A111D2 SM2Mm

I

NBS

PUBLICATIONS

NATL INST OF STANDARDS & TECH R.I.C. IMBSiR 86-3392 A1 11 0254241

Final Report: Technical Contributions

to the Development of Incipient Fault

Detection/Location Instrumentation

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

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

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Eiectrosystems Division

Gaithersburg, MD 20899

April 1986

Sponsored by:

QC lent of Energy

100 f Electric Energy Systems

|ton, DC 20585

86-3392

1986

C. 2

mRESEAnCM

INFOFUMTION CENTER

NBSIR 86-3392

FINAL REPORT: TECHNICAL CONTRIBUTIONS

TO THE DEVELOPMENT OF INCIPIENT FAULT

DETECTION/LOCATION INSTRUMENTATION

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

U S. DEPARTMENT OF COMMERCE

National Bureau of Standards

National Engineering Laboratory

Center for Electronics and Electrical Engineering

Electrosystems Division

Gaithersburg, MD 20899

April 1986

Sponsored by:

Department of Energy

Office of Electric Energy Systems

Washington, DC 20585

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

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

TABLE OF CONTENTS

Page

Table of Contents ill

List of Figures iv

Abstract 1

1. INTRODUCTION 1

2. NBS MEASUREMENT METHODOLOGY AND EARLY RESULTS 4

2.1 Time Domain in Reflectometry Measurements, Errors, and Corrections 7

2.2 Sampling, Windowing, Time-drift and Aliasing 10

2.3 Specific Measurement Techniques Used at NBS 15

2.3.1 Transmission Mode with Matched Resistive Adapters 15

2.3.2 Reflection Mode with Matched Resistive Adapters 17

2.3.3 Reflection Mode Using Abrupt Transition 17

2.3.4 Reflection Mode Using A Tapered Transition 27

2.3.5 Two -Lengths -of- Cable Method 31

3. MEASUREMENT RESULTS 31

ft

4. CONCLUSIONS 39

5. ACKNOWLEDGMENTS 39

6. REFERENCES 40

APPENDIX A A-1

APPENDIX B B-1

APPENDIX C C-1

APPENDIX D Dl-1

iii
LIST OF FIGURES

Page

Figure 1. Block diagram of the time domain reflectometer (TDR) and

data processing hardware 5

Figure 2. Typical TDR response waveform 6

Figure 3. Configuration for a simple reflectometry measurement. ... 8

Figure 4. TDR system connections for a two-step transmission

(substitution) mode of use. The measurement results

from (a) are deconvolved from those resulting from (b)

.

. . 9

Figure 5. Deconvolved transfer function results showing the effects

of delay time drifts. (See text for explanations.) .... 12

Figure 6. Error caused by sweep speed changes during the measurement

sequence. x(t) is the analytical function sampled at time

intervals T = r where r is an arbitrary unit of time. y(t)

is the same analytical function sampled at time intervals

T = r/1.01 13

Figure 7. Effect of sweep speed errors and changes on laboratory

deconvolved data. Compare to the results of figure 6 ... 14

Figure 8. The use of "L" t^rpe attenuators for approximate inipedance

matching and reducing the undesirable reflections at the

cable interfaces 16

Figure 9. Attenuation as a function of frequency of a pair of "L”

type attenuators (adaptors) used in making HV cable

measurements 18

Figure 10. Circuit configuration for making TDR cable measurements

incorporating the "L" type resistive adaptors 19

Figure 11. Pulse response with and without a cable when using the

resistive-adaptor circuit configuration shown in

figure 10 20

Figure 12. Equivalent circuits of the two- impedance cable system

where the interconnecting cable represents an abrupt

change of impedance 22

Figure 13. Voltage and pulse response when using an abrupt

transition method of measurement 25

Figure 14. Alternate method for time windowing TDR responses to

eliminate the effects of the interconnecting cable 28

Figure 15. Assembly drawing of the 50 to 37 ohm tapered line

transition section 29

iv

j
Figure 16. TDR response when using a 50-ohm system and a 50 to 37 ohm

tapered transition adaptor 30

Figure 17. Configuration for measuring cable loss using the

two -length method 32

Figure 18. HV-cable loss as a function of frequency using the

abrupt- transition and resistive-adaptor techniques.

(Cable supplied by manufacturer A.) Losses shown as attenuation in units of dB/meter of cable length 33

Figure 19. HV-cable loss as a function of frequency using the

abrupt- transition and resistive-adaptor, and

two-length measurement methods. (Cable supplied by

manufacturer B.) Losses are shown as attenuation in

units of dB/meter length of cable 34

Figure 20. Loss characteristics of the two resistive adaptors as

a function of frequency for three different test pulses. . . 36

Figure 21. HV-cable loss as a function of frequency using the

tapered- transition adaptor and the abrupt- transition

methods. Losses shown in units of dB/meter length of

cable 37

Figure 22. HV-cable loss, with and without semiconductor layers.

Losses shown are in units of dB/meter length of cable. ... 38

v
.•(»-- CSiJV:

. -;c":.-M5-6. rjolis.j: 'hp'i

''

'

,

-

•

'•.'V

*

.

‘/i _

= '• -"tf-y.'.tt' ji e«- .igetii, '. ,

" ' •"

\ A 'T>' _• -•' \*d'/l

1 • ^#‘4i«^\ dh-

'' • ' ?.

*

. %

irf5JSl>^

fin «• ^ *i« *.^**y^. $1

' •

'

SA Sifr- ',

' “ "- V'ft ^ V.:i ... J "•2'Stt^I’V - ' - - -' ‘ ‘ ;^s.'

'

,

.

rr- % ^.c. h m . '^^'-ttn-tt^Jf

• ’ ; ' '•rn\-:ii;' 'O ;'• r*v ;.tr- ad^.^'d.r -

- . _ . .' i

' v^-'

'

' <" ' ;•. V^-^V;‘ :.-,I'

p<. _.

I f
FINAL REPORT: TECHNICAL CONTRIBUTIONS TO THE DEVELOPMENT

OF INCIPIENT FAULT DETECTION/LOCATION INSTRUMENTATION

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

Abstract

The transmission of electrical energy by use of underground cables

is increasing. Fault location techniques have certain limitations;

incipient fault detection and location would help reduce the maintenance

cost of these lines as well as improve the reliability of service. This

report discusses some test results related to RF-probing techniques

applied to high-voltage transmission lines. The high frequency losses

and attenuation in high voltage cables places certain ultimate

limitations on RF-probing techniques for incipient fault detection. Time

domain reflectrometry methods were employed to assess the RF- transmission

properties of high-voltage cables at frequencies as high as 6 GHz. Fast

Fourier transform deconvolution was used to obtain loss measurements as a function of frequency. The loss mechanisms were identified. The

measurement hardware and methods are discussed as well as an analysis

approach leading to the conclusions.

Keywords: deconvolution techniques; fast Fourier transforms; fault location;

high-voltage transmission; incipient faults; RF measurements; RF

properties; time domain reflectometry ; underground cables.

1 . INTRODUCTION

The objective of this NBS program has been to identify and, insofar as practical, remove technical barriers to the development of instrumentation for

use in detecting and locating incipient faults in underground power

transmission systems. This report will describe the results of the NBS

program since its inception in late 1978. Because the work during the period

through 1981 has been previously presented [1-3]^, only the major findings of

that work will be discussed here.

In recent years, there has been increased interest in the underground

transmission of electrical energy. One of the major reasons is economic. In

order to transmit ever increasing amounts of energy efficiently, higher and

higher voltages are required. These higher voltages require wider rights-ofway which are expensive, and in some cases in congested areas, simply are not

available. An alternative to this is to substitute several high-voltage

(e.g., 150 kV) underground cables for the required extra-high-voltage (EHV)

overhead line. These cables require significantly narrower rights-of-way

resulting in greater transmission energy density. The underground cables

could be conventional high-pressure oil- filled cables using wrapped Kraft

paper for the dielectric or they could make use of more recent technological

advancements such as extruded cross-linked polyethylene cables, compressedgas- insulated systems, superconducting cables, wrapped synthetic cables, etc.

^Numbers in brackets refer to the literature references listed at the end of

this report.

1
Besides Che increased energy densities underground transmission would allow,

aesthetic objections to unsightly transmission towers and environmental

problems such as radio and television interference would be eliminated or greatly diminished.

There are disadvantages to underground transmission as well. The cables

themselves are, in general, more costly than their overhead counterparts

partly because of the more complex dielectric system. Transmission losses due

to dielectric heating are a concern for some types of underground transmission

systems. Installation costs can be greater than for overhead systems. These

disadvantages are known and their effect on the system cost is calculable.

This is not the case for the problem of fault location and repair in

underground cables. Without accurate knowledge of the precise fault location,

considerable resources can be spent locating the fault site and making the

repair. The cost to repair the fault can be significant considering the

complexities involved with the splices. Because the downtime for underground

cables is unpredictable, the additional expense of redundant cables has often

proven necessary.

In order to help alleviate the problem of difficult and costly fault

locating and repairing, the Office of Electric Energy Systems of the

Department of Energy (DOE) issued a Request for Proposal (RFP) entitled

"Research and Development of Fault Detection/Location Techniques and/or

Equipment for Underground Power Transmission Cable Systems." This RFP

solicited proposals for the development of instrumentation to detect and

locate incipient faults in various types of underground transmission cable's.

An "incipient fault" is here defined to be the condition within a cable system

in which local insulation degradation is occurring at a significantly higher

than normal rate which, if not corrected, will' cause the cable system to fail.

If instrumentation which could detect and locate incipient faults did

exist, then a major disadvantage of underground power transmission would be

lessened. Assuming the incipient fault instrumentation could provide a warning in a useable time frame that a cable was going to fail (i.e., days as compared to microseconds) , then the defect site could be repaired during a scheduled outage. Repair would be simplified since the location of the

imminent fault site would be known.

As a result of the DOE RFP, contracts were awarded to three different

groups: Purdue University, SRI International, and Westinghouse Corporation.

The various projects funded were for the development of instr'umentation to

detect and locate incipient faults using both radio -frequency (RF) probing of

the cable dielectric and detection of electrical and acoustical noise

emanating from the incipient fault site. A brief description of each of these

three programs will follow. For more information refer to the contractors'

final reports [4-6]

.

The Electrical Engineering School of Purdue University proposed to

develop instriimentation to detect the electrical noise generated by an incipient fault. They assumed that for most forms of incipient faults partial

discharges would be present. Their technique involved using detectors at each

end of a length of cable to detect the electrical noise and maximize the time

correlation of the two signals by using a variable time delay analysis

technique. The amount of time delay necessary would indicate the location of

9
the incipient fault site relative to the two detectors. Purdue University

successfully designed and built the microprocessor-based instrumentation and

demonstrated it by accurately locating discharge sites in long lengths of lowvoltage coaxial cables. Despite fully meeting their program's objectives, the

unavailability of additional funding prevented them from demonstrating their

system on an installed power transmission cable.

SRI International had two separate programs to develop instrumentation to

detect incipient faults using RF-probing techniques. One of these, proposed

by the Remote Measurement Laboratory at SRI, involved using a swept- frequency

probing approach whereby the signal reflected from the incipient fault site

would be mixed with the transmitted signal. An analysis of the mixer output

would, in principle, indicate the location of the incipient fault site. This

approach relied on the assumption that the local cable impedance would be

different at an incipient fault site (e.g., the dielectric constant would be

changed due to impurities, voids, heating, partial discharge, etc.).

Instnamentation was developed incorporating this technique. The design

included means to mathematically counteract the effects of cable dispersion

using data obtained on actual transmission cable systems. SRI International

was not able, within the contract period, to demonstrate the success of this

approach in detecting incipient faults in either a model or actual

transmission cable system.

The second SRI approach was proposed by the Electronics and Radio

Sciences Division. This system was predicated on the assumption that an incipient fault site was an area of electrical nonlinearity. If this is the

qase, introducing two signals of frequencies f and f into the cable will

result in the generation of signals of frequencies (fl+ f2) and (fl- f2) at

the incipient fault site. The time delay between the introduction of the two

signals and the return of the difference- or sum- frequency will yield the

incipient fault site location. A complication arises, however, in that an

incipient fault site may not only be a locale of nonlinear behavior but also a source of partial discharges resulting in noise signals with frequency

components at the sxim-and difference- signals . This would make locating the

incipient fault site much more difficult. This system was not successfully

demonstrated during the contract period.

The R&D Center of the Westinghouse Electric Corporation proposed

determining the feasibility of using acoustic waveguides to detect and locate

incipient fault sites in compressed gas insulated transmission cables.

Similar to Purdue University, the assumption here was that a significant class

of incipient fault sites would involve partial discharges. Measurements were

made on the acoustic spectra of such discharges to determine the frequency

range of high acoustical activity. Next, the propagation properties of

various acoustical waveguides were determined over the same frequency range.

The Westinghouse conclusion was that an incipient fault detector/locator could

be developed for cables up to perhaps one kilometer in length. However, for

more representative lengths, the acoustic waveguides suffered too much

attenuation. Having successfully determined the feasibility of using acoustic

waveguides for incipient fault detection/location, they spent the remaining

time of their contract on acoustical-optical techniques (e.g., using the

acoustic signals generated by the partial discharges to modulate the light

transmission in a fiber optic waveguide). By the conclusion of the project

they had successfully demonstrated such a system in their laboratory. Since

3
the westinghouse Corporation proposal only called for a feasibility study with

no instrumentation development for delivery to the Department of Energy, they

fully met their objectives.

The DOE RFP resulted in the development of some instrumentation and the

demonstration of both the success and failure (or success of limited degree)

of some approaches. Specifically, Purdue University developed instrumentation

to detect and locate incipient faults using a noise correlation with variable

time delay technique. This instrumentation was demonstrated in the laboratory

and was ready for a full-scale test if funding had permitted. Westinghouse

Corporation demonstrated the limited feasibility of using acoustic waveguides

and the more promising approach of acoustical-optical techniques. SRI

International was not able to deliver either of the two instrumentation

packages proposed. Large amounts of data were generated in the attempted

development of this instrximentation which should be useful in the future.

Their lack of success does not imply that those two approaches are necessarily

impractical, although some of the measurements made at NBS and discussed below

indicate some serious limitations for any RF-probing techniques.

The role of the Electrosystems Divison of the National Bureau of

Standards was two-part. First, NBS monitored the efforts of the Department of

Energy contractors with regard to technical progress. Second, NBS provided

measurementsupport where needed. In the first area, site visits were held,

annual progress review meetings were convened, and reports were submitted to

the Department of Energy. With the benefit of these site visits and meetings,

it was apparent that the general area in which NBS could provide technical

support was in determining the RF- transmission characteristics of the various

types of underground cables. The previous annual report [1] and quarterly

report [3] provide an extensive account of the initial efforts in this area. For completeness, a brief summary of the NBS work is included in the next

section, along with subsequent efforts.

2. NBS MEASUREMENT METHODOLOGY AND EARLY RESULTS

The initial measurements involved the use of time-domain-reflectometry

(TDR) techniques to determine the RF properties of the various types of cable

dielectrics. A block diagram of the measurement system is shown in figure 1. The main components of the system were the digital processing oscilloscope and

the "smart" terminal. This enabled waveforms to be digitized and sent to the

terminal for processing. A typical TDR waveform is shown in figure 2. It was shown that TDR measurements can be quite sensitive in detecting small changes

in the cable impedance. For example, the small deformation effect of placing

a mass of 120 grams on a 15-kV extruded dielectric cable was detectable at the

ppm level. Unfortunately, no change in the same cable was discernible after

11 high-voltage breakdowns at one site across the cable dielectric. Whereas

the TDR input pulse has frequency components to the several gigahertz range,

sufficient to allow for detection of the resulting breakdown channel, no change was observed in the TDR response after the breakdowns

.

Extensive effort was made to improve the coupling of the high-frequency

components into the cable using a tapered transition section. While this

measurably improved the high-frequency coupling, the breakdown channel was still not detected. A series of measurements demonstrated conclusively that

the problem was high-frequency attenuation in the cable. That is, for the

4
Computer

Terminal

i

Oscilloscope

Step

Function

Generator

Sampling

Head

50-Ohm

Coaxial Cable

HV Cable Being

Measured

Figure 1. Block diagram of the time domain reflectometer (TDR) and data

processing hardware.
TDR

Response

Figure 2. Typical TDR response waveform.

I

6
most common type of underground cable dielectric, extruded cross-linked

polyethylene with inner and outer layers of semiconducting material, the

intrinsic high-frequency attenuation is too large to permit the detection of

localized dielectric changes such as breakdown channels, voids, metallic

impurities, "water trees," etc. The attenuation prevents RF-probing

techniques from being useful in detecting small "incipient" fault sites. At

this point in the NBS measurement program, RF-probing techniques were not

altogether ruled out for reasons discussed later.

With the above-mentioned equipment, NBS was in a position to provide

accurate data on the RF properties of some selected cable samples which would

enable system design optimization. The purpose here was twofold: to provide

the most accurate design data possible; and to confirm the large highfrequency attenuation that was observed in the earlier measurements. These

measurements will be discussed in detail.

2.1 Time Domain Reflectrometry Measurements, Errors, and Corrections

There are two common ways to use the TDR unit, either in a normal

reflectometry mode, or in a transmission or substitution mode. Figure 3 shows

the configuration for a reflectometry measurement. Here the step function

waveform passes through the sampling oscilloscope before leaving the 50 -ohm

measurement system. At the measurement reference plane, the pulse enters the

cable under test, which usually has an impedance other than 50 ohms. The step

waveform propagates through the cable, and after being reflected by the short

circuit termination', returns to the oscilloscope for viewing. Distortions are . produced in the waveform due to undesired reflections at the measurement

reference plane and are a major source of error. It will be shown -later in

the paper that errors introduced when the waveform passes to the 'right through

this plane are not compensated when the waveform returns to the left; hence,

corrections are needed.

Figure 4 shows the measurement system being used in the transmission or substitution mode. Here the step function waveform is first measured without

the cable (a) to establish a reference which includes information about the

actual generated waveform. A second measurement is then made after inserting

the high-voltage cable between the generator and the sampling oscilloscope.

By measuring the waveform output of the cable, (b) , the reference can be

deconvolved from it leaving only information unique to the cable. However,

six pieces of information are combined in this result and it may be ambiguous.

The desired result is the attenuation and total phase shift of the cable.

Included are the reflection losses and phase shifts at each of the reference

planes in figure 4(b) . It has already been alluded to that this distortion

produced at the reference plane is not the same entering and leaving the

unknown cable. But under some conditions an average effect can be calculated

and this artificial average can be used on both reference planes. Still, one average reflection loss and an average phase shift remain which are not part

of the desired information about the cable, and for which a correction must be

made

.

The error caused by a reflection can be measured and corrected to some

degree. This could be done in either the time domain or the frequency domain.

The problem of multiple reflections can, in most cases, be resolved more

easily in the time domain.

7
50-Ohm

HV

Cable

Being

Coaxial

Measured

Cable I/ 5 § o « O c

?1£ o

</)5 0) = ^ = c 0) D 0) c - 1-05 5 ® ;r u CC

gj

cr

O)

13

1/1

t13 OJ

>)u

OJ

OJ

s_

OJQ.

!=

U1

S_o

4-

n3

S_r:03co

C_3

OO

OJo

03

u_ 8
Measurement

Reference

Plane

1

1 step

Function

Generator

1

1 Sampling

1

1

1

Oscilloscope

a) Measurement of Reference Waveform.

HV Cable Being

Measured

Step

Function

Generator

Sampling

Oscilloscope

Measurement

Reference

Planes

b) Measurement of Cable Output Waveform.

gure 4. TDR system connections for a two-step transmission (substitution)

mode of use. The measurement results from (a) are deconvolved from those resulting from (b).

9
Consider the arrangement shown by figure 3. As the step waveform returns

from the short circuit and intercepts the reference plane, the difference in

impedance gives rise to a secondary reflection moving again down the cable

toward the short. The process will be repeated many times giving rise to a somewhat repetitive series of step functions. This causes the spectrum of the

original step function to be enhanced or suppressed at harmonics of the

repetition frequency in a way which is determined mainly by the length of the

cable and the severity of end reflections. Again, this is not desired

information and contaminates the measurement in a way which is difficult to

correct in the frequency domain.

Time domain measurement resolves this problem by "time windowing." The

only information that enters the measurement system is that which appears in a viewing time window, e.g., that which appears on an oscilloscope screen. If

there is enough time between the occurence of the desired signal and the

beginning of multiple reflections, the undesired signal can be delayed beyond

the observation window and does not contaminate the measurement. Time

windowing becomes difficult when the desired and undesired signals overlap in

time. Although some computer processing can be done to separate the signals

using techniques such as Prony's algorithm [7] or homomorphic deconvolution,

it is usually simpler to change the physical arrangement to allow more time

between the desired and undesired signals. For example, if multiple

reflections become a problem in the reflectometry mode of figure 3, it might

be possible to use a longer cable under test, allowing more time for the

reflections to return to the measurement system. On the other hand, consider

that a longer cable would have more attenuation and phase shift causing the

desired signal to become longer by the same ratio as the increase in time

between desired and. undesired waveforms so that ’the two still remain

overlapping.

Experiments have shown that in order to correct the effects of either the

simple input reflection or the multiple reflections, the additional

computations necessary introduce significant noise into the result and

therefore increase the uncertainty. So it seems reasonable to try to remove

the reflections by using some kind of impedance matching interface at the

reference plane. Several approaches have been used and the results will be

described later in this report.

2.2 Sampling, Windowing, Time -drift, and Aliasing

It was desirable to measure the attenuation of several power distribution

cables as a function of frequency. Time domain analysis was used to take

advantage of time windowing to remove reflections . The frequency domain

information was computed using a modified Fast Fourier Transform [8,9]. The

process of acquiring and digitizing the waveform introduced several errors.

Consider the time viewing window discussed above to be the trace on an oscilloscope screen. The easiest error to visualize is the uncertainty in

location of the step- like waveform along the time baseline. There are time

delay circuits built into an oscilloscope that an operator can use to position

the waveform to some desired location of the screen. Due to changes in

temperature or line voltage, this delay may change with time, and actually

move the waveform slightly. Some measurements are not sensitive to this time

delay drift, while others exhibit undesired errors with as little as

10
0.2 percent time shift (of full-sweep duration). The amount of drift can be

reduced by allowing several hours for the equipment to thermally stabilize.

In addition, for those measurements which require high precision delays,

software was developed which can measure the delay error in the digitized

waveforms and compute new waveforms that are time coincident. Time delays can

be corrected to less than 0.01 percent error. The curves in figure 5(a) and

(b) are taken from measured results using a method sensitive to time delay

drift. The method uses four acquired time domain waveforms, but these were

chosen to result in a deconvolved transfer function magnitude of nearly 0 dB.

Notice the somewhat cyclic noise in (a) with excursions greater than 1.0 dB.

These are due to a time delay shift of only a few tenths of a percent. After

computer correction of the delay error, the transfer function is much better

behaved as in (b) . Curve (c) is the result of an ideal measurement not

sensitive to this source of error. How this feature is used is described

later in the report.

A second source of error which occurs during waveform acquisition is

caused by an inaccurate knowledge of the sweep speed [10]

.

This has been the

subject of two papers (Appendices A and B) . The computer receives nominal

sweep speed information from the dial settings on the oscilloscope but the

actual sweep speed is determined by the electronics and may not agree. Even

worse, the sweep speed may not remain constant during the several acquisitions

needed for a single measurement. Figure 6 shows computer simulated results of

sweep speed drift. Curves (a) and (b) are identical computer generated step

waveforms except that the time base for (b) is one percent faster than for

(a)

.

Curve (a) was considered the input to a perfect lossless network,

"(b) was considered the output,, and the two were deconvolved. Without the time

shift, the two waveforms would have remained identical and the deconvolved

waveform should have been unity (0 dB) for all frequencies in the spectrum.

The one percent error in time actually produced the sloping spectral response

in (c)

,

producing 0.6 dB error at 10 percent of the normalized Nyquist

frequency. The usable frequency range for actual measured waveforms usually

lies between 10 and 20 percent of Nyquist frequency. So, the one percent

sweep time error could produce between 0.5 dB and 1.0 dB error in the

deconvolved spectrum. A software package was included which evaluates the

slope of (c)

,

and computes and corrects the sweep time error. Figure 7 shows

the same effect in real measured waveforms. Curve (a) is the deconvolved

spectrum of two time domain waveforms having the same sweep rate. Curve (b)

indicates the seriousness of a 1.0 percent error in sweep rate and the

corrected waveform appears in (c)

.

Probably the least obvious source of error in acquiring and digitizing

waveforms is aliasing. The waveform being acquired is sampled and stored

during the digitizing process. If too few samples are taken along the

waveform, the real shape is poorly described by the data and the resulting

spectrum will be distorted. This distortion is known as aliasing.

The obvious solution is to increase the sampling rate until aliasing is

reduced to an acceptable amount. However, there may be limitations set by Che

oscilloscope or acquisition system. Some have a fixed momber of samples

across the screen (e.g., 512 samples) or at least a maximum (e.g., up Co 2048

samples) set by the computer. If a waveform has many rapid transitions and

there are too few samples residing on these to adequately sample, it may be

possible to sweep faster, spreading out these rapid changes, and in chis way

11
Frequency (MHz) (Max; 10% of

Nyquist Frequency)

Figure 5. Deconvolved transfer function results showing the effects of delay

time drifts. (See text for explanations.)

12
(b)

Figure 6. Error caused by sweep speed changes during the measurement sequence.

x(t) Is the analytical function sampled at time Intervals T = t where

T Is an arbitrary unit of time. y(t) Is the same analytical function

sampled at time Intervals T = x/1,01.

13
14

Figure

7.

Effect

of

sweep

speed

errors

and

changes

on

laboratory

deconvolved

data.

Compare

to

the

results

of

figure

6.
permitting more samples for each transition. On the other hand, if there are some slowly changing portions of the waveform, it may be necessary to slow the

sweep speed so that all the important parts of the waveform appear in the time

window. The real difficulty becomes apparent in making cable measurements;

one portion of the waveform contains a veiry rapid transition while the other

portion is very slowly changing. Both portions contain important information

and it is often not possible to select one sweep speed that can present the

waveform properly. The rapid transition can be sampled properly by increasing

the sampling rate but only if there is no upper limit. Even then, there will

be many more samples than necessary on the slowly varying portion. Some

sampling oscilloscopes allow a variable sampling rate faster in the portion of

the waveform that change rapidly, and slower elsewhere. If the problem is

severe, it may not be possible to make the measurement in the time domain.

2.3 Specific Measurement Techniques Used at NBS

2.3.1 Transmission Mode with Matched Resistive Adapters

The simplest measurement configuration is the transmission mode shown in

figure 4. As was pointed out, there is a difficulty with reflections if the

cable is not the same impedance as the measuring system. It is possible to

match these impedances using simple resistive adapters. This was the first

approach.

The impedances of several cables were estimated by using time domain

reflectometry . A pair of "L" attenuators was built for each of the various

impedances using the design criterion that they would minimize reflections

with the least amount of attenuation. Figure 8 demonstrates the use of these

adapters. As described previously, a reference measurement is taken as in (a)

which includes information about the generator, measurement system and both

adpaters . This is deconvolved from measurement (b) leaving only the

characteristics of the cable. If the cable impedance is , then the

resistors and R

2

are calculated as follows.

Assuming that < 50 ohms, which was true for all cables tested,

- 50/[l - Z^/50]^/^

- Z^/(l -

As an example, one cable tested has an impedance Z^ - 37.0 ohms. This

requires that R.j^— 25.5 ohms and R

2 - 72.6 ohms. Adapters were built using

metal film resistors, with a parallel pair of 51-ohm units to approximate the

25. 5 -ohm resistor. These were connected to the center conductor of a BNC type

connector. Three 300-ohm resistors and a 270-ohm resistor were mounted

radially to approximate the 72.6-ohm shunt resistor. The physical layout was chosen to be roughly coaxial. Using these resistors, the calculated

attenuation of the pair of adapters is an appreciable 9.8 dB.

15
Impedance

of

Cable

to

be

Measured

16

Figure

8.

The

use

of

"L"

type

attenuators

for

approximate

impedance

matching

and

reducing

the

undesirable

reflections

at

the

cable

interfaces.
Considering the large loss in the adapters, excessive errors can be

predicted when the cable loss is very small. Suppose the cable loss at a certain frequency is only 0.1 dB. If the measurement is made in accordance

with figure 8, the loss in the cable would be the difference between the total

attenuation in (b) and (a) (i.e., 9.9 - 9.8 dB) . Since the desired quantity

is only one percent of the measured quantity, an uncertainty of less than one percent is required for the results to be meaningful. Such accuracy is

pressing the capabilities of the time domain measurement system, so the method

is best used only to measure large attenuations.

To evaluate the useful frequency range of the adapters, a substitution

measurement was made using the adapted pair as the unknown. Results shown in

figure 9 indicate that they have a constant attenuation of about 9.8 dB for

all useful frequencies. Even the variation above 400 MHz can be deconvolved

out of a measurement as long as the attenuation does not absorb too much of

the useful signal. The adapters have been used in measurements up to 2 GHz.

For large values of attenuation this measurement technique is relatively

easy to perform and yields results having low noise and small uncertainties.

It can be used on any length cable without concern for multiple reflections.

It is the one technique that could work equally well in the frequency domain.

Results of three sets of measurements taken with these adapters on a commonly used distribution cable showed that the attenuation is a linear

function of frequency, and this was true for almost all cables tested. It was

clear that the smaller values of attenuation deviate more from the, straight

line than the larger values, supporting the earlier claim that measurements in

this lower range are reaching the accuracy limit of the measurement system.

2.3.2 Reflection Mode with Matched Resistive Adapter

Figure 10 is a modified version of figure 3 with the addition of the

resistive adapter. The waveform that is viewed on the oscilloscope in (a) is

comprised of two parts, as shown in figure 11(a); the output from the step

generator passing through the oscilloscope toward the resistive adapter, and

the wave reflected from the short returning to the oscilloscope by way of the

adapter. The second part contains the information about the original

generated step waveform, the oscilloscope transfer function, the round trip

transfer function of the adapter and the short circuit termination. The first

part of the waveform does not contain this information and is time windowed

out as shown. The configuration in figure 10(b) contains all the information

of (a) plus a round trip transfer function of the cable as shown in figure

11(b), so that deconvolving (a) from (b) gives the cable characteristics. It

is important to recall that this attenuation will be twice as large as the one way- trip measured in the transmission mode.

2.3.3 Reflection Mode Using Abrupt Transition

The reflectometry mode depicted in figure 3 does not make use of matching

adapters and avoids the initial expense and time required to construct them.

But it should be clear by now that reflections could reduce the accuracy of

such a measurement and it is more convenient to use the matching adapters once

they are built. On the other hand, it has been shown that the losses in the

adapters can cause large errors when measuring cables with small attenuation,

17
Attenu.?tion

(dB)

Frequency (MHz)

I- i <ju ro 9 - Attenuation as a function of frequency of a pair of "L" type

attenuators (adaptors) used in maKing HV cable measurements.

I A

18
c

o

r-5|

o O E

JC « o

CO O I-

•5 i o «

Og

il£ 0)

W •“

L9

Figure

10.

Circuit

configuration

for

making

TOR

cable

measurements

incorporating

the

"L"

type

resistive

adaptors.
Generated

Step

(a) Without Cable I

Waveform Reflected

Usable

Time

Window

(b) With Cable

Figure 11. Pulse response with and without a cable when using the

resisti ve-adaptor circuit configuration shown in figure 10.

20
say less than 1 dB. For these lower attenuations and for quick evaluations,

it is useful to make a direct measurement without adapters (referred to as an

"abrupt transition" herein) and correct the result for the reflections.

First, consider how large these errors might be. It is straightforward

to calculate the reflection error as a step waveform passes across such an

abrupt transition. The equivalent circuits are shown in figure 12. In each

circuit, the transmission line is considered a Thevenin's equivalent circuit

with the source impedance equal to the line surge impedance just prior to the

plane defining the location of the equivalent circuit, and the load impedance

equal to the line surge impedance just after the plane. The Thevenin's source

voltage can be calculated from the load voltage and remains the same as long

as the source remains in the same cable . In each case , only the wave

travelling in one direction is considered as if it could be time windowed out

and separated. Also, only the first reflection from the abrupt junction is

considered. Multiple reflections are time windowed out of the problem.

For simplicity, consider both transmission lines to be lossless and their

impedances to be resistive (actually nearly resistive) . Beginning with

circuit (a), assign a source voltage V = e; the actual line voltage must be

e/2 because the source and load impedances are equal. At the abrupt junction

(b)

,

the source voltage is still that of the 50-ohm line, that is e, but the

voltage in the cable is now

e Z

V - — c 50 + Z ’

. . c

by simple voltage divider action. Once the wave has propagated into the

unknown cable (c)

,

the measured voltage remains the same (V ) but the new

c source becomes the unknown cable instead of the 50-ohm transmission line.

Therefore a new source voltage must be calculated from the actual load

voltage

.

Assume that the step wave is reflected from the open circuit termination

without attenuation. The same rules apply for the wave moving to the left (d)

and (e)

.

To calculate the transfer function of the abrupt transition,

consider that the equivalent circuits are resistive and, therefore, the

transfer function will be constant with frequency. The magnitude of the

transfer function is simply the dividing ratio of the equivalent circuit. It

is defined by

Transfer Function (TF) - Input Voltage

For the wave moving to the right.

V

TF - —

R V

50

eZ /(50 + Z ) c c_

e/2

2Z

(50 + Z)

For the wave moving to the left.

21
Measurement I

Reference

50U

Plane

Q>>

(0

o>c

fl) >

(0

V. J-C

0) ' '

<Df— CD

4->

U

OJ 03

i. "O

OJ OJQ- s E=

oj M-

+->

O

oo

O) Ln CD

!Z OJ .03 1—

J2l

U

03U +-> o.

OJU i_ c

03 03 •a

OJ c

o. 03

*r* 00 1 -M o C 2 OJ

4-) 00

OJ

O) S- -e Q.

+j OJ 4-o OJ .

00 Jd

+-> 03

•1

U

C5u CD

s_

C

— •1

u +-) o

+-> OJ c c

OJ e 1

o

03

u > i_

•r— OJ

:c -(-> ^3“ LU r—

c\j

OJ

i_CD

22
V 2(50)

TF = —

L V

c

100 eZ /(50 + Z ) c c eZ^/(50 + Z^) (50 + Z ) c

Notice that the transfer function is simply the voltage divider ratio across

the transition and is different in the two directions. This will be an

important consideration when developing the algorithm to correct the

reflection error.

Next consider the transmission loss that a wave suffers while passing

through an abrupt transition. (Strictly speaking, this is not an attenuation

since the transmission line and cable were asstimed to be lossless, but is due

to reflection loss.) The important point to consider is that the normal

equation for losses cannot be used. That is, loss = 20 log IV /V. I is not

valid because it tacitly assumes that the input and output impedances are

equal and have divided out in the ratio. Also, in general, V out and V in are complex so the magnitude of the ratio is needed. The correct approach

involves the input and output volt-ampere product, but since our equivalent

2 circuits are resistive, this simplifies to power calculated as V /R. So,

loss = 10 log

out out

2 ^ . /R.in

If this relationship is ,used with the voltages on either side of the

transition, the one-way loss' is

loss - 10 log

4(50Z ) c (50 + Z )^

c

and this is true regardless of the direction the wave propagates

.

On the other hand, the round trip transmission loss can be calculated

calling V the input and the output and both are in a 50 -ohm transmission

line. So, using

loss - 20 log ("^^^50 )

loss — 20 log

4(50)Z

(50 + Z )' c

and this is precisely twice the one-way loss as it should be.

Based on this reasoning and understanding that the round Crip transfer

function for the transition is precisely the voltage ratio,

( 1 )

23
4(50)Z

c TF =

2 (50 + Z ) c

it is permissible to construct an artificial one-way transfer function, TF,

which is simply the square root of the round trip TF, as

This is the geometric mean of the two real TFs and produces the correct value

of the one-way transmission loss using

This feature makes it simpler to perform the loss calculations if it is used

carefully

.

As an example, if the cable impedance were 37.50 ohms , the round trip loss

calculated using eq (1) amounts to 0.18 dB. One mustseriously question

whether the error is large enough to warrant correction. It certainly seems advisable when the attenuation being measured is less than 1 dB , and this is

the same range of attenuation for which the resistive adapters produce

significant errors.

Finally, let us generate the correct algorithm for the abrupt transition.

Now assume that the 50-ohm transmission line is a standard 50-ohm impedance

and is lossless, but the unknown cable impedance is not well known and has

losses to be measured. The configuration is shown in figure 13. The round

trip loss in the cable might be calculated from

is measured by the sampling oscilloscope as it propagates toward the

transition. Two usable reflections return, one from the transition and the

second from the open (or short) circuit termination at the far end of the

cable. This second reflection contains information about cable attenuation

and the round trip transmission loss of the transition. Basically the

correction algorithm must take the total measured loss and subtract the abrupt

transition loss.

Although the measurement is made in the time domain to take advantage of

time windowing to separate the various reflections , the correction algorithm

is done in the frequency domain. The voltages shown in figure 13 are the

spectral components of the actual waveform at one given frequency. Because of

the time windowing, the spectrum can be separated into single frequency

TF' = 7TF = 2750 Z

c (50 + Z ) c

loss = 20 logjTF'

I

( 2 )

loss = 20 log (V^ /V^) . However, V and V, are not directly measurable. Instead, a a b

(3)

step-like waveform

24
son

Cable

C

uwm o

"S

.t2,E

C 3 E o O E

x; •=: 0)

(0

O h- Eo

25

Figure

13.

Voltage

and

pulse

response

when

using

an

abrupt

transition

method

of

measurement.
complex spectral component from the generator as it approaches the reference

plane. is the portion of that is reflected back into the 50-ohm system,

and is the portion that enters the unknown cable. Voltage has made a round trip through the cable and approaches the reference plane. and

are the reflected and measured portions of , respectively.

To calculate the attenuation of the cable, it is sufficient to consider

power flow. The total attenuation and the reflection losses in the cable are given by

Total Power Loss = 20 log (V /V ) m^ g

This is valid since both Vmgand V are measured in the 50 -ohm system. The

reflection loss can be calculated as the ratio of the power propagated into

the cable divided by the power incident on the transition plane.

Reflection loss = 10 log

However, the cable impedance is not well known. It is easier to see that

the propagated power is the simple difference between the incident and

reflected power, or

Reflection loss = 10 log

= 10 log

Since this is the loss for a single pass through the transition plane, and it

has been shown that the attenuation is the same in either direction, the total

reflection loss is simply twice this number. Therefore, the attenuation of

the cable is just the difference between the total loss and the reflection

loss, or

/50 - V^/50

_Sl I- 7^50

g

2 2 2 (V - V )/V

, g r g

Net Attenuation = 20 log (V /V ) - 20 log f(V^ - V^)/V^

j

, ni g \ ® ^ S /

= 20 log (V V /(V^ - V^)) . (4) ^ V m g g

r /

Because this is based on a power relationship, the magnitude of the

appropriate spectral component can be used in the formula rather than the

complex voltage. However, it is also possible to calculate the complex

26
voltages V and V, in terms of V , V , and V and substitute directly into

a b g r m

eq (3) with identical results.

This calculation must be repeated for each frequency in the spectrum and

the BASIC program that accomplishes this is given in Appendix C. The waveform

is shown in figure 13 and is time windowed three times as shown. Portion (a)

is portion (b) is and portion (c) is V^.

If the waveform cannot be properly time windowed as shown in figure 13,

an alternate method shown in figure 14 can be used. Waveform (a) is taken

with a 50-ohm termination on the reference plane. Waveform (b) , (c) is taken

with the unknown cable on the reference plane but time windowed appropriately.

The (a) is V^, (b) minus (a) is V^, while (c) produces as before.

When a 50-ohm termination is not available that mates onto the reference

plane, the condition can be approximated by measuring a short (d) and open (e)

and taking half the sum of the two. This method is available in the software

package listed in Appendix D.

2.3.4 Reflection Mode Using a Tapered Transition

The ideal way to measure cable characteristics would be to use a lossless

impedance matching device between the measurement system and the unknown

cable, for example, a broadband transformer. These tests used a tapered

transition, consisting of a section of rigid transmission line with a center

conductor whose diameter increased uniformly along its- length transforming the

impedance from 50 ohms to 37.3 ohms. Figure 15 shows an assembly drawing of

the transition section. The right end has a high quality 50-ohm coaxial

connector on it, modified to connect to the stepped 50-ohm center conductor

and adapter sleeve. The TDR system connects to this coaxial connector. The

left end of the 35-cm long tapered section connects to the power transmission

line's center conductor. The slit section of the outer conductor clamps over

the outside of the power transmission line.

The tapered line is useful as a lossless transformer for frequencies

whose wavelengths are less than the length of the transition [11] . For

frequencies whose wavelengths are considerably longer, the taper looks like an abrupt transition. This can be seen in an approximate way from the time

domain waveform, figure 16. Portion (a) is just the initial step waveform as before. Portion (b) is the reflection from the taper and is a linear ramp

joining the voltage of the 50-ohm system to the voltage in the unknown cable

(approximately 37.5 ohms). Waveform (c) is the reflection from the unknown

cable and its short circuit termination. It is apparent that the transition

has a reflection and that its time characteristics are slower than the initial

step input. Also, considering that the spectrum for a step decreases

inversely with frequency, while for a ramp, it decreases as the inverse

squared, the reflected ramp waveform should have much smaller high frequency

components than the incident step, or conversely, the taper must be matching

the cable to the system better at high frequencies than at low. This

conclusion is also expressed in the reference [11].

27
Relative

TDR

Response

Time

Figure 14. Alternate method for time windowing TDR responses to eliminate the

effects of the Interconnecting cable.

28
29

Figure

15.

Assembly

drawing

of

the

50

to

37

ohm

tapered

line

transition

sect i

on.
Tapered

Transition

Section

O)c

'35

CD0) n

(Z O

“O

0)

(0

OS

0) t

0>E

I30

Figure

16.

TDR

response

when

using a

50-ohm

system

anda

50

to

37

ohm

tapered

transition

adaptor.
Over the frequency range that the taper functions well as a matching

transformer, the measurement can be made identically as with the transmission

and reflection modes using matched resistive adapters (sections 2.3.1 and

2.3.2 of this report). For very low frequencies, the taper can be considered

an abrupt transition and can be used as described in the previous section.

Frequencies in the range between these two extremes present some unique

problems and have not been completely analyzed. The methods described herein

will not function as desired for those intermediate frequencies.

2.3.5 Two -Lengths -of -Cable Method

Another method which is conceptually simple depends on measuring two

lengths of unknown cable as in figure 17. The "short length" measurement in

(a) includes information about the generated step waveform, the oscilloscope

response, the transition characteristics, and the attenuation of the shorter

length of cable. The measurement in (b) contains all of (a) plus the

attenuation of the additional length of cable. Deconvolving (a) from (b) by

frequency domain division gives the attenuation of the additional length of

cable. All other effects including the transition are removed from the

measurement providing that the waveform can be time windowed as in (a) and

(b) . Only part of the waveform is used and multiple reflections must be

excluded. Multiple reflections are characteristic of the length of the cable

and therefore different for the two lengths. During deconvolution, only those

effects which are identical for the two measurements can cancel, so both sets

of multiple reflections would contribute error into the result.

This method works well if the two lengths are not grossly different. The

time window must be long enough to capture the entire time response of the

longer cable. The same time window must be used for the short length and so

it must be short enough so that multiple reflections would not appear in the

window. The ratio of two lengths always had to be less than four. Other

cables with less loss might permit a larger ratio.

3. MEASUREMENT RESULTS

Several cables were obtained from each of four different manufacturers

and selected ones were measured for attenuation using the five methods

described above. Some of these results are given here to support general

conclusions

Figures 18 and 19 are plots of the log attenuation versus log frequency

for several cables and measurement methods. The log- log plot is used because

the attenuation is expected to be a function of some power of the frequency

and should plot to a straight line whose slope is that power. In general, the

attenuation in dB turned out to be a linear function of frequency so that the

straight lines on log- log paper have a slope of approximately one.

Two major loss mechanisms were considered for these cables; the resistive

skin-effect loss in the center conductor and the outer braid, and the

dielectric loss. Skin effect losses are known to increase as the square root

of frequency and plots with slopes of 1/2 would have been expected. Since

this was not normally found in the measurements, it was concluded that the

attenuation was principally that related to dielectric loss.

31
c

o

(Q

.ti .£

r E

o O E £ » (D

CO O H

c

o

+-* o

o

o

cc

o

c

LU

E

o

o

n

(Q

o

u. O

t

V

E

H

asuodsay yai

aAiieiay O)

c_

z:

ZTi

32

Configuration

for

measuring

cable

loss

using

the

two-length

method.
oo

COooooo

>»oc0) 3

O’0) w

u.

33

Figure

18.

HV-cable

loss

asa

function

of

frequency

using

the

abrupt-transition

and

resistive-adaptor

techniques.

(Cable

supplied

by

manufacturer

A.)

Losses

shown

as

attenuation

in

units

of

dB/meter

of

cable

length.
Frequency (MHz)

Figure 19. HV-cable loss as a function of frequency using the abrupttransition, the resistive-adaptor, and two-length measurement

methods. (Cable supplied by manufacturer B.) Losses are shown as attenuation in units of dB/meter length of cable.

3000

34
Figure 18 shows the results taken from a cable of manufacturer A. The

skid wires were removed and replaced with copper braid. The data marked with

a dashed line was taken using an abrupt transition and it fits a straight line

of slope 1.2 quite well. The data taken with the resistive adapters is drawn

with a solid line and seems to be composed of at least two straight sections,

the higher loss portion which nearly matches the abrupt transition curve and

the lower attenuation curve with a slope of about 0.88. This two-slope curve

is also evident in figure 19 for a cable from manufacturer B, and seems to be

characteristic of measurement made with these particular resistive adapters.

(The skid wires were left on this cable and no braid was used.) It appears to

be the result of a 0.3 dB constant systematic error added to the normal

measurement

.

To help determine the source of this error, the adapter characteristics

were measured using the time domain system. Two adapters were coupled

together forming a 50-ohm attenuator. As can be seen in figure 20, the

measured attenuation is 9.8 dB for all frequencies up to 400 MHz. The

calculated atteniiation is 9.8 dB, showing excellent agreement. This did not

provide a clue to the source of the 0.3 dB error which is still unresolved.

Figure 19 also shows results of a two -length measurement and is in only fair

agreement with the abrupt transition measurements.

Figure 21 shows data taken with the tapered transition compared with

abrupt transition data. Note how the two agree well at higher frequencies

where the taper matches well.

•It was important to decide if the loss was really due to the lossy

dielectric, and if so, what part of the cable was producing such large

attenuation. The loss of a one -meter length with various portions of the

dielectric removed was measured. In each case, a copper braid was pulled over

the cable. Figure 22 shows the losses (1) of the original cable, (2) of the

same cable with outer semiconductor layer removed, and (3) the same cable with

both inner and outer semiconductor removed and a copper rod replacing the

original aluminum conductor. Two conclusions are obvious. First, the cable

is six times lossier when both semiconductor layers are in place than when

they are removed. Second, a meter length of cross-linked polythylene cable

still is very lossy (1 dB at 1.5 GHz). All three curves have nearly the same

slope at lower frequencies. The slope of the curve for the cable with the

inner semiconductor removed has an obvious change of slope at about 1.5 GHz.

The steeper slope indicates that a second source of loss is becoming dominant

above this frequency. The source of this loss is not known, but it may be a skin effect loss at the surface of the copper raid due to the higher loss of

the solder layer plating the copper. It seems likely that it was also present

in the other cable configurations but was not so obvious because of their

higher dielectric losses.

An idea was proposed to propagate a microwave signal through the cable in

such a mode that practically all the energy was confined to the less lossy

polyethylene and would not penetrate the semiconductor near the metal

conductors. This last experiment indicates that at the frequencies required

to propagate for long distances, only the largest diameter cables could be

considered. For the small diameter cables (3-6 cm)

,

the frequencies must be

above 10 GHz. This compares to ordinary TEM propagation at 1 GHz at similar

losses for larger cables. The testing of small diameter cables is not

35
o

(gp) uojienuauv

36

Figure

20.

Loss

characteristics

of

the

two

resistive

adaptors

as

a

function

of

frequency

for

three

different

test

pulses.
Attenuation

(dB)

1

I I I / I I I I I I I I L .1 I l I '30 100 300 1000 3000

Frequency (MHz)

Figure 21. HV-cable loss as a function of frequency using the taperedtransition adaptor and the abrupt-transition methods. Losses shown

in units of dB/meter length of cable.

37
o

o

(aP) uoi;Bnu0UV

38

Figure

22.

HV-cable

loss,

with

and

without

semiconductor

layers.

Losses

shown

are

in

units

of

dB/meter

length

of

cable.
practical for long distances. However, it may become useful for short

distance cable evaluation.

4. CONCLUSIONS

The Department of Energy sponsored program on incipient fault

detection/location has resulted in significant contributions that should be

utilized in the future. Purdue University's time -delay noise correlator

passed all laboratory tests and appeared to be fully capable of meeting the

DOE objectives. Westinghouse has determined that acoustical -optical

techniques appear promising for the detection and location of incipient faults

in compressed gas - insulated cables. SRI has obtained vast amounts of data on

the propagation properties of several cables under actual field conditions.

They have explored the use of two different RF-probing techniques for

incipient fault detection/location. NBS has demonstrated some fundamental

limitations of using reflectometry approaches in extruded polyethylene cables.

In the process, good data on the attenuation of a variety of distribution

cables have been obtained. It appears that the largest source of loss in

these cables are the two semiconductor layers. Unfortunately, they are

required for satisfactory cable performance under high-voltage conditions.

The prospect of launching waveguide modes in these cables which would not

"see” the inner and outer semiconductor layers was briefly explored. The

results looked promising. It may be shown later that the attenuation is still

too high for incipient fault detection over appreciable distances, but the

waveguide approach might still be beneficial for cable manufacturers as an

online defect detector.

5 . ACKNOWLEDGMENTS

This work was sponsored by the Office of Electric Energy Systems of the

Department of Energy; Mr. Russell Eaton was the technical coordinator. The

cooperation of several cable manufacturers is appreciated, namely, Reynolds

Metals Company, Electrical Division, of Richmond, Virginia, Phelps-Dodge

Company, Yonkers, New York, Piralli Cable Company, Union, New Jersey, and the

Okanite Company, Ramsey, New Jersey. The Potomac Edison Company also provided

some cable samples which had been taken out of service. The authors would

also like to express thanks to Mrs. Barbara L. Frey who prepared this

manuscript

.

39
6 . REFERENCES

[1] Anderson, W.E., Ramboz , J.D., 1980 Annual Report. Technical

Contributions to the Development of Incipient Fault Detection/Location

Instrumentation, NBSIR 81-2235, Nat. Bur. Stand., March 1981.

[2] Anderson, W.E., Ramboz, J.D., Ondrejka, R.A.

,

The detection of incipient

faults in transmission cables using time domain reflectometry techniques:

technical challenges, IEEE Trans. Power Apparatus and Systems, vol.

PAS-101, No. 7, July 1982, pp . 928-1934.

[3] Hebner, R.E., Development of Power System Measurements - -Quarterly Report

January 1981 to March 31, 1981, NBSIR 81-2283, Nat. Bur. Stand., April

1981, pp. 4-7.

[4] Weeks, W.L., Final Report, Detection and Location of Incipient Faults on Power Cables, Contract No. ET 78C013214, Electrical Engineering School,

Purdue Research Foundation, February 1981.

[5] SRI International Final Report, not available at this date.

[6] Harrold, R.T.

,

Acoustic Waveguide Technique for Sensing Incipient Faults

in Underground Power Transmission Cables, DOE Contract No.

ET-78-C-01-2867

,

Westinghouse R&D Center.

[7] Van Blaric\am, M.L., Mittra, , A technique for extracting the poles and

residues of a system directly from its transient response, IEEE Ant. and

Prop., vol. AP-32, November 1975.

[8] Samulon, H. A., Spectrum analysis of transient response curves, Proc

.

IRE, vol. 39, February 1981, pp . 175-186.

[9] Waldmeyer, J., "Fast Fourier transform for step-like functions: The

synthesis of three apparently different methods," IEEE Trans., Inst.

Meas .

,

vol. IM-29, No. 1, (1980), pp . 36-39.

[10] Ramboz, J.D., Ondrejka, A.R.

,

Anderson, W.E., Sampling-rate drift

problems in transfer function analysis of electrical power cables, Proc.

of the Waveform Recorder Seminar, Ed. R.A. Lawton, Nat. Bur. Stand.

SP-634, June 1982, pp. 47-53.

[11] Skilling, H.H.

,

Electric Transmission Lines, First Ed., McGraw-Hill,

(1951) pp. 353-355.

40
Appendix A

Sampling- Rate Drift Problems in

Transfer Function Analysis of Electrical Power Cables

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

Reprinted from NBS Special Publication 634, Proceedings of the Waveform Recorder

Seminar, Edited by R.A. Lawton, June 1982.

A-1
.iiiilij^* .r:rs.»* .,«i ..

^

"TT" ..

''.'!n.;\ .-^< ' '-; !<j ,/l.r " .ii.-.:. i.y-v •'.->

v/O '

f

4,

I

'

' ®.."'

. '• ;i v<” '.i.fi'vr,' ,

' ; , k\ . a.

' ':' ./ /' ••: Cry

•

‘''V'*’,

' '% f .y.

v-';‘ ^' • "v^- ;^'^..,/ -•

'«n$ . , ; ; n^,r

. ,,

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

if icif 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-refl ectometry 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 tor

correcting the data are discussed and illustrated.

Keywords: sampl i ng-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 characteri sties 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 refl 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 correspond! ng 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- refl ectometry (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 sampl i ng-rate drift.

* Electrosystems Division, NBS, Washington, DC 20234

** Electromagnetic Technology Division, NBS, Boulder, CO 80303

A-2
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)

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.

A-3
TDR

Response

1r

T = 0 Minutes

Fig. 3. Erroneous cable attenuation results

due to sample-time drift.

Fig. 2. Typical TDR response waveforms for

two collection cycles.

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 10% 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’ resu-lt led the

authors to examine sampling-rate drift.

3. Sampling-Rate Shifted Data

Electronic sampl ing 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

No Shift

Shifted

Unshifted

Waveform

Shifted

Waveform

Sample-Time Interval

Fig. 4. An arbitrary rising waveform with and without bOmp! i ng-t ime drift.

A- 4
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

At 2 , 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 NAt 2 s 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 NAti, as indicated by the open dots. For ex- ample, for an increase in the sampling period from At^ to At 2 , 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.

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/(m2 + 100)1/2] + 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 sampl i ng-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 "dror>n" is clearly present and is entirely the result of the 1* shift in

sampling rate. A-5
Fig. 6. Analytically-generated wave forms having similar characteristics to typical TDR responses,

the lower waveform being time-shifted by 1%.

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 sampl ing-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 0(1)

which has the "droop" removed.

0(1) = {(I*A2-M)*[B(M+1 )-B(M)] + B(M) (2)

where 0(1) 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

^2 is a correcting factor derived from the slope.

A6
The correcting term ^2 ‘'s 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 ''s 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):

0(1) = 0(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

20%

Nyquist

Frequency

Frequency

Fig. 8. Corrected attenuation of the data shown in fig. 7.

to 20* of the Nyquist frequency.

CQ

“O

C

o

CO3

CO

<

+ 1r

For real TOR 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 lOA shows the

attenuation plot that resulted when no rate-shift correction was applied. Figure lOB shows the

corrected attenuation which removed the effect of the "droop" in an attempt to improve the results.

<D

(AC

o

Q.

0)O

CCcca

hFig. 9. Two TOR response waveforms, the second having a time shift of 0.1%

with respect to the first.

A-7
Frequency

(10% of Nyquist Frequency)

Fig. lOA. (Left) Attenuation results from waveforms shown in fig. 9 containing a sampling-time drift of 0.1?;.

Fig. lOB. (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 sampl ing-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.

Empi rical ly-deri ved 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 0 etecti on/Location Instrumentation, NBSIR 81-2235, Nat. Bur. Stand.,

March 1981.

A-8
1

iw.i'M V; 'l„

i.-.. « '.'^<v *|'.'%iiil®Wl ' '"

,

,

. '

r:

n' M

m®''

j--'- #

' %.^

t;

I . *' T , " Tflw"' ' \ ; ^ ,D'

i

)

vVC : ,.' ic;>l -

<*« M

f

3*r’* w*' ” . 1

'

' <*'.•*>•. ->v-t “^t r*" ' :’w r ':i»i^

' w . f- , v» -;•?'* . V . • 4V>^ »»5T< V''- > , •• fr 'if.'-J MW.-^ TV W?r ' •»'-> -

•.

‘ 1-t

' 'f.i . 5l.fli. - m*“-. c

••

V .

' ':t '••i--i-':;-r‘. 'v ^i».#i- • »• jk '

«

• _

. .‘a-^ rv !<•.-

;•>-? -fi X i

' ..,5 '^"' vffix 'i ';:' » ,,. -i--

, <'>.

)“ ! ;c* '-{r' ’ifi''' ’fet '• / ,

'/ :

' .. « * -i • H « }i 't'3: ; ixv ; S.V i’

;.•

' \t>i. i yi&.'i ',^:^aa>?i >• •, :'<;! H' ; 7wi; ;

;ji. ?>3 ^rs •>!«: •.'? 'fc4«i^ . .ip-!fi-''‘isfc-V'

•' '*••'•. «

'

. -(ftlTri 9/?7 ''^' ',>^3>'(l!i«l' WVfv; ^' '' i ''',{»,.; -fx'^ •<

; li'"'* i i - r

•

iKS ic-i *5>> U'^PV'..v ,'u «3tCVw* /'rvV7 :?vU;:-.- ?'.' . 'v-r? ^ii* 'i,» »

I .. . nu I

' ^S*rt' >

iT^

H' ^ 7 i iS A3 i H' ;7wi‘ ^4-.. ; *,';' ;y I’S'i A ,.i . ^ V. .,1f>>

<' 1

' ''.{M,‘-f>^’ '<

; I -r 1V*I7 9ii '* 'l 1'

as

”.0 O’** ! •I*.

i-., ?i."t :.:?<;« HW<1 "tTlS ' JM' *>?«*«; »P ,^o*'*'t*-t.

t t.

' iC- M'$r.: ::

' '•*

. w^'?2 9>r <

oHi:* . aV> 4* 'IVM A* >» ‘ > WTf

fS'"

j; : . .

C**»T.

', m

V:' - . "

< ,'*

-1-1 »<i?

Hk .

. r““"‘
Appendix B

The Effects of Sampling-Rate Drift on Transfer Function Measurements

W. E. Anderson and J. Hagler

National Bureau of Standards

Washington, DC

B-1
THE EFFECTS OF SAhP LING-RATE GRIFT ON TRANSFER FUNCTION ^EASIJREf€NTS

wilHan E. Anderson, Member IEEE Janes Hagler, Non-Menber

National Bureau of Standards

Washington, DC 20234

ABSTRACT

Digital sampling using waveform recorders represents a powerful and valuable technique in the field

of high voltage measurements. It enables a researcher

to study transient behavior by forming a replica of the actual event using the sampled data. This replica

nay not represent the actual event because of errors caused by the sampling process which may range from

quantizing errors in the waveform recorder's analogto-digital converter to aliasing caused by too few

samples.

For precise determination of the transfer function,

the stability of the waveform recorder’s "clock" poses

a limitation. Uncertainties in this "clock" will

result in similar uncertainties in the frequency domain

response.

The problems associated with the instabilities of

this "clock" (called sampling-rate drift) are presented.

Examples are shown for both actual data and a sampled

analytical waveform. Mathematical techniques for re- moving the effect of this drift are presented and

their limitations discussed.

Introduction

Digital waveform recorders (i.e., waveform recorders which use digital electronics to sample and store waveforms) have seen increased usage in measurement

applications in the electric power industry. Traditionally researchers measuring electrical waveforms

had to rely on a photograph of an oscilloscope trace

to store the waveform for later analysis. This subsequent analysis (e.g., a risetime calculation) re- quired time-consuming and often relatively inaccurate measurements with a ruler. With a digital waveform

recorder, all that has changed. The waveform recorder

can transfer the sampled waveform to a computer for

immediate analysis. Although these recorders are valuable for steady-state measurements, they are particularly useful for high voltage impulse and other

transient measurements [1].

While most researchers are familiar with oscilloscopes and can use then without difficulties, the use

of a digital waveform recorder can lead to errors, some of them quite subtle. The purpose of this paper

is not to list all the problems generic to the use of

waveform recorders, which has already been done by

others [2]. However, a presentation of a couple of the problems will illustrate the point that waveform

recorders should be used with care.

First, in order to avoid a problem called "aliasing," the bandwidth of the measured signal must be less than one half the sampling frequency of the waveform recorder [3]. For example, a 1-Wz waveform re- corder sampling a waveform having frequency components

through, say 10 Wz , will work in the sense that a waveform will be recorded. But this waveform will be an incorrect representation of the original waveform

and the uninitiated researcher may not be aware of the

problem at all. Second, uncertainties in the amplitudes

of the sample values are a problem. A typical amplitude

resolution for a waveform recorder is 1 part in 512. This resolution is limited by the analoq-to-digital

converter in the waveform recorder. In addition, digitizing errors occur, such as those caused by quantization noise, integral and differential nonlinearity,

offset, etc. Also, the calibration of the dynamic

performance of the converters poses a challenge. As a result, the amplitude accuracy of waveform recorders

is difficult to establish. These problems are subtle

in that the researcher may have little knowledge of their occurrence. Sampling-rate drift is a similar

problem and can have serious consequences in a par- ticular class of measurements.

The time base or "clock" in a digital waveform

recorder determines the sampling rate (number of samples

per unit time) of the instrument. This "clock" could

be a ramp generator or a quartz oscillator. If the

"clock" or time base varies, then the sampling rate

will also vary. This variation can lead to serious

problems when making transfer function measurements using time domain techniques. In such measurements a voltage step is applied to the system to be measured.

Both the input voltage and resulting output response

are recorded. Discrete Fourier transforms of the two digitized waveforms are then calculated and the ratio

of the magnitude of the frequency components of the

output to the frequency components of the input yield

the transfer function. If sampling-rate drift has occurred between the measurement of the input and

output waveforms, then the resulting transfer function

calculation will be compromised.

As an example consider figure 1. The lower waveform x(t) can represent the input to the system to be measured. The upper waveform y(t), instead of being

the output of the system, in this case also represents

the input. In the time domain they look very ruch

identical. If the two waveforms both represent the same input signal, then the ratio of their Fourier

transforms should be unity over the entire frequency

spectrum. Figure 2 shows the transfer function

h(o») for the two waveforms in figure 1 (see (R)

below). While the result could be interpreted as high-frequency roll-off, the real culprit is samplingrate drift. This example will be discussed in more

B-2
Experimental Considerations

Figure 1. x(t) and y(t) show two actual sampled waveforms taken one minute apart.

Figure 2. h(o)) shows the effect of sampling-rate

drift for the two sampled waveforms in figure 1. Note the roll-off with increasing frequency.

detail later in this paper. For the researcher interested in power spectrum measurements, sampling-rate

drift is not much of a problem in that the shapes of

the time- and frequency-domain waveforms are only

slightly affected. The problem occurs In transfer

function-type measurements where ratios of waveforms

are calculated.

Besides alerting the power engineering community

that this problem can occur, this paper also discusses

in some detail what can be done to identify data affected by sampling-rate drift and what corrections can

be made to the data to minimize the effect of the

drift. Recommendations are then given as to the best

ways to deal with this problem.

The effects of sampling-rate drift were first re- ported by Ramboz , et al. [‘l-l. They were attempting to make high precision measurements (±0.1 dB) of the

transfer functions of various power cables using a voltage step generator. In a typical experiment, the

response in the time-domain to a voltage step was recorded after transmission through a length of the

cable to be measured. The measurement was then re- peated but with a longer length of the cable. Fourier

transforms of the two time-domain responses were calculated and the ratio of the second to the first yielded

the transfer function of the additional length of cable.

The resulting transfer functions sometimes showed rolloff or even gain, which were not observed in repeat

measurements and were, therefore, a measurement artifact

and not indicative of the properties of the power

cable being measured. Subsequent work revealed that

this measurement artifact was caused by a drift in the

time-base or "clock" of the waveform recorder which

resulted in a drift in the sampling rate.

The waveform recorder used in this early work and

for this paper was a digital processing oscilloscope.

The sweepspeed of the oscilloscope controls the sampling

rate. To determine the transfer function of the cable

under test, the response of the cable to a voltage step

is required. A voltage step generator is used to provide

the signal to the cable and the oscilloscope digitizes

the cable response by taking 512 uniformly spaced (in

time) samples across the waveform with an amplitude

resolution of 1 part in 1024. The digitized waveform

is then transferred to a computer for processing. The

experiment consists of acquiring two waveforms. The

first waveform is the response of the system consisting

of the output impedance of the step generator, the

signal cable connecting the generator to the power

cable under test, the electrical connector between

the signal and power cables, and some length of power

cable. The second waveform is the response of the same system as the first but includes a longer length

of cable. Therefore, the Fourier transform of the

second waveform divided by the Fourier transform of

the first waveform will give the transfer function of only the extra length of power cable. The effects of the signal cable, electrical connectors, etc., common

to both measurements will cancel. Discrete Fourier

transform software based on a modification of the fastFourier transform algorithm suitable for step-like waveforms was used to calculate the transfer function [5].

In the original measurements, having anticipated

some of the problems associated with instrumental

drift, care was taken to leave the digital processing

oscilloscope on for several hours before taking data.

Despite these precautions, problems caused by samplingrate drift were apparent in the computed transfer

function. Although the sampling-rate drift was small,

the precision of the measurement was large (±0.1 dB)

so the effects were apparent. (The effects of samplingrate drift are a function of both the size of the

drift and the rate of roll-off of the waveform in the

frequency domain -- see next section.)

For the data presented in this paper, the same instrumentation was used. However, to emphasize the

sampling-rate drift problem, the measurements were

taken immediately after the oscilloscope was turned

on. The other difference is that, unlike the initial

measurements, both measurements were made on the same length of cable. This was done to focus on errors due

to sampling-rate drift without having the additional

complexity due to the sample response.

B-3
It should also be noted that the fast Fourier

transforn used gives values for the discrete Fourier

transforn of x(t) at 256 points. The graphs of Fourier

transforns and h(u) in this paper are drawn in "analog form" although, of course, they are discrete

functions. In addition, the graphs of h(u) are shown

only for the first 70 of the 256 conputed points (i.e.,

frequencies up to 70/256 of the Nyquist frequency).

The higher frequency portion of the graphs exhibits a large noise component for real data due to the fact

that numbers close to zero are being divided by each

other. Neither time, frequency, nor amplitude scales

are shown on the graphs because they are totally arbitrary for the purposes of this discussion.

Theoretical Considerations

Recall that for a two-terminal pair network, the

voltage transfer function H(ju) is defined as:

= Vo(jo))/Vi(ju)). (1)

where Vo(jw) is the output voltage and V-j (joj) is the

input voltage in the frequency domain. Measurements of the transfer function are frequently, and conveniently,

performed in the time domain by measuring the step response. The unit step response is related to the

voltage transfer function through the inverse Laplace

transform

(Note: It is assumed that the sampling rate is constant

during the sampling of each of the two waveforms but has changed between the acquisition of the first and second waveforms.) Thus, in sampling the second waveform, the waveform recorder "thinks" it is sampling

at times T, 2T, ••• when it is actually sampling at times aT, 2aT, The relation between the two sampled waveforms is then y(nT) = x(naT) for n = 1,2,3, •••.

In other words, sampling from waveform y(t) with a sampling interval of oT is equivalent to sampling

from x(at) with a sampling interval of T. Recall

that the Fourier transform X(u)) of the waveform x(t)

is given by m

x(a>) = ; x(t)e-j<^dt. (4) 0

Likewise the Fourier transform Y(oj) is given by

Y(uj) = f y(t)e"j‘^dt. (5) 0

From the preceding discussion, y(t)

x(ot) thereby

corresponds to

00

Y(i*)) = / x( ot)e"i (6) 0

A change of variable t = at, results in

g(t) = L-M(l/j‘-)Hi(ju.)-},

_ (2)

where H]^(j(i)) is the normalized voltage transfer

function. It is therefore recognized that equation

(1) is the frequency domain analogue of the convolution

equati on

t Vq(^) = / Vi (t-T)g'(t)dT, (3) 0

where g'(r) is the impulse response function. In general, then, the application of equations (1) or (3)

requires the measurement of two quantities (using

either two different instruments at the same time or the same instrument at two different times) and thus,

if there is a sampling-rate drift, an error can occur.

The consequences of sampling-rate drift can be

examined mathematically. Suppose the two waveforms

x(t) and y(t) (both zero for t < o) are sampled at sampling intervals T, yielding digitized values x(T),

x(2T), ••• and y(T), y(2T), •••. For convenience the

transfer function h(io) is used in this paper where

h(iD) = 20 log ( 1 Y( w) j /| X(w) I ) where Y(o)) is the Fourier

transform of y(t). If the two waveforms x(t) and y(t)

are identical (as would be the ideal case if the waveforms are generated under the same experimental conditions), the two sampled waveforms x(T), X(2T), ••• and

y(T), Y(2T), ••• will be identical and h((o) would

equal zero. In practice there is always some noise

present in the system but h(iD) would still be expected

to be close to zero, and fairly evenly distributed

about zero (at least at low frequencies).

Now consider the case where sampling-rate drift

has occurred. That is, the second waveform y(t) is identical to the first waveform x(t), but the waveform

recorder's "clock" has changed so that when it registers

one unit of time, a units of time have actually passed.

Y(a.) = (1/a) / x(T)e-j(“/«)^ dT (7)

Y(«) = (l/a)X(o)/a). W

To simplify the discussion, consider the case where

a < 1 (i. e., the sampling rate has increased by a factor of a or equivalently the sampling interval

has decreased by a). Then

h(o.) = 20 log (tY(o.)l/lX(a,)l (9)

or

h(o.) = 20 log (a-llX(a)/a)|/|(X(a,)|). (10)

If I X(o)/a) I /| X((d) I is less than a, then h((u) will be less than zero. That is, if 1 X((d)| decreases rapidly

enough with increasing frequency, then the system will

appear to be exhibiting roll-off.

In other words, a sampling-rate drift of 1/a

(a corresponding sampling interval change from T to

oT) where a < 1 can result in an apparent roll-off

in the frequency domain. This roll-off depends quantitatively on how fast lX((u)| is decreasing with increasing frequency and on the sampling-rate drift

1/a.

To illustrate the effect of one percent sampling

rate drift, consider the analytical function

x(t) = (t-256.5)

(t-256.5)^ + Idb

+ K, ( 11 )

where K is chosen so that x(0) = 0. This function was chosen because its shape is similar to the real waveforms to be discussed later. In figure 3, the lower

B-4
Figure 3. x(t) is the analytical function in (11) sanpled at tine intervals T = x where x is an arbitrary unit of time. y(t) is the sane analytical function sampled at tine intervals T = X /I. 01.

graph shows (11) sampled at t = 1, 2, ••• 512 (in units

of time arbitrarily given as x). The upper graph

shows (11) sampled at t = (1.01)"^ x 1, (1.01)-^ x 2,

(1.01)"^ X 512. Note the similarity of the two graphs in figure 3 despite the 1.01 sampling-rate

drift. Figures 4 and 5 show, respectively, the transform X(uj) of x(t) sampled at t *1,2, ••• 512, and the

roll-off exhibited by the function h(u). This example

also illustrates the effect of sampling-rate drift

Figure 4.

Figure 5. h(aj) shows the effect of sample-rate drift

for the analytical waveform in (11).

qualitatively. The second waveform, because of the

faster sampling rate, is sampled at smaller time

intervals. This will make the steep rise of (11)

appear to be less steep for the second waveform y(t)

than for the first waveform x(t). The high-frequency

components of the second waveform will therefore oe less, resulting in h(o)) < 0.

Software Corrections

A researcher performing transfer function or similar types of measurements using digital sampling

techniques should immediately suspect sampling-rate

drift if results similar to figure 2 are obtained.

Once this problem is identified, it should be either

eliminated or corrections applied to remove the effect.

While it may be straightforward to eliminate the pro- blem (e.g., by uSing a more stable system clock):

correcting data with this problem is a challenge.

Several methods have been 'proposed. These methods, as well as their limitations, will be discussed.

The first correction scheme was proposed by Ramboz

,

et al. [4], This is a frequency domain correction,

which centers the graph of h(u)) = 20 log( | Y(u) j /| X(od) |

)

about zero. The approach is to use the average slope of the first few points of h((D) to obtain a correction

factor since, for most systems, one expects h(u)) to

be flat at low frequencies. While this approach does

force h(u) to be flat at low frequencies, it does

nothing to correct for h(u) at higher frequencies.

From (10) it is apparent that a simple slope change

can not completely correct h(u>) for drift.

The approaches taken here are based on the fact

that, in these measurements, the first 100 or so points

of the sampled time-domain waveforms should be the same for both measured waveforms. These data points

represent the measured response between the voltage

step generator unit and the cable being measured. If no sampling-rate drift has occurred, these points will

be identical. By contracting or expanding the sampling

interval of the second waveform with the aid, for

example, of linear or cubic interpolation, the first

100 points of the second waveform should align with

the first 100 points of the first waveform. There is one major complication, however. The two waveforms

are often horizontally displaced with respect to one another (i.e., the "step" does not occur at the same horizontal position on the oscilloscope screen). The

approach taken to align the waveforms was to do a least squares fit of the two waveforms by first sliding

the second waveform left or right until the correct

horizontal displacement was determined, and then doing

a least squares fit by expanding or contracting the

sampling interval of the second waveform to agree with

the first. Unfortunately, these two operations are

X(w) is the discrete Fotjrier transform of the sampled analytical waveform in figure 3.

R-5 1
not independent, i.e., the best fit sanpl ing-rate

drift correction is dependent on the horizontal displacenent correction and vice versa.

To illustrate this point graphically, consider the

following waveforms x(t) and y(t) shown in figure 6. The second is obtained from the first merely by changing

the sampling time interval by a factor a> 1, i.e.,

y(t) * x(at). One could assume that the point "t = 0"

is incorrectly located on the graph of y(t) and "slide"

the graph of y(t) to the right to obtain the best

least squares fit of x(t) to y(t). The results of the

"sliding" are shown in figure 7. Expansion of the

y(t) time scale would then yield a correction. But this correction is wrong because for this example, the

original zeros are in alignment and only a time-scale

expansion of y(t) in figure 6 is required. These two approaches will yield different corrections. The

translation and drifting correction cannot be applied

independently.

y(t)

t —

Figure 6. x(t) and y(t) represent waveforms obtained

by sampling the same hypothetical waveform

at two differing sample rates.

A more suitable approach to this correction problem

may be to consider digitized samples x(T), •••, x(512T)

andy(T), •••, y(512T). The problem which needs to

be treated mathematically is to minimize (in sand 0) the expression

100

«(a,0) = S |x(nT)-;(naT+0)l2, (12) n=l

where y is calculated as follows: find k so that

kT < onT+0 < (k+l)T. Then y(onT+0) is an appropriately interpolated value between y(kT) and y((k+l)T). It should be noted that if 0 < 0, the expression *( 0, 0 ) is evaluated by interchanging the roles of x(t) and y(t).

To minimize *( 0, 0 ) in both a and 0 simultaneously,

we used code based on Marquardt's algorithm [6] which

is used to minimize a nonlinear sum of squares in a relatively small number of iteration steps. For ana- lytically generated, translated, and shifted waveforms,

such as shown in figure 3, this method performed well.

The values given by the algorithm for a and 0 were

found to be close to the actual a and 0 which had been

used to generate the analytical waveforms and

h(o)) was nearly zero. However, for real digitized

data, this approach was not as successful in giving

values which indicated improvement. The criterion for

judging improvement was to observe the graph of h(u) for the corrected waveforms and to see if this graph was more "centered about 0" than the graph

of h(o)) for the uncorrected waveforms. The reasons why improvement in real data were difficult to obtain

are threefold: (1) noise in the data tends to "flatten"

the graph of the function *( 01

, 0 ) and the minimum of

(a, 0 ) need not give the best correction factors a and 0; (2) the interpolation scheme adds error to the comparison; and (3) inputting incorrect initial

guesses to the computer program can lead to "spurious"

local minima, corresponding to the problems with first

"sliding" then "expanding" discussed above.

Figure 7. y(t) in figure 6 has been translated to the Figure 3. x(t) and y(t) show two real sampled waveright to minimize the difference between the forms taken one minute apart, two curves. B-6
The difficulty with software correction can be illustrated with the most extreme real data which were

gathered. Figure 8 shows two waveform readings taken

1 minute apart shortly after the oscilloscope was turned on. The transform X(u) of the first waveform

is illustrated in figure 9, and the function

h(u) for these two waveforms is shown in figure 10. Figure 11 shows the function h^(j(a)) for the correction obtained by first finding the best translation,

then the best drift. The factors were a = 0.999,

IX(o;)l

Figure 9. X(uj) is the discrete Fourier transform of

the sampled waveform x(t) in figure 8.

Figure 12. hr^(w) was calculated after using cor- rections obtained by the Varquardt algorithm. The high-frequency roll-off has vanished.

S

= -15.4. No real improvement is apparent. Figure 12 shows the function hn((o) for the best correction obtained from the code which uses Marquardt's algorithm.

Here, a = 0.73 and 3 = 0.37, approximately. While the

function hp,(u) exhibits the desired properties, ac- cepting these results means accepting an almost 30%

drift in the time scale. This may not be unreasonable

for an oscilloscope during the first minute or two

after turn on. In some other examples, h^(<i>) has shown little improvement over h^d(u).

Conclusion

. For, precise transfer function measurements, errors caused by sampling-rate drift can pose a problem. Cor- rections in the frequency domain are straightforward

but require a priori knowledge of the transfer functions

and are also not complete. Corrections in the time

domain do not require this prior knowledge and are theoretically possible. Our results show that time

domain corrections work well for analytical waveforms

but are less reliable for actual data. The conclusion

is that the preferred way to handle the problem of

sampling-rate drift is to prevent its occurrence by

using a stable external clock instead of the internal

time base of the waveform recorder.

Figure 10. h((i)) shows the effect of sampling-rate

drift for the two waveforms in figure 1. Note the roll-off with increasing frequency.

Acknowledgments

The authors are indebted to John Ramboz , Arthur

Ondrejka, and Robert E. Hebner for their technical

contributions to this work, and to Betty Meiselman and

Barbara Frey for the manuscript preparation.

References

[ 1 ]

[ 2 ]

[3]

R. Malewski, "Digital Techniques in High-Voltage

Measurements," IEEE Trans. Power Aoo. Svst., Vol

PAS-101 pp. 45084517; 1982.

Proceedings

edited by R, Spec. Publ.

of the Waveform

Lawton

,

Nat . Bur. 634; 1981 October.

Rec order

Stand.

Seminar,

(U.S.),

C. Shannon, "Communication in the Presence of Noise," Proceedings of the IRE, Vol. 37, pp. 10-22;

1949.

Figure 11. ht^ was calculated by using corrections ob- [^]

tained by first finding the best horizontal

translation of y(t) and then the best

drift. No real improvement over figure 10

is apparent.

J. Ramboz, A. Ondrejka, and W. Anderson, "Sampling-Rate Drift Problems in Transfer Function

Analysis of Electrical Power Cables," P roceedi nqs

of the Waveform Recorder Seminar , Nat. Pur. Stand.

(U.S.), Spec. Publ. 634, pp. 47-53; 1981.

B-7
[5] W. Anderson and J. Ratnboz, 19S0 Annual Report;

Technical Contributions to the Hevelopnent of~

Incipient Fault rietection/Locati on Instrunentation,

flat. Rur. Stand. (U.S. ), NBStR 81-2235; IW7

[6] 0. Marquardt, “ An Algorithm for Least-Squares

Estimation of Nonlinear Parameters," J.Soc. Indust.

Appl. Math., Vol. II, pp. 431-441; 1963.

B-8
Appendix C

BASIC program for transfer function analysis, reflection mode

using an abrupt transition, matched termination.

C-1
1 REM PROGRAM "0DOE/DPO/ARRAYFFT2" 9-30-80 LAST MOD 19-N0V-80

2 REM FFT VERSION BY ANDERSON 9-22-80 (DOE TAPE FILE #4;3-4-81)

3 POLL N,M;3

4 DELETE V,W

5 REM DPO DATA COLLECT

6 GO TO 100

8 REM PLOT DPO DATA

9 GO TO 330

12 REM ARRAY SQUASH

13 GO TO 1000

16 REM PLOT SQUASHED ARRAY

17 GO TO 2000

20 REM DFT ROUTINE

21 GO TO 3000

24 REM ATTEN. PLOT

25 GO^TO 3380

28 REM DFT MAGNITUDE PLOT

29 GO TO 4000

32 REM TRANSFER DATA TO REFERENCE ARRAY

34 GO TO 7080

36 REM SUBTRACT INPUT WAVEFORM TO CABLE FROM REFERENCE WAVEFORM

38 GO TO 7090

40 REM INTERPOLATE NEW WAVEFORM

42 GO TO 5000

44 REM TRANSFER DATA TO TERMINAL

46 GO TO 150

48 REM DIFFERENCE OF TWO WAVES

50 GO TO 400

52 REM MAKE FIRST N SAMPLES EQUAL ZERO

54 GO TO 1100

56 REM DISC INPUT WRITING ROUTINE

57 GO TO 7013

60 REM DISC OUTPUT WRITING ROUTINE

61 OPEN E$;1,"U“,F$

62 GO TO 7050

64 REM READ REFERENCE FROM DISC

66 GO TO 7000

68 REM GENERATE WAVEFORM

69 A9=l

70 GO TO 500

72 REM ADD NOISE TO V ARRAY

74 GO TO 700

100 PAGE

102 GOSUB 9000

104 PRINT "DPO DATA COLLECTION CYCLE"

no DIM W(512)

115 PRINT "HOW MANY AVERAGES? POWER OF 2 GREATER THAN 2"

120 INPUT A1

125 PRINT "WHAT MEMORY?"

130 INPUT D$

135 PRINT 03:"ST0 ";D$

140 G$=D$&'7"

142 G$=G$&D$

144 G$=G$&" "

C-2
145 PRINT (33:"HAV ";G$;A1;" S"

149 RETURN

150 REM TRANSFER DATA TO CALCULATOR

151 DELETE W,V

152 DIM W(512),V(512)

155 PAGE

160 PRINT "DATA FROM WHAT MEMORY?"

162 INPUT D$

164 G$="DP"&D$

166 G$=G$&"?"

175 PRINT 03:G$

180 INPUT 03:W

185 W=W-512

187 G$=D$S"1"

190 PRINT 03:"CHL ";G$

195 PRINT (33:"SCL?"

200 INPUT 03:S$

205 DELETE M,V1,X1

210 V1=VAL(S$)

220 M=1

230 V1=V1*10®(-3*M)

240 W=W*(V1/102.3)

247 G$=D$S"2"

250 PRINT 03;"CHL ";"B2"

260 PRINT @3:"SCL?"

270 INPUT @3;S$

280 X1=VAL(S$)

290 M=P.0S(S$,"S",1)

300 T$=SEG(S$,M-1,1)

310 M=POS("fnunp",T$,l)

320 X1=X1*10©(-3*M)

321 T=X1*10/512

322 W(1)=W(2)

323 W=W-W(1)

324 HOME

325 RETURN

330 V2=65

332 V3=130

334 V4=50

336 V5=80

340 CALL "MIN", W, Ml, II

346 CALL "MAX", W, M2, II 350 WINDOW 1,512, Ml, M2

354 VIEWPORT V2,V3,V4,V5

356 PAGE

357 PRINT "ENTER TEST CONDITIONS; MAX OF ONE LINE

358 INPUT A$

360 PAGE

370 CALL "DISP",W

375 AXIS 512/10, VI

380 HOME

381 GOSUB 9000

382 A$="TEST COND.:"&A$

384 PRINT A$;"J"

C-3
390 PRINT "TIME BASE SETTING: s/DIV"

395 PRINT "VERT. SENS. SETTING: RH0/DIV";"r'

399 RETURN

400 REM DIFFERENCE BETWEEN TWO WAVEFORMS

401 DELETE W,V

402 DIM W(512) ,V(512)

405 PAGE

407 PRINT "WHAT TWO MEMORIES SHALL I READ FROM? (M,N=M-N)"

408 INPUT D$,J$

410 GOSUB 164

415 V=W

420 D$=J$

425 GOSUB 164

430 V=V-W

435 W=V

499 RETURN

500 REM GENERATE WAVEFORM

505 PAGE

510 DELETE M,V1 ,X1,T,W,A,B

520 DIM W(512)

530 M=1

532 Vl=l

534 Xl=l

536 T=1

550 PRINT "WHAT SLOPE FACTOR? (USUALLY >10)"

560 INPUT A

570 PRINT "WHAT LINEARITY FACTOR? (USUALLY >1)"

580 INPUT B 590 A=A®B

600 FOR N=1 TO 512

610 M=N-256.5

620 W(N)=M/(M©2®B+A)©(0.5/B)

630 NEXT N 640 W=W-W(1)

699 RETURN

700 REM ADD NOISE TO V ARRAY

710 PRINT "WHAT AMPLITUDE NOISE? (1*0 dB S/N)"

720 INPUT A8

725 D9=512/A9

728 FOR 1=1 TO D9

730 A7=RND(1)

740 A6=RND(1)

750 IF A7=>0.5 THEN 770

760 A6=-A6

770 V(I)=V(I)+A6*A8

780 NEXT I 790 RETURN

999 REM ARRAY SQUASH SUBROUTNE

1000 HOME

1001 PRINT "JJJJJJJJJJJJJJJJJJ"

1002 PRINT "REDUCTION FACTOR; 1,2,4,8,16,32? "; 1004 INPUT A9

1005 DELETE V

1008 D9=512/A9

C-4
1010 DIM V(D9)

1015 Q2=0

1020 FOR Ql=l TO 512 STEP A9

1030 Q2=Q2+1

1040 V(Q2)=W(Q1)

1050 NEXT Q1

1052 T1=T*A9

1060 RETURN

1100 REM INITIAL ZEROS

1110 PRINT "MAKE ZERO UP TO WHICH SAMPLE POINT?"

1120 INPUT A7

1130 FOR N=1 TO A7

1140 W(N)=0

1150 NEXT N 1160 A7=A7+1

1170 A8=W(A7)

1180 FOR N=A7 TO 512

1190 W(N)=W(N)-A8

1200 NEXT N 1300 RETURN

2000 V6=V(1)

2001 REM PLOT. ARRAY V (SQUASHED ARRAY)

2006 V(1)=0

2010 CALL "MAX", V, M2, II 2020 CALL "MIN", V, Ml, II 2030 WINDOW 1,Q2,M1,M2

2035 VIEWPORT 65,130,10,40

2040 CALL "DISP",V

2050 AXIS (Q2-1)/10,V1

2052 V(1)=V6

2055 HOME

2056 PRINT

2060 RETURN

3000 DELETE X,Y,M,P,R,C,D

3001 REM BEGIN FFT ROUTINE

3010 PAGE

3012 CALL "TIME",T$

3014 PRINT T$

3016 PRINT A$

3021 F1=1/(2*T1)

3022 PRINT "THE MAXIMUM ANALYSIS FREQUENCY IS " ;F1/1000000; " MHz"

3106 D8=D9/2+l

3107 DIM X(D8),Y(D8),M(D8),P(D8),D(D8)

3109 PRINT "A SET OF ";D9/2;" FREQUENCY POINTS WILL BE CALCULATED" ; "J"

3110 REM *** BEGIN CALCULATION***

3111 M=0

3112 P=0

3113 D=0

3115 F9=F1*2/D9

3120 CALL "FFT",V

3130 CALL "UNLEAV",V,X,Y

3132 PRINT "FREQ.", "MAGNITUDE", "PHASE, DEG", "ATTEN,dB RE M(l)"

3134 PRINT

3135 P9=2*PI/D9

C-5
3136 PRINT @32,26:0

3137 K2=0

3138 Kl=8

3140 FOR K=2 TO D8

3150 X(K)=X(K)+W(512)/2

3160 Y(K)=Y(K)-W(512)*SIN(P9*(K-l))/(2-2*C0S(P9*(K-l)))

3170 M(K)=SQR(X(K)©2+Y(K)©2)/(2*F1)

3180 P(K)=180/PI*ATN(Y(K)/X(K))

3190 D(K)=20*LGT(M(K)/M(2))

3200 PRINT (K-1)*F9/1000000,M(K),P(K),D(K)

3205 IF Kl=34 THEN 3340

3208 K1=K1+1

3210 NEXT K 3330 GO TO 3348

3340 IF K2>0 THEN 3342

3341 COPY

3342 FOR N=1 TO 1000

3343 NEXT N 3344 PAGE

3345 Kl=l

3346 K2=l

3347 GO TO 3210

3348 PRINT "GGGGGG"

3350 RETURN

3380 REM BEGIN OF ATTENUATION PLOT; +-45 dB

3385 VIEWPORT 25,120,5,65

3390 WINDOW 2,08,-45,45

3400 PAGE

3410 AXIS 8,5

3420 MOVE 2,D(2)

3430 FOR 1=2 TO D8

3440 DRAW I,D(I)

3450 NEXT I 3460 HOME

3470 RETURN

4000 PAGE

4001 REM BEGIN OF MAGNITUDE PLOT

4012 CALL "MAX", M, M3, II 4013 PRINT " THE MAXIMUM VALUE IS ";M3;" AT LOCATION ";I1;"^"

4020 PRINT "ENTER THE MIN AND MAX AMPLITUDE LIMITS FOR PLOT: " 4030 INPUT W3,W4

4040 VIEWPORT 25,120,5,65

4050 WINDOW 2,D8,W3,W4

4060 AXIS (D8-2)/10,W4/10

4070 MOVE 2,M(2)

4080 FOR 1=2 TO D8

4090 DRAW I,M(I)

4100 NEXT I 4110 HOME

4120 RETURN

5000 REM INTERPOLATE NEW WAVEFORM

5005 DELETE V,M

5008 DIM V(512)

C-6
5010 HOME

5020 PRINT "JJJJJJJJJJJJJJJJJJ"

5030 PRINT "TIME CHANGE EACTOR? C"1)"

5040 INPUT A9

5050 V(1)=0

5060 FOR N=2 TO 512

5070 M=INT(N*A9)

5072 IF M<512 THEN 5080

5074 V(N)=V(N-1)

5076 GO TO 5090

5080 V(N)=(N*A9-M)*(W(M+1)-W(M))+W(M)

5090 NEXT N 5092 V(512)=V(511)

5094 DELETE W

5096 DIM W(512)

5098 W=V

5100 RETURN

6100 DELETE 1,2

6101 DELETE 999

6103 DELETE 2001

6104 DELETE 3001

6105 DELETE 3110

6106 DELETE 4001

6108 DELETE 5 6109 DELETE 6100,6109

7000 REM DISC READING ROUTINE

7001 DELETE M

7004 PRINT "SOURCE OF REFERENCE DATA? UNIT

7005 INPUT Z 7006 PRINT "WAVEFORM FILE NAME?"

7007 INPUT E$

7008 OPEN E$;1,"R",F$

7009 READ #1:A$,D8,F1

7010 DIM M(D8)

7011 READ #1:M

7012 CLOSE 1 7013 REM DISC WRITING ROUTINE

7014 PRINT "DISC WRITING ROUTINE"

7015 PRINT "UNIT?"

7016 INPUT Z 7017 CALL "UNIT",Z

7020 PRINT "DISC FILE NAME(e.g. DPO/WAVEl)

7030 INPUT E$

7035 CREATE E$;2500,0

7040 OPEN E$;1,"F",F$

7050 WRITE #1:A$,D8,F1,M

7060 CLOSE 1 7070 RETURN

7080 REM TRANSFER DATA TO REFERENCE ARRAY

7081 PAGE

7082 DIM U(512)

7084 FOR 1=1 TO 512

7086 U(I)=W(I)

7088 NEXT I

C-7
7089 RETURN

7090 REM SUBTRACT INPUT WAVEFORM TO CABLE FROM REFERENCE WAVEFORM

7091 PAGE

7092 FOR 1=1 TO 512

7094 W(I)=W(I)-U(I)

7096 NEXT I 7098 RETURN

9000 CALL *'TIME",B$

9010 PRINT B$

9030 RETURN

9999 END

C-8
Appendix D

Part I

ASIC program for transfer function analysis, reflection made using an abrupt

ransition, mismatched termination. Main program requires use of program given

n Appendix D, Part II to be appended under program control.

Dl-l
1 REM MEASURE TF THROUGH ABRUPT TRANSITION. FILE 6 10 FEB 81

2 REM FFT VERSION BY ANDERSON 9-22-80 PROGRAM "0D0E/DP0/TFABRUPT2"

3 POLL N,M;3

4 REM BEGIN

6 GO TO 100

8 REM TRANSFER DATA AND CONTINUE

9 GO TO 290

12 REM PLOT SINGLE WAVEFORM

14 GO TO 1600

16 REM CORRECT TIME SHIFT ERROR

17 GO TO 820

20 REM DFT ROUTINE

21 GO TO 4930

24 REM MAKE FIRST N SAMPLES OF ARRAY D ZERO

26 GO TO 1700

56 REM DISC INPUT WRITING ROUTINE

57 GO TO 5810

60 REM DISC OUTPUT WRITING ROUTINE

61 OPEN E$;1,”U",F$

62 GO TO 5900

64 REM READ REFERENCE FROM DISC

66 GO TO 5700

100 REM BEGIN MAIN PROGRAM

no PAGE

120 REM ACQUIRE DATA • 130 PRINT "READY WITH OPEN CIRCUIT WAVEFORM?(Y)

140 INPUT 1$

150 D$="A"

160 GOSUB 4000

170 PRINT "READY WITH SHORT CIRCUIT WAVEFORM?( Y)

180 INPUT 1$

190 D$="B"

200 GOSUB 4000

210 PRINT "READY WITH INPUT WAVEFORM? (Y)

220 INPUT 1$

230 D$="C"

240 GOSUB 4000

250 PRINT "READY WITH OUTPUT WAVEFORM?( Y)

260 INPUT 1$

270 D$="D"

280 GOSUB 4000

290 REM TRANSFER DATA TO CALC.

295 R1=0

300 DIM A(512), 8(512), C(512),V(512),W(512)

310 D$="A"

320 GOSUB 4180

330 A=W

340 D$="B"

350 GOSUB 4180

360 B=W

370 D$="C"

380 GOSUB 4180

390 C=W

400 D$="D"

Dl-2
410 GOSUB 4180

420 V=W

430 REM PLOT WAVEFORMS

440 PAGE

450 PRINT "ENTER TEST CONDITIONS;MAX OF ONE LINE

460 INPUT A$

470 PAGE

520 REM PLOT MEM A

530 VIEWPORT 5,60,50,80

540 W=A

550 GOSUB 4460

552 WINDOW 0,130,0,100

555 VIEWPORT 0,130,0,100

560 MOVE 6,83

570 PRINT USING 575:M2

575 IMAGE "ARRAY A;MAX VAL : " ,FD .4D , " mV"

580 REM PLOT MEM B 590 VIEWPORT 5,60,10,40

600 W=B

610 GOSUB 4460

612 WINDOW 0,130,0,100

615 VIEWPORT 0,130,0,100

620 MOVE 6,43

630 PRINT USING 635:M2

635 IMAGE "ARRAY B;MAX VAL: ",FD.4D," mV"

640 REM PLOT MEM C

650 VIEWPORT 70,125,50,80

660 W=C

670 GOSUB 4460

672 WINDOW 0,130,0,100

675 VIEWPORT 0,130,0,100

680 MOVE 71,83

690 PRINT USING 695:M2

695 IMAGE "ARRAY C;MAX VAL : " ,FD.4D ," mV"

700 REM PLOT MEM D 710 VIEWPORT 70,125,10,40

720 W=V

730 GOSUB 4460

732 WINDOW 0,130,0,100

735 VIEWPORT 0,130,0,100

740 MOVE 71,43

750 PRINT USING 755:M2

755 IMAGE "ARRAY D;MAX VAL: ",FD.4D," mV"

760 HOME

770 GOSUB 5930

780 A$="TEST COND:"&A$

790 PRINT A$

800 PRINT "TIME BASE SEHING: ";X1;" s/DIV"

810 COPY

812 IF R1=0 THEN 820

815 RETURN

820 REM CORRECT TIME ERROR

825 PRINT "DO YOU WANT TIME CORRECTION? ( Y ,N)

827 INPUT 1$

Dl-3
828 IF I$="N" THEN 1180

830 Rl=l

840 W=A-B

850 GOSUB 6000

860 PRINT "WAVEFORM A-B"

870 CALL "MAX", B, M2, II 900 W=A

910 V=B

920 GOSUB 6050

930 PRINT "TIME ERROR IN A-B IS ";I7;" SAMPLE POINTS"

940 PRINT "DO YOU WANT TO CORRECT THIS?(Y,N)"

950 INPUT 1$

960 IF I$="N" THEN 990

970 GOSUB 6210

975 A=V

980 GO TO 820

990 W=C-B

1000 GOSUB 6000

1010 PRINT "WAVEFORM C-B"

1020 W=C

1030 V=B

1040 GOSUB 6050

1050 PRINT "TIME ERROR IN C-B IS ";I7;" SAMPLE POINTS"

1060 PRINT "DO YOU WANT TO CORRECT THIS?(Y,N)"

1070 INPUT 1$

1080 IF I$="N" THEN 1120

1090 GOSUB 6210

1100 C=V

1110 GO TO 990

1120 W=A-C

1130 GOSUB 6000

1140 PRINT "WAVEFORM A-C"

1150 PRINT "ANYMORE CORRECTIONS?{Y ,N)

1160 INPUT 1$

1170 IF I$="Y" THEN 820

1180 REM CALCULATE WAVEFORM DIFFERENCES

1190 W=A-C

1200 A=A-B

1210 C=C-B

1220 B=W

1223 D$="D"

1225 GOSUB 4180

1227 V=W

1228 GOSUB 1700

1230 GOSUB 430

1240 PRINT "SHALL I DO DFT?{Y,N)"

1250 INPUT 1$

1260 IF I$="Y" THEN 1280

1270 RETURN

1280 DELETE 110,1280

1290 DELETE 4000,4660

1291 DELETE 1600,1820

1295 DELETE 6050,6300

1296 DELETE 1290,1296

Dl-4
1300 FIND 7 1310 APPEND 100

1315 GO TO 100

1320 END

1600 GO TO 6000

1700 REM WAVEFORM LEADING ZERO ROUTINE

1710 PRINT "DO YOU WANT LEADING ZERO ROUTINE?( Y ,N)

1720 INPUT 1$

1730 IF I$="N" THEN 1820

1740 PRINT "MAKE ARRAY D ZERO UP TO WHICH SAMPLE?(MAX 512)"

1750 INPUT 17

1760 FOR 1=1 TO 17

1770 V(I)=0

1780 NEXT I 1785 17=17+1

1787 V7=V(I7)

1790 FOR 1=17 TO 512

1800 V(I)=V(I)-V7

1810 NEXT I 1820 RETURN

4000 PAGE

4010 GOSUB 5930

4020 PRINT "DPO DATA COLLECTION CYCLE"

4030 DIM W(512)

4040 PRINT "HOW MANY AVERAGES? POWER OF 2 > 2.0"

4050 INPUT A1

4080 PRINT @3:"ST0 ";D$

4090 G$=D$&"/"

4100 G$=G$&D$

4110 G$=G$a" " 4120 PRINT @3:"HAV ";G$;A1;" S"

4130 RETURN

4140 REM TRANSFER DATA TO CALC.

4180 G$="DP"&D$

4190 G$=G$^"?"

4200 PRINT @3:G$

4210 INPUT @3:W

4220 W=W-512

4230 G$=D$&"1"

4240 PRINT 03:"CHL ";G$

4250 PRINT (33:"SCL?"

4260 INPUT 03:S$

4270 DELETE M,V1,X1

4280 V1=VAL(S$)

4290 M=1

4300 V1=V1*10®(-3*M)

4310 W=W*(V1/102.3)

4320 G$=D$&"2"

4330 PRINT @3:"CHL ";"B2"

4340 PRINT 03:"SCL?"

4350 INPUT @3:S$

4360 X1=VAL(S$)

4370 M=P0S(S$,"S",1)

4380 T$=SEG(S$,M-1,1)

DL-5
4390 M=P0S(‘'munp",T$,l)

4400 X1=X1*10©(-3*M)

4410 T=X1*10/512

4420 W(1)=W(2)

4430 W=W-W(1)

4450 RETURN

4460 REM PLOTTING ROUTINE

4500 CALL "MIN", W, Ml, II 4510 CALL "MAX", W, M2, II 4520 WINDOW 1,512, Ml, M2

4580 CALL "DISP",W

4590 AXIS 512/10, VI

4660 RETURN

5380 PAGE

5810 REM DISC WRITING ROUTINE

5820 PRINT "DISC WRITING ROUTINE"

5830 PRINT "UNIT?"

5840 INPUT Z 5850 CALL "UNIT",Z

5860 PRINT "DISC FILE NAME(e.g. DPO/WAVEl)"

5870 INPUT E$

5880 CREATE E$; 2500,0

5890 OPEN E$;1,"F",F$

5900 WRITE #1:A$,D8,F1,M

5910 CLOSE 1 5920 RETURN

5930 CALL "TIME",B$

5940 PRINT B$

5950 RETURN

5960 END

6000 REM PLOT SINGLE WAVEFORM

6005 PAGE

6010 VIEWPORT 5,125,5,95

6020 GOSUB 4460

6030 HOME

6040 RETURN

6050 REM COMPARE TIMES OF TWO WAVEFORMS

6055 17=0

6057 Jl=2

6058 Kl=2

6060 FOR 1=1 TO 9

6070 I1=I*M2/10

6080 FOR J=J1 TO 512

6090 IF W(J)>I1 THEN 6095

6093 NEXT J 6095 J1=J-1

6100 I5=J-1+(I1-W(J-1))/(W(J)-W(J-1))

6110 FOR K=K1 TO 512

6130 IF V(K)>I1 THEN 6150

6140 NEXT K 6150 K1=K-1

6160 I6=K-1+(I1-V(K-1))/(V(K)-V(K-1))

6170 17=17+15-16

6180 NEXT I

Dl-6
6190 17=17/9

6200 RETURN

6210 REM CORRECT TIME ERROR

6220 FOR 1=1 TO 512

6230 I8=INT(I+I7)

6240 IF I8>0 THEN 6260

6250 V(I)=W(I)

6255 GO TO 6295

6260 IF I8<512 THEN 6290

6270 V(I)=V(I-1)

6280 GO TO 6295

6290 V(I)=W(I8)+{I+I7-I8)*{W(I8+1)-W(I8))

6295 NEXT I 6300 RETURN

Dl-7
'

:'l

'' V

, , ! ^ ‘ ]

! •> 1

(ii

m:

I )V ,0^up

'

. 1

' ootd

r: i'
Appendix D

Part II

BASIC program appends to that given in Appendix D, Part I.

D2-1
100 REM-APPEND PROGRAM-CALC ABRUPT TRANSITION TF (TAPE FILE #6)

101 REM- (PROGRAM "ODOE/DPO/TFABAPPEND"

105 PAGE

no REM CALC SPECTRA FOUR WAVEFORMS

120 W=A

125 PRINT "SPECTRUM A"

130 GOSUB 2780

140 A=W

150 W=B

155 PRINT "SPECTRUM B"

160 GOSUB 2780

170 B=W

180 W=C

185 PRINT "SPECTRUM C"

190 GOSUB 2780

200 C=W

210 W=V

215 PRINT "SPECTRUM D"

220 GOSUB 2780

230 V=W

240 REM CALC TRANSFER FUNCTION

250 FOR K=1 TO 512

260 W(K)=A(K)+V(K)-B(K)-C(K)

270 NEXT K 272 W(1)=W(3)

273 W(2)=W(4)

280 REM PRINT&GRAPH

282 K2=0

283 Kl=8

285 PAGE

286 CALL "TIME",T$

287 PRINT T$

290 PRINT "FREQ. "/'MAGNITUDE", "PHASE, DEG"

295 PRINT

300 PRINT 032,26:0

305 W2=20*LGT(2)

310 FOR K=1 TO 511 STEP 2

320 Wl=(K-l)*F9/2000000

330 W(K)=W(K)-W2

340 PRINT Wl,W(K)/2,W(K+l)/2

350 IF Kl=34 THEN 390

360 K1=K1+1

370 NEXT K 380 GO TO 470

390 IF K2>0 THEN 410

400 COPY

405 GO TO 430

410 FOR N=1 TO 1000

420 NEXT N 430 PAGE

440 Kl=l

450 K2=l

460 GO TO 370

470 PRINT "GGGGGG"

D2-2
475 FOR N=1 TO 1000

476 NEXT N 480 H$="WAVE RETURNING FROM CABLE END/WAVE INTO CABLE"

500 PAGE

510 GOSUB 1600

520 END

1000 PRINT "WAVEFORM READ ROUTINE"

1010 PRINT "UNIT?"

1020 INPUT F 1030 CALL "UNIT",F

1040 PRINT "WAVEFORM FILE NAME?"

1050 INPUT A$

1060 OPEN A$;2,"R",F$

1070 READ #2:G$,L,F1

1090 READ #2:A

1100 READ #2:H$,L,F1

1120 READ #2:B

1130 READ #2:G$,L,F1

1150 READ #2:C

1160 READ #2:G$,L,F1

1170 READ #2:D

1200 CLOSE 2

1210 RETURN

1600 REM BEGIN RATIO PLOT

1610 PAGE

1615 PRINT "GRAPH ";A$

1517 CALL "TIME",T$ , 1618 PRINT T$

°

1620 PRINT "WHAT PERCENT OF POINTS SHOULD BE PLOTTED?";

1630 INPUT LI

1640 L1=INT(512*L1/100)

1650 CALL "MIN", C, M3, II

1655 PRINT

1660 PRINT "THE MINIMUM VALUE IS ";M3;" AT LOCATION ";I1

1670 CALL "MAX", C, M3, II 1680 PRINT "THE MAXIMUM VALUE IS ";M3;" AT LOCATION ";I1

1690 PRINT "ENTER THE MIN AND MAX AMPLITUDE LIMITS FOR PLOT

1700 INPUT W3,W4

1710 VIEWPORT 25,120,5,65

1720 WINDOW 1,L1,W3,W4

1730 AXIS (Ll-2)/10,(W4-W3)/10

1740 MOVE 1,W(1)

1750 FOR 1=3 TO LI STEP 2

1760 DRAW I,W(I)

1770 NEXT I 1780 HOME

1786 HOME

1787 PRINT "JJJJJJJJ"

1788 PRINT "PLOTTING LOG ";H$

1790 RETURN

1800 REM 5 POINT LINEAR FILTERING ROUTINE

1810 D3=C(1)

1820 02=C(2)

1830 FOR N=3 TO 40

D2-3
1840 Dl=(C(N-2)+C(N-l)+C(N)+C(N+l)+C(N+2) )/5

1850 C(N-2)=D3

1860 D3=D2

1870 D2=D1

1880 NEXT N 1890 RETURN

1900 REM CALC REFERENCE FROM SIGNAL PLUS HALF THE TRANSFER FUNCTION

1910 FOR 1=2 TO L 1920 C(I)=SQR(A(I)*B(I))

1930 NEXT I 1940 C(1)=C(2)

1950 RETURN

1960 REM RECORD RESULTS ON DISC

1970 PRINT "UNIT?"

1980 INPUT Z

1990 CALL "UNIT",Z

2000 PRINT "DISC FILE NAME (eg DPO/REFERl)"

2010 INPUT E$

2020 CREATE E$; 2500,0

2030 OPEN E$;1,"F",F$

2040 A$=SEG(E$,5,8)

2050 WRITE #1:A$,L,F1,C

2060 CLOSE 1 2070 RETURN

2080 FOR 1=1 TO 1000

2090 NEXT I 2100 RETURN

2110 REM MODIFY SPECTRUM FREQUENCY

2120 PAGE

2130 PRINT "WHAT FREQUENCY CHANGE FACT0R?C"1)

2140 INPUT A2

2150 C(1)=B(1)

2160 FOR 1=2 TO L 2170 M=INT(I*A2)

2180 IF M<L THEN 2210

2190 C(I)=C(I-1)

2200 GO TO 2220

2210 C(I)=((I*A2-M)*(B(M+1)-B(M))+B(M))*A2

2220 NEXT I 2230 RETURN

2370 REM MEASURE TIME DRIFT IN REFERENCE

2380 PAGE

2390 CALL "TIME",T$

2400 PRINT T$

2410 VIEWPORT 25,120,5,65

2420 WINDOW 1,55, -1,1

2430 AXIS 5,0.2

2440 S=0

2450 S1=20*LGT(C(1)/A(1))

2460 MOVE 1,S1

2470 FOR 1=1 TO 50

2480 S2=20*LGT(C(I+1)/A(I+1))

2490 IF I>16 THEN 2510

2500 S=S+(S2-S1)*(17-I)

D2-4
2510 DRAW I, SI

2520 S1=S2

2530 NEXT I 2540 S=S/136

2550 HOME

2560 PRINT "JJJVERTICAL RANGE IS -1,1 dB”

2570 PRINT "AVERAGE SLOPE IS ";S;" dB PER POINT"

2580 PRINT "TO CORRECT SPECTRUM MULTIPLY BY ";S+1

2590 PRINT "SHALL I TEST THIS CORRECTION? (Y,N)"

2600 INPUT 1$

2610 IF I$="N" THEN 2750

2620 PRINT "WHAT FREQUENCY CORRECTION FACTOR?"

2630 INPUT A2

2640 DIM D(L)

2650 D(1)=C(1)

2660 FOR 1=2 TO L 2670 M=INT(I*A2)

2680 IF M<L THEN 2710

2690 D(I)=D(I-1)

2700 GO TO 2720

2710 D(I)=((I*A2-M)*(C(M+1)-C(M))+C(M))*A2

2720 NEXT I 2730 C=D

2740 GO TO 2380

2750 RETURN

2760 END

2780 REM BEGIN FFT ROUTINE

2790 DELETE X,Y

2810 CALL "TIME",T$

2820 PRINT T$

2830 PRINT A$

2840 F1=1/(2*T)

2850 PRINT "THE MAXIMUM ANALYSIS FREQUENCY IS " ;F1/1000000 ; " MHz"

2880 PRINT "A SET OF 256 FREQUENCY POINTS WILL BE CALCULATED" ; "J"

2890 REM *** BEGIN CALCULATION***

2920 W1=W(512)

2930 F9=F1*2/512

2940 CALL "FFT",W

2980 P9=2*PI/512

3000 K2=0

3010 Kl=8

3020 FOR K=3 TO 511 STEP 2

3030 X=W(K)+Wl/2

3035 K3=(K-l)/2

3040 Y=W(K+l)-Wl*SIN(P9*K3)/(2-2*C0S(P9*K3)

)

3050 W(K)=20*LGT(SQR(X©2+Y®2)/(2*F1)

)

3060 W(K+1)=180/PI*ATN(Y/X)

3070 NEXT K 3080 W(1)=W(3)

3090 W(2)=W(4)

3100 RETURN

3230 PAGE

3240 REM DISC WRITING ROUTINE

3250 PRINT "DISC WRITING ROUTINE"

D2-5
3260 PRINT "UNIT?"

3270 INPUT Z 3280 CALL "UNIT",Z

3290 PRINT "DISC FILE NAME(e.g. DPO/WAVEl)"

3300 INPUT E$

3310 CREATE E$;2500,0

3320 OPEN E$;1,"F",F$

3330 WRITE #1 : A$ ,D8,F1 ,M

3340 CLOSE 1 3350 RETURN

3360 CALL "TIME",B$

3370 PRINT B$

3380 RETURN

3390 END

3400 REM PLOT SINGLE WAVEFORM

3410 PAGE

3420 VIEWPORT 5,125,5,95

3430 GOSUB 4460

3440 HOME

3450 RETURN

6000 GO TO 1600

D2-6
N3S-114A Rg'.. 2-30

U.S. OEPT. OF COMM. 1. PUBulCATlON OR 2. Performing Organ. Report No. 3. Puclication Date BIBLIOGRAPHIC DATA

REPORT NO,

NBSIR 86-3392 722 July 1986

SHhtl '.See instruczionsi

4. TITLE AND SUBTITLE

Final Report: Technical Contributions to the Development

of Incipient Fault Detection/Location Instrumentation

5. AUTHOR(S)

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

6. PERFORMING ORGANI ZATION ( I f joint or other than N BS. see in struction s) 7. ContracL^Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report S. Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street, City, State. ZIP)

Department of Energy

Office of Electric Energy Systems

Washington, DC 20585

10.

SUPPLEMENTARY NOTES

I j Document describes a computer program; SF-185, FlPS Software Summary, is attached.

11.

ABSTRACT (A 200-‘r^ord or less factual summary of most significant information. If document includes a si gnificant

bi biiography or literature survey, mention it here)

The transmission of electrical energy by* use of underground cables is increasing.

Fault location techniques have certain limitations; incipient fault detection

and location would help reduce the maintenance cost of these lines as well as improve the reliability of service. This report discusses some test results

related to RF-probing techniques applied to high-voltage transmission lines. The

high frequency losses and attenuation in high voltage cables places certain

ultimate limitations on RF-probing techniques for incipient fault detection.

Time domain ref lectrometry methods were employed to assess the RF-transmission

properties of high voltage cables at frequencies as high as 6 GHz. Fast Fourier

transform deconvolution were used to obtain loss measurements as a function of

frequency. The loss mechanisms were identified. The measurement hardware and

methods are discussed as well as analysis approach leading to the conclusions.

12.

KEY WORDS (Six to twelve entries; alphabetical order; capi tali ze only proper names; and separate key words by semicolon si deconvolution techniques; fast Fourier transformers; fault location;

transmission; incipient faults; RF measurements; RF properties; time

raf lactoroatr-y ;—underaraumd .cah.le.s

13.

availability

Unl imi ted

I I For Official Distribution. Do Not Release to NTIS

I I Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C.

20402.

high-voltage

domain

14. NO. OF

PRINTED PAGES

35

15. Price

’

Order From National Technical Information Service ^NTIS), Springfield. VA. 22161

Omm-OC 904i-p-«0
II
J