signal processing on the output data [1-4]. Sinusoidal stimuli of high purity

that are uncorrelated with the sampling frequency are often used for this purpose since they are well-defined signals easily generated and characterized over a wide frequency range. Figure 1 shows a test system with a sinusoidal input as the stimulus. The final output from this test is

the rms signal-to-noise ratio (S/N ratio) or a related number, the effective number of bits of

the instrument. As will be shown later, the quantizing error of an ideal n-bit waveform recorder

results in a S/N ratio of 6.02n +1.76 decibels. Deviations from this ideal value are an indication

that there are errors in the test instrument in addition to the inherent quantizing errors associated

with an ideal digitizer. Using the measurement approach indicated in figure 1, the S/N ratio can

be calculated from the digital output code using either frequency or time domain analysis.

In the frequency domain, the S/N ratio is calculated from a set of m output code words, where

m is a power-of-two from 16 to 1024, by weighting the data with a Hanning window, and performing a Fast Fourier Transform to obtain the magnitude spectrum needed for the calculation. In the time

domain, where the power-of-two restriction does not apply, a sinewave of the form y = A + B sin (CX+D)

is fitted via a nonlinear least squares computer program to the digital output data, and this

fitted curve is compared with the original digitized data to calculate the S/N ratio. Finally,

the concept of the "effective number of bits" of the test instrument can be employed. If a waveform recorder behaves like a perfect digitizer, then its only error is the quantizing noise.

If the S/N ratio is measured, the effective number of bits n^ can be calculated from

(S/N) measured = 6.02ni + 1.76.

7
2. Quantizing Error

In figure 2 the transfer function of an ideal 3-bit analog-to-digital converter is shown

along with the quantizing error or noise of the converter. Let Q = the voltage corresponding to one least significant bit (LSB) of the converter, FSR = full-scale range of the converter, then

Q = FSR/2 n for an n-bit converter. For each digital output code word there is a continuum of

analog input voltages that range from -Q/2 to +Q/2. The quantizing error is the difference

between the analog input and the analog value computed from the digital output code. As shown

in figure 2, the quantizing error can be represented as a sawtooth waveform with amplitudes from

+Q/2 to -Q/2 in each quantizing interval . As illustrated in figure 3, the rms value of this

waveform is calculated to be Q//12.

3. RMS Signal-to-Noise Ratio

Let S = V//2 be the rms value of a sinewave input signal of peak value V.

If V is a full-scale input signal applied to a bipolar range digitizer, then

s

= FSR _ Q2

n

2/2 2/2

LetJN be the rms quantizing error or noise of the digitizer, which has been shown to be equal to Q//12, then the S/N ratio of this ideal n bit digitizer is

S/N Q(2

n

" 1 )//2

Q//T2

and in decibels, 20 log(S/N) = 6.02n + 1.76.

For a signal V less than full scale,

or, in decibels

S/N . 2 "-< « ^R

20 log (S/N) = 6.02n + 1.76 + 20 log j^L.

4. Computation of S/N Ratio in Frequency Domain

The S/N ratio was computed using the Fast Fourier Transform by taking the rms value of the

largest signal spectral line and dividing it by the rms value of the remaining lines. The

magnitude of the Kth spectral line is given by

= ^(Kth real coefficient) 2 + (Kth imaginary coefficient) 2

and the S/N ratio by

S/N _ rms value of largest signal spectral line .

' rms value of remaining lines

The K = 1 line corresponds to the dc component and is omitted. Separate static tests can be used

to examine and identify the effects of dc offset errors.

8
It was also found necessary to introduce other correction factors to compensate for errors caused by the use of a window function. Since there are generally not an integral number of

periods of the input waveform in the data window due to the power-of-two restriction, a tapering

or window function [5] is applied to the data set to reduce the leakage phenomena. Even when

using a Hanning window function of the form y = 0.5 (1-cosx), spectral leakage into adjacent

frequencies is not completely eliminated. This is illustrated in figure 4 for the worst case where the number of periods in the data window is an integer plus one-half. A number of spectral

lines on each side of the fundamental are deleted from the noise computation because they are contaminated with leakage from the fundamental. The noise is computed from the equation

To establish an average value or "noise floor" of in the ideal case, consider all Mj^'s = M,

and let N = Q//12.

In figures 10 and 12, the data is scaled to a range of ±1 voTt to allow comparison of different

test ranges; M =-89.1 dB for these figures. Thus, based on result s ob tained from the graph

shown in figure 4, spectral lines with amplitudes greater than 2Q//12m were not included in

the noise computation.

Also associated with the window function is the processing loss, which is a fixed value

as depicted in figure 5. This figure shows the spectrum of the function y = sin 4X + sin 32X

where there is an integral number of periods in the data set, and no tapering function is applied,

which is equivalent to using a rectangular window. If sin 4X is considered to be the signal,

and sin 32X the noise, then the S/N ratio is zero dB. After a Hanning window function is applied

to the same data set, and the identical set of computations are performed, the resulting S/N

ratio is -1.76 dB. If the number of periods in the data set is not an integral number, an additional error is incurred which varies with the remaining fractional period and is a maximum

at 0.5 period. This pickett fence or scallop effect is depicted in figure 6 when a Hanning

window function is used, and has a maximum value of -1.42 dB. For an integral number of periods

in the data set, the measured value of the fundamental (and other periodic functions) will be one- half (-6.02 dB) of the actual value. As the remaining fractional period in the data set increases

from zero to one-half, this attenuation increases from -6.02 to -7.44 dB. If the fractional

number of periods in the data set is known, a correction can be applied for this effect.

Another result of using the Hanning window is that if a dc offset exists in the data, this

introduces a low frequency component into the first line (K = 2) of the spectrum. Therefore, this

line was also deleted from the noise in these calculations. Finally, a factor was used that

multiplied the measured noise by a number proportional to the number of spectral lines deleted

around the fundamental to compensate for the lost lines. This factor was

Then

and

M = 2Q//12m.

H = yjlW(m -2 (number of deleted lines)).

9
H can cause an error in the noise computation if, for instance, one spectral line contributes

the majority of the noise. This line then gets weighted by the factor H, and the resulting noise

computation is too high.

5. Computation of S/N Ratio in Time Domain

An alternative to the frequency domain method is to analyze the data in the time domain [6].

This approach involves fitting a sinewave of the form y = A + B sin (CX + D) to the digital

output code from the waveform recorder using a nonlinear least squares fit program [7]. This

fitted curve is then assumed to represent the original input waveform. A fit of a sinewave to a set of digital output codes is shown in figure 7. For the ideal digitizer, the residuals (fitted curve - output code) should fall within the range of ±0.5 LSB. The S/N ratio is then calculated

from

and the effective number of bits can be calculated as previously shown, or from the equation

Nonlinear curve fitting requires preliminary estimates of the parameters A, B, C, and D; the closer the initial guess the faster the program converges to a final value. A pre-fit program

estimates these parameters (offset, amplitude, frequency, and phase) from the maximum data point,

minimum data point, and the zero crossings. A commercial software regression analysis package

based on Marquardt's nonlinear least squares method then performs a fit of the data to the sinewave

function.

The residuals from an ideal 4-bit simulation are also shown in figure 7. Figure 8 is a computer printout of results based on a 10-bit simulation, with the errors expressed in LSB's.

This printout gives the ideal value of the S/N ratio for a full-scale input (61.96 dB) and also

the ideal value computed from the 90 percent of full-scale amplitude (61.05 dB), as determined

by the equations given in section 3. The measured value of S/N ratio (60.95 dB) was determined

using the curve fit routine and for a perfect digitizer, should be equal to the ideal 90 percent

of full-scale value. The maximum error is 0.525, and the rms error is 0.292, which is close to the theoretical value of Q//12 = 0.289.

6. Effect of Errors On S/N Ratio

The effects that some types of errors have on the S/N ratio have been analyzed by modeling

with a computer an n-bit successive approximation, offset binary coded analog-to-digital converter.

The first type of error studied involves a one LSB quadratic nonl inearity, shown in figure 9. The error function Q-QX^ is the deviation from the ideal transfer characteristic caused by a nonl inearity in the converter. The input variable X is normalized and has the range -1 to +1.

For an input of the form X = A sin wt, this error could be expected to produce a second harmonic

spectral line in the output spectrum which has an rms value of Q/2/2 for a full-scale input

voltage. The value of the noise can then be computed as being approximately equal to

20 log(S/N) - 20 log rms (amplitude fitted sinewave)

rms (sum of residuals)

n-, = n - log rms (sum of_resi duals) . Q//T2

* Vq2 /12 + (Q/2/2T2 = 0 46Q

and the S/N ratio should be

20 log(S/N) = 6.02n - 2.3 dB.

10
For the simulation results given in figure 10, the internal digital-to-analog converter of the

model was assumed to have a one LSB quadratic nonl i neari ty . For a 10-bit digitizer, a value of

57.9 dB is calculated compared with ~58.0 dB obtained with the simulation.

The second type of error studied involves bit errors, an example of which is a one LSB error in

the second bit as shown in figure 11. As in the previous example, N is the rms total of the quantizing

noise and other errors, given by

While this computation gives the correct value for the noise produced by an error in bit 2,

a S/N ratio test will give a lower value. Such tests fail to take into account that the spectra

associated with the cyclic occurrence of the second bit contains a fundamental frequency component

of the applied sinusoidal input. Therefore, this fundamental component is necessarily measured

as signal rather than noise, producing an overestimate of true S/N ratio. This situation exists

for other bit adjustment errors also, for instance, the cycling of bit one (most significant

bit) follows a square wave of the same frequency as the applied sinusoidal input. If this bit

has an adjustment error of 1.0Q, then the rms contribution to the fundamental spectral line caused

by this error is 0.45Q, and the rms sum of the contributions of all remaining spectral lines

is 0.22Q. As an example, a simulation with a 10-bit converter having a one LSB error in the

second bit produced a S/N ratio of 57.1 dB which compares with 55.9 dB, calculated using

N = 0.58Q. Numerous other errors can also be expected to affect the S/N ratio.

7. Test Results

Three waveform recorders were tested with both time domain and frequency domain analysis

of the data. Due to computer memory limitations, a maximum of 256 data points were

fitted by the time domain method. Fast Fourier Transforms were performed on 1024 data points,

and subsets of these were used in the time domain solutions. Runs were made at various test

frequencies, and in many cases amplitudes of both 50 and 90 percent of full scale were used.

Figure 12 shows the results of a frequency domain test on a 10-bit recorder which had a maximum sampling rate of 500 kHz. Figure 13 is a plot of the residuals from the curve fit for

this test; a four LSB outlier is easily seen. A printout from the time domain analysis at a different frequency is shown in figure 14. Note that the maximum outlier has become slightly

smaller, as reflected by the larger number of effective bits.

Plots of the effective number of bits vs frequency are shown in figures 15 through 17.

Data from the 500 kHz 10-bit recorder plotted in figure 15 shows the 90 percent of full-scale

values gave better results than the 50 percent of full-scale values. Data from a medium speed

10-bit recorder with a maximum sampling rate of 10 MHz is plotted in figure 16. Finally, data

from an 8-bit 100 MHz recorder is shown in figure 17. Glitches observed in the output data

at the faster sampling rates probably account for the deterioration in the effective number of

bits at higher frequencies. These instruments were not tested at frequencies greater than

one-fifth of the maximum sampling rate.

8. Conclusions

The above tests show that the time domain and frequency domain methods of calculating the

effective number of bits give similar results. The frequency domain approach is computationally

faster by virtue of Fast Fourier Transform routines, but restricts the number of data points to

a power-of-two. The time domain method has no restriction on the number of data points, does not

require a window function to control leakage, but does require subjective decisions by the operator

in estimating a preliminary fit of the data, and is susceptible to a poor fit if not monitored.

Harmonics of the fundamental input frequency are easily identifiable in the frequency domain

method, but are difficult to detect from a time domain curve fit. Outliers in the data set are difficult to detect in the magnitude spectrum resulting from the frequency domain method, while a simple examination of the residuals computed from the time domain curve fit will easily point

these out. Both methods obscure errors that result in fundamental frequency components as described

in section 6.

11
9. References

[1] Pretzel, G., Dynamic testing of high-speed A/D converters. J. Solid-State Physics.

SC-13(3): 368-370; June 1978.

[2] Burton, P. B., Checking A/D converter linearity analog dialogue. 13(2): 10; 1979.

[3] Pratt, B., Test A/D converters digitally. Electronic Design. 25: 86-88;

December 6, 1975.

[4] Ramirez, R. W., Digitizer specifications and their applications to waveforms.

Electronics Test. 4(9): 74-80, September 1981.

[5] Harris, F. J., On the use of windows for harmonic analysis with the discrete

Fourier Transform. Proc. IEEE. 66(1): 51-83; January 1978.

[6] DeWitt, L., Dynamic testing reveals overall digitizer performance. Handshake,

Tektronix Publication: 9-12; 1981, Spring/Summer.

[7] Daniel, C; Wood, F. S., Fitting equations to data. New York: John Wiley

and Sons; 1980, 458 p.

LIST OF FIGURES

Figure 1. General measurement approach

Figure 2. Quantizing error of ideal converter

Figure 3. Quantizing error calculation

Figure 4. Leakage effect from Hanning window

Figure 5. Hanning window processing loss

Figure 6. Hanning window - pickett fence effect

Figure 7. Time domain approach: sinewave fit to output data, and determination

of residuals

Figure 8. Results of time domain analysis of an ideal simulated, 10-bit recorder

Figure 9. Quadratic nonlinearity error

Figure 10. Spectra of a 10-bit recorder having quadratic nonlinearity shown in fig. 9.

Figure 11. Second bit error

Figure 12. Frequency domain test results: 10-bit recorder with maximum sampling rate of 500 kHz

Figure 13. Residuals from time domain test: 10-bit recorder with 500 kHz sampling

rate, 1 kHz test frequency

Figure 14. Results of time domain analysis of 10-bit recorder with maximum sampling

rate of 500 kHz

Figure 15. Results from both time and frequency domain tests: 10-bit recorder

with 500 kHz sampling rate

Figure 16. Results from both time and frequency domain tests: 10-bit recorder

with 10 MHz sampling rate

Figure 17. Results from both time and frequency domain tests: 8-bit recorder with

100 MHz sampling rate

L2
SINE

WAVE

SOURCE

ANTIALIASING

FILTER

)

WAVEFORM

RECORDER

r >

PIGITAL

SIGNAL

PROCESSING

Figure 1. General measurement approach

IDEAL 3-BIT A/D CONVERTER

UJo

o

3

£LI-3

O

0.5 1.5 2.5 3.5

INPUT VOLTAGE

UJ3

QUANTIZING ERROR

C-T/2.Q/2)

H ONE QUANTIZING INTERVAL

E=-QX/T FOR

X FROM -T/2 TO T/2

'runs T/2

-C1/T) E

2dX Q2/12

-T/2

Figure 2. Quantizing error of ideal converter

Figure 3. Quantizing error calculation

13
14
FOURIER SPECTRA

RECTANGULAR WINDOW

0 Y=SINC4X)+SINC32X)

S=SINC4X>

N=SINC32X5

20LO6CS/N>=20LOGC 1/O=0 DB

32

HANNING WINDOW

S=0 .5/VT

N=V 0 . 25T2+0 . 5T2+0 . 25T2/VT

20LO6CS/N}=-1 .76 DB

Figure 5. Hanning window processing loss

DB ATTENUATION

5.5

6.0

6.5

7.0

7.5

FRACTIONAL PART OF

PERIOD IN WINDOW

Figure 6. Hanning window - pickett fence effect

15
OUTPUT CODE

IN LSB's

16

LSB's

RESIDUALS

+0.5

-0.5

«*

* it

* * *

* ***

* *

TIME

Figure 7. Time domain approach: sinewave fit to output data, and determination

of residuals

************ TIME DOMAIN ANALYSIS ***************

OF A SINE WAVE INPUT TO A DIGITIZER

IDEAL rms S/N RATIO FOR A 10 BIT CONVERTER WITH

A FULL SCALE SINE WAVE INPUT IS 61.96 DECIBELS

MEASURED rms S/N RATIO IS 60.95 DECIBELS

EFFECTIVE BITS ARE 9.984

FOR THE 90.00 PERCENT OF FULL SCALE SINE WAVE

USED IN THIS TEST.. THE THEORETICAL rms S/N RATIO

IS 61 .05 DECIBELS

MAX POSITIVE ERROR IS 0.498659

MAX POSITIVE ERROR LOCATION IS 185

MAX NEGATIVE ERROR IS -0.524760

MAX NEGATIVE ERROR LOCATION IS 165

RMS ERROR IS 0.291913

10 BIT SIMULATION

256 DATA POINTS

8.274 PERIODS

Figure 8. Results of time domain analysis of an ideal simulated, 10-bit recorder

L6
r>

a.

h-3O

H

CDH

7 FULL

8 SCALE

ANALOG INPUT

Figure 9. Quadratic nonlinearity error

AMPLITUDE

PECIBELS

ar

-20"

-40-

-60"

-60"

-I 00

FAST FOURIER TRANSFORM MAGNITUDE SPECTRUM

ONE LSB QUADRATIC NONLINEARITY

INPUT « 99X OF FULL SCALE

PERIODS: 55.60

S/N RATIO: 57.96 DB

EFFECTIVE BITS= 9.35

1 92 253 320

SPECTRUM LINE NUMBER

Figure 10. Spectra of a 10-bit recorder having quadratic nonlinearity shown in fig. 9.

17
AMPLITUDE

DECIBELS

0 r

-20

-40

-60 -

-80

-100

FAST FOURIER TRANSFORM MAGNITUDE SPECTRUM

RMS S/N RATIO TEST

IB BIT £00 KHZ RECORDER

FS TEST RANGE IS 10.00 VOLTS SINUSOIDUAL INPUT IS 2.56 VOLTS

INPUT FREQUENCY IS E0 KHZ SAMPLING RATE IS 530 KHZ TAPER- 0.50

NUMBER OF DATA POINTS IS 1024 THEORETICAL S/N BASED ON AMPLITUDE IS 56.15 DB MEASURED S/N RATIO- 47.17 DB EFFECTIVE BITS- 8.509

OCT. 1981

SPECTRUM LINE NUMBER

Figure 12. Frequency domain test results: 10-bit recorder with maximum samplinq rate of 500 kHz

18
ERROR

LSB'S

RESIDUALS

+ 1.0-

0.0

* **

x Tt * ,~ * x*

* J£ * * * »t ** **

it**

-1 .0 "

-2.0 -

-3.0

it *

itit

*~ »% it

. it it

** * *

it *

it X* * ***

it*

it* *

:X *M * *

X

XXX ^ 7TX

it **

-

it

**

it *> *

-4.0

0 32 64 96 128

TIME

',] (68 192 224

Figure 13. Residuals from time domain test: 10-bit recorder with 500 kHz sampling

rate, 1 kHz test frequency

************ TIME DOMAIN ANALYSIS ***************

OF A SINE WAVE INPUT TO A DIGITIZER

IDEAL rms S/N RATIO FOR A 10 BIT CONVERTER WITH

A FULL SCALE SINE WAVE INPUT IS 61 .96 DECIBELS

MEASURED rms S/N RATIO IS 49.78 DECIBELS

EFFECTIVE BITS ARE 8.957

FOR THE 50.64 PERCENT OF FULL SCALE SINE WAVE

USED IN THIS TEST. THE THEORETICAL rms S/N RATIO

IS 56.06 DECIBELS

MAX POSITIVE ERROR IS 1 . 386669

MAX POSITIVE ERROR LOCATION IS 134

MAX NEGATIVE ERROR IS -3.230074

MAX NEGATIVE ERROR LOCATION IS 176

RMS ERROR IS 0.594861

10 BIT RECORDER MAXIMUM SAMPLING RATE 500 KHZ

INPUT 10 KHZ, SAMPLING RATE 50 KHZ

FSR 10 VOLTS, 256 DATA POINTS

Figure 14. Results of time domain analysis of 10-bit recorder with maximum sampling

rate of 500 kHz

19
Figure 15. Results from both time and frequency domain tests: 10-bit recorder

with 500 kHz sampling rate

EFFECTIVE BITS VS. FREQUENCY

10

9

6

i

^ 50*

r—

i

90% -» Ni Q

o-FFT

o -TIME

DOMAIN

1 KHZ 18 KHZ 108 KHZ 1 MHZ

Figure 16. Results from both time and frequency domain tests: 10-bit recorder with 10 MHz sampling rate

20
EFFECTIVE BITS VS. FREQUENCY

8

7 h

2.

i

i

p=

,

5

i

>

o -FFT

-TIME

DOMAIN

0.01 MHZ 0.1 MHZ 1 MHZ 10 MHZ

Figure 17. Results from both time and frequency domain tests: 100 MHz sampling rate

8-bit recorder with

)

21

CHARACTERIZING THE DYNAMIC PERFORMANCE OF WAVEFORM DIGITIZERS

Philip S. Crosby

Tektronix , Inc . The obvious question that comes to mind when one considers using a waveform digitizer for a specific application is: "Is it good enough?".

The answer to that question has two states; yes or no. However, the number

of states that the code sequence of a digitizer can occupy can become

astronomical in a pretty short time. Thus, the characterization of a digitizer must become an exercise in data reduction, coupled with careful con- sideration and selection of allowable test stimuli. The test stimulus

should have low entropy, that is, the number of coefficients needed to

describe it fully should be small in number.

There is very little that can be said about a sinewave; this will

be shown to be of considerable advantage for our purpose. In an absolute

sense, the only two properties that a sinewave has are amplitude and frequency. However, a sinewave applied to a digitizer must be represented

by two additional properties, phase and D.C. offset. Therefore, we can perhaps envision a process downstream from the digitizer where the operator might push a button marked "sinewave" and out come the four numbers:

Amplitude - A Phase - 0 Frequency - F D.C. Off est - D These values having been computed from a sample sequence:

{s}

It is obvious that sequence {s} must contain at least four terms,

but the upper limit on the number of terms is unbounded.

Now, if we distrusted magic buttons and wanted to see if the se- quence, {s}, really produced those values, we could work backwards.

ts}. . = D + A-Sin( { i

}

• F + 0) test

Where

{i} = 0, 1 • 2n , 2j_2_k , ... , (N-l )

• 2 n FNs FNs FNs And

F

g = sampling frequency

N = number of samples in sequence {s}

This enables us to produce an error sequence, .{e}

{e} = ROUND( {s } . . ) - {s

}

test

Where the function, ROUND, is a rounding function.

It can be shown that the function tied to the button marked "sinewave"

can be recursively optimized by recycling {s} - ^ s ^ test through the function

and updating the coefficients A , F , (21 , and D until the R.M.S. value of

{s} -{ s i test has sensibly reached a minimum value. At this point, the R.M.S.

value of {e} should express the sample-by-sample difference between the

digitizer being used and an ideal digitizer, providing the errors in the

digitizer do not cause the measured parameters A , F , 0 , and D to systematically interact.

23
Comparisons between this method and more complex methods that

place restrictions on frequency or phase values and/or require sample

sortinq have indicated that this method correlates very well with

other methods. Also, the measurements of the sinewave properties aqree

very closely with externally measured properties (note that 0 is the

only parameter that is difficult to verify externally).

Now, we miqht ask, "What properties of the diqitizer are actually

beinq measured ? By chanqinq the frequency of the sinewaves, we can

qet a measure of effective bits vs. frequency, but what actually qoes

on and what relevance does it have with respect to measurements of a more complex waveform?"

That is a qood question that demands an answer. Unfortunately, the answer that can be offered is not a complete one, but it is the best

one we can think of, and, perhaps as qood an answer as we may qet

with any test method.

Diqitizers really have three classes of errors:

1. Quantization Error - this is customarily treated simply a rounding error, but in reality, we must include two other components:

A. The errors due to nonlinear quantization thresholds.

B. The errors due to sampled analoq noise.

These errors are independent of the sinewave frequency and

represent a kind of baseline accuracy the sum of which can be

inferred from the test method described herein.

2. Aperture Jitter

This is the characteristic that is usually measured by samplinq

a rapidly risinq (or falling) voltaqe. This would normally be

expected to produce an error value that increased linearly with

respect to frequency. This characteristic is inferred by measurinq

the variance of sample values over many repetitions of the ;test

siqnal . Note that the mean value is seldom measured.

This error component is usually associated with time jitter in

the strobe pathway. It is certainly real, but is probably less

siqnificant than the next term to be described, which has rec- eived little attention.

3. Siqnal -Dependent Aperture Errors.

Any diqitizer must explicitly or implicitly sample the input

siqnal . This samplinq operation involves the variation of a parameter which must be a component of a low-pass filter, if the

hold mode is to have any meaninq. For most samplers, this parametric variation occurs most rapidly when the time derivative

of the siqnal beinq sampled is zero. If the time derivative is

non-zero, then the "on" resistance of a samplinq bridqe or the

1/Gm of a strobed comparator is usually hiqher than its optimum

value. This produces a consistent increase in what miqht be called

the "analoq set-up time" of the diqitizer. This error is nearly

proportional to the square of the dV/dt of the siqnal. This

suqqests that our sine-wave test should indicate an error that

is proportional to the square of the frequency-amplitude product .

Our analyses of various diqitizers indicate that this third error term quickly becomes dominant as the frequency is increased.

It is also easy to see how the existence of this error type could

have been missed in the course of makinq aperture jitter measurements, since this kind of error would result in *-he mean sample

value havinq been shifted.

24
ADVANTAGES

This test method allows the evaluation of digitizer distortion at any

frequency that can be generated by a sinewave generator. No special relationship between the generator and the sample clock need be set up. Results can

be plotted in a manner similar to the plots of frequency response of analog

systems. Furthermore, the measurements that must be made in order to infer

the effective bits measure may be sued seperately to describe the conventional

frequency response and to diagnose the conversion errors more fully.

While it is true that rather involved processing of the sample data

is necessary, once that analysis method has been put in place, many types

of digitizers may be tested in the same manner. POSSIBLE CONCERNS

Although the performance of the digitizer can be assessed relative to

sinewave inputs, are there other, more complex waveforms that could produce

unexpected errors? The answer would seem to be, "no", providing that the signal

being digitized is truly reconstructable . The proposed method can be used

for signal frequencies up to nearly one half of the sampling freguency. That

involves sampling time derivatives that must at least be equal to the highest

values that can be contained in any reconstructable signal at any portion

of the dynamic range . It is possible that the best fitted sine wave that can be computed

from the sample record may differ significantly in phase, amplitude or D.C.

offset (a significant frequency error is very unlikely). The amplitude and

D.C. offset errors can be detected independently without too much effort, but

the measurement of phase is likely to be somewhat more difficult. This area

has not been investigated as completely as might be hoped, but digitizers

that have performed well according to the "effective bits" measure have been

used in some extremely phase-sensitive applications (group delay measurements,

for example) and have acheived accuracies that were within predicted limits.

ACKNOWLEDGEMENTS

The first and most important, of course, is to Lyle Ochs , who developed

the concept in the first place. The author's role in this paper has been more

in the way of evaluation rather than invention. Thanks also to John Lewis,

Dale Jordan and Jim Prouty, who provided me with tools to independently test

Lyle ' s method

.

25

Measurement of the Transient Versus Steady-State

Response of Waveform Recorders

T. M. Souders and D. R. Flach

El ectrosystems Division

National Bureau of Standards

Washington, DC 20234

A simple test method is proposed in which the transient and steady-state responses

of waveform recorders are compared. The transient signals employed in this method are single period sinusoids accurately characterized in terms of a steady-state sine wave from

which they are derived. Digital recordings of the transient and steady-state waveforms

are made with the test instrument and are subsequently compared. Differences are analyzed

using time-domain digital processing. A gated S/H amplifier is used to produce the single

period transients from a sine-wave input. Techniques are presented for generating the

appropriate gating pulses, and for accurately comparing the transient and steady-state

waveforms. Test results are included for three different instruments, having up to 10 bits of resolution and conversion rates to 100 MHz.

Key words: analog-to-digital converter; digital processing; dynamic testing; sine-wave

testing; transient digitizer; transient response; waveform recorder.

Introducti on

Dynamic testing of waveform recorders is most commonly performed with steady-state, sinusoidal

stimuli [1,2,3]. The advantages of such approaches are many: accurate sinusoidal waveforms are among the easiest to generate, they are rather easily related to other waveforms through Fourier

analysis (assuming the system is linear), and applicable hardware and software analysis techniques

are readily available to perform spectral analysis, time domain analysis, signal-to-noise ratio

calculations, etc. However, waveform recorders are frequently employed to measure transient rather

than steady-state phenomena. Therefore, it is desirable to relate the transient response to the more easily measured steady-state response.

A simple test method is proposed in which the transient and steady-state responses are compared, as illustrated in Fig. 1. The transient signals employed in this method are single

period sinusoids accurately characterized in terms of a steady-state sine-wave from which they are derived. Digital recordings of the transient and steady-state waveforms are made with the test

instrument and are subsequently compared. Differences are analyzed using time-domain digital

processi ng.

Implementation

The single-period sinusoids can be accurately generated from the steady-state sine wave by

using a sample/hold (S/H) amplifier placed in the track mode for a single period, as shown in

Fig. 2. Digital circuitry shown in the upper part of the figure is included to generate the

appropriate S/H mode control, and a resistive divider at the bottom is added to provide an accurate

means of monitoring the S/H amplifier's performance. The digital mode control signal is derived

from the trigger output which is a standard feature on many commercial signal generators. The

timing relationships in this and subsequent trigger signal stages are shown in Fig. 3. The

trigger output signal is first passed through a commercial variable digital delay circuit, which

permits the trigger to be delayed with respect to the sine-wave output. In this way, the sine wave

can be gated at different phase angles to provide transient wave shapes such as those illustrated

in Fig. 4. Next, the delayed trigger is applied to the block labeled "^N" (Fig. 2). The first

stage of this block is a symmetrical divide-by-2, which produces a string of positive pulses, each

having a duration equal to that of the reference sine-wave period. This waveform is subsequently

divided by 10, producing a ripple carry output from the divider which is a rectangular pulse

having a duration again equal to the sine-wave period, and occurring once every 20 periods of the

sine wave. This ripple carry output signal is used to control the S/H amplifier, and to trigger

the waveform recorder under test. With a mode control signal thus developed, single sinusoidal

periods can be gated through the S/H amplifier, commencing (and ending) at any arbitrary phase

angle, with a 5 percent duty cycle.

27
Since the objective is to measure the response to transient versus steady-state waveforms,

it is important to accurately characterize the transient sinusoid in terms of the steady-state

input waveform from which it is derived. Absolute characterization of the two waveforms is not required. An error signal proportional to the difference between the transient and steady-state

signals can be obtained with the circuitry shown at the bottom of Fig. 2. This is readily

accomplished by selecting a gain of -1 for the S/H amplifier, and using a matched 1/1 resistive

divider connected as illustrated in the figure. An oscilloscope at the node connecting the two resistors monitors a voltage equal to one half the algebraic sum of the input and output voltages.

While this voltage tracks the input during the hold mode (when the output voltage is fixed), it

represents only the error signal between input and output during the track mode, when the transient

signal is developed. Diode bounding at the measurement node minimizes the overdrive of the

oscilloscope during the hold mode, permitting quicker recovery in the subsequent track mode.

This has proved adequate for settling time measurements to be made with an uncertainty of

approximately 1 mV; however, measurements to higher accuracy may require further signal limiting.

Since the steady-state as well as the transient waveforms are sampled at the output, the

steady-state input waveform to the S/H amplifier serves only as a reference with which to compare

the other two test waveforms. If the S/H amplifier produces negligible distortion at the test

frequency, then comparisons can easily be made by first trimming the resistive divider to produce

a null at the measurement node while in the track mode, under steady-state conditions. This

requires matching the divider ratio to compensate for the dynamic gain error, and adding a small

shunt capacitance across one resistor to balance the phase delay through the amplifier. Once the

divider is thus trimmed, any subsequent error signals measured in the transient mode indicate

the differences between the transient and steady-state waveforms as they appear at the waveform

recorder's input.

The results of such measurements can be seen in the oscilloscope photographs reproduced in

Fig. 5. Note that the error voltage (which is twice the indicated voltage) settles to within

approximately 40 mV in 100 ns, and within 5 mV in 200 ns, for a 20-V peak-to-peak transient.

These values represent errors of 2 LSB's and 0.25 LSB magnitude, respectively, for a 10-bit

recorder having 20-V full-scale range.

Measurement of the waveform recorder response to the transient versus steady-state signals is

made by first selecting the steady-state signal via the mode control switch in Fig. 2. The

recorder is then armed and subsequently triggered by the next mode control signal. All encodings

following this trigger signal are thereby stored. The resulting data set is then transferred to the controlling computer, the mode control switch is set to select the transient signal, and the

encoding and data transfer processes are repeated. Differences between the steady-state and

transient responses are then simply calculated by subtracting the second data set from the first,

as illustrated in Fig. 1.

Error Sources

The success of this measurement process is dependent upon the validity of three assumptions:

1. That the differences between the transient and steady-state waveforms, measured as discussed above, are negligibly small.

2. That the signal source is sufficiently stable that no appreciable change in waveform

takes place between successive applications of the steady-state and the transient inputs

3. That the two recorded sampled data sets are taken from identical segments of the two waveforms, i.e., that there is no timing skew between them.

The first assumption is tested as previously discussed. If significant errors are measured

between the transient and steady-state waveforms, corrections can possibly be applied by using

the recorder-under-test to digitize the error signal at the resistive divider's measurement

node, and subtracting the recorded data from the final measurement. This method requires a high

input impedance to the recorder so that the resistive divider is not loaded, and assumes that

the error signal can be measured on a more sensitive range, to minimize the effects of errors in

the test unit.

The second assumption can be tested by observing the cycle-to-cycle and longer term stability

of the waveform peaks and zero crossings at high gain on a storage oscilloscope. A sensitive

differential preamplifier with adjustable dc bias is useful for this measurement. Waveform

instability was found to contribute negligible errors (<0.02%) in tests of 8- and 10-bit recorders.

28
Unfortunately, the final assumption will generally not be valid using the test method

illustrated in Fig. 2. The difficulty arises because the encoding process of the recorder under

test is generally controlled by an internal clock which runs asynchronously with the input and

trigger signals. The result is that the first recorded encoding will be delayed with respect to the trigger signal by a random duration At<j<At, where At is the conversion time of the

recorder under test. Subsequent encodings will take place at times (with respect to the trigger

command) given by At<j +nAt, where n represents the nth encoding following the trigger.

Since At^ randomly changes with each new trigger command, subsequent data sets will be displaced

in time with respect to each other by a duration given by -At<Atd'<At. All corresponding

samples from the two data sets will be displaced by this same amount, therefore, the amplitude

displacement between corresponding samples will, to a first approximation, be equal to the time

derivative of the waveform at that location, multiplied by the time displacement. For a sinusoidal

test waveform Y = A sin(wt), an error signal will be generated by this time displacement, given by

wAAtd' COS(o)t).

This effect can be minimized or eliminated by appropriate modifications to the basic test

technique. While in principle the error source can be eliminated by phase-locking the recorder's

sampling instants to the trigger signal, this may not always be feasible in practice. A simple

approach is to minimize the error by averaging a number of consecutive pairs of data sets, each

pair containing a steady-state and a transient sample set. Assuming the recorder's time base is

independent of the test signal, then the values of At<j should be randomly distributed about the

average value, within the limits of -At/2 and +At/2. It can be shown that the standard

deviation of the mean of n such sample sets is giv en by At//1 2n. Therefore, the standard

deviation of the mean amplitude is given by wAAt//12n.

Results

The transient versus steady-state response of three different instruments has been measured

using the techniques outlined above, and typical error plots from these tests are presented in

figures 6-8. The three instruments are respectively, a 10-bit, 10-MHz sampling rate waveform

recorder, a 10-bit, 500-kHz digital storage oscilloscope, and an 8-bit, 100-MHz waveform recorder.

In each of the tests, some data averaging was performed to reduce the error caused by time skew.

Unfortunately, since the mode control switch (Fig. 2) had not been automated, an operator was

required to manually throw this switch for each new pair of waveforms, with the ensuing boredom

resulting in some cases in fewer data sets than desirable. Thus, while Figs. 6(a-d) represent

true errors, the remaining figures still contain strong time-skew components. Figure 6, for

example, shows various offset and distortion errors as large as 2-3 LSB's. These represent true

transient versus steady-state response errors, and are likely due to thermal unbalances occurring

within the test instrument. Other effects which have the appearance of high frequency noise

bursts are also present in this figure. These appear randomly in both the steady-state and

transient representations, and therefore are not due to differences in response to the two

signals. On the other hand, it is readily apparent that the errors plotted in Figs. 7(a-b) are

90° out of phase with the input signal (see inset), and are therefore predominantly due to time-skew rather than being true errors, and, in figure 8, a combination of time-skew errors

and an offset are present. In these figures, therefore, further averaging is required.

References

1. "Test A/D Converters Digitally," Bill Pratt, Electronic Design, No. 25, Dec. 6, 1975.

2. "Dynamic Testing Reveals Overall Digitizer Performance," Handshake Spring/Summer 1981,

pp. 9-12, Tektronix, Inc.

3. "Digitizer Specifications and Their Applications to Waveforms," R. W. Ramirez, Electronics

Test, Sept. 1981.

29
(a)

(b)

WAVEFORM STORE

Z> AND

RECORDER PROCESS

(a)-(b)

PLOT

Figure 1. Basic test method.

VARIABLE

DIGITAL ->

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TRIG.

OUT

SINEWAVE

GEN.

OUTPUT

STEADYSTATE

MODE I CONTROL

S/H

AMPLIFIER

TRIGGER

r INPUT

WAVEFORM

RECORDER

STORE

AND

PROCESS

-o SCOPE

Figure 2. Test circuitry for generating and comparing transient and steady-state waveforms

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Figure 5. Oscilloscope photographs showing

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b) Error signal observed at "scope" terminal in Fig. 2, while transient waveform

shown in a) is produced at S/H amplifier output. Marker indicates commencement

of track mode control level. (Vertical scale is 10 mV/div.; horizontal scale

is 200 ns/div.).

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+12.8

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Figure 8. Transient minus steady-state response of an 8-bit, 100 MHz waveform recorder,

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34
CALIBRATION TECHNIQUES FOR A LARGE COMPUTERIZED WAVEFORM RECORDING SYSTEM

W. B. Boyer

Sand i a National Laboratories

Albuquerque, New Mexico 87185

A transient waveform recording and processing facility has been developed for the

Sandla Particle Beam Fusion Accelerator, PBFA I. Signals from diagnostic monitors on the

accelerator and associated experiments consist of transient pulses of 10-1000 ns duration

and I to 5000 volts peak amplitude. The waveform recording system consists of 44 Tektronix

79I2AD Transient Digitizers interfaced to a HP-1000/45 minicomputer. The facility also

contains computer-controlled calibration, switching, and attenuation devices. The calibration and switching hardware can route either precision dc voltages or precision frequency

frequency periodic signals to the attenuators and digitizers. Software has been developed

to automatically calibrate the attenuators and digitizers and store the curves in disc

files. These data are used to calibrate waveforms recorded from accelerator experiments.

The facility cable system Is also calibrated for frequency response using the 79l2AD's in a semiautomatic mode. Waveform calibration consists of averaging to center of trace, linear

amplitude adjustment, nonlinear sweep speed processing, and cable frequency response compensation. System tests indicate that waveforms can be calibrated to an amplitude accuracy

of + 3 percent. Signals recorded from different monitors can be aligned In time to within

+ .4 ns.

1. Introduction

A computerized, on-line data acquisition and processing facility has been developed to support

Sandla 's Particle Beam Fusion Accelerator, PBFA I. D3 A transient waveform recording system constitutes a major part of this facility. This paper describes methods used to calibrate and verify the

performance of the waveform recording system.

2. Accelerators

PBFA I has 36 Independent beam lines and Is capable of delivering 30 terawatts and I mega joule in a 2 or 4 megavolt, 35 ns pulse Into a target chamber. C2J The accelerator can be configured to generate either electrons or Ions. The objective Is to deliver sufficient beam energy to demonstrate the

scientific feasibility of Inertlal confinement fusion. A cutaway drawing of PBFA I Is shown in Figure

I. The data acquisition facility also supports the SuperMITE accelerator which Is used for testing

advanced pulsed power components for PBFA It. A third machine, MABE, Is currently being brought online. MABE is a prototype for advanced weapons effects simulation accelerators.

3. Data Signals

The waveform recorders digitize signals produced by voltage, current, and radiation monitors on both the accelerators and associated experiments. These signals are fast transient pulses of 10 to

1000 ns duration and I to 5000 volt peak amplitude. These waveforms must be recorded In the presence

of EMP levels generated by dl/dt and dv/dt of I0 15 amps and volts per second.

4. Waveform Recording System

A block diagram of a typical waveform recording channel is shown In Figure 2. The cable run from

the monitor to the waveform recorders consists of 120 feet of RG-214 and 150 feet of RG-331 coaxial

cable. This Is about the minimum length which will reach all portions of the accelerator with equal

length cable runs and also provide flexibility In jumpering between monitors and waveform recorders.

The facility has 44 Tektronix 79I2AD Transient Digitizers with 7AI6P programmable vertical amplifiers and 7B90P programmable time bases. The vertical amplifier has a specified minimum bandwidth of

200 MHz. This Is adequate for recording virtually all accelerator and experiment diagnostic

signals.

35
Data signals from up to three different experiments are cabled to the input ports of a computercontrolled, four-position coax rotary switch module. Signals with amplitude greater than 500 volts

are first attentuated by specially designed high power 5X attenuators.

The output signal from the coax switch Is fed into a programmable attenuator. A fiducial timing

marker pulse can then be added to the data signal via a wideband isolating power adder. In some cases, the fiducial signal is routed to the 79I2AD vertical amplifier B channel, and timing Information is only recorded during the preshot baseline check.

Both the 79l2AD's and the fiducial pulse generator are triggered by a special Trigger pulse

generator. The trigger generator is triggered by some event in +he accelerator.

An HP-1000/45 minicomputer controls the coax switches, programmable attenuators, 79I2AD transient

recorders, and the trigger generator.

5. Calibration System

The computer controlled calibration system is shown in Figure 3. A Tektronix 1340 Data Coupler

contains vertical and horizontal reference signal generator cards as well as digital output cards for

controlling the coax switch matrices.

The vertical reference card can generate sensed dc voltages of 0, .01, .025, .050, . . . , 1.0,

and 2.5 volts. Actual outputs have been measured to + . I percent. These values are used to compute

vertical calibration factors. The vertical reference generator is used to automatically calibrate the

7AI6P vertical amplifiers, wideband couplers, and programmable attentuators.

The 7AI6P vertical amplifiers are computer calibrated by injecting a single known dc voltage

into the input and measuring the deflection. This process is averaged over four tries. Linear deflection is assumed. Each of the six sections in the programmable attenuators is also computer calibrated

by injecting known dc voltages into the unit and measuring output with the associated transient

recorder. Fixed attenuators are manually calibrated using dc power supplies and voltmeters. All dc

equipment is corrected to + . I percent using a calibrated Fluke 382A dc voltage reference source.

The horizontal reference card can generate periodic signals with frequencies in the range 0.25 Hz to 125.0 MHz In a .25 , .625, 1.25 sequence. Period accuracy is specified at .02$. The horizontal

reference signal is used to compute time base sweep curves. The calibration software locates zero crossings on the waveform and generates a calibration curve of time vs. zero crossing addresses. The

data acquisition program uses this curve to process recorded signals. The curve Is assumed to be

nonlinear. The time at which each signal sample point occurs Is computed by a double sliding parabolic

interpolation. C3H The signal data points are transformed into an array of data points occurring at a fixed sample rate by linear Interpolation.

Cable runs are calibrated by a hybrid computer/manual technique. A fast rise step pulse is injected directly into a digitizer and recorded. The same pulse is then injected into the cable run

to be calibrated and recorded by the transient recorder. A constrained deconvo I utlon process is used to compute a compensating impulse response function for the cable run. The recorded data signal

Is convolved with this Impulse response to compensate for cable losses.

The automatic data acquisition program uses the calibration factors described above to process

each recorded waveform. The overall accuracy of this system was checked as follows. A 150 V, 50 ns rectangular pulse was recorded by a transient digitizer. This signal was then manually calibrated

using deflection factors determined by the Fluke 382A reference source. The same pulse was Injected

Into the Input of a cable run. It was recorded and processed by the data acquisition program. A least squares comparison was made of the two waveforms. The overal I scale error was .4 percent and

the standard deviation normalized to the peak level was 2.8 percent. The undegraded signal, recorded

degraded signal, and calibrated signal are shown in Figure 4. An overlay plot is shown in the fourth

quadrant.

Time measurement accuracy of calibrated waveforms has also been measured. The 62.5 MHz periodic

waveform from the horizontal reference signal generator card was digitized on a 79I2AD. The waveform

was calibrated using the time base calibration information. The resulting signal is shown in Figure 5. The period of each cycle of this signal was measured by locating alternate zero crossing times. Linear

interpolation was used when no sample actually equalled zero. Cumulative zero crossing times were

also computed. The resulting data and errors are shown in Table I. All individual cycle errors are

less than 2.5 percent and the total cumulative error is .259 percent.

Accurate alignment in time of signals recorded on different digitizers is critical for analyzing

accelerator and experiment performance. Alignment Information Is recorded by placing a narrow fiducial

36
timing marker on each trace when a baseline is taken. The data acquisition software locates the peak

of the fiducial pulse.

After each signal is time calibrated, the leading edge is truncated at a time equal to the distance to the fidu peak plus one-half of a division. This truncation aligns all signals in time.

Tests have been made to determine the accuracy of the data recording system in aligning signals.

A pulse generator with ten 20 ns wide outputs simultaneous to within .1 ns was used. The pulses were

injected Into the Input of the cable run and recorded by the 79l2AD's at 10 ns/dlv. The waveforms

were processed by the data acquisition software. This process was repeated five times to separate

fixed time delays from shot-to-shot jitters. Fixed time delays are caused by unequal cable lengths.

Least squares comparison fits were made of different signals over the same shot to measure diff- erences in arrival times. These arrival times were averaged over all shots to get fixed time delays.

The fixed time delays were removed and the arrival times were analyzed for different signals over the

same shot and for the same signal over different shots. The results are that the expected alignment

error for different signals on a given shot was .26 ns with a worst case spread of -96 ns. The expected shot-to-shot alignment error was .33 ns with a worst case spread of 1.04 ns.

The most significant source of timing error is the software process of locating the peak of the

fiducial timing marker pulse. Digitization noise results in an expected error of about + 1.5 sample.

At 10 ns/dlv (.2 ns/sample), this is + .3 ns.

6. Uncorrected Errors

There are two prime sources of amplitude error inherent in the 79I2AD transient digitizer. The

first Is nonreproduci b I e wideband noise. This noise is illustrated in Figure 6. This signal is the

result of acquiring two baselines from a digitizer and subtracting them. The vertical axis is in units of 79I2AD digitization levels. There are 512 possible levels.

The second source of error is reproducible, low frequency, sweep geometry error. This problem is

illustrated in Figure 7.

Baseline traces were averaged 21 times at three different vertical positions. Note the position

dependent low frequency oscillations. This error may be removed by performing a geometry distortion

correction on the digitized data. This is a difficult process and is not done in the PBFA I system

since the predominant error Is caused by the wideband noise.

The PBFA I system also does not compensate for nonlinear vertical amplifier deflections. This

effect was measured by manually injecting dc voltages and digitizing the traces. The average value

was computed for each trace. This procedure was performed with the trace initially positioned at the

top, middle, and bottom of the screen. The results in all three cases were essentially identical.

The curve of deflection vs. voltage for the trace initially in the middle of the screen is shown

in Figure 8. A least squares fitted straight line is also shown. The deviations of the measured data

points from the fitted line are shown in Table 2. The table shows that non linearity errors in the

vertical deflection system are insignificant compared to low and high frequency noise.

7. Conclusion

The waveform recording system described above has been operational on PBFA I and SuperMITE since

January 1980. Automated calibration techniques have been developed for linear amplitude attenuations,

nonlinear time base sweeps, and frequency-dependent cable losses. Applying these correction factors

to digitized waveforms results in signals accurate to within 3 percent in both amplitude and time.

Additional error corrections cannot substantially Increase performance on single shot pulses due to the inherent digitization errors.

37
This work was supported by the U. S. Department of Energy under contract DE-AC04-76-0P00789.

References

Hi] W. B. Boyer, "Data Recording Techniques for the Sandia Particle Beam Fusion Accelerator,"

Workshop on Measurement of Electrical Quantities In Pulse Power Systems, National Bureau o Standards, Boulder, Colorado, March 1981.

C2] G. Yonas, "Pulsed Power Particle Beam Fusion Research," IAEA Technical Committee on InertI Confinement Fusion, Osaka, Japan, November 1979.

C3] M. E. Bauder, Operations and Maintenance Documentation for Program PLBRD, Sandia National

Laboratories Report No. TC-TM-70- 1 14, 1970.

38
Figure I. Cutaway artist's conception of PBFA I.

39
PBFA-I WAVEFORM RECORDING CHANNEL

HIGH POWER

ATTENUATORS

PBFA-I SIGNAL 5X

SUPERMITE

SIGNAL

MABE SIGNAL > 5X —1

COAX

SWITCH

PROGRAMMABLE WIDEBAND

ATTENUATOR ISOLATING DATA COUPLER

7912AD TRANSIENT

DIGITIZER

0-®3DB

4

7k

7A16P

AMP

7B90P

TIME BASE

~7f~

1 OF 44

CHANNELS

DATA COUPLER

PBFA-I TRIGGER

SUPERMITE TRIGGER

MABE TRIGGER

COAX

SWITCH

V

7\

FIDUCIAL TIMING PULSE GENERATOR

TRIGGER

GENERATOR

HP-1000/45

COMPUTER

-> ANALOG LINE ±> DIGITAL LINE

Figure 2. Block diagram of a typical waveform recording channel.

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Figure 4. Waveforms used to test overall system calibration performance: (a) undegraded pulse

recorded at digitizer and manually calibrated- Co) pulse recorded through cables;

(c) calibrated, cable compensated, slgojl; and (d) overlay of (a) and (c).

42
1.0

-1.0

0.0 0.4 0.8 1.2 1.6 2-0

TIME - seconds (x 10~7

)

Figure 5. Digitized periodic signal from horizontal reference

I. Time period measurement accuracy For 62.5 MHz (+ .02 percent) per I odi c

Cycle

Actual

Period

ns

Measured

Period

ns % Error

Cumu lati ve Cyc le Time

ns

Measur ed

Cumulative

Time

ns 5

I Error

I 1 6. 000 16. I 15 .721 16.000 16. 1 15 .721

2 1 6. 000 16.208 1 .299 32.000 32.323 1 .0 10

3 16.000 16.203 1 .266 48.000 48.526 1 .096

4 16.000 15.963 .231 64.000 64.489 .764

5 1 6. 000 I5.6I5 2.407 80.000 80. 104 . 130

6 16.000 1 6. 084 .525 96.000 96. 188 . 196

7 16.000 15.947 .329 1 12.000 1 12. 135 . 12!

8 16.000 16. I45 .905 128.000 128.280 .219

9 1 6. 000 1 6 . 299 1 .871 144.000 144.579 .402

10 16.000 15.835 1 .030 160.000 160.415 .259

43
0 2 4 6 8 10

TIME - seconds (x 10~8

)

Figure 6. Wideband noise left over after subtracting two 79I2AD baselines.

44
Figure 7. Vertical position dependent, low frequency 79I2AD noise.

Each signal Is averaged over 21 traces.

45
5 |

1 11 11

1

1

1 r

0 1 ' I i I i I i 1 1 -4 -2 0 2 4 6

APPLIED DC VOLTAGE - volts (x 10°)

Figure 8. Vertical amplifier deflection data. Both the actual measured

points (*) and least squares straightline fit are shown.

Table 2. Vertical amplifier non linearity test data for trace positioned in the middle of the screen

Voltage

Measured

Def I ection

Fitted

Def I ect ion Di f ference

-3.50V 30.53 31 .05 -.48

-3.00V 62. 16 62.72 -.56

-2.00V I26.5 1 26.0 + .5

-I .00V I89.9 I89.4 + .5

0.00V 253.5 252.8 + .7

I .00V 3I6.3 3I6. I + .2

2.00V 379.3 379.4 -.1

3.00V 442.4 442.8 -.4

3.50V 474.2 474.4 -.2

46
SAMPLING-RATE DRIFT PROBLEMS IN TRANSFER FUNCTION ANALYSIS OF ELECTRICAL POWER CABLES

J. D. Ramboz, A. R. Ondrejka, W. E. Anderson

National Bureau of Standards

Washington, D.C. 20234

An examination of measurement problems caused by sampling-rate drift has been initiated at the

National Bureau of Standards. This work arose from the study of degradation in underground power

distribution and transmission cables, where precise measurements of radio-frequency dispersion characteristics (i.e., attenuation and phase delay as a function of frequency) are necessary. Cable dispersion results are obtained using time-domain-reflectometry and fast Fourier transform methods and

spectra obtained from different data sets are compared. But because the data are necessarily taken

at different times, drifts in sampling rate can occur and cause erroneous results in the frequency

domain. Measurement methods for the detection of sampling rate drifts and computation methods for

correcting the data are discussed and illustrated.

Keywords: sampl ing-rate drift; digital sampling; deconvolution; fast Fourier transforms;

1. Introduction

There is an increasing interest in underground electric power transmission and distribution

which is growing from environmental and economic concerns. Fault location in buried power cables

can present technically challenging problems, especially when it is required that the fault site be

located accurately at some great distance from the measuring location. There is an additional interest by the utilities in being able to use the same buried cables for communication purposes. Both

of these needs require a knowledge of the rf propogation characteristics of the cable.

An experimental program had been initiated at the National Bureau of Standards to determine the

rf characteristics of power cables using time-domain ref 1 ectometry (TDR). A thorough examination of

the systematic sources of error using TDR techniques revealed the problem of sampling-rate drift and

the effects such drift can have on the measured transfer function of the cable.

In the time domain, the effects of sampling-rate drift are readily apparent. Basically, in

experiments of this sort, two different time-domain waveforms are acquired. One, for example, would

correspond to the pulse response of a known length of cable and the second would correspond to a longer length of the same cable. The parts of the pulse-response waveforms corresponding to the

output impedance of the pulse generator, the connection between the pulse generator and the cable,

and the response of the shorter length of cable should be identical. If they are not, sampling-rate

drift has occurred. If the two waveforms are then transformed to the frequency domain and divided

to obtain the transfer function of the extra length of cable, errors will result. Based on the

expected behavior of the cable, the transfer function can be corrected to minimize the effects of

sampling-rate drift.

Sampling-rate drifts are discussed, along with their effects, and a method to correct this type

of error is given. Analytical generation of typical TDR-type waveforms is used in the discussion to

aid in the understanding of the problem and to show the effects of the correction process. Real

data is then examined before and after corrections are applied.

2. Power Cable RF Attenuation Measurement Process

One method to measure the radio-frequency (rf) attenuation of underground power cables over a wide band of frequencies is to employ time-domain-reflectometry (TDR) techniques in conjunction with

Fourier analysis. A method used by the authors requires that a length of cable be pulsed and the

TDR response be recorded. A known change then is made in the length of the cable being measured and

a second TDR response recorded. The data collection and analysis process are diagrammed in figure

1. The change of measured response between the two recorded waveforms can be related to the change

of length and, thus, attenuation per unit length can be calculated. Specific details of the measurement process relating to coupling the cables and other miscellany are the subject of a forthcoming

paper. This discussion is aimed more directly to the data analysis and, specifically, the effects

of a sampling-rate drift.

* Electrosystems Division, NBS, Washington, DC 20234

* Electromagnetic Technology Division, NBS, Boulder, CO 80303

4 7
Referring to figure 1, the recorded waveforms are each amplitude shifted in a software process

so that the two recorded waveforms, shown by figure 2, begin at zero amplitude, rise through a steplike function, and then continue at some positive amplitude. The data originally began at a non- zero value because of offsets in the measuring instrumentation, some of which were intentionally

introduced to improve amplitude resolution. However, the particular fast Fourier transform (FFT)

Acquire

Waveform

No. 1

Amplitude

Shift

I

FFT

Acquire

Waveform

No. 2

Amplitude

Shift

FFT

Disk Files

Array Division

(No. 2)/(No. 1)

I Spectra

Shift Test

I

Spectra

Correction

Corrected

Array Quotient

Fig. 1. The data collection and analysis process steps.

algorithm used in this analysis requires that the beginning points of the waveform be made zero. After the amplitude shift, an FFT result is obtained for each of the two waveforms and these results

are stored on computer disk files. An array division corresponding to the deconvolution in the time

domain is then done. The logarithm of the magnitude of this quotient is scaled to place the results

in normalized attenuation units of dB per unit length of cable.

Figure 2 shows two recorded TDR response waveforms (already amplitude shifted) which were obtained from the cable measurement setup. No changes were made in the setup arrangement and, therefore, the two waveforms should be the same. The second waveform was taken 44 minutes after the

first. Processing these two waveforms yielded the results shown in figure 3. Attenuation is given over a ±1 dB range and the frequency is shown over a range from 0 to 128 GHz, which results from a time interval between samples of about 2 ps and a total of 512 sample points. It is not expected

that useful data can be obtained for frequencies beyond 10 to 20% of the Nyquist frequency because

of noise and, in this instance, band limited frequency content of the TDR pulses. The pulse re- sponses shown in figure 2 have rise times of the order of 35 ps, which should contain measurable

frequency components up to the 15 to 20 GHz range.

48
100 ps/Division

Fig. 2. Typical TDR response waveforms for

two collection cycles.

Fig. 3. Erroneous cable attenuation results

due to sample-time drift.

If the recorded waveforms as shown in figure 2 were identical, the array division would yield a straight line of 0 dB over the entire frequency range up to the Nyquist frequency (and, indeed, if one uses this technique, the identical data can be analyzed in the two analysis "channels" to verify

that the software is functioning correctly). Note, however, in figure 3 that the attenuation as computed shows a value more than -1 dB at a frequency less than }0% of the Nyquist where, in fact, a straight line of 0 dB over the range would be expected. If interpreted literally, a negative attenuation represents a system gain which, for these experiments, is not possible. This result led the

authors to examine sampling-rate drift.

3. Sampling-Rate Shifted Data

Electronic sampl i ng devices, such as the TDR equipment, sample a waveform at periodic intervals,

either as a function of linear ramp sweep circuits or by some system "clock." In either instance,

if the sweep-speed or clock rate changes from one set of measurements to a second set, then the "true" waveform is "time distorted" by this sampling-rate drift. It is assumed for purposes of this discussion that the time interval, or period between each individual sample of one "sweep" or data-gathering cycle, is constant and that for a second cycle, the period is also constant but not necessarily

the same as the first. This is illustrated in figure 4. An arbitrary rising waveshape is shown as an "unshifted" waveform with the sampling occurring at times indicated by the solid dots. The time

0

0)C

o

Q.

</> <D

No Shift

Shifted

Unshifted

Waveform

Shifted

Waveform

Sample-Time Interval

Fig. 4. An arbitrary rising waveform with and without sampling-time drift,

49
interval between individual samples is shown as At] on the time scale identified as "no shift."

Here each At] is equal for the entire data collection cycle. If, at some later time, a second

data set is collected where a change has occurred in the sampling rate, as shown by figure 4 as At2> time distortion occurs. Bear in mind that it is exactly the same waveform that is being

measured but because of the change in sampling rate, the apparent waveshape as shown by the "shifted"

waveform results. Any particular sample is made at time NAt2, where N is the Nth sample, on the

unshifted waveform as indicated by the vertical line from the "shifted" time axis. It is assumed,

however, that the measurement was made at a time NAtj, as indicated by the open dots. For ex- ample, for an increase in the sampling period from Atj to At2, an apparent faster rising waveshape results. The same phenomenon occurs on an ordinary oscilloscope if a constant and repetitive

waveform is being observed and the horizontal sweep speed is decreased a small amount; the waveshape

appears to have a faster rise time to the observer. Figure 5 shows an exaggerated example on a typical TDR response for two different sampling times. One rise time appears faster than the other;

however, this was due purely to a change made in the sample-time interval between the time sweeps.

Time, 200 ps/Division

Fig. 5. An exaggerated example of a typical TDR response waveform sampled at two different rates.

When the subsequent data processing occurs, it is assumed that the sampling-time intervals were

the same for the two recorded waveforms. However, because of a sampling-rate drift, one waveform

appears to be "steeper" than the other. This waveform, in turn, when processed through Fourier

analysis, contains more high frequency components than the "slower" (or unshifted) waveform. When

the array quotient is obtained from two "apparently" different spectra, erroneous results such as those shown in figure 3 are obtained.

For measurements of cable attenuation, precision of the order a few tenths of one dB are often

required. It has been observed that a sampling-rate drift of only a few tenths of 1% can cause results

such as shown in figure 3; these are considered unusable.

To characterize the process, an analytically-generated waveform was used. The expression is

shown by eq. (1 )

.

W(I) = [M/(M 2 + 100)!/2] + c (1)

where M = I - 256.5.

The function is generated for an array of 512 points and is symmetrically centered in and around

the center point of 256.5. The expression W(I) is in an array notation where I varies from 1 to 512

in steps of 1. The constant, C, is chosen to force the first point to zero amplitude so that it may

be operated on by the subsequent FFT computations.

Figure 6 shows two computed waveforms having step-like transitions similar to those of actual TDR responses. The waveforms were generated using eq. (1). The lower waveform has been time-shifted

by an amount 1% with respect to the upper waveform. This simulates a typical sampling-rate drift

situation.

Figure 7 is the result of the array division process as discussed previously. The ordinate is plotted for a range of ±1 dB and the abscissa is given for a frequency range from 0 Hz to 20% of

the Nyquist frequency. The "dro^" is clearly present and is entirely the result of the 1% shift in sampling rate.

50
a>

</> c

o

Q_

c/> Q)

DC

QCQ

Unshifted

Waveform

Shifted 1 %

Fig. 6.

J I L-L-£J I I I I I Time

Analytically-generated wave forms having similar characteristics to typical TDR responses,

the lower waveform being time-shifted by 1%.

00

C

mwmo

<3

0)

<

+ 1

-1

20%

Nyquist

Frequency

Frequency

Fig. 7. Attenuation versus frequency from the waveforms shown in fig. 6; erroneous due to sampling-time drift.

The response droops when the second of the two time-domain waveforms is shifted to appear as a slower rising pulse (i.e., sampling rate is faster), and conversely, the attenuation plot would rise

when the sampling rate for the second wave form is slower. Had no sampling-rate drift occurred (as

in a perfect measuring system), then the attenuation plot would be a straight level line at 0 dB over the entire frequency range. For the set of measurements made by the authors, it was judged

more advantageous to correct the "rate-drift" problem in software in the frequency domain rather

than to try to eliminate the drift from the sampling hardware, or to correct for it in time-domain

software. Because it is known that typical sampling-rate drifts result in attenuation responses

such as shown in figure 7, it was predicted that expanding or compressing one of the two frequency

spectra would, in effect, compensate for the rate drift and would, in turn, force the attenuation

back to zero for some reference condition over the frequency range of interest. An expression shown

in eq. (2) operates on an array B(M) such that the array division results in a corrected array D(I)

which has the "droop" removed.

0(1) = {(I*A

2 -M)*[B(M+1)-B(M)] + B(M) }*A2 _I/32

(2)

where D(I) is the Ith point in the corrected array,

I is an integer, 1<I<512,

M is the integer part of (I*A2) for 1<I<512,

B(M) is the Mth point in the uncorrected array, and

A? is a correcting factor derived from the slope.

51
The correcting term A2

is derived from the slope of the uncorrected attenuation response (figure

7). A weighted mean slope is calculated from 33 points, starting with the third array point B(3)

and continuing to point B ( 35) . The weighting is such that the individual slopes received weighting

factors inversely proportional to the order; thus, the lower points influence the results more heavily than do the higher points. This was done because the amount of noise increases as the order

becomes higher and this weighting scheme reduces the effect of noise. The term A2 is equal to

1 + the mean slope.

The process using eq. (2) adds a small positive shift to the process and this can be removed by

using the following empirically derived relationship (shown in array notation):

D(I) = D(I)-[16*(1-A2 )]. (3)

Figure 8 is the corrected attenuation plot of the uncorrected attenuation shown in figure 7. Here the response has been corrected to be within approximately ±0.05 dB over a frequency range up to 20% of the Nyquist frequency.

00

"D

C

o

3

m

+ 1

©

- 1 -

20%

Nyquist

Frequency

=F=f=

Frequency

Fig. 8. Corrected attenuation of the data shown in fig. 7,

For real TDR data, a pulse such as shown in figure 9 was obtained from the laboratory. A second

response was obtained which had a synthesized sampling-rate shift of 0.1%. Figure 1 OA shows the

attenuation plot that resulted when no rate-shift correction was applied. Figure 1 OB shows the

corrected attenuation which removed the effect of the "droop" in an attempt to improve the results.

0)

(/) c

o

CD oc 1

DCQ

I -L

Unshifted

Waveform

hifted 0.1 %

J L 100 ps/Division

Fig. 9. Two TDR response waveforms, the second having a time shift of 0.1%

with respect to the first.

52
1 1r

\—lO

i -1

Frequency

(10% of Nyquist Frequency)

Fig. 10A. (Left) Attenuation results from waveforms shown in fig. 9 containing a sampling-time drift of 0.1%.

Fig. 10B. (Right) Corrected attenuation results using technique discussed.

The techniques discussed above analyzed a TDR response which had been "time-shifted". In practice responses are compared for two different experimental conditions (e.g., two different cable

lengths). The overall TDR response for the second test condition can be markedly different from the

first because of the increased cable length. The part of the time-domain response representing the

impedance transitions between the TDR generator and the cable under study however should be constant

for both measurements and the only change in response would be due to a sampling-rate drift. It is

from the analysis of this data that sampling-rate drift can be determined and a correction factor

estimated.

4. Conclusions

Errors in transfer function analysis, which result from digital techniques where the samplingrate drifts between sets of measurements, can be minimized by applying a correction factor in the

frequency domain. Analytical examples are shown that demonstrate the effect when such drifts occur. Empirically-derived equations are given which, when applied to the array quotient, correct for the

effects of the time drift. In analytical examples, errors of several dB can be corrected to the

order of 0.1 dB or less.

Most of the relationships given in this paper were derived empirically. Their applicability,

therefore, depends on the details of the process studied and the apparatus used. They are intended

only to illustrate the errors which can be produced by sampling-rate drift and to suggest an approach

to the correction of these errors. It is presumed, however, that more general and more rigorous

correction algorithms can be derived. The correction appears to be a direct function of TDR pulse

characteristics and this complicates the possible solution. A thorough examination of the samplingrate drift needs to be completed.

5. Acknowledgments

This work was sponsored by the Office of Electric Energy Systems of the Department of Energy.

6. References

1. W.E. Anderson, J.D. Ramboz, 1980 Annual Report. Technical Contributions to the Development

of Incipient Fault Detection/Location Instrumentation, NBSIR 81-2235, Nat. Bur. Stand.,

March 1981.

53

Automatic Pulse Parameter Determination

with the Computer Augmented Oscilloscope System*

A. A. Guido, L. Fulkerson, P. E. Stuckert

IBM Thomas J. Watson Research Center

P. O. Box 218

Yorktown Heights, New York 10598

The Computer Augumented Oscilloscope System (CAOS) is a special computer terminal

facility intended for laboratory experiments involving waveforms and their interpretation. The

system provides digital acquisition of waveform data, system control and calibration, data

analysis, and graphic and alphanumeric display.

Pulse parameter determination requires the use of all system capabilities since a)

hardware and software options must be chosen or controlled, b) the pulse waveform must be

digitized, c) the appropriate analytical algorithms must be applied to the data and d) the results of analysis must be displayed. Specific attention is given to the algorithms required for pulse

parameter determination and a new procedure for determining base and top magnitude of a pulse waveform is presented.

Key Words: automated oscilloscope; computer aided measurement; laboratory automation; pulse analysis;

pulse waveform analysis; waveform analysis; waveform recording.

Introduction

A significant trend toward the automation of laboratory experiments has emerged in the past several

years. This trend has origins in the realization that automation frequently improves efficiency, permits the

execution of experiments that otherwise could not be performed and minimizes the amount of detail with

which the experimenter must cope.

The Computer Augmented Oscilloscope System (CAOS) provides automation for the laboratory

experimenter who is concerned with waveforms and their interpretation. Figure 1 shows the CAOS

laboratory ensemble, which includes a modified sampling oscilloscope, the CAOS terminal and the telephone

data set that couples the ensemble to a remote computer. CAOS hardware, its features and its operation

have been described previously [1] and the following operational summary is adequate in this paper. By

appropriate entries on the terminal's alphameric and function keyboards, an experimenter may invoke

programs which:

• digitize and store in the computer a waveform displayed on the oscilloscope;

• analyze the waveform data thus stored;

• display raw waveform data;

• display calculated graphical results;

*Copyright 1971 by International Business Machines Corporation; reprinted with permission.

55
Figure 1 CAOS laboratory ensemble.

• display calculated numerical results;

• calibrate an oscilloscope sampling channel;

• display instructional or diagnostic information; and

• permit the specification of options to be used in the execution of programs.

All of the operations listed above are, in effect, self-terminating. When an operation terminates, the

oscilloscope is available for use in its conventional stand-alone fashion.

CAOS has potential application in numerous experimental situations. With suitable software the

system can emulate a number of conventional laboratory instruments (e.g., spectrum analyzer, distortion

analyzer, phase meter, etc.). Beyond emulation, and solely as a function of the analysis and display software,

the system permits the development of new techniques [2] and instruments. This paper describes one such

instrument, a pulse parameter analyzer. An algorithm for determining the base and top magnitudes of a waveform is discussed and some examples of pulse parameter determination are given.

Pulse Parameter Analysis

Typically, pulse parameter analysis involves the evaluation of a waveform which is displayed on an

oscilloscope or an x-y plotter. Figure 2 shows a pulse waveform and the reference lines and points which the

experimenter, either literally or figuratively, superimposes on the waveform in the course of the analytical process. Using these superimposed geometrical constructs, the experimenter determines the magnitude of the

parameters of interest. The entire process entails considerable subjective judgment.

56
Time origin

Figure 2 Pulse waveform nomenclature.

Some instruments (e.g., the Tektronix Type 567 Digital Readout Oscilloscope) provide a degree of

automatic parameter determination, but no instrument, to our knowledge, provides automatic determination

of the eleven major pulse parameters which are underlined in Fig. 2. More importantly, no known instrument incorporates adequate techniques for determining base magnitude and top magnitude, the two crucial

parameters on which all other parameter determinations depend.

Pulse Waveform Nomenclature

Figure 2 shows the nomenclature used throughout this paper. The eleven pulse parameters to be

determined are underlined and all other reference lines and points required in intermediate steps are

identified. Although the nomenclature in Fig. 2 appears somewhat novel, the authors use it because it is the

only available nomenclature that is complete, internally consistent and general enough to satisfy all needs.

The nomenclature of Fig. 2 does not imply any new procedure in pulse parameter analysis which, quite

conventionally, involves the sequential determination of:

1) base magnitude,

2) top magnitude,

3) pulse amplitude,

4) proximal, mesial, and distal line locations either: a) as percentages of the pulse amplitude, or

b) as absolute values,

5) proximal, mesial and distal point locations on the first and last transitions, and

6) the magnitudes of all other parameters from computed differences between appropriate line and/or

point pairs.

57
Base and Top Magnitude Determination

The sequence that is outlined immediately above illustrates the importance of the base and top

magnitude determinations. They are the first parameters evaluated, and their values are prerequisite to all other evaluations. Conventional methods for determining these two parameters involve either:

• estimates of their magnitudes by the experimenter from his observation of, or his graphical constructions

on, the waveform, or

• location of single points on the waveform base and the waveform top by some procedure, where the

magnitudes of the point so located are taken to be the base and top magnitudes.

The first technique is fraught with undesirable subjective factors, and the second can lead to bizarre

results when applied to the "dirty" pulse waveforms frequently encountered in practice. Clearly, a technique

which eliminates subjective judgment and which yield "reasonable" and consistent results for a wide variety

of pulse waveforms is needed.

CAOS software incorporates an algorithm for the determination of base and top magnitudes that was

first suggested by a former colleague, K. Maling [3]. This algorithm is based on the determination of the

probability density of the waveform data within the pulse waveform epoch and is closely related to a technique independently suggested by Boatwright [4]. A graphical description of the algorithm follows:

1) Assume that a pulse waveform, such as that shown in Fig. 3(a), has a superimposed rectangular grid in which each elementary rectangle has dimensions A*1 and Am.

2) Construct the initial probability distribution histogram as follows:

a) for each horizontal stripe (of width Aw) count the number of elementary rectangles through

which the waveform passes. b) at the magnitude corresponding to the location of the horizontal stripe, draw a histogram

element whose length is proportional to the count. (This procedure yields the truncated bimodal

distribution of Fig. 3(b) in which P' B and P' T

are identified.)

58
3) Count the number of transitions in the pulse waveform. (In Fig. 3(a) there are 2.)

4) Subtract the count obtained in 3, above, from each histogram element of Fig. 3(b) to produce the tinal probability distribution histogram, Fig. 3(c). This procedure removes contributions from the transitions and produces the two separate truncated distributions PB and PT

. 5) Calculate the values of the means and the modes, in m, of PB

(and PT

). Either the mean or mode of

PB

(or P T) may be chosen as the base (or top) magnitude.

The previous graphical presentation yields crude results, but as A/ and Am become smaller the

magnitudes of the means (or modes) of PT and PB become more refined measures of the base and top

magnitudes. The technique is particularly applicable in CAOS since A/ is equal to the number of waveform

sample points and Am is determined by the resolution of the A/D converter which digitizes the magnitude of

each sampled point.

The algorithm given above yields two possible values for the base (or top) magnitude, and a choice

must be made. However, one additional factor is pertinent. The probability density algorithm is inappropriate, and sometimes fails for pulse waveforms that have bases (or tops) of substantially zero duration (e.g.,

sawtooth waveforms, exponential waveforms, etc.). In these cases the peak value of the waveform is the

appropriate choice. In the CAOS pulse parameter determination program, which is discussed in a later section, the authors resolve the choice between mean, mode and peak by providing independent selection for

base magnitude and top magnitude wherein for each:

• the mode of the probability distribution corresponding to the pulse base (or top) is the default option.

This option should be taken when results that are consistent with conventional observed results for pulse

waveforms with bases (or tops) of significant duration are desired.

• the peak magnitude of the waveform base (or top) is included as a selectable option which, in general,

should be taken when a base (or top) has substantially zero duration.

• the mean of the probability distribution corresponding to the pulse base (or top) is also included as a selectable option. This option should be taken when results having the highest possible precision for pulse

waveforms with bases (or tops) of significant duration are desired.

CAOS Programming System

Before describing the pulse parameter determination program used with CAOS, a brief description of

the CAOS Programming System (CAPS) and its interaction with an application program, the computer and

the terminal is necessary. Figure 4 shows a system block diagram in which the information flow between the

major constituents is indicated. As described in a previous paper [1], the CAOS terminal hardware executes

a set of wired-in instructions in response to information (i.e., commands and, where applicable, data) from

the computer. Typically, any useful CAOS operation entails the execution of a sequence of these wired-in

instructions. Sequences for all such operations are included in the CAPS software, a library of FORTRAN

routines which may be called by any application program. Typical examples are:

• DIGA (or DIGB) - digitize the waveform on Channel A (or B) of the oscilloscope.

. CALAKY (or CALBKY) - calibrate Channel A (or B).

• ERASTR - erase a specified storage screen.

• WRTLIN - write a line of EBCDIC text on a specified storage screen.

• RDLINE - read a line of EBCDIC text entered via the alphanumeric keyboard.

In addition, CAPS contains interpretive and supervisory routines which activate applications programs

in response to keyboard entries.

59
Laboratory Experimenter —* «"

Sampling

oscilloscope Keyboards andindicators

CAOS

terminal

Telephone link

Computer

IBM 360 Model 44

Software

Information flow for data acquisition, control and display

CAPS

Information

flow for data analysis

Application program

Figure 4 System block diagram.

An application program may contain up to 24 routines, each of which is associated with one of the 24

available function keys. Figure 5 shows the function keyboard overlay card for the pulse parameter

determination program. With this card inserted, CAPS interprets each function key depression as a call for

the execution of a specific routine in its associated application program. CAPS thus renders the CAOS

terminal totally transparent to the user, who needs no knowledge of the detailed workings of the terminal or

the software, both of which are completely masked. CAPS also minimizes core requirements since only it and the application routine associated with a single key must be present in the memory at any time. CAPS

provides a high degree of interaction since:

• the sequence of operations is determined by the user's actuation of the function keyboard, and

• conversational features in CAPS, or in an application program, guide and prompt the user with instructional or diagnostic messages.

The CAOS library currently contains application programs for time-jitter correction, spectrum analysis,

deconvolution and signal averaging in addition to the program for pulse parameter determination. New

application programs, as required, may be written in FORTRAN and added to the library.

Pulse Parameter Determination Program

The program for pulse parameter determination (PPD) is invoked by inserting the overlay card shown

in Fig. 5 in the terminal. PPD makes extensive use of terminal displays, for example, when the operator

depresses "Choose Mode" (key 21) and enters a "1" via the alphanumeric keyboard, the display shown in Fig. 6 results. Modes 1 through 4 comprise, in effect, an interactive instruction manual for the operation of

PPD and the terminal itself. Space limitations preclude the presentation here of the 8 displays which these

60
• • •

« PPD- PULSE PARAMETER DETERMINATION

CHOOSE MODE (1-4) • * • < t ft ANALYZE A B

AVERAGE ft 8 ANALYZE %>. mi

A B CHOOSE

OPTIONS SCOPE

ONLY mCALIBRATE m9, mi A B CHOOSE

DISPLAY mi •

^^20'ft^^F24

Figure 5 Function keyboard overlay card.

*PPD-OPERATING MODES (1-5) Ml

! DISPLAY OF MODES AVAILABLE WHEN OPERATING WITH *PPD (IE, THIS DISPLAY)

.

2 FOR SPECIFYING USE OF ADDITIONAL 681

AND 611 SCOPES FOR DISPLAY.

3 GENERAL DESCRIPTION OF CAOS OPERATION, ABBREVIATIONS, DISPLAYS, ETC.

4 DISPLAY OF COMMENTS AND BASIC INSTRUCTIONS FOR ,*PPD.

5 EXECUTE * PPD. THIS MODE IS INVOKED

ONLY BY A VALID HE, EXECUTABLE) SEQUENCE OF KEY DEPRESSIONS ON THE FUNCTION KEYBOARD LEFT HALF (KEYS 1 - 1 2)

.

HIT FK/MK

Figure 6 Mode 1 display.

*PPD-OPTION LIST 2 OF 4

JO CHOOSE: : TYPE A B 3IE

• ALL DEFAULTS THIS PAGE A .OLD SELECTION THIS PAGE B BASE PARTS TO BE USED IN, r - -CALC. OF BASE MAGNITUDE:

.FIRST AND LAST (D) E 0 0

.FIRST ONLY F -BASE MAGNITUDE ALGORITHM:.

-PROB. DENSITY-MODE (0) H 0 0

. PR0B. OENSITY-MEAN I

. PEAK J -TOP MAGNITUDE ALGORITHM:

.PROB. DENSITY-MODE (D) L - 0 0 .PROB. DENSITY-MEAN M

. PEAK N

HIT RK/FK/MK

Figure 7 Typical option list display.

61
four modes contain. The operator, as a function of his familiarity with the PPD program and the terminal,

may execute any or all of these modes or he may proceed directly to Mode 5, the PPD program proper. All

displays have the following features in common with the display of Fig. 6:

• The top line always contains a page title and the mode and/ or page numbers.

• The bottom line always contains abbreviated instructions for exiting from the page (i.e., in Fig. 6, "HIT

FK/MK").

Mode 5, the PPD program proper, is executed with the 8 active keys on the left half of the function

keyboard (see Fig. 5). Typical operation begins with:

1) execution of "Choose Display" (key 12) which provides an interactive control display through which

the operator may format the display of results from the PPD program. The default (i.e., complete)

display will be provided if no options are exercised.

2) execution of "Choose Options" (key 11) which provides interactive control displays through which the

operator may exercise a number of data acquisition and analysis options. Again, default options are taken if the operator makes no specific choices.

Figure 7 shows a typical page of the PPD option list in which all default options are indicated by

"(D)." By typing the specified alphabetic characters the operator may for either or both oscilloscope

channels:

• select all default options on the page;

• retain his previous option selection;

• specify whether the determination of base magnitude shall be based on:

a) both sections of the pulse waveform base, or

b) that section of the base which precedes the first transition;

• specify whether the base (or top) magnitude shall be calculated as: a) the mode of its probability distribution,

b) the mean of its probability distribution, or

c) the peak magnitude of the pulse waveform.

Again, space limitations preclude showing the complete PPD option list which provides the following

additional options:

• whether calibration of the sampling channel shall be

a) continuous, or

b) under manual control from the function keyboard;

• whether waveform averaging shall be

a) continuous, or

b) under manual control from the function keyboard (default);

• whether the pulse waveform analysis shall be based on:

a) the entire waveform (default) or

b) on a specified continuous portion of the waveform;

• whether the base magnitude shall be

a) assumed to be zero (default);

b) determined on an absolute basis, or

c) assigned a specific value;

• whether the time origin shall be

a) assumed to be zero (default), or

b) assigned a specified value;

• whether the locations of the proximal, mesial, and distal lines shall be

a) at 10%, 50% and 90%, respectively, of the pulse amplitude (default),

b) at specified percentages of the pulse amplitude, or

c) at specified magnitudes;

• whether the polarity of the pulse waveform shall be

62
a) automatically determined by the program (default), or

b) specified by the operator;

• whether attenuation external to the oscilloscope shall be assumed

a) to be zero (default), or

b) to be a specified value.

When the operator has completed executing the option list — an operation which can take negligible to significant time, depending on the number of default options which must be overridden — he executes the

PPD program by depressing one of keys 2 through 4 or 6 through 8 (in Fig. 5) for each operation required.

The operator may revert to conventional stand-alone oscilloscope operation at any time by depressing the

"Scope Only" (key 23).

Examples of PPD Operation

Space limitations preclude a comprehensive description of all modes of PPD operation with the

sampling oscilloscope. The authors, instead, present a limited set of examples which illustrate PPD operation

in general and indicate the degree of precision which can be achieved with CAOS. Throughout this section

the discussion of numerical results is solely in terms of precision, that is, "... the degree of mutual agreement

characteristic of independent measurements of a single quantity yielded by repeated applications of the

[measurement] process under specified conditions ..." [5].

Table 1 lists the hardware conditions and PPD software options for three types of test (A, B, and C)

which were performed 9 times in a one-week period. Figures 8, 9 and 10 show the results of the first of

these tests wherein:

Table 1 Test conditions and options.

Type A

Pulse source

Repetition frequency

Pulse distorting circuit Sampling head

Oscilloscope settings Vertical sensitivity Horizontal sensitivity

Number of sampling points

Triggering

PPD operation

Analyze A (key 2 in Fig. 5). All default options except

magnitude were computed a density histograms.

(Fig. 8) Hewlett Packard Model

21 5A Pulse Generator

60 kHz

Passive RLC network

Tektronix S-2 (75 psec)

100 mV/cm

10 nsec/cm

800

External from pulse source

lat base magnitude and top

the means of the probability

Type B (Fig. 9) Same as Type A, above, except:

Vertical sensitivity—10 mV/cm.

External attenuation of 20 dB (nominal) inserted between

pulse distorting circuit and sampling head.

Type C (Fig. 10) Same as Type B. above, except

:

PPD operation—Average and analyze A (key 3 in Fig. 5) with 10 digitizations of the waveform specified.

63
• Figures 8(a), 9(a) and 10(a) show the pulse waveform data which were analyzed by the PPD program.

Figures 8(a) and 9(a) show the waveform data from one digitization; sampling noise at the 10 mV/cm

sensitivity is evident as in the latter. Figure 10(a) is the average of 10 digitized waveforms, each of which was similar to that shown in Fig. 9(a). Figures 8(b), 9(b) and 10(b) show the probability density

histograms of the corresponding waveforms. For these figures the display routine adjusted the histogram

data to provide a maximum horizontal deflection of 8 cm. The histograms, while exhibiting similar

characteristics, are distinctly different, Fig. 9(b) begin markedly different from the other two.

• Figures 8(c), 9(c) and 10(c) show the calculated pulse parameter displays provided by PPD using the

techniques, options, and algorithms described in previous sections. Note that, despite the differences

between the waveform data and the significant differences between their histograms, the numerical results are in relatively close agreement.

64
Table 2 lists the salient results from Figs. 8(c), 9(c) and 10(c) and shows the variations (in percent of

full scale) for all 9 executions of the three types of test described in Table 1. In Table 2 the extreme

variations for each of the four major parameters are set in bold-face type. Long-term precisions of the order

of ±0.5% of full scale, or better, are achieved throughout. As was expected, the Type B tests contribute a majority (6) of the extreme variations. Further, all nine runs, with the exception of run 7, were made after

all equipment had been on for one-half to one hour. Run 7, which contributes 4 of the 8 extreme values in Table 2, was made after all equipment had been on for approximately six hours.

Table 2 Long term variations in indicated pulse parameters. Type A test arbilrarily taken as reference. Vertical full scale —800 mV; Horizontal full scale—100 nsec. Extreme variations for parameters are set in bold-face type.

Variations in percent oj full scale Data jor Run No. 1 Run numbers

1 3 4 5 6 7 8 9

Pulse amplitude

Type A 439.722 mV +0 187 +0.250 +0 324 +0.450 +0 444 +0.570 +0.286 +0.273

TypeB 437.370 mV* —0.294 -0 123 -0.055 +0 105 +0.011 -0 134 +0.106 -0.178 -0. 193 TypeC 437.990 mV* -0.217 +0 107 +0. 121 +0 332 +0.160 +0 160 +0.366 +0.008 +0.241

First transition duration Type A 4.083 nsec +0 063 -0.016 +0 049 +0.083 +0 048 +0.147 +0.038 +0.006

Type B 4.027 nsec -0.056 +0 056 —0.155 +0 135 +0.043 -0 018 +0.157 +0.045 -0.088

Type C 4. 123 nsec +0.040 +0 062 -0.042 +0. 038 +0.092 +0. 006 +0.035 +0. 121 +0.081

Last transition duration Type A 4.388 nsec +0 038 +0.077 +0 013 +0.016 +0 141 +0.069 +0.046 +0.070

TypeB 4.492 nsec +0.104 —

0

099 -0.062 +0 069 +0.003 +0 171 +0.176 +0.032 -0.090

Type C 4.471 nsec +0.083 +0 077 +0.058 +0 059 +0.023 +0 157 +0.056 +0.085 +0.110

Pulse duration Type A 44.058 nsec +0 182 +0.009 +0 036 -0. 128 +0 045 -0.358 +0.308 +0.136

TypeB 44.034 nsec -0.024 +0 027 -0. 170 +0 159 -0.272 +0 034 —0.762 -0.302 +0.078

Type C 43.961 nsec -0.097 +0 063 -0.086 +0 021 -0. 109 -0 064 -0.315 -0.251 +0. 155

•Indicated data multiplied by 10.

The results summarized in Table 2 indicated that the operation of CAOS (and all other hardware)

under the PPD program was approaching a state of statistical control, insofar as precision was concerned.

The sample sizes are of course, too small to warrant any firm conclusions.

Hence, an additional program was written which executed the Type A test 100 times and computed the mean values and standard deviations for the four major pulse parameters. The results are tabulated in Table

3.

Table 3 Short term variations in indicated pulse parameters. Statistics on 100 Type A tests. Vertical full scale—800 mV;

horizontal full-scale—100 nsec.

Pulse parameter

Mean

(in units shown) Standard deviation

(in units shown) Standard deviation

(in % oj full scale)

Pulse amplitude 445.974 mV 0.593 mV 0.0741

First transition duration 4.16860 nsec 0.03252 nsec 0.03252

Last transition duration 4.52299 nsec 0.03199 nsec 0.03199

Pulse duration 44.4658 nsec 0.0826 nsec 0.0826

65
The data in Tables 2 and 3, unfortunately, are only indicative of the precision that CAOS, or similar

instruments, can bring to the pulse waveform measurement art. In all of the data presented variations from a variety of sources are combined. These sources of variation, in an estimated order of their contributions are:

1) the vertical and horizontal circuits of the sampling oscilloscope,

2) the pulse generator,

3 ) the A/D converter in the CAOS terminal,

4) the 20 dB attenuator,

5) the pulse distorting circuit, and

6) the interconnecting cables and connectors.

Variations due to items 3 through 6, above, are amenable to evaluation and control, but variations due

to item 2, the pulse generator, are a formidable obstacle to find all conclusions relative to the precision

provided by CAOS.

Precision and Accuracy

The discussion in the previous section considered precision only; some final comments on accuracy are

in order. As Eisenhart concisely puts it, "...accuracy requires precision, but precision does not necessarily

imply accuracy" [5]. The data presented in this paper demonstrate that CAOS and the PPD program provide

precision pulse parameter determinations. But precision, valuable as it is as a prerequisite to accuracy, is only the first step. The second step from precision to accuracy is far from trivial, since it requires the

development of a) pulse (or transition) generators and b) time mark generators whose characteristics are known to accuracies consistent with the precision CAOS provides.

As described elsewhere [1], the CAOS vertical calibration hardware provides dc calibration in the

voltage (or vertical) axis of the oscilloscope. Useful as this feature is, it does not provide for determination

of the transient response of the sampling channels. Sampling oscilloscopes with bandwidths in the 20 GHz

region are currently available. Consequently, a pulse generator with a transition duration in the 5 to 10 psec

range is required before an algorithm that compensates for oscilloscope frequency response can be included

in CAOS software. Horizontal (i.e., sweep linearity) calibration of CAOS is, of course, possible with

external oscillators or time mark generators of suitable accuracy.

Conclusions

The data presented in this paper — using pulse parameter determination as a vehicle ~ demonstrate the

precision which can be realized by augmenting the sampling oscilloscope with appropriate digital processing.

Since the CAOS hardware and procedures for acquiring waveform data are invariant, other digital processing

algorithms that preserve and exploit the inherent system precision in other types of waveform analysis ensue.

In addition to the program for pulse parameter determination, programs for spectrum analysis, convolution

and deconvolution, digital filtering, and time jitter correction are available to the CAOS user. Programs for

distortion analysis, circuit delay analysis, integration and others are envisioned and will be added as the need

develops.

Digital systems for data acquisition, control, analysis and display are commonplace in industry and in laboratories. The oscilloscope, very probably, is the one instrument most used in the development of such

systems. It is ironic that this versatile instrument itself is only now being given a degree of precision and

greater versatility through automation of the type that CAOS provides.

66
It is a pleasure to acknowledge the encouragement and support of J. S. Birnbaum and the technical

assistance of R. J. Arculeo and W. L. Keller.

References and Notes

[1] P. E. Stuckert, "Computer Augmented Oscilloscope System," IEEE Trans. Inst. Meas. IM-18, 299

(1969).

[2] B. J. Elliott, "A System for Precise Observations on Repetitive Picosecond Pulse Waveforms," IEEE

Trans. Inst. Meas. IM-19, 391 (1970).

[3] K. Maling is now located at the Systems Development Division Laboratory Poughkeepsie, New York.

[4] J. T. Boatwright, "Random Sampling - A Statistical Measurement Approach," IEEE WESCON

Technical Papers, Vol. 10, paper 23/4, 1966.

[5] C. Eisenhart, "Realistic Evaluation of the Precision and Accuracy of Instrument Calibration Systems,"

/. Res. Nat. Bureau Stand. Eng. Inst. 67C, 172 (1963).

67

Status of Reference Waveform Standards Development at NBS

J. R. Andrews*

Picosecond Pulse Laboratory

Lafayette, Colorado 80026

N. S. Nahman and Barry A. Bell**

National Bureau of Standards

Boulder, Colorado 80303

ABSTRACT

NBS has developed a (step-like) pulse generator for use as a transfer standard

for transition duration (10% - 90%), t^. The generator consists of a tunnel

diode step-like generator (t = 20 ps) driving a low pass filter. Three filters

are available for t = 50, 100, and 200 ps. The low-pass filters, of NBS

design, are 30 cm long, 7 mm diameter, coaxial lines filled with a lossy

Debye-type liquid dielectric. The mathematical model describing these low pass

filters is quite accurate. The necessary parameters for the model can be

obtained from independent measurements. The complete available output waveform

into a matched load (50 ohms) can be predicted to within less than 1.5%. A

companion step-like generator is presently under development to provide

well-known top and baselines with a transition duration of less than one nanosecond.

Key Words: Calibration; reference waveform generators; rise time; time domain

measurements; transfer standards; transition duration; waveform generation;

waveform measurements.

INTRODUCTION

The two objectives of the reference waveform standards development projects have been to develop two independent pulse generators for use as transfer standards for the pulse parameters:

(1) transition duration and (2) base and topline, respectively. The status of these projects are discussed below in Sections 1 and 2.

* J. R. Andrews formerly with the Electromagnetic Technology Division, National Bureau of

Standards, Boulder, Colorado.

** Barry A. Bell on detail from the Electrosystems Division, National Bureau of Standards,

Washington, D.C.

69
I. TRANSITION DURATION TRANSFER STANDARD

1. 1 Objective and Concept

The objective of NBS in this project was to develop a pulse generator suitable for use as a transfer standard for transition duration. The specific requirements were: (1) step-like pulse,

(2) transition duration of the order of 100 ps, (3) smooth, gaussian-like transition, and (4) clean

baseline and topline. The concept chosen for the implementation was to use a tunnel diode to generate a fast, (y 25 ps) , but not necessarily well known, step waveform. The fast transition is

then slowed down using a known low-pass filter. If the step response of the filter is 10 times

slower than the driving pulse, then the transition duration of the output pulse from the composite

generator is approximately within 0.5% by the step response of the filter alone. This follows from

a gaussian filter model excited by a step-like gaussian input signal. The output signal would be

step-like and have a transition duration, TD~, given by

where TD^ and TD^ are the transition duration of the input signal and the step-response of the

filter, respectively. For TD equal to one-tenth of TD„ , TD„ is approximately equal to 1.005 TD«

.

Some pulse equipment manufacturers in the past have made low-pass filters which were designed

for a clean time domain response. Some of these commercial filters were found to have a serious

defect. The leading edge of their step response was distorted with many small glitches, figure 1. These glitches were readily observable using a 20 ps tunnel diode pulse generator and a 20 ps sampling oscilloscope. They were caused by multiple paths and reflections from the various elements

used to construct the filter.

Another filter that has been proposed [1] is a long length of coaxial cable. The skin effect

gives a loss proportional to\/f". The pulse response of a cable is usually quite clean, but it is

also unsuitable due to the extremely slow approach to its final value (commonly referred to as dribble-up), figure 2. Furthermore, low pass filters with a sharp cut-off frequency are also

unsuitable due to ringing and overshoot in their time domain responses, figure 3, [2]. NBS has

found that a suitable time domain filter for transition durations from 50 ps to 500 ps can be

obtained from a coaxial line with a lossy dielectric [3].

A lossy, distributed filter was chosen by NBS for use as a transfer standard [3]. It consists

of a coaxial line filled with a lossy liquid dielectric.

The dielectric is a dilute solution of 2-Heptanone in Heptane. The Heptane solvent is

non-polar and essentially loss-less. The 2-Heptanone solute has a polar molecular structure and

1.2 Selection of Filter

1.3 Filter Model

obeys the Debye dielectric equations [4]. The behavior versus frequency of the real (e') and

70
imaginary (e") parts of the dielectric function (e) are shown in figure 4. is the dielectric

constant of the non-polar Heptane. e', e" and the time constant x are functions of the molal

concentration of the 2-Heptanone in the Heptane.

Figure 5 shows the per unit length equivalent circuit of a coaxial line with a Debye-type

dielectric. s is the complex frequency. L is the normal series inductance, k is the skin effect

constant for the metal conductors. + is the normal low frequency shunt capacitance

(proportional to e^) , t is the relaxation time constant of the polar solution.

The transfer function, H(s), of a transmission line of length I terminated

characteristic impedance, Z (s), is given by

H(s) = V (s)/V. (s) = e "Y(s) '^ out in

where y( s ) is the propagation function, y and Z are defined in terms of the series impedance per

unit length, Z(s), and the shunt admittance per unit length, Y(s).

Y (s) = v/ Z(s)Y(sT (2)

Z q

(s) = >/z(s)/Y(s) (3)

Z(s) = sL + k yjs (4)

Y(s) = sC(s) (5)

C(s) = A e(s) (6)

e ' - e

' e (jco) = e'(w) - je (a)) = + _o °° ^

1 + JWT

By varying the molar concentrations, and x are varied and as a result, Z^ and y can be

adjusted. The effect of varying concentration on the step response transition duration is vividly

demonstrated in figure 6.

Using eq. (1), and equivalent circuits for the connectors the complete step response waveform,

figure 7, of a Debye line filter can be predicted. Note the clean, gaussian-like transition. The

various filter parameters can be determined from independent measurements. k is a function of the

line diameters and the metal conductivity. is determined by 1 kHz capacitance bridge

measurements, e' is determined by the index of refraction of Heptane. L and A are determined by

in its

(1)

71
the line diameters. With and known, by analyzing experimental time domain data [5] and/or

frequency domain data [6] in terms of eq. (7), the value of t can be determined.

1 . 4 Hardware

Figure 8 is a photograph of an NBS Debye line low-pass filter with a tunnel diode step

generator attached. Three different filters have been designed and developed for transition

durations of 50 ps, 100 ps and 200 ps . A 30 cm, 7 mm diameter coaxial air line is used. Different

molal solutions are used in each of the three models. The center conductor diameter is varied to maintain a 50 ohm impedance in each model. Modified APC-7 connectors are used. The center

conductor support bead was modified to provide a leak-proof seal.

The dielectric characteristics of the fluids used are quite temperature sensitive. The

temperature coefficient of the transition duration is approximately 1%/ C. Thus, it was necessary

to provide temperature regulation to better than 0.1°C. The filters are operated at 30°C and are only intended to be operated in a standard laboratory environment. Heaters and temperature sensors

are installed in the filter box.

Also enclosed in the box is the necessary plumbing and valve for filling the line and an expansion bellows to compensate for fluid expansion and contraction due to temperature extremes

encountered during shipping.

The tunnel diode (TD) used to drive the filter is of commercial manufacture. The TD bias

supply and trigger pulse generator is an NBS design which is superior to commercially available

units, figure 9. The NBS bias supply has the advantage that it automatically compensates the TD bias current for changing TD conditions such as temperature, various electrical loads ranging from a short to an open circuit and even using a different TD. The trigger pulse circuits were designed so that they introduced negligible distortion to the TD step-like pulse as shown in figure 10a. This was a considerable improvement over the commercial bias supply which added a 5%, 1/2 ns linear ramp

distortion prior to the abrupt transition of the TD.

1 . 5 Waveforms

Deconvolved, measured output waveforms from the tunnel diode and the 50 ps, 100 ps, and 200 ps

filters are shown in figure 10. Figure 11 is the predicted, available, reference waveform,

e (t) , into a 50Q load from the TD/100 ps low-pass filter combination. It was obtained by

aconvolving the tunnel diode waveform with the filter impulse response function. The tunnel diode

waveform, figure 10a, was first obtained by deconvolution of the measured TD waveform and a model of

the sampling oscilloscope used to make the measurement. The deconvolution technique [8,9] and

sampler model [10] were developed at NBS.

Figure 12 is included to demonstrate the agreement between theory and experiment. The solid

curve, e (t), is the mathematically predicted waveform (TD/100 ps filter), while the dotted one,

3. e (t), is the actual measured waveform. It is meaningful to compare two similar waveforms to m

72
determine the difference between them [11]. The difference between these two waveforms, d(t), is

shown for a 2 ns time window. The RMS difference was 0.4% while the maximum difference was 1.4%.

II. TOP AND BASELINE TRANSFER STANDARD

2 . 1 Objective and Concept

The objective for this NBS project is to develop a step-like pulse generator suitable for use

as a transfer standard for both baseline and topline. The generator is to provide known baseline

and topline magnitudes and to possess a predictable transition duration of less than one nanosecond.

A laboratory experimental model or prototype has been built and is presently being modeled and

evaluated using computer simulation. The information presented below describes the prototype

generator and preliminary waveform data.

The basic concept of the generator, hereafter called the flat-pulse generator, is illustrated

in figure 13. A known DC current, I, drives a terminated transmission line having the HF parameters: Characteristic impedance, R^, and a velocity of propagation, v. The DC current

produces a topline magnitude of IR^ volts. At t=0, the current generator is switched-of f , and the

transmission line output voltage, e(t) decreases to the baseline magnitude of zero. The step-like

waveform, e(t), then provides known top and baseline magnitudes.

2 . 2 Pulse Generator

The flat-pulse generator block diagram is shown in figure 14. A crystal clock (10 MHz) drives

logic countdown and delay circuits to produce a trigger output pulse and a delayed main pulse. The

repetition rate is variable from 1 KHz to 1 MHz while the delay circuit produces selectable delays

of 100 ns from zero to 300 ns. Oscillograms of the main output pulse are shown in figure 15 while

figure 16 shows the output pulse as measured by the NBS Automatic Pulse Measurement System [12,13].

The pulse parameter magnitudes and amplitude values given in figure 16 should be multiplied by a factor of 2, e.g., the pulse amplitude is 511.486 millivolts. The magnitude histogram is given in

the left hand side of figure 16 and attests to the flatness of the pulse. The prototype generator

is shown in figure 17.

SUMMARY

The status of NBS reference waveform generator development has been presented. Two generators

have been described, one being a transfer standard for pulse transition duration (50, 100, and 200

ps) , and the other is a transfer standard for topline and baseline (nominally 0.5 and zero volts,

respectively) having a predictable transition duration of less than one nanosecond. The development

of the transition duration transfer standard has been completed while the top/baseline generator is

in the prototype evaluation stage of development.

73
REFERENCES

1. McCaa, Jr., W. D. ; Nahman, N.S. Generation of reference waveforms by uniform lossytransmission lines. IEEE Trans. Instrum. & Meas. IM-19(4) 382-390; 1970 Nov.

2. Blinchikoff, H. J.; Zverev, A. I. Filtering in the time and frequency domains. New York: J. Wiley and Sons; 1976.

3. Nahman, N.S.; Jickling, R. ; Holt, D. Reference waveform generation using Debye dielectric

dispersion. Nat. Bur. Stand. (U.S.) NBSIR 73-304; 1972.

4. Debye, P.: Polar molecules. Chemical Catalog Co.; 1929. (Also Dover Publications, New York).

5. Bagozzi, R. P.; Ives, W. R. ; Nahman, N.S. Determination of the dielectric relaxation time in a Debye binary liquid by pulse measurements. Progress in Radio Science 1966-69, V.2, 257-265,

URSI Brussels, 1971.

6. Von Hippel , A.; Dielectrics and waves. Wiley, New York, 1954.

7. Von Hippel, A.; Dielectric materials and applications, Wiley, 1954.

8. Nahman, N.S.; Guillaume, M.E. Deconvolution of time domain waveforms in the presence of noise.

Nat. Bureau of Stand. (U.S.) Technical Note 1047; 1981 October.

9. Guillaume, Michel E. ; Bizeul, Jean-Claude. "Mesure de la response impulsionelle d'um milieu de

transmission: application aux fibres optiques" (Impulse response of a transmission medium:

application to optical fibers), Annales des Telecommunications; 36(3-4), 1/8-8/8; 1981

March-April.

10. Riad, S. M. ; Nahman, N.S. Modeling of the feed-through wideband sampling head. IEEE-MTT, Int. Microwave Symposium Conf. Digest, Ottawa, Canada, 1978, June 27-29.

11. Nahman, N. S. Error criteria and the use of reference waveforms. Proceedings of the ATE

Seminar/Exhibit, Pasadena, CA. 1981, Jan. Benwill Publications Corp., Boston, MA. 02215; pp IV-21 to IV-28.

12. Gans , W. L. Present capabilities of the NBS automatic pulse measurement system. IEEE

IM-25(4), 384-388; 1976 Dec.

13. Nahman, N.S.; et.al. Applications of time-domain methods to microwave measurements. IEE Proc. 127(Pt. H, No. 2); 99-106; 1980 April.

74
e(t)

Figure 1. Commercial 2ns transition duration

standard. Note small steps on the

leading edge. The lower curve shows

the leading edge on a faster time

scale.

e(t) ;

t

Figure 2. Step response of a typical coaxial cable

with skin effect loss. Note the long

dribble-up, i.e., the slow approach to

the final value, E.

75
f (t)

> t

Figure 3. Typical step response, f(t) of a low

pass filter having a sharp cut-off

frequency.

o

Figure 4. Debye type dielectric function.

76
sL

T- C,/05

Figure 5. Per unit length equivalent

circuit of a transmission

line with Debye type

dielectric.

Figure 6. Step response transition duration versus Debye dielectric doping.

77
250 ps 500

Figure 7. Step response of a Debye dielectric, coaxial

low pass filter.

78
79
30
Figure 10. Measured and deconvolved waveforms from

the (a) tunnel diode and the (b) 50 ps,

(c) 100 ps, and (d) 200 ps low pass

filters.

81
® 250 ps 500 ps

Figure 11. Available Reference Waveform into a

50 ohm load from the TD/100 ps filter

combination, e a

(t).

82
Figure 12. Overlay of a predicted 100 ps reference

waveform, e„(t), and the actual measured

waveform (dotted line), em(t) and their

resultant difference, d(t). The waveforms

are aligned so that their 50% values coincide

with each other.

83
i(t) Transmission Line. HF parameters

R , v.

o

R e(t)

Figure 13. The basic concept of the flat-pulse generator. A known

DC current, I, is applied to a transmission line load and

then switched-off to establish a known step-like voltage,

e(t).

84
3

CU a,

CD

u 3 H 3

•H 3 o

co cm CU U CO 4J CU iH

•X) 3 CxO 3

cu cx (50 >> 4J •H

CO 3 M

rH

O

H

CU Q

OO

m

4-» J= 3 O

CU 4-1 H •H 3 c/3

4-» ,3 3 O

CU 4-1 rJ -H 3 c/: U 3OI 4-! 33O

CO 4J •H3ou

•HO

CO rH

CU O 3

CU rH o O o o CO

rJ CN 3.

>> 4J

CO 3 O

rH o o O

CUu o Q rH

#» oN

cu rH

4-1 o rH

CO t-l 4-1 o 1 3 4J a. o

CU c_>

N

E3

rH

Uo

4-1

CUC

0)603I u

CO rH

<4H

01 XI

4-1

4-1oi

5-i 60

CO •HT3

CJO

rH

cuu3

60

•H

85
Figure 15. Main pulse output of the flat pulse generator. The lower

oscillogram sweep rate is five times that of the upper one. See figure 16 for vertical/horizontal scales.

86
87
U.S. GOVERNMENT PRINTING OFFICE: 1982-0-360-997/2151 38
NBS-114A (REV. 8-78)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS SP 634

2, Gov't Accession No.

4. TITLE AND SUBTITLE

Proceedings of the Waveform Recorder Seminar

Proceedings of the Seminar on Waveform Recorder Measurement

Needs and Techniques for Evaluation/Calibration,

held in Boulder, CO, Oct. 15, 1981

t. Recipient's Access iw No,

5. Publication Date June 1982

$. Performing Organization Code

7. AUTHOR(S)

Robert A. Lawton, Editor

8. Performing Organ. Report No.

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, DC 20234

10. Project/Task/Work Unit No.

12. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, city, state, ZIP)

Same as Item 9.

11. Contract/Grant No.

13. Type of Report & Period Covered Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

Library of Congress Catalog Card Number: 82-6QQ552

I j - jcument describes a computer program; SF-185, Fl PS Software Summary, is attached.

16. ABSTRACT (A 200-word or leas factual summary of moat significant information. If document includes a significant bibliography or

literature survey, mention it here.)

In the past, for the most part, precision electromagnetic measurements were concerned with the measurement of parameters for sinusoidal (or steady state) excitation and response, e.g., magnitude,

phase, and power. One reason for the popularity of frequency domain measurement was that in this domain only one complete data point need be recorded to constitute a useful measurement. Recording

a thousand data points as required for precision time domain waveform measurements simply was not feasible. Today such frequency domain measurements are still important but now share their importance with transient pulse time domain measurements. With the emergence of integrated circuit components for (1) sampling or analog to digital conversion, (2) storage, and (3) control, real time digital waveform recording is now practical and widespread in usage. Furthermore, by coupling waveform recording components to minicomputers and microprocessors integrated circuitry it is now possible to record single events using compact systems (instruments) which acquire, record, process,

and analyze transient signals. In fact, the incorporation of digital computation integrated

circuitry appears to be a major driving force in expanding the role of waveform measurements in the academic, industrial and scientific communities.

We at the National Bureau of Standards are charged with the responsibility of encouraging the orderly "development of consistent standards and measurement techniques. We have been actively

engaged in waveform standards development for some time now and the papers in these proceedings will give a sample of what NBS and others in the waveform community have dene already. The afternoon session consisted of a workshop which addressed the questions: Where do we go from here? and Why?, culminating in the selection of a steering committee for the development of standards for waveform recorders.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the firat letter of the first key word unless a proper name;

separated by semicolons)

converters; electromagnetics; encoders; pulse; waveform generation; waveform

measurements; waveform recorder; standards.

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