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National Bureau of Standards

NBS

PUBLICATIONS

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NBS Technical Note

High Voltage

Divider and

Resistor Calibrations

Martin Misakian Ma

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TM he National Bureau of Standards' was established by an act of Congress on March 3, 1901. The

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JlATIONAi. BUREAU

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NBS Technical Note 1215 C. X.

High Voltage

Divider and

Resistor Calibrations

Martin Misakian

Electrosystems Division Center for Electronics and

Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Gaithersburg. MD 20899

Issued July 1985

U.S. Depardnent of Commerce

Malcolm Baldrige, Secretary National Bureau of Standards

Ernest Ambler, Director
National Bureau of Standards U.S. Government Printing Office For sale by the Superintendent

Technical Note 1215 Washington: 1985 of Documents,

Natl. Bur Stand. (U.S.). U.S. Government Printing Office. Tech. Note 1215, 31 pages Washington, DC 20402

(July 1985)

CODEN: NBTNAE
TABLE OF CONTENTS

Page

LIST OF FIGURES iv

LIST OF TABLES v

Abstract 1

1. INTRODUCTION 1

2. DESCRIPTION OF SERVICE 1

3. CALIBRATION APPARATUS AND MEASUREMENT APPROACH 2

3.1 Standard High Voltage Resistors 4

3.2 Standard Low Voltage Resistors 4

3.3 Galvanometer Sensitivity 7 3.4 Guard System 7

4. MAINTENANCE OF STANDARD RESISTORS 9

4.1 Calibration of Park Resistors 9

4.1.1 Early Measurements 9

4.1.2 Recent Measurements and Practices 15

4.2 Calibration of Low Voltage Resistors 17

5. OPERATING PROCEDURES 20

5.1 Calibration and System Checks 20

5.2 Uncertainty of Calibration 20

6. FORMAT OF CALIBRATION REPORT 21

7. ACKNOWLEDGMENTS 21

8. REFERENCES AND NOTES 24

APPENDIX 25

1 1

1
LIST OF FIGURES

Page

Figure 1. Schematic view of Wheatstone bridge circuit

for calibration of high voltage dividers 3

Figure 2. Stacked Park resistors form standard high

voltage resistor R^ in figure 1. Polyethylene sheet under base covers metal

guard plate 5

Figure 3. Standard low-voltage resistors supported on NBS-type stand with amalgamated surfaces.

Resistors on stand and calibrated decade box

form resistor R|\| in figure 1. Also shown

are the galvanometer switch and

galvanometer. Polyethylene sheets which

sandwich a guard plate can also be seen 6

Figure 4. Schematic view of guard system. The leakage

resistance to ground is shown connected in

parallel with resistor R^ 8

Figure 5. Measurements of a-j for Park resistor 156881

for the years 1967 to 1973 10

Figure 6. Measurements of a-j for Park resistor 156882

for the years 1967 to 1973 10

Figure 7. Measurements of a-j for Park resistor 156883

for the years 1967 to 1973 11

Figure 8. Measurements of a-j for Park resistor 156884

for the years 1967 to 1973 11

Figure 9. Histogram of a-j in parts-per-mil 1 ion (ppm)

for Park resistor 156881 during the years

1967-1973. The dashed line is a calculated

histogram assuming a Gaussian distribution

and is described in the text 12

Figure 10. Histogram showing number of measurements of

a-j in parts-per-mil lion (ppm) for Park

resistor 156882 during the years 1967-1973.

The dashed line is a calculated histogram

assuming a Gaussian distribution and is

described in text 13

IV
LIST OF FIGURES (continued)

Page

Figure 11. Histogram showing number of measurements of

ai in parts-per-million (ppm) for Park

resistor 156884 during the years 1967-1973.

The dashed line is a calculated histogram

assuming a Gaussian distribution and is

described in text. The dotted line is a calculated histogram which excludes the data

for 1969 14

Figure 12. High voltage measurements of a-j for Park

resistor 156884 during checks of the

calibration apparatus for the years 1980 to

1984 18

Figure 13. Histogram of a^ in parts-per-million (ppm)

for Park resistor 156884 during checks of

calibration apparatus at high voltage for the

years 1980-1984. The data of 1980 are indicated with diagonal lines 19

Figure 14. Format of calibration report for high voltage

dc dividers 23

LIST OF TABLES

Page

Table 1. Summary of Park Resistor Measurements 16

Table 2. Summary of Calibration Uncertainties (ppm) 22

HIGH VOLTAGE DIVIDER AND RESISTOR CALIBRATIONS

M. Misakian

Abstract

An NBS calibration service for determining the ratio of highvoltage dc dividers and the resistance of high-voltage resistors is

described. Calibrations are performed with a Wheatstone bridge

apparatus with a simple guard system. Sources of systematic error are identified and methods for characterizing the NBS standard highvoltage resistors are discussed. Ratio and resistance values can be

determined between the voltages of 10 kV and 150 kV with an uncertainty of less than ±0,01%.

Keywords: calibration service; dc; high voltage; NBS; resistor;

voltage divider.

1. INTRODUCTION

The laboratory applications of direct-current (dc) high voltages range from

fundamental studies, such as elementary particle physics and electrical

discharges in dielectrics, to more applied studies such as insulation tests with

systems containing large amounts of capacitance (e.g., high voltage cables and

capacitors). Technical uses of high dc voltages include the generation of

x-rays, electrostatic precipitation, paint spraying, and the transmission of

electrical energy.

High dc voltages frequently are measured with resistive voltage dividers.

The dividers typically have one or two low-voltage connections with

corresponding ratios. This report describes a calibration service at NBS for

high-voltage dividers and resistors that are of sufficient accuracy to be

regarded as transfer standards. Devices calibrated at NBS are normally used as standards in industrial and government laboratories.

2, DESCRIPTION OF SERVICE

A calibration service is maintained at NBS for the determination of dc

voltage ratios of resistive dividers and their total resistance. The

calibration service is normally available for applied voltages from 10 kV to

150 kV, The calibrations are performed with an apparatus that permits

measurement of the ratio with an uncertainty of less than +0.01%. To assure adequate sensitivity at the lowest applied voltage levels, calibrations are normally performed on dividers with ratios of 100,000:1 or smaller; the low

voltage resistance is also restricted to 10,000 ohms or less.

Resistive dividers are acceptable for calibration only if they are corona-free at the operating voltage and are designed to have small temperature

and voltage coefficients. Specifically, a device is not generally suitable for

calibration by NBS if these coefficients produce a change in the ratio of 0.1%

over the normal range of operating voltages. At a given voltage, dividers

should not exhibit instabilities in their ratio values in excess of 0.005%. NBS

staff can provide some assistance in the identification of intermediate

calibration laboratories capable of determining the ratios of less accurate

voltage dividers.
A typical calibration consists of monitoring the divider ratio with a fixed

voltage continuously applied for 15 minutes. Ratio determinations are made

every three minutes. The measurements are performed at two voltages selected by

the customer to determine the effects of voltage and heating on the divider

ratio. The tests begin at each voltage when the divider is at room temperature. Ratio measurements can be made for different functions of time or voltage by special arrangement.

Dividers can be hand -carried or shipped to NBS. If they are shipped, they

should be packaged in sturdy reusable containers. The design of many high

voltage dividers makes them vulnerable to shear-type forces. Therefore,

provisions should be made to minimize the likelihood of damage due to such

forces when the device is in the shipping container.

A calibration service is also maintained for resistors designed for dc

high-voltage applications. This service is for corona-free resistors designed

for dc operation between 10 kV and 150 kV. The measurement uncertainties and

cautions about shipping damage are the same for resistors as they are for

voltage dividers.

3. CALIBRATION APPARATUS AND MEASUREMENT APPROACH

Measurements of divider ratios are performed with a Wheatstone bridge

apparatus shown schematically in figure 1. Resistors Rx and Ry are resistors in the divider that is being tested and resistirs R^ and R^ are fixed and variable standard resistors, respectively, maintained at NBS. As

suggested by the point of high voltage application, Rx and Rf^ are high

voltage resistors and Rx and Rf^ are low voltage resistors. The detector g is a sensitive galvanometer with resistance G, indicated schematically in

figure 1 by Rq.

The ratio of the divider under test is determined by nulling the

galvanometer and using the well-known relationship between the resistances under

this condition [1] to calculate the ratio. That is, when the bridge is balanced

XjN = X2M (1)

where X^ is the resistance of Rx , N is the resistance Rf^, etc. (subscripts

denote values of respective resistors). Using elementary algebra, eq (1) can be

rewritten to yield the ratio of the divider under test.

Ratio = (Xi+ X2)/X2= (M+N)/N (2)

The bridge, when balanced, introduces negligible burden on the divider

under test. The user is thus cautioned that introduction of a resistance across

the low side of the divider with, for example, a digital voltmeter will change

the ratio. Upon request, calibrations of the divider can be performed with a burden provided by the user on the low side of the divider. By replacing Rx

with a known standard resistor, the bridge circuit in figure 1 can also be used

to determine the value of an unknown high voltage resistor, Rx , using eq (1).

Equations (1) and (2) imply that the uncertainties associated with

determining unknown ratio and resistance values are related to the uncertainties

in the values of the standard resistors. An additional consideration is the

sensitivity of the galvanometer. The resistors and galvanometer used in the NBS

calibration apparatus as well as a simple guard system to detect leakage

currents are described below.
HIGH VOLTAGE

Figure 1. Schematic view of Wheatstone bridge circuit for calibration of high

voltage dividers.
3.1 Standard High Voltage Resistors

Resistor R\j[ in figure 1 typically consists of three 100 megohm Park

resistors [2] connected in series (Serial Nos. 156881, 156882, 156883). The

characteristics of the Park resistor are briefly described here; a more detailed

account is given in Reference 2. Each Park resistor is made of 100 one-megohm

wire-wound resistors connected in series and arranged to form a vertical helix

between a ground plate and high voltage electrode. By removing the ground

plates it is possible to stack several Park resistors in series as shown in

figure 2.

During application of high voltage to the Wheatstone bridge, changes in

resistance can occur in the high voltage resistors because of (i) heating of the

resistance wire, (ii) leakage of current over insulating surfaces used to

support the resistor and, (iii) corona discharges. Each 1 megohm resistor in

the Park resistor has a temperature coefficient of less than

±2 parts-per-mill ion (ppm)/°C near room temperature, and resistors with

temperature coefficients of opposite sign have been paired to minimize changes

in resistance due to heating. The estimated temperature coefficient of the NBS

Park resistors is less than 0.4 ppm/°C and temperature changes anticipated

during calibrations up to 150 kV for three Park resistors in series should

produce a resistance change of less than 10 ppm [2].

Leakage current over insulating surfaces and current due to corona both

effectively introduce resistances that are in parallel with the high voltage

resistor. Precautions taken in the design of the Park resistor to minimize

these possible problems include the use of electrically biased metal shields to

enclose resistor pairs to eliminate corona and the use of a corona ring at the

top of each Park resistor (fig. 2). The effectiveness of these precautions is

checked by simultaneously measuring the current entering at the top of the Park

resistor and the current exiting at the bottom of the resistor under high

voltage conditions. At 100 kV, the currents differed by less than the estimated

measurement uncertainty of 20 ppm. At 50 kV, the maximum voltage normally

applied to the Park resistors, the difference is less than 10 ppm [2]. Using

Ohm's law, it is readily shown that the difference in current at 50 kV results

in an uncertainty of less than 10 ppm in the value of each Park resistor.

3.2 Standard Low Voltage Resistors

Resistor R[^ in figure 1 consists of Rosa-type standard resistors [3]

connected in series with a calibrated resistance box which can be varied from

to 10000 ohms in steps of 0.01 ohm. The standard resistors have elements made

from a low temperature-coefficient alloy which are sealed in metal containers

filled with moisture-free oil. Each resistor is connected into the bridge

circuit with two copper arms that are supported on an NBS-type stand with

amalgamated surfaces [3] in order to minimize contact resistances. The contact

resistances at the amalgamated surfaces are of order 1 x 10"^ ohms [3]. Strips

of copper 2-cm wide and 0.076-cm thick are used to connect the resistance box to

the standard low voltage resistors and to ground. The resistance of the copper

strips can be calculated and is of order 0.0006 ohm. The contact resistances at

the binding posts are estimated to be of order 0.001 ohm or less [2]. These

resistances are negligibly small compared to the resistance of Ri\| which is

typically 3000 ohms or more. Changes in the value of R^ due to heating are also negligible because of the small power that is dissipated, typically less

than 2.5 x 10"^ watt. The resistance change is expected to be less than

1 ppm [4]. Figure 3 shows the arrangement of the standard low voltage

resistors, stand, and resistance box.

4
Park

resistors

Top polyethylene

sheet

Guard plate

Figure 2. Stacked Park resistors form standard high voltage resistor R^ in

figure 1. Polyethylene sheet under base covers metal guard plate,
Galvanometer

Switch for

galvanometer and

guard system

Polyethylene

sheets

Guard plate

NBS type stand

"^^SS—Standard resistor

Decade box

Figure 3. Standard low-voltage resistors supported on NBS-type stand with

amalgamated surfaces. Resistors on stand and calibrated decade box

form resistor R|\| in figure 1. Also shown are the galvanometer

switch and galvanometer. Polyethylene sheets which sandwich a guard

plate can also be seen.
3.3 Galvanometer Sensitivity

The sensitivity of the galvanometer influences the uncertainty associated

with determining the null condition and thus the ratio or resistance of the

device being tested. The galvanometer used in the NBS Wheatstone bridge

indicates a 1 nm deflection for 0.002 uA of current. When the bridge is

slightly unbalanced, the current through the galvanometer aIq is given by [1]

Alg = VaN/{M+No}{G[1+(X2/Xi)>X2+No} (3)

where V is the high voltage, and aN is the change in N from the null value, Nq.

For typical values of X^ equal to 100 megohms, X2 equal to 1000 ohms, M equal to

300 megohms, Nq equal to 3000 ohms, and G equal to 560 ohms [5],

Alg = 7.31 X 10-1^ V aN. (4)

The lowest voltage normally used during calibrations is 10 kV and the

corresponding galvanometer current is

Alg = 7.31 X 10-^ aN. (5)

Thus, a change in N of about 0.28 ohm will produce a galvanometer current of

0.002 yA and a deflection of 1 mn in the galvanometer display. Using a magnifying glass to view the galvanometer scale, a displacement of less than

0.1 irn can be discerned. A 0.1 mm change in the galvanometer display

corresponds to a change in N of less than 0.03 ohm or 10 ppm. At higher

voltages the null condition can be determined with greater precision. For

example, when V is equal to 50 kV, a galvanometer deflection corresponding to a change in N of 0.01 ohm or 3.3 ppm is readily seen.

3.4 Guard System

The NBS calibration apparatus is equipped with a simple guard system which

is designed to intercept leakage currents to ground. Portions of the guard

system can be seen in figures 2 and 3. The Park resistors and standard low

voltage resistors are located or supported on sheets of high density

polyethylene. Beneath each polyethylene sheet is a metal plate (portions of the

guard system) and beneath the metal plate is yet another layer of polyethylene.

A similar combination of polyethylene sheets and a metal plate is located under

the divider or resistor being tested. Through a switching system, leakage

currents which reach the metal plates can be routed through the galvanometer.

The connection of the guard plates to the galvanometer is equivalent to

connecting the leakage resistances to ground (i.e., bottom layer of

polyethylene, table, floor tile, etc.) in parallel with the low side resistors

in the bridge. Figure 4 is a schematic view of the guard system when connected

to the right side of the galvanometer.

If leakage currents occur across dielectric surfaces because, for example,

of high humidity, the guard system shown in figure 4 provides a means to

determine its magnitude. By noting the change in the value of Rf^ necessary to

rebalance the bridge, when the guard system is connected to the galvanometer,

and the resistances X2 and N in the bridge, an estimate of the leakage

resistance to ground can also be made. The practice at NBS is to routinely

check for the presence of leakage currents during each calibration and to
HIGH VOLTAGE

DIELECTRIC SURFACES,

POLYETHYLENE SHEET

METAL PLATES

.POLYETHYLENE

y SHEET, TABLE, ETC.

Figure 4. Schematic view of guard system. The leakage resistance to ground is

shown connected in parallel with resistor R^.
postpone data acquisition if significant leakage currents due to humid

conditions (i.e., relative humidity greater than about 55%) are present.

4. MAINTENANCE OF STANDARD RESISTORS

4.1 Calibration of Park Resistors

4.1.1 Early Measurements

Two methods were originally employed to determine the resistance values of

the Park resistors. Both methods involve measurements at low voltage which,

because of the low temperature coefficient of the Park resistor and freedom from corona and leakage paths, can be taken to be applicable to high voltage

conditions.

In the first approach, the resistance of each 1 megohm resistor was measured with a Wheatstone bridge and standard low voltage resistors. The total

resistance was taken to be the sum of the resistances.

In the second approach, the Park resistor was partitioned into ten

10-megohffi sections. These ten sections were then connected in parallel to form

a 1-megohm resistor. By measuring the parallel resistance (using a Wheatstone

bridge with standard low voltage resistors), it was possible to compute the

resistance of all ten sections in series because the resistance of each section

was within 0.1% of 10 megohms. This procedure, used previously by Wenner [4]

and others, is described in further detail in the Appendix. The resistance

values obtained using the partitioning approach, for temperatures ranging from

23°C to 26°C, were found to be in agreement with the value obtained by summing

the 100 1-megohm resistors within 15 ppm [2].

Since the measurements reported by Park in the early 1960's, the resistance

of each NBS Park resistor has been measured periodically using the partitioning

technique noted above. The 1-megohm, partitioned. Park resistor is compared

with a standard, 1-megohm, wire-wound resistor using a Wheatstone bridge

circuit [6], The uncertainty in the value of the 1-megohm standard resistor

used during the comparison is estimated to be less than ±10 ppm [6,7].

Figures 5 through 8 show measurements of the departure, a-j , from the

nominal 100 megohm value in parts-per-mil 1 ion, for each of the NBS Park

resistors for the years 1967 to 1973. The values of ai obtained in the year

1969 are higher than those obtained in other years, but no well defined trend in

the resistance values is evident. Most of the values of a^ for each resistor

are contained in a band that is about 30 ppm. These early measurements show

that the resistance values remain relatively stable over a period of years.

Figures 9 through 11 show the d-\ data as histograms for three of the Park

resistors. The fourth Park resistor (serial number 156883) is discussed further

below. Calculated histograms, assuming a Gaussian distribution [8], are also

shown in figures 9 to 11 with dashed lines. Each bar of the calculated

histogram has been obtained using an expression of the type

a. +1.5

/

^ n f(a) da

a. -0.5

where f(a) is the Gaussian probability function
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1973.

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Figure 6. Measurements of a^ for Park resistor 156882 for the years 1967 to

1973.

in
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100

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1967 1968 1969 1970 1971 1972 1973

YEAR

Figure 7. Measurements of a^ for Park resistor 156883 for the years 1<567 to

1973.

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CL •r- TO —Q-T3 M l_ - O) Z3 O)

-C -QO c to •r- -•-> O «3 t_ to

•1- "O +-> •r— r— to jc r- OJ • 1—

•1- ^ -c T3 E 1- OJ 1 c +-> t_ TO TO cu • •r— 1

Q.CO to 3 1 1^ to U

to CTi 3 1

+-> <-• (O TO

C- 1 o O

ro r^ a.Ko <c TO

CTi c .-< CD to

•1— c •r—

(/) •1—

•I- t_ E 0) <a ro Z3 c

O) to •f— 4- >> to I— O <o

OJ o E sz E 0) <o •-> TO 4-> (- t_ «-> a> en C7> o o c o -o . M -1- »-> en

to t_ to O) to

•- 3 •r- x: (Ti

Ol

o>

A0N3n03dJ

14
f(a) = (l/a/2iT)exp[-(a-a)2/2&2-j

n is equal to the number of measurements

a-j is the departure from nominal in ppm for the ith measurement

J is the average departure from nominal

o, the standard deviation, is given by

o = [{n-l)-i 5;(a.-a-)2]i/2 . i=l ^

In figures 9-11, the 1969 data are indicated with bars containing diagonal

lines. A summary of the data^ showing the number of data points, n, the average

departure from 100 megohms, a, and the standard deviation, a, are given in

table 1.

As noted earlier, the 1969 data are higher than for other years and it is

found to have a significant effect on the Gaussian distribution used to fit the

data of Park resistor 156884. However, in light of some recent measurements of

Park resistor 156884, which are discussed in Section 4.1.2, the likelihood that

a systematic error was present when the 1969 results were obtained seems high.

Figure 11 shows the effect on the calculated histogram when the 1969 data are excluded in the statistical analysis for Park resistor 156884.

In addition to the low-voltage measurements, intercomparisons between the

Park resistors were made in 1978 at high voltage using a Wheatstone bridge

circuit. The results of these measurements were consistent with the

measurements presented in tab]_e 1, i.e., the measured values are typically

within 10 ppm of the average a.

While the resistance values of the fourth Park resistor (156883) presented

in figure 7 show no trend between the years 1967 and 1973, the overheating of one section of ten 1-megohm resistors in 1975 resulted in a resistance change of

about 40 ppm. Several subsequent measurements of this resistor in 1975 using

the partitioning technique indicated a departure from nominal, ai , of

150 ppm. Measurements performed in 1978, with voltages between 100 V and 500 V,

indicated values of a-\ between 154 and 157 ppm with an uncertainty of less

than ±20 ppm.

4.1.2 Recent Measurements and Practices

The early measurements of Park resistors 156881 and 156882 indicate that

the resistance values have remained stable frocn 1967 to 1973 within about

±15 ppm. The observed variations can be attributed, in great part, to random

measurement errors and the uncertainty in the value of the standard resistor

used for comparison when employing the partitioning technique.

Measurements of the Park resistors in 1984 have been performed by comparing

the partitioned Park resistors with a standard 1 megohm resistor using a precision digital ohmmeter. These measurement results are also given in table 1 and reveal shifts in resistance values from the historic averages of

approximately 18 ppm and 9 ppm for resistors 156881 and 156882, respectively.

15
Table 1. Summary of Park Resistor Measurements

Recent Measured Values

DIVIDER n a (ppm) a (ppm) of ai(year)

156881 25 106.5 7.7 125(1984)d

156882 31 67.5 7.2 77(1984)d

1568841 32 118.5 10.9 117(1978)C; 128(1984)d

156884*^ 24 114.5 5.3

156883 - - - 150(1975); 154(1984)^

b - excluding 1969 data

c - measurement performed in Electrical Measurements and Standards Division with

uncertainty of less than ±20 ppm

d - comparison with a 1-megohm standard resistor using precision ohmmeter

16
The most recent measurement of Park resistor 156883 yields a value of 154 ppm

for ai which is 4 ppm higher than its 1975 value. As noted in Section 3.1,

resistor Rm consists of Park resistors 156881, 156882, and 156883. Thus, the

change in resistor R^ amounts to about 11 ppm which is small relative to the

total uncertainty quoted in NBS calibration reports (see Section 5.2).

The 1984 resistance value of Park resistor 156884 (table 1) also differs

from its historical average by about 11 ppm. The changes in resistors 156884

and Rm (156881, 156882, and 156883) since about 1978 went undetected because

the procedure used to monitor the values of the Park resistors was insensitive

to comparable simultaneous changes in these resistors. Since 1980 the

calibration apparatus has been checked several times annually by measuring the

resistance of Park resistors 156884 at high voltage, typically near 50 kV. This

is done by replacing the unknown resistor Rx (fig. 1) with Park resistor

156884 and using a standard low voltage resistor for Rx . During these system

checks, the value of resistor 156884 was calculated with eq (1) using the

pre-1984 value of resistor R^. Checks of th^e apparatus since 1980 have

yielded an average departure from nominal (a) of 121 ppm (a = 8 ppm) which is in

good agreement with the pre-1984 value of resistor 156884 determined with the

partitioning technique. Figure 12 shows high voltage measurements of the

departure, a-j , from the nominal 100 megohm value in parts-per-mill ion for

resistor 156884 during checks of the calibration apparatus from 1980 to 1984.

Figure 13 presents the data of figure 12 as a histogram. If the 1984 value of

resistor Rfvj had been used to calculate the value of Park resistor 156884 at

high voltage, its value would be larger by about 11 ppm (i.e., ac;130) and in

agreement with the latest determination of resistor 156884 using the

partitioning technique. Thus, it appears that resistor R[i\ (156881, 156882,

156883) and resistor 156884 have both increased slightly in value since 1978 and

the change has gone undetected because the check procedure is insensitive to

simultaneous changes of these resistors (X^ and M in eq (1)). The above

observation suggests that resistors R^ and 156884 be measured annually using

the partitioning technique, and this practice has been instituted again at NBS.

The data in figures 12 and 13 include several anomalously high values in

1980, reminiscent of the 1969 measurements of a] for Park resistor 156884.

The 1980 data are indicated with diagonal lines in figure 13. A recent

examination of the individual 1-megohm resistors of Park resistor 156884 has

revealed several questionable electrical connections and the earlier

intermittent high values of d-\ may have been due to these poor connections and

mechanical handling of the resistor. The questionable connectj_ons have been

replaced. If the ai measurements of 1980 are not considered, a becomes

118 ppm (a = 4 ppm) and all the remaining measurements are within 9 ppm of the

average.

4.2 Calibration of Low Voltage Resistors

The standard, NBS, low-voltage resistors are periodically calibrated in the

Electricity Division at NBS. The calibration procedures are described in detail

elsewhere [3,4] and are not discussed here. The low-voltage resistors that are most frequently used during calibrations of high-voltage dividers have nominal

values of 1 kilohm and 10 kilohm. The calibration uncertainties are less than

±5 ppm and ±7 ppm for the 1 kilohm and 10 kilohm resistors respectively and take

into account random errors (3 times the standard deviation), temperature

uncertainty, errors in drift rate, leakage, pressure variation, and dielectric

absorption [9]. Calibration records of the 1 kilohm and 10 kilohm NBS resistors

show that since 1967 the resistance values of all but one resistor have changed

by less than 6 ppm.

17
E

a

a

(0

1 yJVt —

1

e

., ,

, ., , ^ —rPARK S/N 156884

140

_

o

o _

130 - eo

o o

-<

—

o o e —

120

- o

o

o

o

e ooo oo o

o

ooo

s

o

e

o

~

110 ^

•

o

1 1

1 I 1980 1981 1982

YEAR

1983 1984

Figure 12. High voltage measurements of aj for Park resistor 156884 during

checks of the calibration apparatus for the years 1980 to 1984.

18
1—

r o

00

00m

CO

cc<

0. E_ Z

(0 UJ O o F <

CM - CM QC

O

Q.

X

HIo

<D rt 04 A0N3n03Hd o

t/> ^ t_ 00 'C 00 <D o >> to • T-H q; i/» jr O)

t_ +-> c o •<—

l-> t_ r—

«/>O

•1— *- ,—

</1 fD

O) d) c

i;- CD

O

(D CD

-i<f 4_> (U

t_ r— 'r~ eo o -o

Cl. > ^ i- x: !-> O rn-i- >- •i- 2

x:

*»-^ -c E +J OJ Q. m 4-j O. T ^

VIu

73 •<-

C 4-> -C o ITS C • r- t_ •>- f— 'C f— Cl Q.' •1— Q. t. E1 /O (T3

t_

C

O

O) o oc n. ..- <y- 1 4-> «-<

«/) t3

•»-> £_ l*. <- jQ O

<tj ^ c 1— <t: (Z +-= c O <T3 •f— "C

>f-

•1—

O Q;

»o JZ

</1 1—

V4- Js^ O o

0) . c= x: "^

f3

u oc

(- CTi cn cnt—1 o c • -> •r- O (/I t. 00 • r- 3 Cr^ 3r C '-'

CO

f-t

O)

19
The resistance box which is part of the low-voUage resistance Rf^i in

figure 1 is also periodically calibrated in the Electricity Division. The

corrections for the settings normally used have remained stable for many years.

For example, the corrections for resistance settings less than 100 ohms changed

by less than 0.005 ohm (less than 1.7 ppm of N) from 1964 to 1976.

5. OPERATING PROCEDURES

5.1 Calibration of Dividers and System Checks

As discussed in Sections 2 and 3, measurements of high-voltage divider

ratios are performed with the Wheatstone bridge circuit shown in figure 1. In addition to the ratio measurement, the total resistance of a divider is usually

measured as described in Section 3 and reported. The low side resistance of the

divider is also measured by comparison with an NBS standard resistor.

Measurements of the total resistance and low-side resistance permit the

calculation of the ratio which can then be compared with the value measured at

high voltage. This independent determination of the ratio serves as a check on the ratio measurements and the associated calculations. A check of the

calculations is made by at least two staff members during the review process for

the calibration report. As discussed in Section 4.1.2 the calibration apparatus

is checked regularly (i.e., more than six times annually) by measuring the

resistance of Park resistor 156884 at high voltage.

A check for leakage currents across certain insulating surfaces of the

calibration apparatus is also routinely performed during calibrations. The

guard system used for this check is described in Section 3.4.

5.2 Uncertainty of Calibration

The various sources of uncertainty associated with the NBS calibration

system which have previously been described are

(i) value of resistor R^ (Sections 3.1, 4.1.1, 4.1.2)

(ii) value of resistor R^ (Section 4.2)

(iii) galvanometer sensitivity (Section 3.3)

(iv) lead resistance (Section 3.2)

(v) heating of R(v| (Section 3.1)

(vi ) heating of R^ (Section 3.2).

The largest single uncertainty is that associated with the value of

resistor Rf^ (Park resistors 156881, 156882, 156883) and is taken to be the

root -mean-square (rms) of three times the standard deviation of the Park

resistor measurements (<8 ppm, table 1) [10], the uncertainty in the value of

the Park resistors due to the possibility of leakage currents (Section 3.1,

<10 ppm, ref. 10 again applies), and the uncertainty associated with the value

of the standard resistor used during comparisons with the partitioning technique

(<10 ppm, see ref. 6);this amounts to less than 28 ppm. It is assumed that the

scatter in the measurements of the Park resistors is due to random sources of error and independent of the uncertainties associated with the determination of

the value of the standard resistor. A tabulation of the various uncertainties,

in ppm, and the total rms value is given in table 2. The total uncertainty

amounts to less than 33 ppm. Repeated measurements of the ratio for the same voltage divider, under nearly identical conditions of temperature and humidity,

yield results that are the same within about 3 ppm. What portion of this

variation is already accounted for by the uncertainties in table 1 is not

20
clear. However, its exclusion from table 2 does not significantly affect the

total uncertainty [11]. The uncertainty in NBS calibration reports is

given as 100 ppm.

6. FORMAT OF CALIBRATION REPORT

An example of a Report of Calibration for a high-voltage divider calibrated

at NBS is shown in figure 14. In addition to the measurements, the room temperature, relative humidity, and the fact that all tests begin with the

divider at room temperature are noted.

7. ACKNOWLEDGMENTS

The author wishes to acknowledge many helpful discussions with Ralph Kotter

and his efforts in locating and correcting the poor electrical connection in

Park resistor 156884. The assistance of Barbara Frey during preparation of the

manuscript is also greatly appreciated.

21
Table 2. Summary of Calibration Uncertainties (ppm)

Value of resistor R^ <28

Value of resistor Rf^ <7

Galvanometer sensitivity <10

Lead resistance <1

Heating of resistors R^,^ and R

^

<1_1

Total rms uncertainty <33

22
formnss-ms

(mv. i>-n>

U.S. DEPARTMENT OF COMMERCE

NATIONAL BUREAU OF STANDARDS

WASHINGTON, O.C. aOZM

REPORT OF CALIBRATION

VOLTAGE DIVIDER (Manufacturer, model, serial number)

Submitted by

(Name and address)

Measurements of the ratio between the voltage applied to the high-voltage

terminal and that at the 1-volt tap and of the total resistance were made with direct voltage in August 1984 at a room temperature of about 23°C

and a relative humidity of about 50%. The results are given in the

following table:

Voltage Ratio Total Resistance

(1-volt tap) (megohms)

Elapsed Time Applied Voltage Applied Voltage

(minutes) 30 kV 60 kV 60 kV

3 99977 99978 100.099

6 99977 99978 100.099

9 99977 99978

12 99978 99978

15 99978 99978

The ratios and resistance values shown in the table were recorded at the indicated times after application of the high voltage. The voltage was turned off after each test to permit the return of the divider to room temperature.

The values of the ratio and resistance in the table have been obtained with

an NBS calibration system which has an uncertainty of less than ±0.01%. The uncertainty quoted here should not be interpreted as the accuracy of the

device under test, and it should be noted that the ratio and resistance

values reflect the performance of the divider at the time of the tests and

not the long-term stability. It should also be noted that the ratio values

have been obtained using a resistance bridge which introduces a neglible

burden on the low side of the divider. Thus, introduction of a resistance

across the low side of the divider with, for example, a digital voltmeter

will change the ratio value.

For the Director

National Engineering Laboratory

Group Leader

Applied Electrical Measurements Electrosystems Division

Figure 14. Format of calibration report for high voltage dc dividers

23
8. REFERENCES AND NOTES

[Ij E. Frank, Electrical Measurement Analysis , (McGraw-Hill, New York, 1959)

p. 231ff.

[2] J. H. Park, Special Shielded Resistor for High-Voltage DC Measurements, J.

Res. Nat. Bur. Stand. (U.S.), Vol. 6CC, pp. 19-24, 1962.

[3] P. P. B. Brooks, Calibration Procedures for Direct-Current Resistance

Apparatus, National Bureau of Standards Monograph 39, 1962. Available as Report. No. CUM 7510804 from NTIS, Springfield, VA 22161.

[4] F. Wenner, Methods, Apparatus, and Procedures for the Comparison of

Precision Standard Resistors, J. Res. Nat. Bur. Stand. (U.S.), Vol. 25,

pp. 229-294, 1940.

[5] The resistance u of the galvanometer is actually slightly less than

560 ohms because of a critical damping resistor of 25000 ohms that is in

parallel with G.

[6] The standard 1-megohm resistor consists of ten, 100-kilohm, wire-wound

resistors connected in series and is contained in an oil bath. The value

of the 1 megohm resistor is also determined with the partitioning technique

and comparison with a 10 kilohm standard resistor. The 10 kilohm standard

resistors are calibrated in the Electrical Measurements and Standards

Division at NBS with an uncertainty of less than 7 ppm. The resistance

value is corrected for temperature at the time of the comparisons. As

noted in the Appendix, the partitioning technique, in theory, introduces

less than an additional 2 ppm uncertainty.

[7] It is interesting to note that the precision of the comparison need not be

high if the difference between the values of the standard and unknown

resistor is small. For example, if the values of the standard 1 megohm

resistor and partitioned Park resistor are within 100 ppm of each other, a "1% comparison" will yield a value for the partitioned Park resistor that

is uncertain to 1 ppm in terms of the standard resistor value.

[8] H. 0. Young, Statistical Treatment of Experimental Dat a, (McGraw-Hill, New

York, 1962), Chapter III.

[9] Norman Belecki, private communication.

[10] The 8 ppm uncertainty is not divided by /T because of the high correlation

of resistors 156881, 156882, and 156883.

[11] It should be noted that the spread in the value of the resistance for Park

resistor 156884 from 1980 to 1984 (less than ±9 ppm) can be accounted for

by the uncertainties listed in table 2. The configuration of low voltage

resistors in the bridge (e.g., choice of standard low voltage resistor for

X2) as well as the values of the low voltage resistors (i.e., use of

JOOO-ohm or 10000-ohm resistors) can, in theory, explain uncertainties as large as tlO ppm.

24
APPENDIX

Consider ten resistors, each of nominal value x, and connected in series.

The total resistance is

X. = y x(l+b.) A.l

S V ' 1

'

where b-j is the departure from the nominal resistance value for the ith

resistor and the summation over i is from 1 to 10; it is assumed that b-j is

less than 0.1%. Equation A.l can be rewritten

X^ = lOx + X ^ b.

= 10x[l + I{b./10)]

= 10x[l + y] A.

where y

= j;(b./10).

Next, the ten resistors are considered as being connected in parallel. The

parallel resistance is

(l/X ) =

I (l/x)(l+b )'i (l/x) J(l+b )"'

^ i i

= (l/x) I(l-b.) = (10/x) - (l/x)

I b.

:. (10/x)[l-J(b /lO)] A.

i

For bi < 0.1%, the terms dropped in deriving eq (A. 3) will be less than

1 ppm. From eq (A. 3)

Xp . (x/10)[l-^{b./10)]'^ . (x/10)[l+j:{b./10)]

^ (x/10)[l+u] A.

The terms dropped in obtaining eq (A. 4) amount to less than 1 ppm.

A comparison of eqs (A. 2) and (A. 4) reveals that because of the

approximations made in arriving at eq (A. 4), the departure from the nominal

value when the resistors are connected in parallel and in series is the same within 2 ppm. Therefore, to determine within 2 ppm the total resistance of ten

10-megohm resistors connected in series (i.e., x=10 megohms), the parallel

resistance, Xp, is first measured and then multiplied by 100.

25
NBS-n4A (REV. 2-8C) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET (See instructions)

1. PUBLICATION OR

REPORT NO.

NBS/TN-1215

2. Performing Organ. Report No, 3. Publication Date July 1985

4. TITLE AND SUBTITLE

High-Voltage Divider and Resistor Calibrations

5. AUTHOR(S)

Martin Misakian

6. PERFORMING ORGANIZATION (If joint or other thon NBS, see instructions)

NATIONAL BUREAU OF STANDARDS

U.S. DEPARTMENT OF COMMERCE

GAITHERSBURG, MD 20899

7. Contract/Grant No.

8. Type of Report & Period Covered

Final

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City, State. ZIP)

National Bureau of Standards

Gaithersburg, MD 20899

10. SUPPLEMENTARY NOTES

1^^ Document describes a computer program; SF-185, PIPS Software Summary, is attached.

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

bibliograpliy or literature survey, mention it here) An NBS calibration service for determining the ratio of high voltage dc dividers and

the resistance of high voltage resistors is described. Calibrations are performed with

a Wheatstone bridge apparatus with a simple guard system. Sources of systematic error

are identified and methods for characterizing the NBS standard high voltage resistors

are discussed. Ratio and resistance values can be determined between the voltages of

10 kV and 150 kV with an uncertainty of less than +0.01%.

12. KE^< WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

calibration service; dc; high voltage; NBS; resistor; voltage divider.

13. AVAILABILITY

I X| Unlimited

I I For Official Distribution. Do Not Release to NTIS

g^ Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402. Q^ Order From National Technical Information Service (NTIS), Springfield, VA, 22161

14. NO, OF

PRINTED PAGES

31

15. Price

USCOMM-DC 6043-P80
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