NBSIR 75-775

Electrical Measurement of High

Voltage Pulses in Diagnostic

X-ray Units

Robert E. Hebner, Jr.

Electricity Division

Institute for Basic Standards

National Bureau of Standards

November 1, 1975

Interim Report

Food and Drug Administration Order FDA-1AG 224-74-6039

FDA Technical Consultant: Thomas Lee

Prepared for Bureau of Radiological Health

Food and Drug Administration

Rockvllle, Maryland 20852

NBSIR 75-775

ELECTRICAL MEASUREMENT OF HIGH

VOLTAGE PULSES IN DIAGNOSTIC

X-RAY UNITS

Robert E. Hebner, Jr.

Electricity Division

Institute for Basic Standards

National Bureau of Standards

November 1, 1 975

Interim Report

Food and Drug Administration Order FDA-1AG 224-74-6039

FDA Technical Consultant: Thomas Lee

Prepared for Bureau of Radiological Health

Food and Drug Administration

Rockville, Maryland 20852

U.S. DEPARTMENT OF COMMERCE, Rogers C.B. Morton, Secretary

James A. Baker, III, Under Secretary

Dr. Betsy Ancker>Johnson, Assistant Secretary for Science arid Technology

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Acting Director

TABLE OF CONTENTS

I. INTRODUCTION 1

II. PRELIMINARY CONSIDERATIONS 2

III. PERFORMANCE CHARACTERISTICS OF COMMERCIALLY

AVAILABIE RESISTOR DIVIDERS 3

IV. CONCLUSIONS ik

V. REFERENCES IT

VI . ACKNOWLEDGMENTS l8

APPENDIX 1 "ELECTRICAL MEASUREMENT OF THE PULSED VOLTAGE

IN DIAGNOSTIC X-RAY UNITS" 19

APPENDIX 2 "FEASIBILITY OF USING ELECTRO-OPTIC KERR EFFECT

FOR THE MEASUREMENT OF HIGH VOLTAGE PULSES IN DIAGNOSTIC

X-RAY UNITS" 35

I. Introduction

The purpose of this work was to develop a technique for the calibration

of dividers used to measure high voltage pulses in diagnostic x-rayunits. At present, three somewhat different techniques for the

determination of the peak voltage in an x-ray unit are used. -'-"9 The

first is to infer the peak voltage level from the measurement of an appropriate parameter of the emitted x-ray spectrum. The second is to

infer the peak voltage level from a measurement of the quantity of

radiation transmitted through preselected thickness of an absorber.

The final technique is to measure the peak voltage using a divider to

provide a low voltage replica of the high voltage signal. The relative

advantages of each of the methods have been discussed '''' and the

consistency—under a limited range of voltage and time—of the three

methods, when used to measure the same voltage waveform, has been

determined. The scope of this work was limited solely to an assessment

of calibration techniques for dividers currently in use.

The investigation focused on four areas. These were the divider ratio

under direct voltage, the frequency dependence of the ratio, the

voltage dependence of the ratio and the effect of self-heating on the

device. Sixteen dividers were investigated and there was substantial

variation among the devices tested. A few of the dividers were excellent

under all test conditions. While most of the dividers had the expected

ratio under direct voltage, some had unacceptably large variations of

the divider ratio when the frequency of the applied voltage was varied.

This could lead to a measurement error, particularly during relatively

short puilses. No significant errors due to self-heating or voltage

level were detected in the devices tested.

As a result of this work, a calibration procedure was developed. This

procedure includes three different measurements. The first is a determination of the divider ratio under moderately high—nominally

25 kV—direct voltage. The second is a determination of the frequency

response up to 10^ Hz under low voltage. The final measurement is a determination of the variation of the divider ratio with changes of the

applied voltage level.

This report provides measurement details and resiilts of the tests

discussed above. Section II provides technical background information

and a consistent vocabulary with which the test results can be

discussed. Section III provides a description of the measurements

which were performed and some typical measurement results. Section IV

summarizes the information gained from these tests. This report also

contains two appendices. The first discusses conventional and electrooptical methods of measuring the high voltage pulses, while the second

is a more detailed analysis of the feasibility of electro-optic measurement of these voltage pulses. Both of the appendices were previously

circulated to interested parties but were not available for public

distribution.

1
II. Preliminary Considerations

A basic model for the properties of a voltage measurement system has

been used to describe pulse dividers. In this model, the divider is

represented by a matrix relating the output current and voltage to the

input current and voltage. Mathematically this can be represented

V. (oj) in

I. (co) m

AggCco)

(1)

The voltage transfer function, H(a)), is defined for I (w) = 0, i.e..

H(a)) = V (u))/V.(w)| = l/A^.Co)) . (2) ° I (o)) = 0

The divider ratio, N, is defined as

N = A^^(O) = lim . (3) w 0

It should be noted that all of the matrix elements in Eq. 1 are, in

general, complex numbers. If the elements, A_j^j((jj), are known, the

performance of the divider is well characterized. Measurement systems

are designed so that the ratio of the input to the output voltage can be represented as a single real number. The divider ratio as defined

by Eq. 3 has this property and is the quantity which has traditionally

been used in the description of dividers used to measure the voltage

in diagnostic x-ray units. For the divider ratio to be a valid

quantity, however, it is necessary that |a (a))| not differ significantly

from N over the frequency range of interest. In this report,

measurements of the frequency dependence are discussed.

A second point to consider is that for dividers used to measure the

voltage pulses in diagnostic x-ray units it is desirable to minimize

I^^(co). In other words, because of the high output impedance of the

high voltage source, the high voltage level is not independent of the

current. To keep the current as small as possible, the resistance

of the high impedance portion of the divider is typically of order

10^ Q. Because the divider has extremely high resistance, the effects

of stray capacitance will become significant at relatively low

frequency. For example, a stray capacitance of 3 pF would present an impedance of only 10" Q. at 500 Hz. It is, therefore, necessary to

consider the effects of stray and compensation capacitance when an assessment is made of the divider performance.

2
The experiments reported here were designed to determine the divider

ratio as defined by Eq. 3. The element A-|^^(0) was determined under

direct voltage and A^^(w) was measured at 50, 100, 500, 1000, 5000 and

10,000 Hz. To verify the linearity of the divider and therefore the

applicability of Eq. 1, experiments were also performed to verify that

A-|^^(oj) had no voltage dependence, i.e., that A^^(u)) is independent of

V^^((jo), and that the errors due to self-heating were negligible, i.e.,

A,-, (to) is independent of the integral f I. • V. dt

»

11 •'mm

One of the measuring circuits developed to perform the necessary

measurements was called an active divider. The design and construction

of this device are discussed briefly in Section III. The operational

behavior of this device can, however, be discussed in terms of the

formalism presented above. As can be seen from Eqs. 1-3, the

definition of the conventional divider ratio is predicated upon the

assumption that ^^('j'^) - 0. In practice it is usually sufficient for

I^^(aj) >> I^((jL)). This criterion puts conflicting demands upon the

divider. As was noted earlier, it is necessary to minimize

To have a well defined divider ratio, however, it would be desirable

to have a large I. (w) so that the divider ratio would be relatively in ^ independent of the input impedance of the measuring device attached

to the output terminals of the divider. To accomplish these conflicting

requirements, active divider circuits were constructed. An active

divider is simply a conventional divider arranged so that the high

impedance element of the divider serves as the input to an operational

amplifier and the low impedance element serves as the amplifier

feedback impedance. In terms of Eq. 1, this circuit configuration

makes A^^^'^) ~ ^ ^'^^ ^22^^^ ~ ^' ^^^"^^ "^^^ voltage transfer ratio

and the divider ratio are decoupled from the output current.

III. Performance Characteristics of Commercially Available

Resistor Dividers

The performance of sixteen resistor dividers was evaluated. The

evaluation consisted of experimentally determining operating parameters

under four different conditions:

a) measurement of self-heating under high direct voltage

b) measiarement of the divider ratio

c) determination of the frequency response for frequencies

up to 10,000 Hz

d) determination of the magnitude of any variation in the

high impedance element with a change in applied voltage.

The effect of self-heating was determined using a standard Wheatstone

bridge circuit. Fig. 1. In this figure, R represents the high

3
or

CO

—

Q CO

Q:

Q 3 h- o

PLY

Q

SUP

•HH

-PU

+^ > W PL o ^

-P

-Pm

^1O

Q) +J

d 0) H U U

-P (U

cd Tli (U H bfl > 03 H -Po

(L) >

+^ >O

P>

H 0 (D

tjDW

H

C 0) P H ^ a H Ph-P p 0 W 0c a 0I 0

tn0

-p

•HO

•H 0 0 cd ^ -P w H

cd o

fcib •H

1^
impedance arm of the divider under test and the other high voltage

element, R , is a well characterized, stable, high voltage resistor

Measuremen? procedure vas to apply a direct voltage of about 25 kV to

the bridge. Every fifteen seconds the variable resistor was adjusted

for a null indication on the detector. Using the value of the known

resistors, the value of was calciilated. Typical values of the

change of resistance with time are shown in Fig. 2. The two plots are

for two different dividers of similar construction from the same manufacturer. Over a five minute interval the change in resistance

was only about 80 ppm. This change is in most cases negligible

because the self-heating of the x-ray tube would require the unit to

be turned off before the variation of the resistance due to selfheating could become a factor. For this reason, more detailed

investigations of the thermal characteristics of the divider were

not undertaken.

Although testing of self-heating was performed at high voltage levels,

the ratio under direct voltage was measured at a low applied voltage,

nominally 125 V. Both the applied voltage and the voltage across the

low impedance arm of the divider were measured using digital voltmeters.

From these meter readings, the ratio was calculated.

The frequency dependence of the divider ratio was determined using the

circuit shown in Fig. 3. The inductive voltage divider is a seven- decade device, the division ratio of which is characterized by an uncertainty of order one part per million of the full scale reading.

The oscillator voltage is of order 10 V rms , so the output from the

resistor divider is of order 10"^ - 10~3 V. The voltmeter was a vector

voltmeter used in the differential input mode. The input impedance for

each channel is rated at 108 Q, shunted by no more than 20 pF. To the

measurement acciiracy required, this input impedance is sufficiently large

so that the measuring device is an insignificant perturbation on the

remainder of the circuit. The vector voltmeter is used to monitor the

magnitude of two components of the difference between the output voltages

of the resistor and inductive dividers. The applied voltage also

provided the reference frequency for the vector voltmeter. The meter was adjusted so that one of the measured components was in phase with the

applied voltage. The other component was thus in quadrature. The voltage

transfer function was determined by adjusting the inductive divider so that the "in phase" component of the applied voltage, as detected by the

vector voltmeter, was zero. The ratio of the divider under test is read

from the setting of the inductive divider. The magnitude of the

quadrature component is measured. In all dividers tested, this voltage

was sufficiently small that it was not a significant contribution to the

magnitude of the voltage transfer function. To gain insight into the

characteristics of this measurement system, it is helpful to analyze an approximate, simple representation of the resistor dividers used. Fig. h.

The high resistance element is Rjj and it is assumed that there is an effective parallel capacitance, Cjj. The low impedance element is also

modeled as a parallel combination of a capacitor, C, and a resistor, R.

F-or this combination the voltage transfer function is given by the

expression
ro

HDZ

CO oI 9 d7 o

'I- o

CDI o

00

-pc

0)aH

<U

<uo

CO •HW >

to

•H CVJO

0)

O -P

(U

O

H

(U •HH

ft

ft

03 -Pc

•H

<u

a; EH

COw

•H
q:o

I-<

-I

-Io

(0o

q:

Oq;

Huj q: . V)q us f~ U ^ Z 111 cr O 3 H

iA^/^/A^AAAAA^yA-[-| I

q:

UJ

UJo>

UJ UJ> O- ft- 00UJ s 3 O Oq >

0)&

-p

CO

111 CD +^

Cj QJ Q)

r* -P

(-1

PI •H 1 -P •rH (U

Pi (H

f^H

+-' rH'CJ

f, 1 /It Pi to

1-3

U

u3

(J •P

1^Co

fn §

M-t ft

ft

(U

m ^

-P

Ch P 0

0) 0 03 •H -P

-P

H

cd 0

+3 f>

(U

to

0) P

ft «H0

<u 0 0

•HP <u a a

(U ft a

00

•H

T
Approximate equivalent circuit of dividers.

8
V /V = s ^ iL

, (1, o

H

which is of the form.

V^/V = a + jB ,

where a represents the "in-phase" and 6 the quadrature component.

For the measurements taken 3 =^ 0, that is

RC + RjjCjj , (6)

or, verbally, the dividers were not perfectly compensated. It should

"be noted that in no case was B sufficiently large so that the

quadrature component caused an error of 1%. This can be expressed

mathematically by the following inequality

2

^ 1 - i-^) < 0.01 . (T) a +6

It should also be noted that in only a few of the dividers tested

did ratio, as a function of frequency, have the functional form given

in Eq. h. To accurately account for the measured frequency response

of the other dividers would require a more complex equivalent

circuit

.

It is appropriate to emphasize that the definition of the divider

ratio, Eq. 3, is consistent with accepted practice^ of calibrating

these dividers by determining the resistance ratio. From Eqs. 3 and U,

N = lim A,, (o)) = (R„ + R)/R . (8)

0) -> 0

-L-L ^

9
So in this case, the divider ratio is indeed the resistance ratio.

The investigation of the frequency response was performed to verifythat this ratio is valid over a sufficiently wide frequency range.

The measured values of |a^^(oj)| for a number of dividers at selected

frequencies are presented in Table 1. The estimated uncertainty of the

measurements of |a (o)) | was ±1% of the indicated value up to 5000 Hz

and ±5^ at 10,000 Hz. The quantity actually measured was the voltage

transfer function—a complex quantity. To facilitate comparison with

the divider ratio, the reciprocal of the magnitude of this quantity is

presented in Table 1.

The final set of experiments was designed to provide an experimental

value for any voltage dependence of the magnitude of high impedance

element. The measurement circuit is shown schematic silly in Fig. 5-

Because the dividers under test were not designed to withstand

continuous full rated voltage, it was necessary to use pulsed high

voltage to determine the voltage dependence. The circuitry employed

a high voltage transformer powered from a variable autotrans former . A

solid-state contactor between the two permitted the application of an integral number of half-cycles of the 60 Hz waveform to the input of

the high voltage transformer.

The high voltage output of the transformer was measured using both the

resistor divider under test and a high voltage divider having a compressed gas capacitor as the high voltage element. A compressed

gas capacitor was chosen because this type of device has voltage induced

variations of capacitance which are typically of order 50 ppm over the

rated voltage range. -'-3 Tests on the individual capacitor used

indicated that its variation was of this order.

The measurement procedure was to apply the same high voltage signal

to the capacitor divider and the divider under test. The output

voltages of the two peak detect and hold modules were then recorded

for each setting of the high voltage over the range of interest.

Fig. 6 shows a typical voltage signal from the capacitor divider and

the response of the peak detect and hold circuit to that signal.

Using these measured voltages a least-squares linear fit was performed

between the two low voltage outputs, that is, the coefficients in

the expression

10
Table 1: Siimmary of the Frequency Dependence of |A^_|^(a))| of the

Devices Studied

DIVIDER FREQUENCY |A^^(a))|

A 0 952:1

50 983:1

100 1,030:1

500 1,060:1

1,000 1,070:1

5,000 1,100:1

10,000 1,100:1

B 0 9,970:1*

50 9,960:1

100 9,960:1

500 10,000:1

1,000 10,000:1

5,000 9,760:1

10,000 8,7^10:1

C 0 9,970:1

50 9,970:1

100 9,970:1

500 10,000:1

1,000 10,000:1

5,000 9,300:1

10,000 7,670:1

D 0 9,9^0:1

50 9,9iiO:l

100 9,950:1

500 9,980:1

1,000 9,980:1

5,000 9,260:1

10,000 7,750:1

E 0 2,l60:l

50 2,090:1

100 2,000:1

500 1,900:1

1,000 1,900:1

5,000 1,900:1

10,000 1,861:1

F 0 1,9^+0:1

50 1,9^0:1

100 1,900:1

500 1,880:1

1,000 1,880:1

5,000 1,880:1

10,000 1,8U0:1

11
Table 1: (continued)

DIVIDER FREQUENCY |A^^(a)) | G 0 1,000:1

50 1,010:1

100 1,010:1

500 l,l60:l

1,000 l,3i+0:l

5,000 853:1

.

, ^

-

, , ; 10,000 695:1

. H . 0 1,000:1

50 1,010:1

100 958:1

500 1,150:1

1,000 1,2)+0:1

5,000 825:1

10,000 691:1

I 0 10,000:1*

50 10,000:1

100 10,000:1

500 10,000:1

1,000 10,000:1

5,000 9,960:1

10,000 8,810:1

J ; - 0 952:1

50 1,050:1

100 l,lUO:l

500 3,8UO:l

' 1,000 3,^30:1

' 5,000 2,U80:1

10,000 2,2U0:1

,

. K 0

50 7,690:1*

100 5,350:1*

' \ , . 500 3,210:1*

1,000 3,120:1*

5,000 3,690:1*

10,000 14,590:1*

The uncertainty characteristic of these measurements was not determined.

It is unlikely, however, that the uncertainty which characterizes these

. is significantly larger than the uncertainty in the other measurements.

12
Ok

PEAK

DETECT

a

HOLD [A >

8S

C3o 0

tjO c6 -PHO

•H

<U -Po oH

J3 -P 1^

ft <u ft

!> «H -H OO ,C) •H -P -P

-P

O

<U

CO

d) o

•H . . -p

ft

a o

•H

-Paow

bl) •H

13
were determined. In Eq. 11 , V is the output voltage of the divider

X

under test and V is the output voltage of the capacitor divider.

Typical results are shown in Table 2.

A final point concerning the measurement circuit should he mentioned.

In order to match the output impedance of the divider londer test

to the measurement circuit, an active low side for the divider was constructed as was indicated schematically in Fig. 5. The low

impedance of this active divider is the feedback impedance for an operational amplifier while the high impedance element of the divider

under test serves to define the input current to the amplifier. The

ratio of the applied voltage to the output voltage is the negative

of the ratio of the high impedance to the feedback impedance. Because

of the feedback configuration, the output voltage, and hence the

voltage transfer function, is relatively independent of the current

drawn by any instrumentation used to measure the low voltage signal.

IV. Conclusions

The investigation of these devices yielded substantial insight into

the practical behavior of resistor dividers used to measure the

voltage pulses in diagnostic x-ray units. This insight prompted some modification of the calibration procedure for subsequent dividers.

The most surprising result was that, to within ±0.5^, the divider

ratios were voltage independent over the range of voltage from 10 volts

to 75,000 volts. Because individual components in the divider are specified with somewhat larger voltage coefficients than would be

reflected by this measured change, it is recommended that the

investigation of the voltage dependence of the ratio be included in

future calibrations. An additional consistency check that has been

added is a direct voltage calibration at 25 kV. This will serve as a check on the operation of the voltage-dependence measurement

circuit. Fig. 5- . .

.

Although most dividers were adequately compensated, some had

unacceptably large variations of the voltage transfer function with

a change in frequency. With the limited nmber of devices tested,

there was no identifiable correlation between divider manufacturer

or divider design and the frequency variation. It seems likely

that the unsatisfactory frequency response was a result of abuse,

poor quality control, or user modification rather than a flaw in

design.

Ik
III <

Q.o

UJCO o

_loIo

UJ o

CLCO I- U UJ o <o>o

UJ

_l

Q.

Q.<

CDQ

UJ

a:D

CO<

UJ

CO<

croo<<OUIH

oruQ>

CD >Q\EO

CO

q:oX

-pomo

ft

CO

0)^1

-p

03

•H>

•HO

-PH

CJ

cdft • 03 -p O -H

(U o

-p •Ho O t3

rH -P o

ft

-pC 03

0/ -p M O

03 <D -P

rHO

i>>o

-p

0)

03ft

•H

15
Table 2. Summary of the results ot" the determination of the variation of

the high impedance element with a change in applied voltage.

V \vtJXL«oy

X

V ( -iro T + Q ^ CG ' CG

preQicTjeo.

10.30 1.120 1.123

12.17 1.32U I.32U

13.56 l.i+73

15.23 1.656 1.653

IT. 92 1.952 1.9^2

. 19.83 2.1U2 2.li+8

: 21.86 2.363 2.366

23.88 2.58U 2.583

26.57 2.875 2.873

25.08 2.713 2.712

23.60 2.551 2.553

21.72 2.3^6 2.351

19.9^ 2.153 2.160

17.91 1.9^8 1.9^1

"15. 8i; 1.723 1.718

13.95 1.517 1.515

11.78 1.280 1.282

9.I129 1.025 1.029

Coefficients of the fit:

a = 0.015 with a standard deviation of 0.00i+ o

= 0.1076 with a standard deviation of 0.0002

16
References

L. Stanton, D. A. Lightfoot, S. Mann, "A Penetrameter Method for

Field kV Calibration of Diagnostic X-ray Machines" Radiology,

Vol. 87, pp. 87-98, 1966.

P. M. Joseph, "Mathematical Method for Determining kV from X-ray

Attenuation Measiirements" Med. Phys., Vol. 2, pp. 201-207, 1975.

P. M. Joseph, "Experimental Test of a New Method for kV

Measurements" Med. Phys., Vol. 2, pp. 208-212, 1975.

J. C. Giarratano, R. G. Waggener, J. M. Hevezi, and R. J. Shalek,

"A Comparison of Voltage-Divider, Modified Ardran-Crooks

,

and Ge(Li) Spectrometer Methods to Determine the kVp of Diagnostic

X-ray Units" submitted for publication in Med. Phys.

G. M. Ardran and H. E. Crooks, "Checking Diagnostic X-ray Beam

Quality" Br. J. Radiol., Vol. hi, pp. 193-198, I968.

M. Davison and D. Reekie, "Measurement of Peak Voltage in

Diagnostic X-ray Generators" Phys. Med. Biol., Vol. 13, pp. 6U3-65I,

1968.

E. G. Murphy, "Voltage Dividers for Kilovolt Measurements on Diagnostic X-ray Machines" unpublished report to Bureau of

Radiological Health, FDA, Rockville, Maryland.

J. D. Gilbertson and A. G. Fingerhut , "Standardization of

Diagnostic X-ray Generators" Radiology, Vol. 93, pp. 1033-1036,

1969.

E. R. Epp and H. Weiss, "Experimental Study of the Photon Energy

Spectrtmi of Primary Diagnostic X-rays" Phys. Med. Biol., Vol. 11,

pp. 225-238, 1966.

International Research Group Renardieres on Impulse Measuring

Systems, "Facing UHV Measuring Problems" Electra, Vol. 35,

pp. 157-252, 191k.

J. H. Park, "Special Shielded Resistor for High-Voltage D-C

Measurements" Journal of Research NBS, Vol. 66C, pp. 19-2k , 1962.

E. Kuffel and M. Abdullah, "High Voltage Engineering" Pergamon

Press, New York, 1970.

D. L. Hillhouse and A. E. Peterson, "A 300-kV Compressed Gas

Standard Capacitor with Negligible Voltage Dependence" IEEE Trans.

Instru. Meas., Vol. IM-22, pp. I+O8-U16, I97U.

17
VI, Acknowledgments

The author would like to thank 0. Petersons for introducing him to

the idea of using operational amplifiers to obtain well-defined

performance in dividers used to measure high voltages. Fiirthermore

,

he would like to acknowledge that W. A. Bagley performed much of the

fabrication of the circuits used and that J. E. Jones assisted in the

interpretation of the results through the development eind operation

of the computer analysis. The assistance of J. E. Cunningham and

E. D. Sims in the preparation of the manuscript is also recognized.

Finally, the author would like to thank M. Misakian for his careful

reading of the msuiuscript and for many discussions concerning this

measurement problem.

18
APPMDIX I

"Electrical Measurement of the Pulsed Voltage in Diagnostic X-ray Unit

The material in this appendix served as the basis for a talk presented

at a topical meeting on: "Measurement of kVp of Diagnostic X-ray Units

with Emphasis on Ardran and Crookes Technique", Michael Reese Hospital

Chicago, Illinois, December 1, 197^.

19
Electrical Measurement of the Pulsed Voltage in Diagnostic X-ray Units

'

• Robert E. Hebner, Jr.

Electricity Division

' National Bureau of Standards

Washington, D.C. 2023^

Abstract

A pulsed-voltage measurement system based on the electro-optic Kerr

effect has been used to determine the magnitude of the high voltage

pulses in medical x-ray machines. The purpose of this work is to

provide a calibration, under operating conditions, for other voltage

measurement devices. Among the advantages afforded by this approach

are minimization of operator error, optical coupling of the high

voltage circuitry to the detection circuitry, the ability to measure

the potential difference between two points neither of which are grounded and the fact that a Kerr cell presents a very small burden to

the pulse generator.

The dissemination of the calibration is accomplished through a recently

developed active divider which incorporates a conventional bleeder

bank (resistor divider) as the high impedance component. The use of

active circuitry in the low voltage portion of the divider permits

construction of a device with negligibly small output impedance. For

this reason, errors due to the input impedance of the recording device

and due to the impedance of connecting cables are minimized.

Preliminary operating characteristics of both the Kerr system and the

active divider are presented.

Introduction

The aim of this work is to develop, to evaluate, and to disseminate

techniques for the electrical measurement of high voltage pulses

with an imcertainty no greater than ±1%. Two measurement methods have

been developed. One is based on the electro-optic Kerr effect and

the other on the use of active components to improve the measurement

accuracy using a conventional divider. The remainder of this

presentation will be devoted to a discussion of the measurement

principles involved in these approaches including a brief discussion

of the advantages and disadvantages of each technique.

Kerr Effect

To perform a measurement using the electro-optic Kerr effect, it is

necessary to have a substance containing molecules with an electrical

anisotropy. When a voltage is applied, these molecules will tend to

align with the resulting field. The voltage measurement is made by

20
measuring the degree of alignment. Because the molecules tend to align

with the field, the refractive index of the medium in a direction

parallel to the applied field is different from that in the direction

perpendicular to it. To determine this difference a light beam

linearly polarized at an angle of ^5° to the applied field is used.

This results in two equal components, one parallel to the field, one perpendicular to the field. As these two components pass through this

substance, that component parallel to the field travels at a different

speed from that perpendicular to the applied field. Upon passage

through the substance, there is a phase shift between the two component

of the light beam. The phase difference is given by

(j) = 2u / BE (x,y,t) dz (1) o where B is the Kerr coefficient of the material.

If it is assumed that parallel plate geometry is used, Eq. (l) can be rewritten

(}) = 2tt BV^ V/^ , (2)

where V is the applied voltage, d the plate spacing and V is an effective plate length which includes phase shift due to fringing

fields at the electrode edges. This phase shift can be detected as a change in transmittance of the Kerr system if the light beam is

then passed through a polarizer oriented at an angle of 90° to

direction of original polarization. If the phase shift is given by

Eq. (l), the transmittance of the system, I/I , ±s^'>'^ m

I/I = sin^ [1/2 7T (V/V f] (3)

In this equation, V is the applied voltage, a time dependent parameter,

and V , called the cell constant is defined,

m

V = d/(2B£')"^^^ . (H)

m

As the voltage changes, the transmittance through the system changes

and Eq. (3) is the relationship between the applied voltage and the

optical parameter measiired. This equation is graphed in Fig. 1. When

no voltage is applied there is zero transmittance through the system.

As voltage is increased, a maxima is reached; as voltage is further

increased, the transmittance passes through successive maximas and

minimas. One point to be emphasized, which is a strength and in some cases a weakness of the Kerr effect, is that this is nonlinear. At

higher field strengths, or higher applied voltage, the amount of voltag

change necessary to get a 100^ change in transmittance becomes smaller.

21
Fig 1. Graphical representation of the relationship between the transmittance of the optical system and the applied electric field.

22
Because the sensitivity increases with increasing voltage, the Kerr

effect is an attractive method for high voltage measurements. A

schematic of the apparatus is shown in Fig. 2. The light source is

usually a laser. The light beam impinges on a properly oriented

polarizer and passes through a parallel -p late capacitor. This

capacitor is a glass cell containing nitrobenzene. The light beam then

passes through an analyzer and into the photodetector . The indicated

ground connection is optional. The system measures the potential

difference between the plates and does not require reference to ground.

A typical observation of electric field, at an instant during the voltage

pulse, is shown in Fig. 3. This figure shows a large central area of

uniform transmittance indicating an approximately uniform field between

plates. The fringes on either side are due to the edge fields at the

sides of the electrodes. To perform a simple measixrement of the voltage,

a detector is placed at the center so that it records the transmittance

as a fiinction of time as shown in Figs, k and 5- Fig. h shows the

simultaneous divider measurement, upper trace, and the Kerr measurement,

lower trace, of the high voltage in a single phase x-ray unit. It can be seen from the Kerr measurement that the two peaks differ in magnitude,

the first peak being slightly larger than the second.

A similar measurement made on a three phase unit is shown in Fig. 5- The

salient feature of this photograph is the enhancement of the ripple in

the applied high voltage that is evident in the Kerr response. Because

the Kerr response sensitivity increases at higher voltages , the system

responds preferentially to the ripple and not as identifiably to the

average voltage level.

It is useful to summarize the primary advantages and disadvantages of

using the Kerr effect to measure the pulsed voltage in medical x-ray

units. This summary is presented in Table 1.

Table 1. The advantages and disadvantages of using the Kerr effect

for the measurement of the pulsed high voltage in medical

x-ray units.

Advantages Di s advant age s

High impedance

No reference to ground

Optical coupling

Independent errors

Skilled personnel

Not commercially available

Optimized for shorter pulses

23
Schematic diagram of both optical and electrical aspects of

a measurement system based on the electro-optic Kerr effect.

2h
Fig. 3. Transmittance of a Kerr cell (parallel plate geometry) at an instant under the influence of a high voltage impulse. The

numhers on the figure indicate <\>/t\ (Eq. l) for the spatial

region in which each is located.

25
Fig. k. Divider measurement (upper trace) and Kerr measurement (lower

trace) of the high voltage in a single phase x-ray unit.

26
Divider measurement (upper trace) and Kerr measurement (lower

trace) of tlie higii voltage in a three phase x-ray unit. Note

that the ripple is enhanced in the Kerr system measurement

.

27
The first advantage listed is the high impedance of the Kerr system. A

Kerr cell is a capacitor with a capacitance of approximately 100 pF.

This is the same order of magnitude as the stray capacitance in the

x-ray imit. The voltage measurement device is therefore a negligible

addition to the load seen by the voltage generator.

Kerr systems, as presently constructed, are essentially .parallel plate

capacitors. As can be seen from Eq. (l), the quantity measured is the

electric field between the plates. The Kerr system then requires no reference to ground. Direct measurements of the voltage between the

anode and cathode in a medical x-ray unit have been made.

Optical coupling between the high voltage circuitry and the measurement

device offers the advantages both of decreased shock hazard and of the

minimization of ground loop errors.

Finally the errors inherent in Kerr system measurements are different

from the errors that have been identified in the measurement of high

voltage using a divider. This is significant in calibration work because

the applied voltage can be measured using two independent methods. If

the values obtained by the two methods disagree by more than their

combined uncertainties, it is likely that there is an error in one or the

other. If, conversely, the two agree, it is highly unlikely that they

are both in error by the same amount. In this respect the system is

self-checking, thus minimizing the effect of operator error.

The use of the Kerr system is not a panacea. Among the disadvantages

are that the Kerr system requires skilled personnel. It requires

additional training beyond that necessary to operate an oscilloscope or a voltmeter to perform accurate measurements using a system based on the

Kerr effect.

A second disadvantage is that these systems are not now commercially

available. Most systems in operation today were constructed by the

user and lack the user convenience featiires , the documentation and the

availability of repair service that would accompany a commercial unit.

The final drawback is that the Kerr systems have been optimized for

shorter pulses—pulses with characteristic times in the microsecond

range rather than the millisecond and longer pulses that characterize

medical x-ray units.

Active Divider

Fig. 6 indicates schematically a conventional measurement system using a divider. It consists of a divider with its high and low impedance

segments, a low voltage measuring device and an interconnecting cable.

A typical unit would consist of a commercially available bleeder-bank

connected to an oscilloscope through a length of coaxial cable. The

measured frequency response of such a system is shown in Fig. 7- The

28
Fig. 6, Schematic representation of a conventional voltage measurement

system based on a divider. The high impedance arm of the

divider is Z]_, while Z2 is the low impedance arm. The capacitor

indicated by the dashed lines represents the effect of interconnecting cables and the input impedance of the voltage

measuring device is Z-q. Note that these last two impedances are

in parallel with the divider low side.

29
DIVIDER RATIO IS FREQUENCY DEPENDENT

Fig. 7. The measured—at low voltage—frequency response of a commercially available divider.

30
details of the ratio with respect to frequency are, of course,

characteristic of the particular measurement system. Other work has

shown that variations of the ratio of the magnitude shown here are characteristic of a large variety of measurement systems based on bleeder banks. It is in principle possible to compensate the divider so both the high impedance segment and the low impedance segment have the

same RC time constant. This approach frequently requires, however, that

the low voltage measuring device and the interconnecting cable be

dedicated to a specific bleeder bank as their resistance and capacitance

to ground contribute to the net low-side impedance of the divider.

The technique employed here uses an operational amplifier to maintain

the recognized advantages of a compensated divider while minimizing the

effect of cables and the measuring device on the divider ratio. As

indicated in Fig. 8, the low impedance side of the divider serves as the

feedback impedance for the operational amplifier while the high impedance

segment serves to define the input current. The ratio of the applied

voltage to the output voltage is the negative of the ratio of the high

impedance to the feedback impedance. The cable capacitance and the

input impedance of the measuring device have no effect on the voltage

ratio.

Fig. 9 demonstrates the validity of this approach. The upper photograph

shows the step-response of the measurement system whose frequency

response is plotted in Fig. 7. Using the same bleeder bank, the same cable, the same oscilloscope but an active rather than passive low-side,

one obtains the step response shown in the lower photograph. In this

case, the step response is faithfully reproduced indicating a system

with a flat response over a sufficiently wide frequency range to

reproduce the voltage pulses.

Some of the advantages and drawbacks of this approach are shown in

Table II. The advantages include low output impedance so that the

impedance of the cables and measurement instrumentation introduces

negligible error in the voltage measurement. The divider's input

impedance is determined by the bleeder bank. Thus, no unconventional

components are required in the high voltage circuit. The final

advantage is that the active low side uses commercially available

components, i.e., resistors, capacitors, and operational amplifiers.

As with all measurement techniques there are disadvantages. First the

reliability of this device for this specific application is unproven.

Similar systems have, however, proven reliable for the measurement of

60 Hz voltages up to 200 kV. The second disadvantage is that to the author'

knowledge, an active low side is not commercially available.

31
Fig. 8. Schematic representation of an active divider. Note that the

divider low side, Z2 , serves as the feedback impedance for an operational amplifier and is no longer in parallel with any

measuring devices.

32
Fig. 9- The upper photo is the step response of a commercially availahle

bleeder "bani: (vertical scale: V2 in arbitrary iinits; horizontal

scale: time with units 1 ms/division) . Note that there is an overshoot as is predicted "by the frequency response measiirements

in Fig. 7. The lower photo shows the response of the same system when an active low side is used.

33
Table 2. The advantages and disadvantages of using an active divider

for the measurement of the pulsed high voltage in medical

x-ray units.

Advantages Disadvantages

Low output impedance

High input impedance

Uses conventional components

Reliability unproven

Not commercially available

Summary

Two approaches have been used to electrically measure the high voltage

piilses in medical x-ray units. The first is an optically coupled

measurement based on the electro-optic Kerr effect. The other is an active divider which uses operational amplifiers to improve the voltage

measurement using a conventional bleeder bank. Both of these approaches

are capable of performing voltage measurements with an uncertainty no larger than ±1%. The present work centers on the more critical

evaluation of how well the measurement techniques can be transferred

from our laboratory to the people who are interested in using them.

References

1) R. E. Hebner and E. C. Cassidy, "Measurement of 60 Hz Voltages Using

the Kerr Effect" Rev. Sci. Instru. , Vol. 1+3, pp. l839-l8Ul, 1972.

2) E. C. Cassidy, R. E. Hebner, R. J. Sojka and M. Zahn, "Kerr Effect

Studies of an Insulating Liquid Under Varied High-Voltage Conditions"

IEEE Trans. Elec. Insul. , Vol. EI-9 , pp. ^3-56, 191^.

3h
APPENDIX II

Feasibility of Using the Electro-optic Kerr Effect for the

Measurement of the High Voltage Pulses in Diagnostic X-ray Units

This feasibility study was prepared for the Bureau of Radiological Health

and served as the basis for some of the experimental work reported in

Appendix I.

35
Introduction

During the past several years, the Electricity Division of the National

Bureau of Standards has been active in the development of high-voltage

pulse measiirements based on the electro-optic Kerr effect. As a result

of this work the electro-optic Kerr effect is used, in conjunction with

more conventional techniques, in the calibration of dividers used to

measure high voltage pulses. The majority of this work has been

directed toward the measurement of nearly rectangular pulses with a risetime of approximately 1 ys, a duration of less than 50 ys and a peak value of up to 300 kV. At the present time, work is continuing

both at NBS and in other governmental and industrial laboratories to

extend this work to higher voltages and to both longer and shorter

pulses

The primary advantages that have been identified are described in the

following paragraphs.

The first advantage is that sources of error in Kerr measurements are different from those in divider measurements. This is significant in

calibration work because the applied voltage can then be measured by

two independent methods. If values obtained from the two methods

disagree by more than their combined uncertainties, it is likely that

there is an error in one or the other measurements. If, conversely,

the two agree, it is highly unlikely that they are both in error by

the same amount. In this respect, the system is self-checking thus

minimizing the effects of operator error.

Secondly, the detection circuitry is optically connected to the high

voltage circuitry. In addition to reducing ground current error, which

falls under the first advantage, this buffers sensitive detection

circuitry from the energy contained in the high voltage circuit. This

permits the use of a variety of high speed solid-state devices for

detection and data handling. These devices have low tolerance to high

voltage or high current pulses and therefore they have not been

generally accepted in connection with conventional pulse measurement

techniques.

A third advantage is that voltag^ measurements using a Kerr cell do not

have to be referenced to ground. This technique is thus ideally

suited to the measurements of large potential differences between two

points both of which are at high voltage.

The final advantage is that the Kerr cell is a capacitor with a total

capacitance typically in the range from less than one hundred

picofarads to a few hundred picofarads. This means that the Kerr cell

represents a burden which is at worst as small as and typically much

smaller than that represented by a conventional divider.-^ Under some conditions, e.g., when a high voltage source with high output impedance

provides a pulse to a high impedance load, the Kerr cell provides

minimum perturbation on the high voltage pulse shape.

36
The tvo primary disadvantages are, first, that the existing systems

have been designed and constructed to optimize response over a fairly

narrow range of pulse shapes so to apply these techniques to a significantly different pulse requires further development. And second,

pulsed-voltage measurement systems based on the electro-optic Kerr

effect are not, as yet, commercially available. Therefore the technical

support, warranty, etc., usually associated with commercial products

are also not available.

The purpose of this study is to estimate, on the basis of existing

development work, the accuracy expected of a Kerr-effect pulse-voltage

measurement system when it is used to measure two different types of

pulsed high voltage. The first (type A) is a train of pulses made up

of an integral niomber of half-cycles of a 60 Hz sine wave in the form

typical of the unfiltered output of a full wave rectifier. The second

(type B) is an approximately rectangular pulse of risetime less than

1 ms and duration of 1 ms to 6 s.

Results from preliminary studies show a worst case error of

approximately 10% for the first few half-cycles of a type A pulse and

an uncertainty of order 1% for any remaining half-cycles of a type A

pulse and for type B pulses. These estimates are of course preliminary

and may not reflect the uncertainty characteristic of the final device.

The method of arriving at these uncertainty estimates and proposed

techniques for reducing the uncertainties constitute the remainder of

this report.

Theory

In this section the basic principles of the Kerr effect are reviewed.

This section is intended to provide a brief introduction to the

vocabiilary and equations necessary for a discussion of the proposed

measurement system. A schematic of a Kerr system is shown in Fig. 1.

The voltage measurement is based on the fact that molecules with an electrical anisotropy, e.g., non-zero dipole moment, will tend to align

with an applied electric field. The degree of alignment is then a measure of the applied field. In order to measure the degree of

molecular alignment it is further necessary that the index of refraction

of the medium have one value, n^^j^, in a direction parallel to the

applied field and a different value, nj^, in a direction perpendicular

to the field. The quantity n - n, is given by

n - n ^ = XBE^ . (l)

37
e

CO

<=> Z

to

5=1 a. a: CO ^ _j to

CO

CD

CD

to

•I

lO

LLJ 0=LU

C9

ts

CE LLJ o=

LU a_ 3toooCD

CO » 1 I CD j» I CO ^ I

—••—to

=a

—I >-

•a. o CO

O bD

•H

-p

•H

^1 ^

-P

Ti -P H

(U •H

ChO

•H

-PO

0)

-p

<L)

COO

•P

O

+^

•H

-PooH

QJ -P

-P

030

0)U

0)bO

cd PHO

(U •H

cn c3 P4

PM

-P ,?H 03

0)

03 -p Pi o -P ft (U

cij (D Ch :m

(U (U P ?H o3 U CPe O 1^ a <-! cd ^ o

>5

rHft

t3 Eh ft

CJ

W

•H o

03 -p

0) INl 0

bD •H

(i4

38
In "his expression, 3 is zhe Kerr constant of the Eiaterial, X is the

•wavelength of the incident light and E denotes the applied field. In

the coiarse of this discussion, it is necessary to consider two different

electric fields. One is the field applied to the plates of the cell and

this vill be denoted "by the symbol, Z. The other is the electric field

of the light bear:. This field -will be denoted by the symbol, F, For

the remainder of this discussion a coordinate system will be used in

which the light beam propagates in the z-direction and the applied

field Z is in the x-direction.

:nen ce revri"

1 - n = Xui

X y

(2)

In general, the electric field of the light bean: can be written in

terms of two cor:pcnent polarizations

F = F sin (kz + wt) X ox

sin (kz + u)t + (j) ) (3)

polarizec light <j>y is zero.

To predict the respcnse, the phase shift between F and F_ as the

beam propagates through the system must be calc-jla^ed.

The light is not shiz'ted in I'requency as it propagates through the

cell, but the wavelength in the cell differs for the two polarizations;

k = n k

X X

k = n k

y 7

'2.1' where > is the free-space waventmiber, k = -r- . So, the phase shift,

A <J), for linearly polarized light after propagation a distance tiz is

given by

A<j) = (n kAz - cat) - (n kAz - tot) X y

(U) = k (n - n ) Az X y

39
because we are to detect both beams at the same time, t. The total

phase shift after propagating a distance L is given by

L

<l> = ^

j (n - n)dz. ' n X y

2tt (5)

Using Eqs . 2 and 5, we then obtain

= (27T/A) / ABE^dz

Making explicit possible x, y, z and t dependences of E, we obtain

L

4)(x,y,t) = 2tt / BE (x,y,z,t) dz . o

(6)

To use the cell as a voltage measuring device, we will assume that the

light beam is an unexpanded laser beam, diameter - 2mm, which propagates

in the z-direction in the center of the cell. Previous experimental

results have shown that the error in locating the central region is

negligible with respect to other errors, so Eq. (6) can be simplified

(t) = 27T / BE (z,t) dz

o

(T

In order to use the electro-optic Kerr effect for voltage measurement,

it is necessary to further manipixlate Eq. 7- The aim is to calculate

the transmittance of our entire optical system in terms of <^{t). A

very convenient method of doing this is to use the Mueller matrices^

of the components in the optical path,

light beam is unpolarized

It is assumed that the initial

[A,] =

This beam then impinges upon a polarizer oriented at ^5° to the y-axis,

The matrix for this polarizer is

10 10

0 0 0 0

10 10

0 0 0 0

ko
The beam then passes through a 90° retarder oriented at 0° with respect

to the y-axis. The matrix for this retarder is

10 0 0

0 10 0

0 0 0 1

0 0-10

The Kerr cell can then be represented as a retarder which causes a phase shift (j) and is oriented at an angle B with respect to the y-axis,

The appropriate matrix for this type device is

[M3] =

2 2 cos 23 + sin 23 cos <^

sin 26 cos 26 (l-cos <^ )

-sin 23 sin (j>

cos 26 sin 26 (l-cos <}) ) 2 2 sin 26 + cos 26 cos (()

cos 26 sin <})

0

sin 23 sin <^

-cos 26 sin cf)

cos (j)

The beam then passes through a 90° retarder oriented at 90°

matrix is

This

10 0 0

0 10 0

0 0 0-1

0 0 10

Finally the beam exits through a second polarizer oriented at -^5°

to the y-axis

10-10

0 0 0 0

-10 10

0 0 0 0

The output light beam, [A^], is then given by the equation

[A^] = [M^] [M^] [M^] [M^] [M^] [A.] . (8)

hi
Performing the indicated mtiltiplication , one obtains

sm h (|) -sm *s 9

0

The implication of this matrix is that if the source intensity is I the intensity of the beam upon passing through the complete optical

system is given by the relationship

1 = h sin (J) )

(9)

Furthermore the emergent light beam is linearly polarized at an angle

of -k^° . In the development of Eq. 9, it was assumed there was no attenuation. We can relax this requirement somewhat by rewriting (9)

in terms of the maximum transmitted irradiance, I . That is

m

1 = 1 sin (^5 * ) . ' . . m

This equation relates the transmittance of the system, I/I to the

m

phase shift caused by the electro-optic Kerr effect, ^ . It now

remains to relate the phase shift to the applied voltage. To do this,

Eq. 7 is rewritten

L 2

(t)(t) = 2Tr / BE (z,t) dz = 2tt B£' (10)

where d is the plate spacing, V is the applied voltage, J,' is the

effective length of the plates, and B is the Kerr constant of the

liquid. The effective length of the plates is defined as the length

of the plates of an ideal parallel plate capacitor, i.e., no fringing

fields , which would cause the same phase shift as the Kerr cell if the

same voltage were applied. The quantity £' is not a separately

measurable quantity but to within the accuracy necessary depends

only on the geometry of the Kerr cell. It is convenient to define the

quantity, V , where

V = . (11) ^ v^BT"

Then, , ; : ^

,.

' * = TT (^)

' ^

' m

U2
Inserting this into Eq. 10, yields

I/I = sin^ [ijTT (V/V (12)

m m

which is the desired relationship "between the transmittance of the Kerr

system and the applied voltage. Eq. (12) explicitly indicates the

physical significance of the quantity V^. It can be seen that when

V = V , I/I =1. So, V is the smallest applied voltage necessary to

m m m

cause a maximum in the transmittance of the optical system. Calibration

of a Kerr system consists in applying a known voltage, measuring

(I/I ), and using Eq. 12 to calculate V . Once V is known, Eq. 12

is used in the measurement of unknown voltages.

It should also be noted that for a central path, path dimensions small

compared to both the width and spacing of the plates, the Kerr cell can be considered to be an ideal linear retarder with the fast axis

at 90° and an arbitrary phase shift (J> . If in Eq. 8, [M^] is

simplified to reflect this condition and if [M2] and [M|^] are removed,

the same value for [A^] is obtained. Physically this means that if

the light beam is confined to a central path there is no need for the

90° retarders (X/U plates) in the optical system. The Kerr constant,

and therefore the cell constant , depends both on the wavelength of the

incident light and on the temperature of the birefringent medium.

Because the light source to be used is a laser, the wavelength

dependence is significant only when one is using different types of

lasers. The cell constant does, however, change approximately 0.5%/°C

over the range of typical room temperatures. The cell temperature must,

therefore, be monitored.

In suppressing the spatial dependence of the transmittance in Eq. 2,

two important effects have been ignored. The first is the effect of

fringing fields at the edges of the electrodes. Previous work has

shown that this effect will make a negligible contribution to the

error if the light path is consti'ained to a small central region

between the plates.^ The second effect is that the electric field is

distorted by the presence of space charge in the birefringent liquid.^

It will be shown in the following sections of this report that confining

the light path to this same central region should also reduce the

error res\ilting from space charge distortion.

Using the information that has been presented in this section, it is

possible to design a Kerr system with predictable response. To make

explicit the steps in the design of a Kerr system, a sample calculation

follows

.

U3
Sample Calculation

a) Assume the following parameters

V = Maximum Voltage = 300 kV

P . -6

t = High Voltage Pulse Risetime = 10~ s HV

= Detector Bandwidth = 5 x lo'^ Hz

b) As indicated in Fig. 3, an increase in V implies that

the transmittance passes through a series of minima

and ma:!cima. The niomber of detectable maxima, n, is

given approximately by the product of the detector

bandwidth and the high voltage pulse risetime, i.e.,

^ = ^HV

• = 50

In addition,

' V^' • - V 2 ^

m

so

This is the desired value of V to insure that the m maximum applied voltage can be measured with the given

detection system. It is now necessary to choose cell

dimensions so that the cell will have the desired value

of V . m

: c) As nitrobenzene is the most commonly used Kerr fluid,

it is assumed in the remaining discussion that it is the

liquid to be used. To insure that there is no possibility

of electrical breakdown in the cell, it is sufficient

to design so that the field strength remains below

100 kV/cm. This requires a plate spacing, d, of 3 cm.

The necessary plate length, £, can then be determined

from Eq. 11, if for the p\irposes of design it is assumed

that £ = From Eq. 11,

hk
£ = d^/2BV

' m

= (3 X 10~^m/U2.U X 10^V)^/(2)(3.2 x 10 "'"^m/V^)

= 7.8 cm

d) To insure that the field is unifonn in the central

region, it is necessary that the plate width be

greater than the plate spacing. Appropriate plate

dimensions would then be 8 cm length, h cm width,

1 cm thick and 3 cm spacing.

Table I lists the dimensions and operating voltage range of several

cells constructed at NBS. It can be seen from this table that those

cells which were successfully operated at 300 kV have dimensions

similar to those calculated above.

Accuracy Expected in the Measurement of Type A Pulses

To estimate the accuracy of our measurement of type A (full wave

rectified, 60 Hz) pulses, there are two sources of information. The

first is to compare with the accuracy attainable \inder 60 Hz alternating

voltage. The second source of data is the preliminary experiments

performed in cooperation with and in the laboratories of BRH. In

these studies actual x-ray machine voltages of the desired form were

measiired using a Kerr system.

Because there has been a substantial amount of data and analysis at

60 Hz, this report will first consider that situation. The information

from this work will then be applied to the data obtained at BRH. An

example of the accuracy of voltage measurement at 60 Hz is shown in

Fig. 2. In this figure the cell constant (voltage necessary for first

maximum) is plotted against the applied voltage (number of light maxima

in one half cycle). In principle this plot should be a horizontal

straight line. There is however a systematic decrease, with a change

of about 1% as the field strength increased from about 10 kV/cm to

about ho kV/cm. Partially to increase the precision of this work a more exhaustive study3 of the low frequency behavior of nitrobenzene

was imdertaken. This information is summarized in reference 3 and

provides much of the basis for this discussion.

To gain an insight into Fig. 2 it is helpful to consider the data

presented in Fig. ik of reference 3. That data was from a Kerr cell

in which the plate spacing was 0.5 cm. The figure therefore provides

a plot of the electric field as a function of position between the

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plates for field strengths ranging from 20-60 kV/cm. Performing a linear, least-squares fit to the data points one can obtain values

for the slope of the best straight line through the data points.

These values are summarized in Table II.

The primary observations that are made concerning this data are

1) The electric field distribution is approximately linear.

2) The slope of the distribution passes through a maximum at

approximately 30 kV/cm.

In addition, Fig. 12 in reference 3 indicates that the slope of the

plot of the electric field distribution remains approximately constant

during the entire cycle.

These observations are significant because the aim of this work is to

measure the potential difference between the plates. By definition,

the magnitude, V, of the potential difference is given by

r d

V = / E (x) dx .

- . • Q

In this case the integral is an integral from one of the parallel

plates to the other. If

E = A X + B,

then :

V = d (A (|) + B) .

For a linear field then the potential difference between the plates

is merely the value of the electric field at the center of the cell,

multiplied by the plate spacing, d. From this observation, a second

advantage of confining the light to a central path is identified. Not

only are the effects of fringing fields minimized but, if the field is

linear, the effects of space charge are also minimized.

Fig. 2 shows that under 60 Hz alternating voltage these assumptions

hold to a sufficient precision to permit measurement uncertainty of

order ±1%.

Let us now consider the data obtained from measurements of x-ray

machine voltages in the light of the information developed thus far.

The data to be considered are four measurements , each with the same nominal value for the applied voltage but the duration of the pulse

train being one, two, four and eight half-cycles. The result of these

U8
strength

,

x/d- is rrese!i~e5. a~ various values cf ~'r.e arpliei fieli

streng*!':. The ia"a vere *aken the positive ^.p-X'"-'-" of

the appliei voltage.

Field Strength Slope

(kV/cm) (p")r

20 1.21;

30 l.Tl

1*0 l.liU

50 1.2:

60 1 . IC

h9
measurements is presented in Table III. It can "be seen from this table

that there is a significant variation in the peak voltage within each

set of half-cycles. This variation can be attributed to either of two

factors or more likely a combination of both.

The first possibility is that the amplitude fluctuations are real. This

is possible because the high voltage circuit consists essentially of

a step-up transformer supplying a load which is a parallel combination

of a resistor and a capacitor. An appropriate equivalent circuit is an ideal step-up transformer, powering a series RLC circuit. The output

voltage is assumed to be the voltage across the capacitor.

The equation relating the input and output voltage is then

. d V dV

, nV. = LC ^ + RC + V , 1 ,.2 dt o at

where V. and are the input and output voltages, n is the transformer

ratio, and R, L and C are the appropriate values for the resistance,

inductance and capacitance in the equivalent circuit. If V_j^, R, L, and

C were known it would, of course, be possible to solve this equation

for the output voltage. Those quantities were not determined at the

time of the voltage measurement; but it is sufficient for the purposes

of this document to consider the form of the solution when the input

is zero for t < 0 and sinusoidal with constant amplitude for t > 0. In

this case, the output voltage is of the form

—nf

V = V sin (wt-e) + A e sin (3t + 6) . o p

For times t ^ l/a the peak output voltage can be either greater or less

than the steady-state peak output voltage. This effect may contribute

to the fluctuations in the peak values recorded in Table II.

The second possibility is that a is small compared to any relevant

temporal variation of the applied voltage. In this case all peaks in

the output pulse train would be of the same magnitude and the

fluctuations in the measurements would be due to errors in the Kerreffect voltage measurement-system. This would be true if the time for

the space charge distribution to attain its steady-state value is

greater than approximately 8 ms. Assuming that this is true leads to

the error estimate of 10%. If this is the case, there are two

approaches which should reduce this error. The first is to maximize

the purity of the nitrobenzene. It is well documented (see reference 3

and references therein) that particulate and chemical impurities in

the nitrobenzene will reduce the resistivity of nitrobenzene by orders

of magnitude. Of particular importance is the removal of all

50
Table III. Data obtained using a Kerr system to measiire the high

voltage in an x-ray machine having a type A pulse.

Pulse Duration Half-cycle (V/V ) /, -, ^ -, \ m peak

(half cycles) ^

1st 5.052

1st

2nd i+.500

1st i+.T52

2nd k . 498

3rd i+.305

Uth i+.332

1st

2nd *

3rd U.329

hth i^.359

5th i+.323

6th i^.338

Tth

8th

*The photograph was out of focus at the edges so the initial and final

pulses are not resolved.

51
particulate impurities as these should be slower than ionic impurities

in reaching equilibrium.

If this approach is unsuccessful, there are other liquids acceptable for use in Kerr cells which are less susceptible to impurities than

nitrobenzene. The prime candidate for this application would be

a-dichloronaphalene . Its Kerr constant is approximately an order of

magnitude smaller than that of nitrobenzene but it has been used

successfully at NBS imder direct, 60 Hz and piilsed high voltage.

Accuracy Expected under Type B Pulses

The accuracy estimates for measurements of Type B pulses is again

derived from two sources. The first source is the long history of the

operation of Kerr cells \inder direct voltage. It is well docmented

that measiirement uncertainties of order ±1% can be obtained for cells

used to measure direct voltage. The measurements have traditionally

been made using an expanded beam so that the spatial distribution of

the electric field is recorded. In the same manner as discussed in

the previous section, the plots in Figure T of reference 3 suggest

that accurate measurements can be made using a light beam confined to

a central path. Direct voltage conditions are expected to be

representative of the situation when the type B pulse has a duration

of some few seconds.

In addition to measurements under direct voltage, measurements have

been taken where an electric field of strength 20-25 kV/cm was applied

to the Kerr fluid with a risetime of about 1 ms and arbitrarily long

duration. MeasTirements taken during the rise of this pulse are shown

in Figs. 3-6. The steady-state field distribution was identical to

that at I.56U ms . In each of these figures the Kerr fringes are shown

in the circular photographs on the left. The lower trace on the

oscillograph on the right shows the voltage pulse. The upper trace

shows the time when the pulsed laser (light pulse duration 6 ps) was triggered. To within the sensitivity of this experiment,

approximately ±5^» the Kerr response followed the applied voltage.

Conclusions

Although Kerr cells have been successfully used for the measurement

of microsecond duration pulses for a nijmber of years, very little work

has been directed toward accurate measurement of pulses from

millisecond to second duration. Preliminary studies have shown that

a cell which accurately measures short pulses measures the voltage

waveforms of interest here with an uncertainty of no more than ±10^.

Measiirements performed with direct, low frequency alternating and

step voltages indicate that with a carefully constructed cell,

uncertainties of order ±1% should be attainable.

52
t

photographs on the right show the voltage az:c laser light p"_Llses.
t=. 264 ms

t = . 364ms

t=. 464ms

.2ms/cm

4kV/cm

Fig. h. Kerr fringe pattern photographs taken at various instants during

a voltage pulse with a risetime of approximately 1 ms . The

photographs on the right show the voltage and laser light pulses.
t

t=. 564 ms

t=. 764 ms

t=. 964ms

Fig. 5

Inif m

w 0mmm mmm

iiiiitiif -'^ilitMi liSS1

HIIIIKllll mmmH

mlBBH I

mmmsmm 'iili

iiiiiiiiiiii awn

Milk

KfWmw mrarammmwmmmmmmmi

l

IHil

IB

' ,^^y|< -v^p

.2ms/cm

4kV/cm

Kerr fringe pattern photographs taken at various instants during

a voltage pulse with a risetime of approximately 1 ms . The

photographs on the right show the voltage and laser light pulses.

55
t

t = 1.164nns

t--1.364ms

.2ms/cm

t=1.564ms 4kV/cnn

Fig. 6. Kerr fringe pattern photographs taken at various instants during

a voltage pulse with a risetime of approximately 1 ms. The

photographs on the right show the voltage and laser light pulses.

56
It is not anticipated that a peak applied voltage of 200 kV should

cause any particular prohlems . All work performed to date indicates

that for applied voltages in the range of 10-300 kV all effects have

"been field rather than voltage dependent. Scaling has therefore eilways

been successful.

57
References

1. A. J. Schwab, "High Voltage Measurement Techniques", MIT Press,

Cambridge, Massachusetts, pp. 83-85, 1972.

2. W. A. Shurcliff, "Polarized Light", Harvard University Press,

Cambridge, Massachusetts, 1962.

3. E. C. Cassidy, R. E. Hebner, R. J. Sojka and M. Zahn, "Kerr Effect

Studies of an Insulating Liquid under Varied High Voltage

Conditions", IEEE Trans. Elec. Insul., vol. EI-9, pp. i+3-56, 197^.

h. E. C. Cassidy, W. E. Anderson, and S. R. Booker, "Recent

Refinements and Developments in Kerr System Electrical Measurement

Techniques", IEEE Trans, on Instr. and Meas., vol. IM-21,

pp. 50U-5IO, 1972.

5. E. C. Cassidy, H. N. Cones and S. R. Booker, "Development and

Evaluation of Electro-optical High-Voltage Pulse Measurement

Techniques", IEEE Trans, on Instr. and Meas., vol. IM-I9,

pp. 395-i+02, 1970.

6. R. E. Hebner, E. C. Cassidy, "Measurement of 60 Hz Voltages Using

the Kerr Effect", Rev. Sci. Instru. , vol. U3, pp. l839-^l, 1972.

USCOMM-NBS-OC

58
NBS-114A (REV. 7-73)

U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

SHEET

1. PLIIU.ICATION OK RllPORT NO.

NBSIR T5-TT5

2a Clov *i Accession

No.

3. Recipient *.s Accession No.

4. TITLK AND SUHTITLli

Electrical Measurement of High Voltage Pulses In

Diagnostic X-ray Units

5. Publication Date November 1, 1975

6. Performing Organization Code

7. AUTMOR(S)

Robert E. Hebner

8. Performing Organ. Report No. NBSIR 75-775

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

10. Project/Task/Work Unit No. 2IIOU96

11. Contract/Grant No. FDA-IAG 22l+-7^-6039

12. Sponsoring Organization Name and Complete Address (Street, City, State, ZIP)

Bureau of Radiological Health

Food and Drug Administration

5600 Fishers Lane

Rockville, Maryland 20852

13. Type of Report & Period

Covered

Interim 3/7U-9/75

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bibliography or literature survey, mention it here.)

-^The report describes a method of calibrating dividers used to measure high voltage

pulses in diagnostic x-ray \inits. The experimental development emphasized four

areas. These were the divider ratio under direct voltage, the frequency dependence

of the ratio, the voltage dependence of the ratio and the effect of self-heating

on the device. The res\alts of measurements on approximately fifteen different

dividers are summarized.

In addition, this report contains two appendices. The first discusses conventional

_and electro-optical methods of measuring the high voltage pulses, vhile the second

—presents a more detailed analysis of the feasibility of electro-optical measurement

of these pulses.

17. KEY WORDS (six to twelve entries; alphabetical order; capitalize only the first letter of the first key word unless a proper name; separated by semicolons)

Calibration; electricaJ. measurements; electro-optics; frequency response; high voltage;

Kerr effect; operational amplifier; pulses; radiation; safety; x-ray generators; x-rays

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