PUBLICATIONS^

NBSIR 84-2903

An Investigation of the

Uncertainties of the NBS Thermal

Voltage and Current Converters

F. L. Hermach

,9*^ STAND & TECH

AlllOb 3fl7sai

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Basic Standards

Electricity Division

Gaithersburg, MD 20899

April 1985

Final Report, NBS Contract NB81SBCA0711

Submitted February 28, 1983

Revised August 1 984

-QC ^DEPARTMENT OF COMMERCE

100 P*'*^*- O’" STANDARDS

.U56 I 8iJ-2903 i 1985 j

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NBSIR 84-2903

AN INVESTIGATION OF THE

UNCERTAINTIES OF THE NBS THERMAL

VOLTAGE AND CURRENT CONVERTERS

Clc I oo

; to

.

' a -

F. L. Hermach

U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Center for Basic Standards

Electricity Division

Gaithersburg, MD 20899

April 1985

Final Report, NBS Contract NB81SBCA0711

Submitted February 28, 1983

Revised August 1 984

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

NATIONAL BUREAU OF STANDARDS. Ernest Ambler. Diractor

TABLE OF CONTENTS

Page

Summary 1

I . INTRODUCTION 3

A. Scope of Contract and Reports 3

B. Present NBS Standards 3

C. Ranges and Uncertainties of Calibrations ^

II. SYNOPSIS OF THE AC-DC STUDY 5

III. MJTC’s AND COMPARATOR 7

A. Comparator 7

B. Comparison of MJTC’s 10

IV. REFERENCE TE's FOR F^ TVC’s TO 10 kHz 12

V. EXTENSION OF FREQUENCY RANGE 13

A. Thermoelements 13

B. Thermal Voltage Converters 15

VI. EXTENSION OF CURRENT RANGE 16

VII. EXTENSION OF VOLTAGE RANGE 19

VIII. WORKING STANDARDS 23

A. Current Standards 23

B. Voltage Standards 23

IX. THERMOELEMENT REPLACEMENT 24

X. ERROR ANALYSIS - GENERAL REMARKS 25

XI. RANDOM (STATISTICALLY EVALUATED) ERRORS 29

A. MJTC Comparator 29

B. Other Comparators 30

C. Statistical Parameters and Tests 30

D. Pooled Standard Deviations 31

E. Experimental Designs and Tests 31

XII. ESTIMATES OF RESIDUAL SYSTEMATIC ERRORS (Not Statistically

Evaluated) 32

XIII. COMBINATION OF UNCERTAINTIES 33

XIV. CONCLUSIONS 35

A. Uncertainties of the NBS Standards 35

B. Calibration Uncertainties 36

XV. RECOMMENDATIONS 37

A. Maintenance of AC-DC Standards 37

B. Quality Control of the Calibration Process 38

C. Other Recommendations 39
Table of Contents (Continued)

Page

XVI. ACKNOWLEDGEMENTS ^0

REFERENCES 4l

TABLES:

1 Comparison of Four MJTC's

2 Differences Between 1981 & 1976 Evaluations of MJTC's . . . .

3 Results of Comparisons of FX and FY with MJTC’s

^ Results of TVC Tests with Twin Resistors

5 Ampere-Range Comparisons

6 AC-DC Differences of 1 A to 20A TE's

7 Results of Evaluation of FX2 and FY2

8 Comparisons of F^tvC's

9 AC-DC Differences of F^ TVC's with FX2 and FY2

10 Comparisons of Working and Reference Standard TE's

11 AC-DC Differences of Working Standard TE's

12 Comparisons of Fy TVC's

13 AC-DC Differences of Fy TVC's

Ill Pooled Standard Deviations, S_„

pa

15 Estimated Limits of Residual Systematic Uncertainties . . . .

16 Calculation of Uncertainties

17 Summary of Uncertainties of NBS AC-DC Transfer Standards . .

18 Comparison of Estimated Calibration Uncertainties with

Present Allowances

43

45

116

47

48

49

50

51

52

53

54

55

56

57

61

64

65

19 Estimated Uncertainties for Special Tests 66
Table of Contents (Continued)

FIGURES: Page

1 Road Map 6?

2 Comparisons of MJTC's 68

3 50 mA to 5 mA Comparisons 69

50 mA to 1A Comparisons 70

5 Comparator with n-Compensation 71

6 Diagram of EMF Comparator 72

APPENDICES:

1 n-Compensation and n-Measurements . 1-1

2 EMI, Harmonics and DC Offset 2-1

3 Effect of Relay Off-Time 3"1

Effects of Bead Heating 4-1

5 Impedances and Substitution Corrections 5-1

6 Recommendation of the Working Group on the Statement

of Uncertainties presented to Comite International

des Poids et Mesures 6-1

REPRINTS:

References 2, 3 , and 4 R-1

AN INVESTIGATION OF THE UNCERTAINTIES OF THE

NBS THERMAL VOLTAGE AND CURRENT CONVERTERS

SUMMARY

This investigation required a complete redetermination of the ac-dc

differences of the NBS ac-dc transfer standards, from 20 Hz to 100 kHz. It

involved the following steps:

1 . Setting up a new and considerably more accurate set of primary

ac-dc standards, based on multi junction thermal converters (MJTC's) and a precise emf comparator for comparing pairs of standards,

2. Using them to evaluate 5~mA single junction thermoelements (TE's)

and a 10-V thermal voltage converter (TVC), up to 10 kHz,

3. Extending the frequency range by complex "bootstrap" techniques

that were developed for this, and justifying these techniques.

Extending the current and voltage ranges of sets of

reference-standard TE's and TVC's by appropriate build-up methods, up to 20 A

and from 1 to 500 V,

5. Using these reference standards to evaluate the NBS working

standards that serve for calibrating clients' standards,

6. Determining the random errors of each of the above steps,

7. Studying and evaluating residual systematic errors (after known

corrections were applied) by special tests and experimental designs, then

estimating their individual limits (magnitudes).

1
8. Combining these estimates and random errors in a logical way to

arrive at estimates of the uncertainties of each of the many reference and

working standards (following BIPM Committee guidelines),

9. Carrying out a number of largely mathematical studies relating to

the investigation and these sources of ac-dc differences, and, finally,

10. Recommending steps to be taken to improve and insure the continued

accuracy of the NBS calibration program for ac-dc differences.

As a result of this work it is believed that the accuracy of the NBS

standards and the output of its calibration process for ac-dc transfer are on

a much firmer basis than heretofore, with much better documentation.

The studies showed that in certain ranges of voltage, current and

frequency considerable improvement in the calibration accuracy can be

attained — factors of 2 to 5 for high-quality single-range TE's and TVC's.

Considerable improvement should also be possible for commercial multirange

instruments after further study of their stability and other characteristics.

For very special tests, such as international comparisons, accuracies

approaching 1 ppm should be possible.

2
I. INTRODUCTION

A. Scope of Contract and Reports

In brief, this investigation, performed under contract with NBS,

required a theoretical and experimental analysis of the uncertainties in

maintaining and using the NBS ac-dc transfer standards for current and

voltage measurements at frequencies up to 50 kHz, plus suitable documentation

of the study. In effect, the contract required a redetermination of the

NBS ac-dc transfer standards. This was carried out to 100 kHz for voltage

measurements because of frequent calibration requests at the higher

frequency.

The contract was completed and the final report was submitted to NBS in

February 1983. The report was revised and the appendices were added in

August 1984 for publication as an NBS Internal Report.

B. Present NBS Standards

The basic or primary ac-dc transfer standards at NBS at these

frequencies are thermal current and voltage converters, described in [1] and

[2]. The working standards used in the calibration of client thermal voltage

converters (TVC's) are described in [33. Papers [2] and [33 are appended to

this report for ready reference.

Extensive research was carried out at NBS to establish these standards

and verify their accuracy. The basic principles and brief descriptions of

the investigations and of the many special tests required for these

pioneering developments are given in the references. The work described in

[1 3 (1952) established the ac-dc transfer to 0.01/6 (100 ppm) for current

measurements from 1 mA to 20 A and voltage measurements from 0.2 to 750 V at

audio frequencies. In the work described in [23 (1966) a basic set of 5 to

20-mA single-junction thermoelements (TE*s) was evaluated to a few ppm, and

3
two selected TE's were used with special series resistors as thermal voltage

converters up to 500 V to 10 ppm. An emf comparator was developed to compare

the ac-dc differences of pairs of converters to ±2 ppm.

Fifteen comparisons of adjacent or similar ranges are required at each

frequency with this primary set of TVC's (called F^), to verify the build-up

(step-up) from 0.5 to 500V. In [3], Williams described a set of TVC's which

required only 7 comparisons, thus considerably shortening the time required

for routine verification of accuracy. His set (called Fy) is now the working

standard for the determination of ac-dc differences of TVC's sent in to NBS

for calibration. In a later paper [6] he described a similar set of shunts

with two thermoelements (TE's) for evaluating thermal current converters

(TCC's). Because of grounding and capacitance difficulties with the shunts,

however, TE's are still used as the working as well as the reference

standards for TCC calibrations. The contact-type TE's formerly used at 1 A

and above were replaced with insulating-bead types, to eliminate the

troublesome direct coupling between the heater and thermocouple circuits.

The reference TE's from 25 to 500 mA were also made to NBS special

specifications a number of years ago. Each has a Evanohm^ heater, with

Evanohm leads from it to the glass press, to minimize ac-dc differences from

Thomson and Peltier effects, and from the skin effect of the magnetic leads

normally used.

C. Ranges and Uncertainties of Calibrations

The following table shows (for ready reference) the stated uncertainties

actually available in the calibration of client ac-dc converters at the start

of this investigation. It is considered to be very unlikely that the errors would exceed these values.

Certain commercial products or materials are identified in this paper to

specify the experimental procedure adequately. Such identification does not

imply recommendation or endorsement by NBS, nor does it imply that they are necessarily the best available for the purpose.
Frequency

2-5

Hz

5-20

Hz

20-20k

Hz

20-50

kHz

50-100

kHz

0.1-0.

5

MHz

0.5-1

MHz

Voltage limits (V) 50 100 o o o 1000 600 100 100

Current limits (A) 0.05 0.05 202 15

Uncertainty (percent )3

Multirange TVCs 0.02 0.01 0.005 0.007 0.01 0.02 0.03

Coax single range

TVCs

0.02 0.01 0.002 0.003 0.005 0.02 0.03

TCC (.005 to 5 A) 0.02 0.01 0.005 0.01

TCC 05 to 20 A) 0.01 0.02

^200 volts at 20 Hz, increasing to 1000 V at 200 Hz.

^5 amps at 20 Hz, increasing to 20 A at 200 Hz.

^The lower uncertainty applies at the crossover frequencies. Uncertainties

may be increased if the ac-dc differences are large or affected by selfheating.

The larger uncertainties of the multirange converters reflect, in part,

the poorer precision and stability of these more complex but very convenient

instruments

.

II. SYNOPSIS OF THE AC-DC STUDY

Quite a number of years have elapsed since the comparisons were made

which formed the basis for the present accuracy estimates. NBS now has new

types of TE's. A series of comparisons of the NBS current converters was started a few years ago, but has not been completed. For these reasons a meaningful study of uncertainties required setting up a new base (primary)

group of TE's, as well as carrying out new complete series of interrange

comparisons of both the current and voltage standards (reference and working)

for extending the ranges from the base (build-up).

5
The same emf comparator and the same or new types of TE’s could have

been used for the base and for these comparisons, as before. However, it was very desirable to use, instead, a group of the newer multi junction thermal

converters (MJTC’s) and a new comparator, described in [4], (1976), which is

also attached to this report. At that time the ac-dc differences (d*s) of

these 5- to 1 2-V standards were evaluated to 0.5 ppm up to 10 kHz for the MBS

Absolute-Volt Program. However, the converters have not been used since

then. For this study the apparatus was set up again with the MJTC’s to form

an excellent base for directly evaluating the corresponding ranges of the

reference set of thermal voltage converters (TVC’s), and the TE's used in

them as current converters. A considerably better accuracy was thereby

attained. Thus this study was based on the new MJTC’s as primary standards,

with subsequent experimental comparisons with TE’s, which were then used for

the extensions in frequency and range.

Special studies and tests were made to extend the frequency range from

10 to 100 kHz for voltage measurements and to 50 kHz for current measurements. The d’s of the 5-mA reference TE’s from all known causes except bead

heating should theoretically be independent of frequency from 1 kHz up to at

least 100 kHz. To buttress the theory they were compared with other TE’s of

different types and construction, which should also be independent of frequency in this range. As described later in this report, the agreement was excellent

.

Resistors of calculable reactance are used with a pair of the reference

TE’s to form the voltage ranges of the F-| reference set. In the 1966 evaluation [2], agreement of the 5 to 50 V ranges, where the computed reactance

errors were negligible, formed the basis for assigning d’s. Since then evidence of dielectric loss effects has been found. To evaluate them the 1 0-V

range was compared with TVC’s containing resistors of measured ac-dc characteristics, and with two of the MBS 30-MHz TVC’s [5]. These rf TVC’s have

carbon-film resistors, with agreement in d's to 0.15? out to 40 MHz. The

results showed that there was indeed an ac-dc difference in the 10-V F^ re- sistor, but that it was less than 6 ppm, even at 100 kHz.

6
A block diagram of these major steps in the evaluation of the NBS ac-dc

reference and working standards is shown in figure 1

.

Analyses and tests were also made of the important problem of accurately

deducing the d’s of the many ranges of the and Fy TVC sets when the TE's

are replaced, without retesting all of the ranges. Many other analyses were carried out to evaluate systematic errors from known sources in TE's and in

the comparison of TE's. Suitable statistical analyses of random errors were

also carried out, and some additional sources of systematic error were

discovered.

III. MJTC*S AND COMPARATOR

A . Comparator

For this study the precision MJTC comparator and associated equipment

were set up in the NBS AC-DC Laboratory, room A144, MET, which has excellent

temperature stability, with a typical range throughout the day of ±0.6 °C. A

simplified diagram of the comparison circuits and a description of the

procedure for comparing two MJTC's are given in [il]. Briefly, with a resistance divider a fraction of the higher emf of one of the MJTC's is opposed to

the full emf of the other. The small differences are read on a nanovoltmeter

(nVM), with ac, dc direct, dc reversed, and ac, successively applied to the

two heaters at equal time intervals (to minimize the effects of drifts).

From these the difference between the two d's is calculated.

Several important changes and improvements were made so that the

comparator could also be used for TE's. Brief descriptions follow.

(1) In place of oil immersion for the standards, the metal tank was thermally lagged. This was found to be adequate. Oil immersion would have

been impracticable for many of the NBS standards.

7
(2) When the two TE's have equal n’s, (n = lAE/EAI, where I is the

heater current and E the output emf), the steady-state balance is independent

of small changes in the ac and dc supplies, greatly reducing the uncertainty

in the measurement and the need to keep the emf of one of the TE's constant

during a determination. However, n may range from 1.6 to 2.0 for TE's, so that some of these advantages are lost. A simple method of compensating the

comparator for different n's was developed. It is described in appendix 1. With this modification the basic equation for comparing two TE's is

A = d^ - dg = (N^ - N3)/ngEj_, where T refers to the TE with the higher n, to

which the Lindeck potentiometer shown in figure 6 is connected, and S to the

other. and are the average readings of the nVM with dc and ac applied

to the heaters, respectively, and Ej^ is the lowest emf of the two TE's. With

N in nV and E in mV, A is in ppm.

(3) An operational-amplifier integrator and timer (called an "averager") was designed and built to integrate the 1-V output of the nVM for

10 s, and display the average on a DVM. This significantly reduced the

uncertainty from Johnson and nVM noise, and greatly aided the operator.

Typically, repeated 10-s averages fluctuated by less than 1/10th of the

peak-to-peak noise seen in 10 s on the nVM.

(i1) The 11 -kP input resistance of the 3“Stage divider was reduced to

1 kP, by switching out the first stage when two single-junction TE's, with

their low output resistance, were compared. This improved the performance of

the nVM and reduced the Johnson noise of the circuit. The peak-to-peak noise

in 10 s was about 15 nV, about 3.5 times the calculated Johnson noise. This

is 1.5 ppm of the typical 10 mV rated output of a TE, and 5 ppm with the 3~niV

output encountered in interrange comparisons.

(5) Adequate shielding and grounding are very important. All ground

leads were connected to the grounded metal tank in which the TE's were

placed. A bypass capacitor was connected between each lead and the tank, to

reduce any lead-borne interference. Although there was no direct evidence

8
that it was significant, electromagnetic interference (EMI) can be

particularly troublesome at TV frequencies, where leads are near a quarter

wavelength and so pick up electromagnetic energy efficiently.

A simple direct test was devised to see if EMI caused significant

errors. With the TE's and supplies connected, but with all power supply

switches off, a "phantom" ac-dc test is performed, using the formula for A

given in IIIA(2) above with the value of n^E^ to be used in the actual test.

The result should be zero within the random-error limits. As shown in

appendix 2 , this test is sensitive enough to detect significant errors.

( 6 ) If there are ac components in the input, chopper-type dc

electronic nanovoltmeters (such as the one normally used) may be subject to

intermodulation effects which can result in false zero-order (dc) outputs.

These normal-mode errors were noted in the MJTC study [4], and were reduced

by filtering. Careful measurements showed that at the commonly-used

frequencies the ac output of a TE is typically less than 1 yV, and that this

is too small to cause a significant error from this insiduous effect.

(7) About midway in this study, a zener-diode protective circuit,

discussed in section VII, was installed at the input to the TVC’s, to reduce

the possibility of burnout from over-voltages.

A detailed diagram of the comparator, with these changes, is shown in

figure 6 . It is quite similar to the comparator shown in figure 8 of [ 3 ],

attached, and the same precautions in its construction, described in [ 3 ], were taken. The first stage of the divider is set at zero when the Read 2

position of the switch is used. Shielding, polarity markings, and the fine

controls of the Lindeck potentiometer, are not shown. Correct polarity is

assured if the nVm goes upscale (more positive) with the Set key down when

the input to the TVC's or TE's is increased.

The conventional definition of ac-dc difference of a TE is

d = (Ia~^d^^^d» 1(1 is the arithmetic average of the two directions of

the applied dc current required to give the same output emf as the rms

9
current, 1^. From this «• + d), so that an unknown ac current can be

measured directly, if d is known, by observing the emf with applied and

measuring the two polarities of dc current which give the same emf. The same formulas apply for TVC's, with V replacing I.

In a recent paper, however, [7] Inglis has shown that this definition is

in error if the TE has a proportional dc reversal difference, p = |l^-l 2

|/I(j,

with Ei=E 2

» where the subscripts, 1 and 2, refer to the two polarities. He

has proposed a new definition, d^= (1^-1^)/!^, where I^=I^=l 2 and

(E^ +E2)/2=E^. It is free of this error, but can be awkward to use directly,

for ac measurements. The difference between the two definitions is

dependent upon a number of factors. However, for a square-law TE in which p

is well behaved (approximately independent of E), the difference between the

two definitions is only about 3p /8. If p = 5x10 (rather large for a precision TE intended for ac-dc measurements) the difference is less than

0.1 ppm.

At NBS the primary standards are the MJTC's, with p*s much less than

1x10”^. The other TE's are evaluated by the steps shown in figure 1, with

the conventional definition of d.

Additional analysis shows that, with the conventional definition, there

are small error terms which should be added to the basic formula for the NBS

emf comparators when TE's having large dc reversal differences are compared.

However, they are about the same magnitude as the 3p^/8 term just given, and are therefore also negligible for the NBS TE's, which have small and well

behaved p's.

B. Comparison of MJTC's

The ac-dc difference of 4 MJTC's were carefully compared at 6 to 10

volts (limited by voltage ratings) at 30 Hz, 1 kHz and 10 kHz. These are 4 of the 8 that formed the MJTC base described in [4]. The 4 are of different

design and manufacture. This diversity greatly strengthens the confidence in

10
standards, because sources of systematic error are more likely to be

discovered in such comparisons than by simply repeating measurements on one

standard, or comparing like standards.

The results of the evaluations (including repeat tests on different

days) are given in table 1, as d^-dg in ppm for the MJTC's identified as T

and S. The supplementary designations of the MJTC's shown in parenthesis in

the figure, are those given in the 1976 paper.

The pooled standard error, s^, (standard deviation of the average) for

these measurements was 0.16 ppm. If the difference between two averages in

repeat tests is less than /2ts^ (t is Student's t) we have no evidence (at a given confidence level) that the difference is statistically significant. At

a 955^ confidence level for k(n-1) degrees of freedom with k=19 (the number of

averages in table 1), and n=4 (the number of determinations in each),

/?tSg = 1.H X 2.0 X 0.16 = 0.45 ppm. None of the differences between

averages was as large as this.

The results of these measurements at each of the 3 frequencies are shown

more vividly in figure 2. Here the number near the head of each arrow is

d^-dg, where T is the MJTC at the arrowhead. The best estimate for

dcr25-i “‘^044 = M is obtained from the paths between them, giving double

weight to the direct path. The best estimate for dQ^Q is obtained by

assigning to each pertinent arrow half of the discrepancy between M and the sum of the two arrows involving G5C. Similarly is determined. (NPL14

could not be used at 10 kHz because of its magnetic lead wires.)

The value assigned to each MJTC, on the assumption that the average of

all 4 is zero, is shown to the nearest 0.1 ppm in each circle. G10C was not

included in this group because it was compared only with G5C, in early

measurements, which were not repeated.
The same MJTC’s were evaluated in 1976 [M] as part of a larger group.

Table 2 shows the differences between the present assignments and those of

1976. They are gratifyingly small, indicating the high stability as well as

the low ac-dc differences of these thermal converters of different design and

construction.

IV. REFERENCE TE*s FOR F^ TVC*s TO 10 kHz

The first comparisons of the 10-V reference TVC with one of the MJTC's,

and subsequent intercomparisons of TE's, disclosed several problems. The TVC was unstable because of variable contact resistance in its sliding

connectors. Some TE's had a peculiar dependence of ac-dc difference upon the

ac-dc sequence used, differing by as much as 3 Ppm with ac, dc+, dc-, ac applied than with ac, dc-, dc+ , ac applied. Several of the TE's required 15

to 20 s to come within 1 ppm of the final value after the input was switched, even though the off-time of the relay was less than 0.5 ms.

To overcome these problems simple modifications were made in the TVC

connectors and new 5-mA TE's were chosen after extensive screening tests.

Each consisted of two special TE's with Evanohm heaters, welded to the copper

skin of the CuNi lead-in wires to reduce thermoelectric errors.^ The two

heaters were connected in series, as were the two thermocouples, to obtain a rated output of 12 mV. They were temperature compensated by the method used

by Williams [ 3 ].

Two of them, labeled FX and FY, were compared as both current and

voltage converters with two of the MJTC's at 30 Hz, and 1 and 10 kHz, using

the 5

- and 10-V F^ resistors for the TVC tests. The results are shown in

table 3. The third TE, FZ, was compared with FX to 100 kHz.

2Later analysis indicated that welding to the copper instead of the core might

not greatly reduce the Peltier error.

12
The measured d's were gratifyingly small. There was no appreciable d

from Thomson and Peltier effects in the heaters of any of the three TE's.

There were small low-frequency errors at 30 Hz, and evidence of impedance

errors (about 1 ppm at 10 kHz) in the TVC resistors.

To check on possible current-dependent d's at high frequencies, FX and

FY were paralleled and compared with FZ at 5 mA, with excellent agreement.

Puzzling drifts of some single-junction TE's led to a study of transients caused by switching the input voltage during an ac-dc determination.

As shown in appendix 3. if the response of a TE to a step-change in input is

a simple exponential with a time constant, t^, and the relay off-time in

transit is t^, (tQ<<t^) then the proportional change in output emf at a time,

t, after switching (caused by the off time) is p

= t^/t^e^, where a = t/t^.

For the high-speed miniature relays now used, tQ is only 0.^ ms. For a TE

with a t^ of 2 s (fairly typical) a time t=10 s is required to make p<1 ppm.

This is comfortably below the 30 s interval (time before reading nVm) now

used.

The present relays can be used only up to 200V in the circuit, and

high-voltage relays have much longer off times. Longer intervals might then

be required. Surprisingly, for t^ = 4x10”^ s, t=15 s, only a modest in- crease. Thus the excessively long drifts of some TE's are evidence of other

problems, of unknown causes.

V. EXTENSION OF FREQUENCY RANGE

A . Thermoelements

Because of reactances in the complex structure of the 5- and 10-mA

MJTC's, these direct comparisons could not be extended reliably in frequency.

The simpler TE's, with their smaller reactance errors, should have wider

frequency ranges. To verify this, several 5-mA TE's of different

construction and/or manufacture were compared with FX and FY as current

converters from 30 Hz to 50 kHz. Two of them were in the original 1966

13
primary set. All of them have Evanohm heaters and should have low

thermoelectric errors. These were determined from the 1-kHz MJTC tests, and were independent of frequency. The important criterion is that the measured

differences between each pair of TE's should be the same at higher

frequencies, giving strong evidence that reactance and other errors were negligible.

Unfortunately the measurements showed no such agreement. At 50 kHz

discrepancies of up to 4 ppm from the 1 -kHz values were observed. It seemed

likely that some of the differences could be caused by leakage current

through the insulating bead which fastens the hot junction of the

thermocouple of a TE to the center of the heater. [1,2] The bead resistance

is a complex function of frequency and of bead temperature and voltage. This

was verified by making additional measurements with added resistance between

the heaters of the two TE's, which changed the bead voltage of the ungrounded

one. (The thermocouple circuit is grounded at the emf comparator.)

Apparently the bead resistance of these TE's was less at 50 kHz than at

1.6 kHz, where bridge measurements were made earlier (as described in [2]).

Detailed analysis of bead resistance errors, given in appendix 4, led to some surprising conclusions. They showed (1) that bead heating (caused by

leakage current from the heater to the thermocouple through the bead) is

twice as effective in raising the thermocouple temperature as heating from

the heater wire, (2) that if one end of the heater is grounded, no error would be caused by bead heating, and (3) this would be true even if a pair of

equal TE's, with heaters in series, is used, as in FX and FY. (In the

comparisons with the MJTC's described earlier, FX and FY were at the ground

end.

)

With this background, the comparisons of pairs of TE's were made by

following a method used by Williams. They were compared as TVC's with two

nearly identical 30-V series resistors. One end of each of the heaters of

the two TE's under test could then be at ground. Appendix 5C shows that by

repeating the measurements with the resistors interchanged and averaging the
results, errors from small differences in the reactances of the resistors

could be largely eliminated, and the TE’s could be evaluated as current

converters

.

The results of these measurements are shown in table 4. Except at

30 Hz, there was no significant frequency dependence of the average of the 6

TE's up to 50 kHz, with FX as the reference. Thus there is good evidence

that the corrections assigned to FX and FY up to 10 kHz by comparisons with

the MJTC's could be extended without change to 50 kHz.

TE’s are subject to low-frequency errors (1) caused by failure to

integrate the heating effect of the ac current wave correctly. For FX,

d = +0.9 ppm at 5 mA and 30 Hz. From these tests, 30 Hz values could be

assigned to all of the other TE’s.

B. Thermal Voltage Converters

As shown in [2], the ac-dc difference, d^, of a TVC is d^ = d^^ + d^^,

where d^^ = (Z|.-R^)/R^ and d^ = for the same output emf.' In these

equations, is the magnitude of the ac impedance, defined as the ratio of

the input voltage to the current, I, through the ungrounded input of the TE

heater, R^ is the dc resistance, and I^ is the dc current (average for the

two directions) required to give the same output emf as I^. Note that Z^

includes the impedance of both the TE and the series resistor, and that the

equation for d^ is a perfectly general one.

Preliminary comparisons of the mid-ranges of the TVC’s to evaluate high

frequency effects disclosed some disturbingly large differences at 50 and 100

kHz. Calculations showed that the d’s caused by the reactances of the series

resistors should be much less than 1 ppm, and should vary as f^. The

observed differences were roughly proportional to f, suggesting dielectric

losses as the cause. This supposition was strengthened by the -1 .0 ppm

average of F^10-FY and Fi5-FX in the comparisons at 10 kHz with the MJTC's

15
(table 3). The reactance errors should be completely negligible at this

frequency.

To investigate this further, F^io-FY was compared with a special TVC

that Haddad had studied in 1969 for his GWU Master’s thesis under

CutkoskyCl 8] . He had determined the change in impedance (resistive and

reactive components) between 1.6 and 16 kHz. The comparisons indicated that

F-|10-FY had a Ad of about -1.5 ppm.

To carry this to higher frequencies, F^io-FY and F-|20-FX were compared

with the corresponding ranges of the rf Model C TVC’s, which had been

evaluated to 40 MHz[5]. These TVC's have unspiraled carbon film resistors on cylindrical ceramic bases, as distinct from the spiraled metal-film

resistors, of the F^ set, with much smaller possibility of dielectric

effects.

The results of these several tests were not completely concordant, but

all of them pointed strongly to a small but significant d^ in FilO-FY. Later

tests showed that the dg of the resistor alone was about -5 ppm at 100 kHz.

VI. EXTENSION OF CURRENT RANGE

Range extension (build-up) is based on comparisons of adjacent ranges,

so that all are determined in terms of a base or reference range. Evaluating

the validity of the method is, of course, important, and is often very difficult. For these current ranges, the extension was carried out by two

methods, as follows:

(a) From 5 to 1000 mA two almost identical TE's of one range were first

compared. They were then paralleled and compared with each of two TE’s of

the next higher range, and so on. This is the method used in [2] to compare

the 5- to 50-mA TE’s. Like that work, pairs of almost identical

low-reactance resistors were connected in series with the heaters to assure

that the paralleled currents were sufficiently in phase. The analysis of

16
appendix 5E shows that the phase angles of the two paths must be equal to

better than one mrad. This is readily measured on a commercial impedance

comparator, to 100 kHz. When the phase angles are negligible, the basic

formula for this method, taking into account small differences in the

characteristics of the paralleled TE's, is given in appendix II of [2]. This

method has the strong advantage that each TE is used at or near rated

current, so that the results are not affected by current-dependent errors.

(b) Above 1 A the heater resistances are too low to be measured on the

bridge, and mutual inductances can cause serious errors, so a more complex

approach following [1] was necessary. Adjacent-range TE’s were compared at

the rated current of the lower range. To investigate current-dependent d's,

selected ranges were compared with shunted low-range TE’s at frequencies low

enough so that the reactance errors of the shunts were negligible. Each such

comparison was made at two currents. All of the TE’s had Evanohm heaters

with small thermoelectric effects independent of frequency, so that the

extrapolation of current-dependence could safely be made to 50 kHz.

The 5 to 50-mA build-up was made with the MJTC comparator in method (a).

It was convenient to start with a 50-mA (OF-19) MJTC of Wilkin’s later, and

very different design[8]. His calculations showed that this MJTC should have

less than 1 ppm error up to 100 kHz. It agreed with the NPL-14 50-mA MJTC at

30 Hz and 1 kHz to 0.1 ppm, verifying low-frequency concordance. (NPL-14 is

frequency-limited because of skin effect in its magnetic leads.)

The results of these 5- to 50-mA comparisons are shown in figure 3* The

numbers near each arrow are d.p-d3

in ppm, at the four frequencies shown in

the key, where the subscript T designates the TE at the arrowhead. The

columns headed ’’Average” are the averages of the two adjacent TE’s, as determined by the two comparisons of that paralleled pair with the two TE's

above them in the figure. The numbers in each block are the d’s determined

from the intercomparisons (starting with MJTC OF-19), with forced closure of

each triangle. (One third of the closure error is applied to each leg.) The

17
closure errors were very small, requiring adjustments of only 0,3 PPm or less.

The pooled standard deviation Sp^ of the average of four determinations

of d^-dg was only 0.28 ppm. These high precision tests showed excellent

performance in these Evanohm-heater TE*s. At the low end of this rather long

chain of measurements, the values obtained for FZ and FY as current

converters agreed with those previously determined from the 5mA MJTC's to

1 ppm at 20 Hz^ and 50 kHz, and to 0.5 ppm at intermediate frequencies. Thus

systematic errors in the chain were very small indeed.

Of particular interest is the excellent agreement at 1 kHz (better than

0.6 ppm) between the MJTC’s and the average of the two 50 mA and two 25 mA

TE’s.^ Each of these four single-junction converters has an Evanohm heater

and Evanohm stems (lead-in wires) from the heater to the glass press (which serves as a good heat sink). Thus the Peltier as well as Thomson errors of

each TE should be very small. Any residuals would not likely be the same in

all of them, nor the same as those in the MJTC’s. Thus the agreement

provides valuable additional confirmation that the ac-dc differences of the

NBS standards caused by thermoelectric effects are considerably less than

1 ppm.

The fast-acting relays controlling the inputs to the heaters limit the

high precision MJTC comparison equipment to 50 mA or 1 00 V (not simultaneously). For comparisons at higher voltages and currents, the 1966 com- parator [2] was used. The results of the paralleling measurements, method

(a), from 50 mA to 1 A are shown in figure 4, along with a comparison of one

of the 1-A TE’s with FG-1 , a shunted 1 0-mA TE described in [6]. The build-up

is based on a 0 ppm assignment to the average of the two 50-mA TE’s, together

with forced closure of each triangle of tests in the four loops up to 1 A.

^Extrapolated from the 30 Hz measurements.

^At 1 kHz reactance errors and low frequency errors should be negligible.

18
For these measurements, Sp^^ was about 1.7 ppm, practically independent

of frequency. This is not as good as the precision of the MJTC comparator,

but is low enough to meet the needs for high-current calibrations. The

evaluation of FG-1 with the 1-A TE agreed with Williams’ earlier tests [6] to

5 ppm, which is well within the limits of random error for the number of

stages involved.

The results of the comparisons of the 1- to 20-A TE’s by method (b) are shown in table 5. These air-cooled TE's were made by the Weston Company a number of years ago to NBS specifications. Each has an Evanohm heater, with

an insulating bead at the hot junction of the thermocouple. To guard against

current-dependent errors, some of them were compared with Williams’ shunted

TE's. Each comparison was made at two currents, with no consistent evidence

of such dependence, so that the results of table 5 could be combined with the

values assigned to the 1-A TE to determine the d’s of all of the ranges, as shown in table 6.

For these comparisons Sp^ was about 1.7 ppm, again not greatly dependent

on frequency. The TE’s showed rather large d’s at 50 kHz, probably because

of skin effect in the lower ranges, and a peculiar "proximity effect" in the

5 to 20 A ranges. These TE’s have heaters of C-shaped cross section rather

than tubular. For these ranges d was markedly dependent upon the position of

the return lead. [6]

VII. EXTENSION OF VOLTAGE RANGE

The extension from the base 10-V range of the F^ reference set of TVC's

up to the 1 000-V and down to the 0.5-V ranges required 14 adjacent-range

comparisons at each frequency, using the FX and FY TE’s with 13 plug-in

resistors [2]. Unfortunately, shortly after it was completed a major fault

in the ac amplifier burned out both of these excellent TE’s. (A lower-range

TE connected in series with them as a fuse was more rugged.) Subsequently,

19
two unusual sources of error in the ac-dc comparisons were discovered,

casting some doubts on the accuracy of the TVC build-up.

The first of these was an unexpectedly large error caused by a dc offset

voltage, Vqq, In the output of the same direct-coupled ac amplifier. Because

this was only one direction of dc, it would be integrated Incorrectly if the

TE had a dc-reversal difference, g = AE/E, for the two directions of the same

dc voltage. As shown in appendix 2C, the error can be as much as e = gu/2,

— ? — ii where u = V^g/V^. Thus if u=1x10 and g = 5x10 , e can be 2.5 ppm. As

p shown in 2B, this is much larger than the output error e' = q caused by a small proportional error, e^^, in measuring a small harmonic, V^, in an ac

— P wave, Vg, where q

= Vj^/V^. If q

= 1x10 and the error of an rms instrument

in measuring the harmonic is e^ = 5x10”^, the error in measuring the combined

wave is only 0.05 ppm.

The second source of error was an unexpectedly large skin effect in the

brass center conductor of the coaxial connectors. At 100 kHz, a 6-ppm error

was caused by an L-shaped connector sometimes used in front of one of the

0.5-V TE’s in a comparison. The error decreased, of course, for higher

ranges with their higher resistances.

The effects of the dc offset and troublesome dc transients in the amplifier were eliminated by using a wide-range output transformer. The reference

plane in each TVC-comparison was taken as the center of a coaxial "T"

connector to which each of the two TVC*s was thereafter directly connected.

Two new 5-mA TE's, FX2 and FY 2 were assembled to replace FX and FY.

They were evaluated by comparisons with MJTC G44 to 10 kHz and with FZ from

2.5 to 5 mA up to 100 kHz. F^10-FY2 was evaluated at 20 Hz, 1 and 10 kHz

with GH4 as a TVC. Because of the importance of the frequency extension, the

tests described in section V-B were repeated with FY2

. Results of these

extensive measurements are shown in table 7.

20
The results of the interrange comparisons of the set are shown in

table 8, and the values assigned to each range, with d of F^io-FY2 from

table 7 as the basis, are shown in table 9. In the comparisons each TE is

used at two currents, with a series resistor of the given range. If its d^

is current dependent, a correction must be applied at each step. Since

dy-dt+dc (see section V-B), dv2"<^v1 ="^c2"^c1 » currents

corresponding to subscripts 2 and 1 , on the assumption that d^ is not voltage

dependent

.

Unfortunately each of these new TE's has a significant d^, which is also

somewhat current-dependent, as shown by the results in table 7. It was difficult to evaluate the current dependence accurately enough, because of

the low emf’s at the low currents. Any inaccuracy is multiplied by the

number of steps from the 10-V base range to the extreme ranges. To reduce

the uncertainty, an average value of ciQ=dQ 2 ~dQi was calculated from all of

the values for both TE’s from 1 to 100 kHz. Subscript 2 applies at 5 mA and

subscript 1 at either 3-3 or 2.5 mA. This value, +0.8 ppm, was applied

uniformly in calculating the d's in table 9 from the comparisons of table 8.

The tests with FZ showed that it was independent of frequency from 1 to

100 kHz. At 20 Hz the values of d^ were taken directly from table 7.

As a check on the accuracy of this average value for d^^, the ac-dc

difference, dg, of the series resistor of each range was calculated at 1 kHz

by formulas given in appendix 5D, starting with the values of d^ of the TE's

as given in table 7, and d^ as shown at 0.6 V in table 9. At this frequency

each dg should be negligible. The computed values ranged from +0.M to -0.9

ppm, and the average for all voltage ranges, with regard to sign, was only

-0.1 ppm. This is an excellent check indeed.

Both FX2 and FY2 have d^'s which are positive, and so cannot be caused

by Thomson effects in their heaters [1]. Unfortunately they also have

unusually large negative d^'s for their heater impedances (-10 and -12 ppm,

respectively), calculated from the measurements at 1 kHz. These values of d^

21
and are indicative of large Peltier effects at the heater to lead-in

Junctions.

At higher frequencies the even larger dj^ for the 0.6-V ranges (TE's

alone) are caused by skin effect, which increases the resistance of the

magnetic heater leads, causing positive ac-dc differences.

With the TVC set these factors require troublesome corrections, but

do not invalidate the results, as the correlation at 1 kHz shows. Indeed,

they provide excellent checks on the correctness of the basic build-up

formulas.

It is to be noted that these TE's cannot be used interchangeably; i.e.

F^10-FX2 is not known from table 9. Substitution corrections are discussed

in section IX.

The TVC comparisons below 200 V were made with the MJTC comparator.

Because the thermocouple emf's of the higher-range TE in each pair were low

(3 mV or less), the precision was poorer than with 10 mV outputs. The

pooled standard deviation, Sp^^, was 0.52 ppm. The 1966 comparator was used

for the higher voltage ranges, with the original TE's, FX and FY. To avoid

repeating these measurements the substitution formula given in section IX was used to calculate the d^'s with FX2 and FY2

.

A study of protective circuits to guard TVC's from burnout, sparked by

the loss of FX and FY, showed that a simple combination of a pair of

back-to-back zener diodes directly in parallel with the TVC's and a 10-mA

expendable TE in series with the combination should provide adequate

protection against reasonable kinds of over voltages. The zener voltage

should be near, but not less than, twice the supply voltage, and there are limits on the zener resistance and the time constant of the fuse (which is

why a TE was chosen). The method does work well, and TE's of large dc

reversal difference, which are relatively inexpensive, can serve well as fuses, but a CRO across the TVC's is advised, to monitor the wave form.

22
Vlll. WORKING STANDARDS

A. Current StcUidards

The working standards which are used in calibrating thermal converters

sent to NBS were evaluated by direct comparison (heaters in series) with the

corresponding ranges of the reference converters, in the calibration console

normally used for such measurements. This had the advantage of giving direct

information on the precision of calibrating TE's as current converters

(TCC's). Usually the input line to the working standard was grounded. To

check on possible bead resistance errors, some measurements were repeated

with the reference standard at ground. (The ground should never be placed on

the line connecting the two heaters, because capacitance and leakage currents

from the ac and dc sources to ground could cause the two heater currents to

differ .

)

The results of these comparisons are shown in table 10, and the values

assigned to the working standards are shown in table 11. The overall s„_ was p<i

2.4 ppm.

B. Voltage Stcindards

The Frj set of TVC's for calibrating TVC's sent to NBS was evaluated by

adjacent-range comparisons, as in [ 3 ], with the calibration console. The

results are shown in table 12 .

The 10-V range was compared with F^io-FY2 , as the basis for the

build-up. However, insuring the validity of the build-up process is somewhat

more complicated than with the F^ set. Each series resistor is used with

both TE's, Fyl and Fy2, to form two ranges (such as 3 and 6V with the 800-P

resistor). Then, since d^=d^+dQ, the difference between those two ranges is

^v2~^v1 ~^t2~*^t1 '‘’^c2'’^c1 • Thus d^ of each of the two TE's must be evaluated

(at the comparison currents if it is current dependent). Since d^^ depends on

the heater of the TE as well as the resistor, any difference between the two

d^'s should also be evaluated to determine dv2 ~dvi , the correction to be

23
applied at each step of the build-up comparisons. This is quite complicated

unless the reactance terms are negligible as shown in appendix 5B and

discussed in the next section.

Fortunately the d^ variations caused by TE’s decrease with increasing

range. For this build-up of the Fy set, d^ corrections were evaluated from

the comparison of the 6-V and higher ranges at 20 Hz and 1 kHz (where the

efect of dj^ of each heater is negligible). Since the dg*s of the series

resistors are also negligible at these relatively low frequencies, the same

‘^c2~‘^c1'^*^v2~‘^v1 evaluated in each of these comparisons, where d ^2 refers

to Fy1 at 1.25 or 1.6? mA, and d^^ to Fy2 at 5 mA. The average value is less

subject to random errors. For these TVC's each very small. At

20 Hz and at 1 kHz the average of all of them at 6 V or above was 0 ppm.

Thus the d^ 2 “dQi corrections were negligible at these frequencies. They

were taken to be the same at higher frequencies. This assumption was checked

to a few ppm by special tests involving the known F-| TVC’s and the Fyl and

Fy2 TE's. Similarly, the d^ corrections caused by heater impedances were

very small.

The results of the Fy build up are given in table 13. They were checked

by comparing the 1-V and 100-V ranges with the same ranges of the F^ set.

The differences ranged from 2 ppm or less at 1 kHz to 6 ppm at 100 kHz, and

are generally within the random error limits imposed by Sp^, which were

1.2 ppm at 1 kHz and 2.8 ppm at 100 kHz.

IX. THERMOELEMENT REPLACEMENT

It is highly desirable to be able to replace a TE in a TVC set without

recalibrating all of the ranges. The analysis in appendix 5B of the

substitution error which may result shows that the ac-dc differences as current converters, d^, and as voltage converters, d^^ of both the old and new TE's must be known, and the phase angles of the impedances must be less

24
than certain specified limiting values. At NBS, and dy^ can be measured

by comparison with the reference standards, and the phase angles can be

determined closely enough with a commercial impedance comparator to 100 kHz.

If the phase angles are negligible, the change in d^ of a given range of

a TVC set when TE^ is replaced by TE2 (of the same nominal range and input

resistance) is given by

^v2 ^v1 ^^vh2 ^vhl^ ^^c2~^cl^ 9

where R^ and Rg are the nominal values of the heater and series resistances,

Rt=Rh'^^s» ^vh applies to the heater alone.

It is to be noted that as the voltage range is increased, the first term

becomes negligible and the second approaches dQ2 ~dQi

.

If the phase angles are not negligible or cannot be determined, it is

best to repeat the lower inter-range comparisons. Although the phase-angle

term is complicated, the analysis shows that the error in neglecting it will

be less than 1 ppm if the angles of the two TE's are equal to within 0.1 mrad

and the angles of the resistors and the TE’s are less than 5 mrad.

X. ERROR ANALYSIS - GENERAL RDiARKS

These are personal views on various phases of error analysis.

(1) There are many sources of systematic errors in these standards and

in the comparison process. Practically all are independent. Our estimates

of their individual limits, after all known corrections are applied, should

then be added in quadrature as the square root of the sum of their squares

(rss), following Youden [10].

25
(2) Youden recommends adding the estimate of the random errors (such as 2^3 or 3Sa) to the rss of (1) to obtain the total uncertainty.

(3) However, it is evidently desirable to follow the much more recent

guidelines of the BIPM Working Group on the Statement of Uncertainties, in

accordance with B. N. Taylor’s memorandum of August 21, 1981 [11]. This

involves adding all of the components in quadrature, including s^. They are

to be estimated as the equivalent of "standard deviation". For convenience,

the BIPM recommendations are reproduced in appendix 6.

(4) It is generally not feasible to determine a probability distribution for each of these error estimates, even though one feels that the true

value may be nearer the center than at the estimated limits. Thus it is

safer (more conservative) to assume a rectangular distribution, with limits

±b. The standard deviation, a, of such a distribution is b//3*

C. F. Dietrich, of the British Calibration Service, has shown that if rectangular distributions are combined with each other and with a normal (Gaussian)

distribution, the standard deviation of the combination is

As a result of his extensive analysis of such combinations he states that

[ 12 ]

" 4.69 Let us look at this another way round. If we know

the standard deviations of the Gaussian uncertainties of an item of calibration, and thus the total Gaussian standard

deviation, and if we assess the maximum value of each of

the estimated uncertainties, and assume that these have a rectangular distribution, we can at once find the total

standard deviation of the measurements. We can then state

that the probability of an uncertainty lying outside ±2a is

less than 0.0455 or the probability of an uncertainty lying

outside ±3a is less than 0.0027, without having to go to

all the trouble of calculating the combined distribution

and calculating the required probabilities. The correct

26
probabilities will always be less than the corresponding

Gaussian ones having the same tolerance limits and standard

deviation, but usually by only a small amount.”

This very important conclusion provides a simple yet generally realistic

method of combining error estimates. It is on the conservative side (i.e.,

does not underestimate the total).

(5) A very important factor in error analysis is to gain enough

knowledge of, and experience with, the measurement process to be able to find

the (generally hidden) causes of residual uncorrected errors, and to get

reasonable estimates of the error limits. This inevitably takes time.

(6) Because of the difficulty of finding error sources by simply

repeating measurements in the same way, it is very desirable, as is well

known, to vary the conditions of the measurement and note the effects on the

results. The imposed variations should be well beyond the normal limits.

(7) Thus in research to establish the accuracy of physical standards,

every effort should be made to vary or change the associated measuring

equipment. In contrast, as Churchill Eisenhart has emphasized [13], the use

of standards in calibrating others should be considered as a measurement

process which must be kept under statistical control, with only specified

ranges of the variables allowed. The measurement process should be well

documented to insure this through the years.

(8) It is also very desirable in the research phase to make

measurements with different standards and different comparison apparatus,

whenever possible. We know that having different TE*s made in different ways

by different manufacturers can give a lot of confidence in the results if

all of them agree, and can help disclose sources of error if they do not.

27
(9) "Round-Robin" tests of three or more TE's or TVC's of the same

range, and other more complex experimental designs, can also be very valuable

means of disclosing systematic errors, as is well known.

(10) As figure 1 shows, there are several steps in the determination of

the accuracy of the final or working standards of ac-dc difference. It is

well to note that, if corrections are applied at each step for the known

(determinate) errors, the estimates of remaining residual errors (these are estimates not errors) are combined as the square root of the sum of their

squares (rss), not added directly. There is no need for the crippling

"accuracy ratios" or factors of 3/1 to 10/1 in each step, as so often

specified.

(11) Operator mistakes and certain equipment malfunctions are not

amenable to analysis and inference, but can be major sources of error. For

established calibration programs, where the volume of work justifies it, they

can be reduced by computer control and computer verification of important

parameters. They can also be reduced by repeating critical calibrations with

a second operator and a second calibration console, and by the calibration of

check standards in an adequate quality-control program. Having a second

comparator and equipment available has been very helpful in the ac-dc

program, in both the research and calibration phase.

(12) Incorrect procedures, generally stemming from incomplete

understanding, can also be major sources of error. As F. B. Silsbee has

emphasized [1M], the person in charge of a standardizing laboratory must have

a high degree of technical knowledge and competence. This is especially true

for ac-dc difference measurements, which are deceptively simple in principle

but require a person with a sound knowledge of ac circuit theory to detect

and overcome problems.

(13) It is to be expected that the ranges of the reference standards

closest to those of the primary standards will be known with the best

accuracy, and that the accuracy will decrease as both range and frequency are extended. Thus a realistic view of the uncertainty, u, will be that of a

28
rather flat-topped cone in a 3 -dimensional space, with the range and

frequency as x and y coordinates and 1/u as the z (vertical) coordinate. The

views for the working standards will, of course, be similar.

XI. RANDOM (STATISTICALLY EVALUATED) ERRORS

A. MJTC Comparator

A limiting factor in the precision of TE comparisons was the noise level

of the circuit and nanovoltmeter. With the 10-s averager for each reading

and with 120 s required for an ac-dc determination, the pass band of interest

extended from about 0.01 to 0.1 Hz. Both the noise level and the response

time of the nVM were dependent on the source resistance. With these factors

in mind, a number of tests were made to evaluate the effects of noise and

zero drift of the comparator and its nVM on ac-dc measurements, with the two

thermocouple inputs shorted.

The first of these consisted of eyeballing the peak-to-peak excursions

of the nVM for 10 s, while at the same time taking 10-s averages of the nVM

output (expressed in nanovolts of input). The average difference between

these 10-s averages was generally 1 /8th to 1/20th of the average of the

peak-to-peak excursions, a marked improvement. However a better measure of

the effect of noise on the integrated output was obtained by calculating a phantom A' = d.j.-d3 , by the formula given in section III, using groups of

successive 10-s readings and assuming nE = 20 mV. For both the 300 and

1000-nV ranges of the nVM usually used, the average A’ (without regard to

sign) was less than 0.1 ppm.

Similar (although fewer) measurements were made with maximum source

resistance (300S2), and with 30 s between averages, as in a normal ac-dc

comparison. The values of A' ranged up to 0.15 ppm. They would be expected

to be 3-3 times as great with emf's of 3 mV, as in the TVC build-ups. These

29
are the true limiting minimums of random errors imposed by the comparison

process.

B . Other Ccxnparators

Similar tests were not made for the 1966 comparator and for the

calibration console. Both have been in use for long periods of time.

Instead the pooled standard deviations of each were evaluated under the

conditions of the present investigation, for TE and TVC comparisons, as discussed in the next sections.

C. Statistical Parameters and Tests

Four independent determinations were normally made at each frequency in

each comparison of the TE*s, and the average, A^, and its standard deviation,

s^, were computed. Since the same measurement process was involved in many

such tests, pooled standard deviations were computed to increase the precision of estimating the true a. If each of m comparisons has the same number

of determinations, the formula for the pooled standard deviation of the

average is simply

pa

2'i1/2

ai

Preliminary calculations were needed to determine which tests to pool.

Obviously comparisons at low emf's were likely to have larger s^’s than those

at 10 mV. On the other hand tests at different frequencies rarely had

significantly different s^’s.

The pooled ”within-day” s^’s were used to more sharply determine the

significance of differences between averages of measurements repeated on different days. For two measurements the *'t" test, with the formula given in

section III, was simplest. For more measurements, appropriate tests were

used [15].

30
The round-robin triads of figures 3 and 4, the build-up comparisons for

the TVC's, and the comparisons of ampere-range TE’s with shunted TE's at low

frequencies were all examined for evidence of systematic errors.

D. Pooled Standard Deviations

Table 14 shows the values of the pooled standard deviations, Sp^, for

the several paths in the Road Map of figure 1 . Each was grouped by

parameters, such as type of comparator, frequency, and emf level, that were

found to be significant.

The table shows the wide range of Sp^»s from the MJTC’s to the working

standards. These values are combined in section XIII, with the systematic

error estimates of section XII.

E. Experimental Designs and Tests

The sequence of readings in a determination (ac, dc+, dc-, ac, equally

spaced in time) is an example of a simple experimental design that eliminates

the error from linear drifts in the TE's and comparator. Knight and his

coworkers at NPL have used a least-squares fit to the readings in multiple

ac-dc sequences to correct for 2nd and Sr’d order drifts as well. However the

excellent temperature stability in MET A144 at NBS, and the long thermal

time-constant afforded by the thermally- insulated tank in which the TE's are

placed, have made this unnecessary for this investigation. Erratic changes,

chiefly from the nVM, would generally mask small non-linearities.

Experimental designs based on left-right interchanges of two standards

to detect offsets could not be used directly, because of the often large

differences in the emf's of the TE's (as great as 3/1 )• With the MJTC

comparator, the higher emf must be connected to the divider, and the output

of the TE with the higher n must be connected to the potentiometer.

31
Triads of comparisons (round robins) are shown in figures 3 and 4. In

each of these there are two paths from one TE to a second; one direct and the

other via the third TE. If the d2~d^ paths differ by more than (2/5)Spg^,

there is evidence of systematic error at about the 95$ confidence level.

None of these 28 triads showed such evidence. Other more complicated round

robins, used to evaluate TE’s after the loss of FX and FY, also showed small

closure errors.

In the 50 to 5 mA comparisons of figure 3. the values of d for FY and

FZ, obtained after 4 stages from 0F19, were within 1 ppm of those obtained

from the direct MJTC tests at 1 kHz and the subsequent frequency extensions.

XII. ESTIMATES OF RESIDUAL SYSTEMATIC ERRORS

(NOT STATISTICALLY EVALUATED)

There are many known sources of residual errors in the TE’s, TVC’s and

comparator. A listing of those which are significant and of the estimates of

their limits (bounds) is given in ppm (and percent of A = applicable) in table 15 for each of the blocks in the Road Map of figure 1

.

The estimates of limits are given for 1 kHz, where many errors are at a minimum, and for the highest frequency. Unless otherwise noted, equal bounds

are implied; i.e., 0.5 signifies that it is considered to be very unlikely

that the residual error will be outside the range -0.5 to +0.5 ppm.

Many of the bounds were determined from actual measurements or specifications. Others were difficult to estimate, and a few are simply

educated guesses; based, however, on extensive experience in ac-dc

measurements. Some pertinent notes are given at the end of the table.

Almost all of the sources of error are independent (not correlated). The few

correlated sources are discussed in the next section.

32
XIII. COMBINATION OF UNCERTAINTIES

From the basic dimensionless equation given in section III-A

dj - dg + (Njj-N 3

)/ngEj^. Here the exponent of each variable is +1 or -1.

From the theory of errors [16], the propagation-of-error formula for the

fractional standard deviation, Sp, of d^, with uncorrelated variables having

small random errors, reduces to (I where each of the s^^'s is the

fractional standard deviation of an individual factor (considering (Nj^-N^) as

a factor). In accordance with Dietrich [12], the same formula will apply

safely enough for combinations of estimated residual uncertainties^, each

taken to be uniformly distributed between estimated bounds, ±b, with the

standard deviation of each taken as Sj^ = ±bj^//3. These values of Sj^ are the

"equivalent standard deviations" of the BIPM report (appendix 6). Twice the

overall standard deviation, 2s^, is taken as a reasonable measure of the

overall uncertainty. According to Dietrich the probability of a value lying

outside this will be less than 0.05.

This use of 2s^ for the overall uncertainty, Uq, is strongly recommended

by Dunn of the National Research Council of Canada [17], who also recommends

the approach taken by Dietrich to the combination of uncertainties. It seems more appropriate than 3 Sq when many of the sources of error are considered to

be of uniform probability density, since the long tails of the normal

distribution are truncated.

Because of the several successive steps and the three different

comparators used in evaluating the NBS reference and working standards, and

because of the many steps in the extensions of the frequency and other

ranges, the rather straightforward procedure of combining uncertainties from

tables 14 and 15 becomes very involved. The detailed calculations are shown

in table 16. They are generally self-explanatory. The results are the same

as those obtained by adding variances and finding the overall uncertainty as twice the square root of the overall variance. However, no definite

confidence limit is associated with the uncertainty, U.

wi th each other and with Sp. See section X-4.

33
Extreme rigor in making these calculations did not seem warranted,

especially for the smaller U's, which do not effect the rss results very

much.

In the XVC build-up the errors in determining the changes in the d^'s

of the TE's (FX2 and FY2 ) with current level are correlated; i.e., they add

in each step of the build-up. Similarly in the Fy tvC build-up, the errors

in determining the difference between the d^’s of Fy1 and Fy2 at the

particular currents used add at each step. These correlated uncertainties

were separately evaluated in the calculations of table 16.

It is to be noted that in each build-up involving chains of successive

measurements the uncertainty at the end of each chain is given in table 16.

It is difficult to estimate the effects of the uncertainties which

depend on the magnitude of A, particularly for these chains of measurements.

These range from 2.8J of A for the MJTC comparator to 3 .6/6 for the other

comparators. A prudent allowance for them is given in B of table 17.

Fortunately the values of d for the NBS standards are small, so that this is a significant factor in only a few cases.

The values of d and U apply at the currents and voltages shown in the

various tables. At other voltages and currents additional corrections must

be applied to the d's, and the uncertainties will be somewhat greater.

Appropriate currents and voltages were used in evaluating the reference

standards. Fortunately the working standards are rarely used at other than

rated inputs.

34
XIV. CONCLUSIONS

A. Uncertainties of the NBS Standards

The overall results of the calculations of the uncertainties are given

in the important summary table 17. They apply at rated current and voltage,

with the exceptions shown.

Several conclusions can be drawn from this table and the other results

of this study, as follows:

(1) The long-term stability of the d's of the MJTC's is excellent.

This, together with their low d’s and 0.5 ppm uncertainty, amply fulfilled

the hope that they would be superior primary standards of ac-dc difference at

the base frequency of 1 kHz, and over the range from 30 Hz to 10 kHz.

(2) Their accuracy can be transferred to the single-junction TE's at

5 mA and 5 to 10 V to 1 ppm.

(3) The accuracy of these base ranges can be extended to 100 kHz to

better than 2 ppm.

(4) As expected, (see section X-13) the uncertainty of the reference

standards increases with increasing V or I range. The most precise

comparator can only be used to 50 mA or 100 V, so the uncertainty cone has

discontinuities in slope.

(5) As expected, the difficulties of extending the range increase at

higher frequencies, and so do the uncertainties; generally by a factor of 1 .5

to 2 times those at 1 kHz.

(6) As shown in table 16, the random-error component is significant in

almost all comparisons. There is generally a reasonable balance between

35
random and systematic components. However, better precision would be the

first step to improving accuracies.

B. Calibration Uncertainties

(1) If TE*s and TVC's of the same type and quality as the working

standards are calibrated with the calibration console, it would be expected

that the overall uncertainty would be the rss of the working standards from

table 17 and the single step U's of 16-H (minus the Sg of the reference

standard) or 16-1 of table 16. The results of such calculations are given in

table 18, along with the present calibration allowances, from section I-C.

(2) As the table shows, little improvement may be possible for the

coaxial TVC calibrations. For TCC calibrations the differences between the rss uncertainties and the allowances are deceptive. Individual TE's of the same quality as our standards are no longer available in the ampere ranges.

The multirange TVC's with shunts that are commercially available are much

more complex. Experience has indicated that they have larger and less stable

d's than do the single-range TE's and coaxial TVC's.

(3) If NBS is pressed for better accuracy, particularly for TVC's, the

needs might be met by using the uncertainty-cone concept to specify smaller

uncertainties at and near the apex. In this way the basic accuracy at NBS

could be transported via suitable ac-dc transfer standards to the client's

standards laboratory.

(4) Very high accuracies are attainable over limited ranges for very

special tests (such as international comparisons) in which such accuracies

are really needed. They would be made by directly comparing single-range

coaxial TVC's up to 100 V with the resistors and reserve TE's (FA and FB),

or single-junction TE's up to 50 mA with one of the pairs of reference TE's,

using the MJTC comparator in each case. The results of calculations (similar

to those described in B-1 of this section) are shown in table 19, to

substantiate this.

36
(5) A comparison was made of the d’s of the working standards shown in

tables 11 and 13 with the values previously assigned from earlier tests and

presently used in calibration work. For the Fy TVC’s, the largest difference

between the d*s was 23 ppm, on the 600-V range at 100 kHz (the highest

voltage available at this frequency). It was 10 ppm on the 1000-V range at

50 kHz, and much less at most other ranges and frequencies. The average

difference for all ranges at all frequencies (with regard to sign) was only

2 ppm. For the current-measuring TE*s the largest difference between the d's was 36 ppm. The average for all ranges at all frequencies was only 8 ppm.

These low differences attest to both the quality of the earlier measurements

and the stability of the MBS ac-dc transfer standards. They are comfortably

below the uncertainties of calibrations shown in section I-C of this report.

XV. RECOMMENDATIONS

A. Maintenance of AC-DC Standards

(1) The NBS standards are believed, with reason, to be very stable.

However if better accuracy than heretofore is to be maintained, it would be

prudent to compare the working standard TE’s with the reference standards

every three years, and to compare adjacent ranges of the Fj TVC set at

similar intervals. This could be modified by experience — see recommendation B-6.

(2) The difficult and very time-consuming recalibrations of the

reference standards might only be necessary every 9 years, if the 3-year

tests show no significant changes.

(3) Spare F^l and F-j2 modules should be available in case of burnout,

with values d^ and d^ known by prior comparison with the present ones. FA

and FB, an extra pair of 5-mA TE*s with known d^ and d^, are already

available for the F^ reference set. The substitution formulas of section IX

37
should make It possible to calculate the dy's for the other TVC ranges,

without recalibrating each one, when a TE is replaced.

(4) AC-DC differences as large as 9 ppm have been observed even in

Evanohm-heater TE's, so replacements should never be used without

recalibration.

B. Quality Control of the Calibration Process

(1) The principles of quality control given by Eisenhart [13] should be

followed. Check standards should be evaluated periodically in the

calibration console. They should be of the same types as the major kinds of

ac-dc standards normally calibrated. In particular the multirange standard,

which was purchased in part for this purpose, should be put in service, as well as the spare Model F TVC's on which a partial history has already been

garnered.

(2) NBS statisticans should be consulted and should be of major help in

setting up these programs. Careful selection of a few ranges and frequencies

should not make these very important quality-control tests too time-consuming

or onerous.

(3) The waveform and frequency of the applied ac should be observed on

a calibrated CRO in each test, and the frequency setting of the oscillator

should be double-checked to avoid mistakes.

(4) The very simple EMI test described in section III-A should be made

occasionally, especially for low ranges.

(5) A second comparator and associated equipment should always be

available and ready for use as a check against unsuspected (or suspected)

errors. This is particularly valuable when new or modified ac-dc standards

are first tested.

38
(6) As experience with the check standards and the bienniel

calibrations of the working standards is accumulated, the recommended

calibration periods of A-1 for the working and reference standards may safety

be revised.

C . Other Recommendations

(1) Almost all of the TE’s from 5 mA to 20 A were made to our special

order by American manufacturers who no longer make TE's. The MJTC's are not

commercially available at all. All of these now form an unique collection of

well-evaluated reference standards, and should be reserved solely for

evaluating the NBS working standards and for comparisons with other national

laboratories, or for other special test in which the highest accuracy is

really required. The MJTC comparator, with its high precision, should be

available for use when this is really needed.

(2) The new types of solid-state thermoelements (SSTE's) have much

higher emf’s than the conventional TE's, but are subject to the same basic

limitations on ac-dc difference from Thomson, Peltier and other effects. If

Wilkins * -type MJTC's can not be obtained commercially in the near future,

serious consideration should be given to designing and making thin-film

MJTC's by cooperation with other divisions at NBS.

(3) The new values of d for the working standards, from tables 11 and

13, should be used in place of those now in the computer. However any stated

improvement in the calibration uncertainties should be withheld until some checks on the error analyses are made by comparing the NBS working and

reference standard TE's and TVC's in both the calibration and 1966 consoles.

In addition any improvement in the stated uncertainty of the more complex

multirange TVC's and their shunts should await the installation of a quality-control program and further studies of these instruments.

39
XVI. ACKNOWLEDGEMENTS

Sincere thanks are expressed to J. R. Hastings, E. S. Williams,

C. B. Childers, and K. B. Krishnamurthy, who assisted in this investigation,

to N. Belecki for his encouragement and support, to C. Reeve for his helpful

suggestions and review of the statistical procedures, and to T. Lipe for his

review of the entire report.

40
REFERENCES

1 . Thermal Converters as AC-DC Transfer Standards for Current & Voltage

Measurements at Audio Frequencies, F. L. Hermach, Jour. Res. NBS, v. 28,

no. 2, p. 121 , Feb. 1952.

2. Thermal Converters for Audio-Frequency Voltage Measurements of High

Accuracy, F. L. Hermach and E. S. Williams, IEEE Trans, on Instrum. &

Measmt., v. IM-15, p. 260, Dec. 1966.

3. Thermal Voltage Converters & Comparator for Very Accurate AC Voltage

Measurements, E. S. Williams, Jour. Res. NBS, v. 75C, p. 1^15, July-Dee.

1971 .

M. An Investigation of Multijunction Thermal Converters, F. L. Hermach and

D. R. Flach, IEEE Trans, on Instrum. & Measmt., v. IM-25, p. 524, Dec.

1976.

5. Thermal Voltage Converters for Accurate Voltage Measurements to 30

Megacycles per Second, F. L. Hermach and E. S. Williams, AIEE Trans., v. 79-1, p. 200, July 1960.

6. Thermal Current Converters for Accurate AC Current Measurement, E. S.

Williams, IEEE Trans, on Instrum. & Measmt., v. IM-25, p. 519, Dec.

1976.

7. Errors in AC-DC Transfer Arising from a DC Reversal Difference, B. D.

Inglis, Metrologia, v. 17, p. Ill, 1981.

8. Theoretical Analysis of the AC/DC Transfer Difference of the NPL

Multijunction Thermal Converter Over the Frequency Range DC to 100 kHz,

F. J. Wilkins, IEEE Trans, on Instrum. & Measmt., v. IM-21 , p. 334, Nov.

1972.

41
9.

Evaluation of AC-DC Transfer Errors for Thermal Converter-Multiplier

Combinations, B. D. Inglis, Metrologia, v. 16, p. 177, 1980.

10. Uncertainties in Calibrations, W. Youden, IRE Trans. Instrum., v. 1-11,

p. 133» Dec. 1962.

11. Uncertainty Assignment, B. Taylor, Memo for Technical Staff of the NBS

Electricity Division, Aug. 21, 1981.

12. Uncertainty, Calibration, and Probability, C. F. Dietrich, Halsted

Press, 1973.

13 . Realistic Evaluation of the Precision and Accuracy of Instrument

Calibration Systems, C. Eisenhart, J. Res. NBS, v. 67C, p. 161,

Apr- June 1963*

1^. Suggested Practices for Electrical Standardizing Laboratories, F. B.

Silsbee, NBS Circular 578, 1956.

15 . Experimental Statistics, M. G. Natrella, NBS Handbook 91, 1966 (Chapters

3 and 15).

16. Notes on the Use of Propagation of Error Formulas, H. H. Ku, J. Res.

NBS, V. 70c, p. 263 , Oct-Dec 1966.

17 . Measurement Assurance, A. F. Dunn, NRC, Canada, Report 188^3, 1980.

18. A Resistor Calculable from AC to w=10^rad/s, R. J. Haddad, Thesis, GWU

School of Engineering and Applied Science, April 1969.

19 . The Theory of Peltier & Thomson Errors in Thermal AC-DC Transfer

Devices, F. C. Widdis, lEE Monograph ^97M, Jan 1962.

H2
Table 1

Comparisons of Four MJTC's

Jh - (ppm)

V T S 30 Hz 1 kHz 10 kHz Date

10.0 G5C +0.47 +0.15 -0.44 12/08/81

(B10-i|4) (B5-2)

-0.10 12/11/81

6.0 1 o oro 12/11/81

6.0 Gr25-1 G5C +0.32 0.00 -0.29 12/1 1/81

(CIO-1

)

(B5-2)

-0.03 12/14/81

6.0 Gr25-1 G44 +0.17 -0.01 -0.05 12/14/81

(CIO-1

)

(BIO-44)

+0.06 12/18/81

8.0 NPL 14 G44 +0.3^ 12/18/81

(A50-14) (BIO-44)

+0.36 12/18/81

-0.40 +0.27 12/18/81

6.0 Gr25-1 NPL 14 +0.52 -0.22 12/18/81

(CIO-1

)

(A50-14)
Table 2

Differences Between 1981 and 1976 Evaluations of MJTC*S

^81 “ <^76 (PP“)

MJTC 30 Hz 1 kHz 10 kHz

G44 + 0.2 0.0 + 0.1

Gr25-1 0.0 0.0 - 0.11

G5 C + 0.3 - 0.1 + 0.1

G 10 C

-0.3 0.0 0.0

NPL U - 0.2 0.0
Table 3

Results of ConparIsons of FX and FY with MJTC's

TE

or

TVC

I orV 30 Hz

d(ppm)

1 kHz 10 kHz

FX 5 mA - -0.3 -0.2

FX 2.5 mA - 0.0 -0.1

5 V +0.9 -0.4 -1.2

Fi5-FX 3 V -0.1 -0.7 -1.0

FY 5 mA - +0.2 0.0

FY 3 mA - +0.4 -0.2

10-FY 10 V +0.8 -0.3 -0.8

F^ 10-FY 5 V +0.2 +0.1 -1.2

1 F-|5-FX consists of the 5~V resistor of the F-|TVC set, in series with TE FX.

45
Table 4

Results of TVC Tests with Twin Resistors

dT“ds (ppm)

T S 30 Hz 1 kHz 20 kHz 50 kHz

FY FX +0.2 +0.2 0.0 -0.2

B5E77 FX +5.0 +2.6 +3.2 +3.7

F5K9 FX -1 .6 -1 .0 -1 .1 -1 .2

B5EXG1 FX +2.8 + 1 .1 +0.9 + 1.5

A5EP7 FX -0.1 +0.5 -0.5 -1 .3

Average d of

with dpjj =

6 TE's

0.0 +0.6 +0.4 +0.4

NOTE: All tests at 5 mA.

30 Hz results not averaged. See text.

46
Table 5

Ampere-Range Comparisons

dj-ds

T £

1 I

(A) 20 Hz 1 kHz 20 kHz 50 kHz

W20A#7-1 W10A #0-1 10 + 1 + 11 + 17 + 10

W10A#0-1 W5A #5-2 5 -5 -2 0 +16

W10A//0-1 W5A #5-1 5 -6 -6 -6 + 17

W5A #5-2 W3A #4-1 3 +1 -1 +4 +16

W3A #4-1 W2A #3-2 2 +3 0 -7 -1

1

W2A #3-2 W1A #7-2 1 -4 -2 -5 -13

FG3A W3A #4-1 3 -2 0 + 15 +43

FG3A W3A #4-1 2 -4 +1 + 15 +46

FG1A W1A #7-2 1 -3 -2 + 11 +29

FG1 A W1 A #7-2 0.6 +1 0 + 15 +36

FH2A W2A #3-2 1 .2 -2 -2 -12 -40

FH2A W2A #3-2 2.0 0 -14 -33

FH20A W20A #7-1 10 -21 -49

FH20A W20A #7-1 16 -22 -59

NOTE: FG1A, FH2A, FG3A, and FH20A are Williams* shunts with low--range TE' FG and FH.

47
Table 6

AC-DC Differences of 1A to 20A TE*s

d(ppa)

TE

I

(A) 20 Hz 1 kHz 20 kHz 50 kHz

W20A #7-1 10 -5 +5 +14 +10

W10A #0-1 5 -6 -6 -3 0

W5A #5-2 3

-1 -4 -3 -16

W3A #4-1 2 -2 -3 -7 -32

W2A #3-2 1 -5 -3 0 -21

W1 A #7-2 1 -1 -1 +5 -8

W1A #2-2 1 -4 -3 +2 -10
Table 7

Results of Evaluation of FX2 and FY2

TE

or TVC

I orVd(ppm)

20 Hz 1 kHz 10 kHz 20 kHz 50 kHz 100 kHz

IO-FY2 10V +3.9 +2.4 +1.3 +1 .0 +0 .

6

+0.3

7 +2.0 + 1.4 +0.

6

5 + 1.6 + 1 .4 0.0

FY2 5 mA + 4.7 +3.2 +3 • 6 +3.5 +3.9

3.3 +2.8 +2.4 + 2.9

2.5 +2.2 +2.3

FX2

5 mA +3.5 +2.2 +2.4 +2.1 +2.2

3.3 +2.3 + 1.3 + 1.3

2.5 +1.6 +1 .9

49
Table 8

Comparisons of F^tVC's

(FX

g and FY2 TE's)

A - dj-ds (ppm)

T S V 20 Hz 1 kHz 20 kHz 50 kHz 100 kHz

F2OO-FX2 FIOO-FY2 100 - -1.1 +0.2 +1 .H +17.8

FIOO-FY2 F5O-FX2 50 - +0 .

6

-0.8 -2.8 -6.2

F5O-FX2 F3O-FY2 30 - -2.5 -1.6 -2.0 -1.5

F3O-FY2 F2O-FX2 20 -1.3 +0.7 -0.3 0.0 -2.0

F2O-FX2 FIO-FY2 10 -3.8 -1.7 -2.1 -2.9 -6.0

FIO-FY

2 F5-FX2 5 -0.6 +0.2 -0.3 -1.3 -2.5

F5-FX2 F3-FY2 3 -1.6 -0.6 -0.8 -3.1 -6.3

F3-FY2 F2-FX2 2 0.0 +1 .1| +0.7 -1.1 -4.1

F2-FX2 FI-FY2 1 +0.11 + 1.9 +0.7 -3.9 -13.1

F1-FY2 FX2 0.5 + 1.0 +3.11 +H.2 -0.7 -6.1

FX2 FY2 0.5 + 1.2 +1.1 +1.9 +2.2 +2.5

Comparisons with F^1 , FX, and FY in place of FX2 and FY2

F1000-Fy1 F500-FX 500 - -2.0 -15.1 -1.7 -

F500-FX F300-FY 300 - - 0.8 -0.3 -11.1 -33

F300-FY F200-FX 200 - - 0.7 -0.5 -2.3 + 6.7

50
Table 9

AC-DC Differences of F, TVC*s with FX2 and FY2

d(ppm)

TVC V 20 Hz 1 kHz 20 kHz 50 kHz 100 kHz

F1000E-F,^1 500 - +2.7 -11.5 -6.1 -

F5OO-FX2 500 - +2.5 +1 .2 -6.5 -18.6

300 + 1 .7 +0.4 -7.3 -19.4

F3OO-FY2 300 - +3.5 +1.9 -1.8 +15.6

200 — +2.7 + 1.1 -2.6 +1 4.8

F2OO-FX2 200 - +2.4 +0.4 -1 .7 +6.4

100 — + 1 .6 -0.4 -2.5 + 5.6

FIOO-FY2 100 - +2.7 -0.6 -3.9 -12.2

50 — + 1 .9 -1.4 -4.7 -13.0

F5O-FX2 50 - +1.3 -0.6 -1.9 -6.8

30 — +0.5 -1.4 -2.7 -7.6

F3O-FY2 30 +2.6 +3.0 +0.2 -0.7 -6.1

20 +0.7 +2.2 -0.6 -1 .5 -6.9

F2O-FX2 20 +2.0 +1.5 -0.3 -1.5 -4.9

10 +0.1 + 0.7 -1.1 -2.3 -5.7

FIO-FY2 10 +3.9 +2.4 +1.0 +0 .

6

+0.3

5 + 1 .4 + 1 .6 +0.2 -0.2 -0.5

F5-FX2 5 +2.0 +1 .4 +0.5 +1 .1 +2.0

3 + 0.7 +0 .

6

-0.3 +0.3 + 1 .2

F3-FY2 3 +2.3 +1 .2 +0.5 +3.4 +7.5

2 +0.4 + 0.4 -0.3 +2.6 + 6.7

F2-FX2 2 +0.4 -1.0 -1.0 +3.7 + 10.8

1 -1 .5 -1 .8 -1.3 + 3.9 + 10.0

FI-FY2 1 -1.9 -3.7 -2.5 +6.8 +23.1

0.5 -4.4 -4.5 -3.3 + 6.0 +22.3

FX2 0.6 -5.4 -7.9 -7.5 +6.7 +28.4

FY2 0.6 -6.6 -8.9 -9.4 +4.5 +25.9

51
Table 10

Comparisons of Working and Reference Standard TE's

A(ppm)

I

Test Standaird (mA) 20 Hz 1 kHz 20 kHz 50 kHz

A3 #95 FA 5 +5 +2 +9 + 18

GIO #57 B10EP2 10 -5 -5 -4 -3

F20 #1 W25E1 20 -9 -7 -5 +1

W30 #1 W25E1 25 -12 -11 -12 -12

F50 #2 W50E1 50 -37 0 +3 -2

B100 #3 W100E1 100 -18 -20 -20 -24

A250 #M W250E1 250 -19 -22 -28 -44

(A)

W0.5A #0-2 W0.5A #0-1 0.5 -4 -2 -5 -2

W1A #7-1 W1A #2-2 1 0 -2 -1 -4

W2A #8-3 W2A #3-2 2 +3 + 1 +1 -2

W3A #9-2 W3A #4-1 3 +2 -1 -1 -3

W5A #5-1 W5A #5-2 5 -5 -7 -1

1

-13

25 Hz

W10A #0-3 W10A #0-1 10 -6 -5 -13 -28

100 Hz

W20A #1-2 W20A #7-1 16 +3 -10 -18 -14

52
Table 11

AC-DC Differences of Working Standard TE*s

AC-DC Difference (ppm)

TE

I(mA) 20 Hz 1 kHz 20 kHz 50 kHz

A 5 //95 5 + 2 0 +8 + 17

G 10 #57 10 -6 -6 -5 -4

F 20 #1 20 -10 -8 -6 0

W 30 #1 30 -13 -12 -13 -13

F 50 #2 50 -36 -1 + 2 -3

B 100 #3 100 -20 -21 -20 -23

A 250 250 - 2 H -22 -28 -43

(A)

W0 . 5A #0-2 0.5 0 -2 -3 -7

W 1 A #7-1 1 -4 -5 + 1 -14

W2 A #8-3 2 -2 -2 + 1 -23

W3A # 9-2 3 0 -4 -8 -35

W5 A # 5-1 5 -6 -1

1

-14 -29

25 Hz

W10A #0-3 10 -12 -11 -16 -28

100 Hz

W20A # 1-2 16 +8 -5 -4 -4

53
Table 12

Comparisons of Fj tvC's

A - dj-ds (ppm)

T S V 20 Hz 1 kHz 20 kHz 50 kHz 100 kHz

FylOGO-IOE-Fyl Fy600“Fy2 600 - 0 -13 -7 -

Fy500-10C-FYl Fy600~Fy2 500 - 0 -7 + 11 -

Fy500-10D-Fy1 Fy 600“Fy2 500 - 0 0 +35 -

F730 O-F7

I Fy200-Fy2 200 -1 -1 0 + 12 +59

Fy100-Fy1 Fy60~Fy2 60 -1 +1 0 -6 -13

Fy30-Fy1 Fy20-Fy2 20 +1 0 0 +1 -1

FylO-Fyl Fy6-Fy2 6 +2 0 -1 +3 -2

FyS-Fyl Fy2 2 +2 -2 -1 -1 -3

Fy 1 Fy2 1 +1 -4 -4 -1 -3

5 ^
Table 13

TVC

AC-DC

V

Differences of Fy TVC*s

d(ppm)

20 Hz 1 kHz 20 kHz 50 kHz 100 kHz

Fy1000-10E-Fy1 600 - -2 -15 -2 -

Fy500-10C-Fy1 500 - -2 -9 + 16 -

Fy500-10D-Fy1 500 - -2 -2 + 40 -

Fy600-Fy2 500 -2 -2 +5 + il3

Fy300-Fyl 300 -2 -2 + 5 + ii3

Fy200-Fy2 200 -3 -1 -2 -7 -16

Fy100-Fy1 100 -3 -1 -2 -7 -16

Fy60-Fy2 60 -2 -2 -2 -1 -3

Fy30-Fyl 30 -2 -2 -2 -1 -3

Fy20-Fy2 20 -3 -2 -2 -2 -2

Fy10-Fy1 10 -3 -2 -2 -2 -2

Fy6-Fy2 6 -5 -2 -1 -5 0

Fy3-Fy1 3 -5 -2 -1 -5 0

F-jZ 2 -7 0 0 -4 + 3

Fyl 1 -6 -H -5 0

55
Table 14

Pooled Standard Deviations, Sp^

®pa (ppm of input V or I)

Type of Test

Typical

emf (mV) 20 Hz 1 kHz 20 kHz 50 kHz 100 kHz Average

1 . Comparison of

MJTC ’

s

10-40 0.11

(5)1

0.16

(11)

- - - 0.14

2. Comparison of

MJTC's vs. Reference TE's

and 10 FY2

10 0.20

(5)

0.29

(9)

0.25

3 . Extension of

of frequency

range

10 0.23

(5)

0.24

(5)

0.25

(5)

0.24

4. Build upReference TE's

a. 5 to 50 mA 10 0.26

(11)

0.23

(13)

0.35

(11)

0.26

(11)

- 0.28

b. 50 mA to 1A 10 1 .80

(11)

1.68

(16)

1.57

(15)

1.98

(17)

-

1 .76

c. 1A to 20A 5 1 .77

(13)

1 .56

(12)

1.48

(12)

1 .74

(16)

-

1 .64

5 . Build upF^TVC's

a. 0.5 to 100 V 3 0.49

(7)

0.47

(12)

0.52

(12)

0.57

(10)

0.54

(10)

0.52

b. 200 to 1000 V 3

-

1 .71

(4)

1.41

(4)

1.06

(3)

1.55

(2)

1.43

6. Comparison of

Reference and

Working TE's

5 mA - 20 A

10 2.36

(12)

2.77

(12)

2.47

(11)

1 .72

(17)

2.33

7. Build up

F-, TVC's

1 to 1000 V 3 1.58

(6)

1 .20

(9)

2.16

(9)

2.54

(9)

2.79

(9)

2.05

^Values in parentheses are the number of tests.

56
Table 15

Estimated Limits of Residual Systematic Uncertainties

(not evaluated by statistical means)

(See notes at end of table)

Limits, ±b

1 kHz 100 kHz

ppm ^ of A ppm % of i

MJTC Comparator & Equipment

1 . nVm & averager { 2 % of

indication)

2 2

2. Determination of n^ - 2

- 2

3. n-Compensation 0.1 0.1

DC-reversal difference

definitions

0.1 0.1

5. AC effects 0.1 — - 0.2

bo = (Ib2)1/2 0.17 2.8 0.25 2.8

1966 Comparator & Equipment

1 . 1966 evaluation 1.0 - 1.0 - 2. Detector accuracy - 3

- 3

3. Determination of ng - 2

-

2

4. AC effects - — 2.0

*>o 1.0 3.6 2.2 3.6

Calibration-Console

1 . Basic accuracy 1 .0 - 1.0 - 2. Detector accuracy - 3

- 3

3. Determination of ng - 2

- 2

il. AC effects - 2.0

*>o 1.0 3.6 2.2 3.6

Limits, ±b. ppm

1 kHz 50 kHz 100 kHz

MJTC 's

1 . 1976 assignment of group

average 0.3

2. Possible changes 1976-1982 0.1

3. Assignment of G-44 0.1

0.33

57
Table 15 (Continued)

Limits, ±b, ppm

1 kHz 50 kHz 100 kHz

E.

F.

G.

H.

I.

J.

5 mA Reference TE's

1

.

Residual thermoelectric

effects 0.2 0.2

2. High frequency evaluation 0.0 0.5

0.20 0.5^

Fi IOY2 , Base TVC

1 . 1 kHz base 0.2

2. High frequency extension 0.0

t>o 0.2

Reference TE's, build-up

to 50 mA (3 stages)

1 . Bead error (each stage) 0.2 0.3

2. Paralleling error (each stage) 0.1 0.3

each stage b^ 0.22 0.42

Reference TE's, build-up from

50 mA to 1A (il stages)

1

.

Bead error (each stage) 0.2 1 .0

2. Paralleling error (each stage) 0.3 1 .0

3. AC effects (each stage) 0.0 1 .0

each stage b^ 0.36 1.73

Reference TE's, build-up

1

A

- 20A (5 steps)

1 . Dependence of d^ on I (each step) 2.0 2.0

2. AC effects (induced emf's.

etc. ) (each step) 1 .0 3.0

3. Proximity effect (each step) 0.0 2.0

each step b^ 2.2 4.1

Extension of Voltage Range

10 to 0.5 V, 10 to 200 V

ranges (5 steps each)

1 . Residual dependence of d^ on I (correlated) 0.2 0.5

each step b^ 0.2 0.5

58
Table 15 (Continued)

Llalts, ±b, ppm

1 kHz 50 kHz 100 kHz

Extension of V range from 200

to 1000 V range (at 500 V)

(3 steps)

1 . Dependence of d^ on V

(Avg. for 3 steps) 0.5 2.0

2. Dependence of d on I 3. Transfer FX, FY^ to FXp,

0.2 0.5

FY2 0.5 2.0

each step 0.73 2.9

L. Working standard TE*s 5 mA to

20 A range (by comparison with

reference stds, same range)

1 . Bead resistance and other

ac effects 3.0 5.0 5 mA

6.0 10.0 20 A

2. Dependence of d^ on I 2.0 2.0

each step b^ 3.5 5.M 5 mA

6.3 10.1 20 A

M. Working Standards TVC’s (Fy set)

Build-up 10V to 1000V range

(4 steps) and build-down 10V

to IV range (3 steps)

d

(2 of each TE (correlated) 1.0 3.0

Dependence of d^ on V

(high ranges), build-up 0.0 to 0.0 to

0.5 2.0

Adj, error (low ranges),

build-down 0.0 to 0.0 to

0.5 2.0

average, each step b^ 1.1 3.3

59
Table 15 (Continued)

Sections

A, B, & C

E-1 & F-1

G-1 & H-1

G-2 & H-2

1-1

1-3

J-1

K-1

K-3

M-2

M-3

NOTES:

of A errors depend on magnitude of A = d.p-d3

. Hg determined once, but error affects every ac-dc determination.

AC effects are estimated residuals or allowances for rfi,

induced voltages, etc.

Main effects evaluated by comparison with MJTC. These are residuals

.

Estimate of error from finite bead resistance.

Estimate of A0 error, of paralleled TE's, etc.

Variation of d^ with I was not applied in build-up.

Proximity of return lead on current distribution in TE heater.

The error in measuring Ad^ adds at each step.

Self-heating effect on d^,.

Residual substitution error.

See K-1 note.

A0 of Fj TE's. See section VIII-B.

60
Table 16

Calculation of Uncertainties

Se “ Spa or b//3, - 2

S or U (ppm)

1 kHz 50 kHz 100 kHz

A. MJTC G41]

pg

from table 14-1

g

for comparator,

Se Spa 0.16

table 15-A Sg=b//3 0.09

g

MJTC's (15-D) Sg=b//3 0.19

= 2Sq = 2(Z 0.53

B

C

D

Reference 5 mA TE's & F^10Y2

TVC to 100 kHz

Spg (14-2 & 3)

Sg comparator (15-A)

0.29 0.29 0.29

0.09 0.14 0.14

Sg TE's (15-E or F) 0.12 0.31 0.58

«o

= 2S«o 0.65 0.89 1.33

(Uo^ 0.84 1 .04 1 .42

. Reference TE's 10 to 50 mA

(3 stages)

Spa ( 14 . 4 a) per comparison 0.23 0.26

Se comp. (15-A) per comparison 0.09 0.14

Se TE's (15-G) per comparison 0.13 0.24

Because of triads, Uq=0.8 x 2Sq 0.45 0.61 per stage

After 3 stages ^q-^=/3Vq 0.78 1 .05

After 3 stages Ug=(UQ^^ + 1.1 1.5

. Reference TE's 100 mA to 1A

(i| stages)

Spa per comparison 1 .7 2.0

Sg comp. ( 15 -B) per comparison 0.6 1.3

Sg TE's ( 15-H) per comparison 0.2 1 .0

After 1 stage = 0.8 x 2Sq 2.9 4.1

After 4 stages UQ]j=/IfUQ 5.8 8.2

Ug = (UqIi^ + Uq2)1/2 5.9 8.3

61
Table 16 (Continued)

S or U (ppm)

1 kHz 50 kHz 100 kHz

Reference TE's 2A to 20A (at 10A)

(5 steps)

Spg (14-4C) per step 1.6 1 .7

Sg comp. ( 15 -B) per step 0.6 1.3

Sg TE's (15“I) per step 1.3 2.4

After 1 step = 2Sq 4.3 6.4

After 5 steps Uq^ = /SUq 9.6 14

= ^^05^ 11 16

FiTVC's 10 to 0.5V and

10 to 100V (6 and ^1 steps)

Spa (l4-5a) each step a 0.47 0.54

Sg comp. (15“A) each step b 0.09 0.14

Sg TVC's (15-J)

(correlated) each step c 0.11 0.29

After 1 step » 2Sq 0.98 1.26

After 5 steps UQ5»2((5c)^+5(a+b)^)^^^ 2.7 4.2

Up - 2.8 4.4

TVC's 200 to 1000V range

(at 500V) (3 steps)

Spa (I4~5b) each step 1.7 1.6

Sg comp. ( 15 -B) each step 0.6 1.3

Sg TVC's ( 15 -K) each step 0.4 1.7

After 1 step Uq = 2Sq 3.7 5.3

After 3 steps Uq^ = 6.4 9.2

«C-<«03^ Up2)’/2 7.0 10

62
Table 16 (Continued)

S or U (ppm)

1 kHz 50 kHz 100 kHz

H. Working TE's 5mA to 20A range

^ (U-6) 2.8 1 .7

comp. (15-C) 0.6 1 .2

TE's (15-L) 5mA 2.1 3.1

20A 3.6 5.8

Reference TE's (16-B) 5mA 0.4 0.5

(16-E) 20A 5.6 8.2

= 2So 5mA 7.1 7.5

20A 15 21

I. Working Standard TVC's

l6 to 1000V range (5 steps);

10 to IV range (3 steps)

^pa ^ ^ ^

' Sg comp. (15-C) each step b

1 .2 2.8

0.6 1 .2

S TVC's (15-M)

(correlated) each step c 0.6 1 .9

After 1 step Uq = 2Sq 2.9 7.2

After 3 steps UQ2=2((3c)2+3(a+b)2)^^2 7.2 18

(at IV) Uj = (Uq

3^ + 7.2 18

After 5 steps UQ^=2((5c)2+5(a+b)2)^^2 10 26

(at 500V) Uj = (Uq5^ + 10 26

63
Table 17

Summary of Uncertainties of NBS AC-DC Transfer Standards

I. Uncertainties Independent of Magnitude of d

Ua ppm

Standard 1 kHz 50 kHz 100 kHz

MJTC (one of group) 0.53

B Reference base, 5 mA TE’s & 10V TVC 0.84 1 .0 1 .4

C Reference TE: 50 mA range 1 .1 1 .5 D 1A range 5.9 8.3

E 20A range 1

1

16

F Reference TVC: 0.5 & 100V ranges 2.8 4.4

G 1000V range (at 500V) 7.0 10

H Working TE*s: 5 mA range 7.1 7.5

20A range 15 21

I Working TVC’s: 10V range 2.9 7.2

IV range 7.2 18

500V range 10 26

II. Uncertainties dependent on magnitude of d:

For all standards Ug = 0.05d should

Ug < 1 ppm with few exceptions.

be added to U^.

Ill . Uncertainties at 20 Hz are somewhat , but not significantly, greater

than at 1 kHz.

IV. Uncertainties at less than rated V or I require further study. However

the working standards are almost always used at or near rated V or I

.

V. Self-heating effects at 1000V were evaluated in [3].

1 Letters refer to table 16.

64
Table 18

Coaparison of Estimated Calibration Uncertainties with

Present Allowances

U (ppm)

1 kHz 50 kHz

5 mA 20 A 5 mA 20 A

Working standard TE's (l6-H)

Comparison (16-H without Sg of

7.1 15.0 7. 5 21

ref. stds.) 7.1 9.2 5 12

U (rss) 10 18 1

1

24

Present allowance 5 mA - 5A

Present allowance 5A - 20A

50

100

100

200

1 kHz 100 kHz

JV 10V 500V vv 10V 500V

Working standard TVC's (16-1) 7.2 3.0 10 18 7.2 26

Comparison (16-1, one step) 2.9 2.9 2.9 7.2 7.2 7.2

U (rss) 7.8 U.2 10 19 10 27

Present allowance (for coaxial

TVC's)

Present allowance (for multi20 20 20 50 50 50

range TVC's) 50 50 50 100 100 100

NOTE ; This table applies to the evaluation in the NBS Calibration Console of

single-junction TVC*s and single-range TE's of the same quality as the

NBS standards.

65
Table 19

Estimated Uncertainties for Special Tests

(Calibration of a TE or TVC against a reference standard,

with NJTC comparator)

U (piMl)

1 kHz 50 kHz

5 mA 50 mA 5 mA 50 mA

Reference standard TE 5“50 mA 0.9 1 .1 1 .0 1.5

Comparison (1 6B & 16C

of TE's)

without Sg

0.6 0.6 0 .

6

0.6

rss 1 .1 1.2 1 .2 1 .6

1 kHz 100 kHz

jV 10V 100V IV 10V 100V

F^TVC 0.5 - 100V 2.8 0.9 2.8 1.4 4.4

Comparison (1 6-C, all ranges) 0 .

6

0.6 0.6 0.6 0.6 0.6

Substitution uncertainty 0.5 0.5 0.5 2.0 1 .0 2.0

rss 2.9 1 .2 2.9 ^.9 1 .8 4.9

66
Figure 1 . "Road Map"

67
30 Hz 1 kHz

10 kHz

Figure 2

.

Comparisons of hJT’s

68
50 mA

25 mA

10 mA

10 kHz

1 kHz

69
1 A

500 mA

250 mA

100 mA

50 mA

Figure. 50 mA to 1 A Comparisons

Ref.

70
DC DCR

Figure 5. Comparator With n -Compensation

71
72
APPENDIX 1

n-COMPENSATION and n-MEASUREMEMTS

A. Principle of CcxBpensation

The basic circuit of the M.JTC comparator with the n-compensation

resistor, R^,, included is shown in figure 5 . Ep represents an adjustable

Lindeck potentiometer.

At the initial balances, with N= 0 , (N is the reading of the high

impedance nanovoltmeter, nVm) , mE^ = E2 = Ep = V2. (The Ep setting is made

by switching nVm in place of Rj,.) Now if the input voltage V^, is increased

by a small amount, AV^, then AE^/E-] = n-jAVj^/Vj^ and AE2/E2 = n2AV^/Vj^ (from

the definition of n given in section IIIA with replacing I). A small

current then flows in the E2~Ep loop. Because of the voltage divider formed

by R2 and Rj^, AV2 is less than AE2. Thus if n2 is greater than n^ , R^ can be

adjusted until mAE^ = AV2, maintaining N= 0 . This makes the steady-state

balance insensitive to small changes in the supply voltages, and makes it

unnecessary to adjust these voltages to keep one of the emf's constant during

an ac-dc determination, as heretofore required.

From the figure and with the output resistance of the potentiometer

included in R^,, AV2 = qAE2i where q

= Rj,/(R^ + R2) . Since the same AV/V is

applied to both TVC’s

AE. AE^ mAE^

~ qn^mE^

so that q

=

Appendix 1-1
B. Basic TE Equation

Since neither TE has a constant output during a comparison of two TVC's

(or TE*s) the development of the comparator equation given in appendix 2 of

[ 3 ] is not directly applicable. It will be convenient to use a general

equation for a TVC with slightly different ac and dc input voltages, V_ and a V^, applied. We may write, as an identity,

where V^* is the average of the two directions of dc voltage required to

produce the same emf as V^, and is the average of the two directions which

produce an emf, E^^.

Then, from the definitions of n and d, and, since E^ = E^j* ,

Ea - E^

= V , (1 + —-= + d) , to Ist-order terms.

a d nE , d

A similar equation applies for current measurements, with I replacing V.

C . AC-DC Comparisons

From the above basic TVC equation, and with the same voltage applied to

both TVC's, as in fig. 5.

Thus

E 2a

E

2d

E

la

E d-d Id

2

Appendix 1-2
But Ng - V2a and = V

2 d

~ polarity shown, so that

Na-Nd-V2a“V2d""’(^1a"^1d^"'l^^2a"^2d^"'"^^1a"^1d^ • Combining these equations,

and noting that q=n^/n2 and raEi*E2, gives, closely enough.

d,-d2 - q

(e, -E,,) m(E, -E,,) N -N, '2a 2d^ ^ la Id'^ a d

"1®2 n,E2 n,Ej (A 1 B- 1 )

If n^>n2, the potentiometer and R^, are connected across E^ , and the

polarity of the nanovoltmeter is reversed. Rj, is adjusted as before, so that

there is no change in N when is increased. Because of the input

resistance, R^, of the divider, analysis shows that

R + R,

P 1 where R

P

R R

r R +R

r

The comparator formula then becomes

N

-

. H ^

2 1 - n^Ej (A 1 B- 2 )

Equations A 1 B -1 and A 1 B-2 may be written as

- <3 ^ = T S

-

'^a (AlB- 3 )

where the subscript T refers to the TE to which the potentiometer is

connected, and E^j^ refers to the TE with the lowest emf.

Appendix I-3
D. Precautions in n-Measurement

The characteristic, n, is conveniently measured, after the initial

balance is obtained with the set key down, by changing the input quantity, Q,

by about 0 ,\%, noting the change in output emf E, then calculating n=QAE/EAQ.

The usual precautions in measuring small changes should be observed, as in an ac-dc difference test, to avoid errors from drifts etc.

A more insiduous error can occur, however, if the heater alloy of a TE

has even a small temperature coefficient of resistance, a, so that

R=RQ(1+a6), where 0 is the temperature rise above ambient. Then, since V=IR

p for the heater, and 9=kl

dV dl

I dR dlI dR dl dl

^ 2R^akIdI

V I'^R'l'^dlR R

= ^ (1 + 2a6) since R » R

I o

From the definition of n and the above equation

n^^ = ny(1 + 2a0).

For the NiCr alloys normally used in low-range TEs, a can be -1x10“'^ to

_ ji p -2x10 . 0 is usually about 1.5x10 at rated I. Thus n^ and nj^ can differ

by 3 to 6$. For alloys like Evanohm the difference is much smaller.

Thus the appropriate n should be measured and used. Since it enters

only in a difference term with this comparator, small errors in determining

it are not significant unless d-p-dg is large.

Appendix 1-4
E. Square Law Output and RMS Response

It is worth emphasizing that even if n*2, so that with K a constant, a TE inherently responds to the true rms current, I. This can be

shown easily for the simplest case in which all of the heater is at the same constant temperature, 9. Then, equating heat input and output at any

p instant, i R = K^0 = K

2

E . R, and K

2 are generally somewhat dependent on

e, but if the frequency of the heater current, i, is high enough, thermal

inertia keeps 6, and hence E constant. Then term by term integration with

respect to time, t, over one period, T, and division by T, gives, directly,

2

I R=K2E. Because of the temperature dependence of R and K

2 the output is not

2 exactly proportional to I , but it is still a measure of I, the rms current.

This can also be shown to be true under far more general conditions (see

appendix 3 of [ 1 ] )

.

Appendix I -5
rAm

' ^

',^ e,Jl ,#!i«t«^

mmik

f ^^SBeiwt S' riu*^ ; tue ,®1 o» iiiiwiS'^dsm *^lio»^

, >>*. Tv,

" ‘Veft^4i3?t<iC> »«< Ifti .rr»0;-

. - : ' ’ "?-

• -"^ ‘-^ —' ; ^l" »,i •

FsiJ% ,,

r .-iT -». _lM ;f

ttU < vI^T<jqS',
Appendix 2

EMI, Harmonics and DC Offset

A. Test for Line-Borne Electromagnetic Interference (EMI)

Only about 1 yW of heater power, over a wide range of frequency, can produce 0 .^% of rated emf in a typical 5-tnA TE. Thus TE*s are sensitive to

EMI, particularly at TV and FM frequencies. (They were the detectors in

early field-strength meters.) Laboratory leads at these frequencies can transfer radiated energy fairly efficiently to the heaters. Of course if the

leads are twisted or shielded they make very poor antennas. However

shielding is not completely effective, and in areas of high field strength

(up to 1 V/m in some areas) errors can result if the TE responds to currents

at both the main and interfering frequency.

However, because of their square-law characteristics (E=KI^ where I is

the rms current) a small heater current, Ig, at a different frequency than

the main current, does not cause as large an error as the ratio a=Ig/If„

might indicate.

If the response sensitivity is the same at both frequencies

E = KI^ = + a^j

Without Ig, E^ = Thus (e-Ejjj J/E^^

j = AE/Ej„ = a^. With only Ig present,

Eg = Klg^ so that Eg/Ep, = a^.

If a measurement of is desired, AE/E^j is an error term. It can be

evaluated to see if it is significant by making a measurement with all of the

connections in place but with the power supplies producing Ipj turned off.

Appendix 2-1
In the more general case K is somewhat dependent in E, so that the

sensitivity of this test is affected slightly. Also, if both TE’s in an ac-dc comparison respond equally well to currents at both frequencies, there

will be no EMI error. However the EMI test will determine this also.

In the MJTC comparator, RF bypass capacitors (of very low inductance)

are connected from each ungrounded lead to the metal tank to reduce the

possibility of EMI errors. The tank itself is an excellent shield.

B. Effect of Harmonics (see Section VII)

Small amounts of low-order harmonics in the input voltage generally

cause insignificant errors in the measurement of the rms value by a TVC, or

in the comparison of two TVC's. This is a great advantage for true

rms-measuring instruments. This can be shown rather simply for a wave having

a fundamental voltage, , and a single harmonic, Vj^. Then V=(Vi^+V^^)^^^.

Because of reactance, skin effect, etc., the response of the TVC may be

different at the two frequencies, so that E=kV^=k^ V^+k^Vj^^. Let Vj^/Vi = q and

Kh = Ki(l + e^). Then E = k-|V^(l + q^e^^ that the proportional error is

only q^e^.

For several harmonics this becomes Z Qm^®m» where m refers to the order

of the harmonic.

C. DC Offset

The above equations should apply even if the harmonic is of zero order

(dc). However if the TE has a dc reversal difference (which can be caused by

Thomson or Peltier heating) there is an added output, E-K^V^g, proportional

to the first power of any dc offset voltage, V^g, in the ac wave, Vg. Then

E = k(v ^ + V + K V = KV^(l + a os o os ^ E

Appendix 2-2
With a dc voltage, v^, equal to V applied and then reversed, the do

reversal difference in output is AE = 2KqV. Thus

where

g

E

and u Vos

V

Note that this is proportional to the 1st power of u, and that, for a square

law TE, g is twice the value of the proportional dc reversal difference as normally defined (AV/V for constant E).

Appendix 2-3
illllllHK^jK. ^

•‘ii/i ‘ .• > f% iri 10 1 V\Vfet)f*rtiWt) ^ Ifec^ * ’ r/pii^

in# *- -n.i f«iU“ «* t

'“ • -\,---!gP , '. tW' . , *gS2?» 1^’

i>

*'

'

' ' '0 jp(’ U5*

ja

##*• ror

« -'i

! ’> •!»»(?

, %i#9 »<' (!;•

‘ *-v i JB fM« r*»-<?#<i« ''‘'<\tV

oere n r%f»r ji fc<>

‘fl .•r^'.^V^Pil.* i%i>nto in.e t<?fji

V***#*./^* <«i»bion t*»fl *

.^' j? -'-.rM; J,

. |W tn« 49 *^V# ,*
Appendix 3

Effect of Relay Off-Time

Let the response, E, of a TE be approximated by a simple exponential

with a time constant, t^^. Then after the steady-state heater current is

turned off for a time tQ<<t^ (the off-time of the relay when switched), we have

E = Ej.e ° . Ej,(l - WtJ .

Thus AE = E^-E = Eft^/t^.

When the relay is closed (with the same heater current), E recovers to

Ej. exponentially, so that

-t /t

E = E^ - AE e

® °

where tg = t-t^. Then p =[Ef-E)/Ef = b/e^ where b = AE/Ej. = t^/t^ and

a = tg/t(j = t/t^ when tg>>tQ. If p = 1x10 (recovery to 1 ppm), tQ = MxlO"^ s, and t^=2 s, then b = 2x1 0~^ and a=5.3* Thus t = at^^ = 10.4 s.

Interestingly, when t^ = 4x10”^ s, t = 15.2 s to recover to 1 ppm, only

a modest increase for this 10-fold increase in off time.

Appendix 3-1
y*. ,, g^/t# ) eiiu > n<x^ W^fe'art'sJ _||%lOvj

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.

'

- - — - ^ - T'
Appendix 4

Effects of Bead Heating

A. Relative Effectiveness of Bead and Heater Power

Widdis has shown (equation 17 of [19]) that the midpoint temperature

rise,

0JJJ, of the heater of a TE carrying a current, I, taking into account

the heat loss through the thermocouple wires as well as the heater, to heat

p sinks at the ends (all at 0=0) is 0jjj = DS, /2M. Here the very small Peltier

p p and Thomson heating is neglected, D = I p/A K, p and K are the electrical

resistivity and thermal conductivity of the heater, A is the cross sectional

area and 2S, the length of the heater, and M = 1+K^/Kq, where is the sum of

the thermal conductances of the two thermocouple wires in parallel and Kq is

the sum of the conductances of the two halves of the heater.

Since kQ = 2KA/S, and 2pJ,/A = Rj^, the heater resistance, we find that

®ra 2(Kq+K^)

where

If the bead between the heater and the hot junction of the thermocuple

p has a resistance R^, its power dissipation is Pp=It) Rt). The added

temperature rise from this small heating is A0 = P^j/(K.|+Kq). Thus bead power

is twice as effective as heater power in raising the temperature of the hot

junction.

Appendix 4-1
B. AC-DC Difference Caused by Bead Heating

One end of the heater of a TVC is grounded, and the thermocouple circuit

is usually grounded also for safety and to keep the bead voltage low. Thus

half the heater voltage is across the bead. From the formula in section V-B

the significant current is through the ungrounded heater terminal. The

heater power is, to first order terms,

2 2

I, R. i/r.

p - -j—5 * -LJ! (, h 2 2

'

where

a 1

The temperature rise, with the effect of bead power included, is

0 = UP.+ 2UP. = UI.^R. (1-a) + 2Ua^I,^R.

h b 1 h 1b

where

U = 1/2(k^ + k^)

Thus

e = UI,\(1 - a * 2a\/R^) - UI,\

with no error from the bead current, to first order terms.

This will, of course, not be true if neither heater terminal is at

ground.

Appendix 4-2
C. Two TE's in Series

A similar but more involved analysis shows that if two equal

series-connected TE’s are used in a grounded TVC, the resultant output will

also be unaffected by the bead currents.

Appendix M-3
J
Appendix 5

Impedances and Substitution Corrections

Ingles has studied the general impedance relationships in TV's and the

effects of changing TE’s.[9] However the following alternative approach,

with its explicit treatment of phase defect angles, was developed at NBS. It

has been used very effectively for several purposes, and so is given here.

It is analogous to a much earlier unpublished NBS treatment of shunted TE's

for current measurements.

A. Impedance of a TVC

A TVC set with well-defined ac-dc characteristics (independent of the

surroundings) generally consists of a shielded TE in series with one of a group of three-terminal shielded resistors, as shown in fig. 1 of [2]. As

shown in section VI of [2], the ac-dc difference of a combination as a TVC

is, in the present notation, d^ = d^+d^, where d^ = (z^-R^)/R^ and

dc = (lha“^hd^^^hd* these expressions, = Vj^/Iy^, and is the magnitude

of the impedance of the combination, with an applied rms voltage V^^ and a resultant heater current Ij^. Ij^^ and I^^ are the magnitudes of the ac and dc

currents required to produce the same output emf

.

This is a very general equation, applicable for any series resistor and

TE combination. To evaluate the component impedances we may write as an identity

= (V. - V^]/I. + V, /I. = Z + Z, t ^ 1 h“^h hh s h

where V^ is the voltage across the heater. The bars signify either phasors

or complex numbers, and their absence signifies magnitudes.

Appendix 5-1
We may also write

Z /R - 1 + a + Jb and Z. /R. - 1 + c + je

s s n n

with a, b, c and e each much less than unity for a useful TVC. Rg and R^ are

the dc values. Then

S .

1 a * jb t p(i ^ c -> je) ^ ^

1 + P

I K

where p

= R^/Rs* 8 = (a + pc)/(l + p) and h = (b + pe)/(1 + p) . Note that

h = tan the phase defect angle in radians, closely enough, since g

and h are very small. Then to a sufficient approximation

^ - [l * 2g * h^]2i1/2 , h

= 1 + g

+ ~

and

When p ^ 1, h^/2 < 1 x 10"^ if b and e are each less than 1 mrad, so that the phase angle term is negligible. In this case

d^ = g, dg » a, and d^ = c

where dg = (Zg/Rg) - 1, d^ = (Z^/R^) - 1.

Appendix 5-2
B. Substitution Corrections (See Section IX)

Consider two different TE’s of the same nominal R^, each with a known d as a current converter, and a known d^^ as a voltage converter (with no series resistor). The difference in d^ of a TVC range with the same series

resistor, is, if all phase angles are negligible.

D. <

1

D. <

II 82 81 dc2 - dd = p(C2 - Ct)/( 1 + p) + dc2 ' dd .

But

p/(Up) = R^/r^ and C2

- ct = d^2 ” dh1 = (^^^2 “ ~ (^vhi “ dd )

.

Then

0v2

-

‘‘vl R ^^vh2 ^vhl ^ ^ R f^c2 ^c1 ^

' w U

Thus the substitution correction for any range is expressed in terms of

the directly measurable d's of the new and old TE’s as current and voltage

converters

.

If the phase angles are not negligible a term, h^^-h

2 ^, must be added.

This reduces to

2 2

h, -hj - pbCe^-e^) + - e^^)

(1 + p)^

Thus it is zero if ©2 ^ •

If b = 1x1

e^ and e

2

= 2x1 (as rather extreme examples) this

added phase angle correction is less than 1 ppm even at p=1 (low voltage

Appendix 5~3
range). It is much smaller for higher ranges, even if b is larger (as it may

be because of capacitive currents).

At NBS a commercial impedance comparator has been very convenient for

comparing phase angles to better than 1 mrad up to 100 kHz. It is used to screen the series resistors and TE heaters to make sure that their phase

angles are negligible.

C. Interchanged Series Resistors

As explained in section V, two nearly identical 30 V 3~terminal

resistors, and R

2

, of negligible phase angles, in separate coaxial

shields, are connected in series with two nearly identical TE*s. The

resulting TVC's are compared, to evaluate dQ^-dQ2 of the TE’s as current

converters. Then the resistors are interchanged and the comparison is

repeated to essentially eliminate inequalities in the magnitudes of the

reactances of the resistors. For the first measurement, with in series

with TE^ and R

2 in series with TE 2

,

S ^

a^ + pc^ - (a^ + pc^)

1 + p

+ d , - cl - cl c2

For the second measurement, with and R

2 interchanged

. * P=1 -

'^1 * PP2>

. . ^2 1 p

^01 ^02

A. + —2—r =2' *

''01 ‘*02 ‘’01 “o2-

t

since

P1+p

3 = 1- for the usual 0.5 V TE's,

Appendix
A more extended treatment, including the effects of phase angles, leads

to added terms in , ^

2

, e-| and 62* similar to those given in appendix 5B.

They are negligible if they do not exceed the limits given there.

D. AC-DC Difference of Series Resistor

For a given range of a TVC, from the equations of appendix 5A, with all

phase angles negligible,

d + pd, s h

Thus

R. R^

d = (1 +p)(d -d ) - pd. = — (d -d ) - — d, s

^ VC ^h R vc R h

s s

since dj^ = d^j^ - d,^, where d^j^ is the ac-dc difference of the TE as a TVC.

E. Effect of a Small Phase Difference Between the Paralleled Impedances in

the Current Build Up

The current through the single higher-range TE in the build-up is the

phasor sum of the currents through the two paralleled lower-range TEs. It

will differ from the sum of the magnitudes of the two currents, and I2, if

the two are not in phase.

For simplicity let = I-|40, I2 = 12-^ = I-i^e with 0<<1 (in radians).

The bar signifies a phasor quantity, and its absence a scalar. Since is

the reference,

1 =

1.^ ^2 " ^ ^ (cos0+jsine)

= 1 ^[[2 + d‘^/ 2 ] + j0] (neglecting higher order terms in 0)

Appendix 5-5
From this and by continuing to neglect terms in 6^ and higher

I = 21^(1 - e /8)

The proportional difference is

e = (21^ - I)/I = e /8 .

If e = 3x10”*^, 0 = 0.1x10”^ radians

are in parallel,

Since the two impedances, Z, and Z 2

,

l,/0 Z, /JD -

This will be true only if Z 2 Z^4-6. Thus the phase difference between Z^

and Z 2 must be less than Ixio"^ rad to keep the phase error less than about

0.3 ppm.

Appendix 5-6
Appendix 6

RECOMMENDATION

of the Working Group on the Statement of Uncertainties

presented to Comite International des Poids et Mesures

Assignment of experimental uncertainties

RECOMMENDATION INC-1 (1980)

1 . The uncertainty in the result of a measurement generally consists of

several components which may be grouped into two categories according to the

way in which their numerical value is estimated;

A - those which are evaluated by statistical methods,

B - those which are evaluated by other means.

There is not always a simple correspondence between the classification

into categories A or B and the previously used classification into ''random"

and "systematic" uncertainties. The term "systematic uncertainty" can be

misleading and should be avoided.

Any detailed report of the uncertainty should consist of a complete list

of the components, specifying for each the method used to obtain its numerical value.

2. The components in category A are characterized by the estimated

variances, Sj^^, (or the estimated "standard deviations" s^^) and the number of

degrees of freedom, Where appropriate, the estimated covariances should

be given.

3. The components in category B should be characterized by quantities Uj^,

which may be considered as approximations to the corresponding variances, the

existence of which is assumed. The quantities Uj^ may be treated like

Appendix 6-1
variances and the quantities Uj like standard deviations. Where appropriate,

the covariances should be treated in a similar way.

4. The combined uncertainty should be characterized by the numerical value

obtained by applying the usual method for the combination of variances. The

combined uncertainty and its components should be expressed in the form of

"standard deviations”.

5. If, for particular applications, it is necessary to multiply the com- bined uncertainty by a factor to obtain an overall uncertainty, the multiplying factor used must always be stated.

Appendix 6-2
rhermaI Converters for Audio-Frequency Voltage

Measurements of High Accuracy

F. L. HERMACH, fellow, ieee, and E. S. WILLIAMS

Abstract—The ac-dc diiferences of a reference group of thermoelements have been evaluated at audio frequencies to a few parts per

million (ppm) at currents from 5 to 20 mA. A technique for comparing

the ac-dc differences of two thermoelements with an uncertainty of about 2 ppm has been developed. Two 5 mA thermoelements are used with a plug-in set of resistors of computable reactances to form

thermal voltage converters for voltage measurements. With this same

technique adjacent ranges of these converters can be compared to step up from 0.5 to 500 V to better than 10 ppm.

I. Introduction

I

N PRINCIPLE, the current balances which have

been developed to determine the ampere in absolute measure with direct current could also be used with

alternating current. However, the most stable electrical

standards are still the dc standard cell, and 1 ohm resistors, which are not usually designed for ac use. Thus,

ac measurements of current and voltage have, in practice, been based on rms ac-dc transfer standards or comparators. For many decades these were electrodynamic or electrostatic instruments, designed to have the same torque constant with either alternating or direct current (or voltage) applied, making it easier to obtain

a wider frequency range than with instruments like the

current balance which must have a computable torque

constant. More recently, electrothermic instruments

such as thermocouple transfer standards and bolometer

or thermistor bridges have been used. All of these instruments have been highly developed in the national laboratories of several countries to make ac measurements

at audio frequencies to about 100 ppm in combination

with dc standards. The combination possesses a number

of advantages over ac potentiometers (which must also

include a transfer instrument), and over electronic and

other squaring circuits (which must have exact squarelaw characteristics in two quadrants).

Recent advances in operational amplifiers and inductive voltage dividers have made possible wide-range ac power sources with linearity and day-to-day stability

better than 100 ppm. This implies a need for better

accuracy in basic ac-dc transfer standards.

At this accuracy, conventional forms of electrodynamic transfer instruments are limited to power fre- quencies by the effects of inductive and capacitive reManuscript received June 23, 1966. This paper was presented at the 1966 Conference on Precision Electromagnetic Measurements,

Boulder, Colo. This work was supported in part by the Army Metrol- ogy and Calibration Center, I'raukford Arsenal, and the Metrology

Engineering Center, Bureau of .Naval Weapons, Pomona, Calif. The authors are with the Electrical Instruments Section, Electricity Division, National Bureau of Standards, Gaithersburg, Md.

actances in their coils, and electrostatic instruments

have a serious minimum-voltage limitation because of their low torque-weight ratio. Both would require new

means of sensing deflections to obtain precisions of 10

ppm or better. This could be done by measuring the

reactance, which is a function of the deflection of the

instrument. However, a major difficulty would remain —that of vibrations from external forces or from the

cyclic variations of the ac driving torque. Experience

has shown that it is often difficult to control spurious

torques caused by minor mechanical resonances. It is possible that floating the moving system in a liquid of the same density would minimize these difficulties. However, it has seemed to the authors that improved

thermal converters (thermocouple instruments) offer better promise of obtaining an ac-dc transfer accuracy

of 10 ppm or better, and considerable effort has been

concentrated on them over the past five years. This

paper may be considered as a progress report describing

the present group of reference thermoelements and coaxial thermal voltage converters, and the techniques

and equipment which have been developed to compare

them to a few ppm.

II. Thermal Converters

A thermoelement (TE), defined as the simplest type

of thermal converter [l], consists of a heater and ther- mocouple. In its usual form, the heater is a short,

straight wire suspended between two supporting leadin wires in an evacuated glass bulb. The hot junction

of a thermocouple is fastened to the midpoint of the

heater, and is electrically insulated from it with a small

bead. The thermocouple EMF (about 5 to 10 mV for a conventional TE at rated current)' is then a measure

of the heater current. For voltage measurements, a re- sistor is connected in series with the heater to form a thermal voltage converter [l]. At the National Bureau of Standards, fourteen I IN

form the present reference group for ac-dc differencr

Twelve of them (made by four different manufactunTs)

are of conventional design but with he.iters of Evanohm

or Karma (modified nickel-chromium alloys), wliith

have low thermoelectric effects.* 'I'hey were rhos<-n from

* The international system (SI ) of unit-, with its symlK<E i . usr.l m

this paper. Because of their frequent orriirrence, ihr word thrrm.<-lr. ment is abbreviated as TE and therm,il volt.igc converirr .is I \ ( m

this paper.

* Evanohm and Karma ;ire registererl tr,ldem.^rk^ «.f ihr W ill. ,t B. Driver Company and the Drivcr-I l.lrri^ (!om|i.inv. rcsjirr ii\r! , (See Acknowledgments.)
i; 'ft'''!!

•‘I

V

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E^ti'aspassawcSiSs^s?

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M-WtwwfcJ'tMil: m^lmmilk m^.-lim.,am:^d^mf^ •^ i AMUiiUMiBI

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vWdUHi^.
HER MACH AND WILLIAMS: THERMAL CONVERTERS FOR AF VOLTAGE MEASUREMENTS 261

larger groups on the basis of low dc reversal differences

and high bead resistances, and are all mounted in one aluminum enclosure lined with foamed plastic for thermal insulation. Each is supported by its heater

leads, which are soldered directly to binding posts

mounted on the low-loss phenolic top plate of the enclosure, and its thermocouple output leads, which are

soldered to two-pin connectors. The other two thermal

current converters are of a radically different design

having many thermocouples (40 or more) attached to a

bifilar (doubled-back) heater [2]. They were obtained

from their inventor, F. J. Wilkins of the National Physical Laboratory in England.

The fourteen TEs are identified in Table I, along

with certain pertinent characteristics, as well as the ac- dc differences assigned to them at audio frequencies as

a result of the tests to be described.

TABLE I Refurence Thermoelements

Rated Dc Approx. Bead Ad-dc differIcienti- re- heater resis- eiice (ppm)

fication

111“ EMF versaIf length ta licet niA mV ppm mm GQ 20 Hz 2 kHzll MM. 14* 20 25 <10 >1 0 0 MM. 15* 20 25 <10 — >1 0 0 A20E3 20 5 40 5 >1 0 0 A20F.6 20 5 60 5 >1 0 -1

A10E18 10 8 130 5 0.3 -f-6 + 1 A10E19 10 8 160 5 0.5 0 -1

WlOEl 10 7 200 8 0.6 + l +3

W10E2 10 7 <10 8 0.8 -2 0 H10E45 10 8 160 4 >1 -8 -2

A5E8 5 7 10 5 0.7 + 1 -f-1 A5E9 5 6 40 5 0.6 0 -1

F5K9 5 4 20 5 0.5 -3 -2

F5KL? 5 4 260 5 0.5 -2 0 B5E77 5 8 no 6 >1 +6 0

* These can be used at much higher currents.

t A/// for the same EMF.

j At 2 kHz and rated I.

II -Same value assigned at 20 kHz.

III. Thermal Voltage Converters (TVCs)

Each of a new set of TVCs developed at NBS for this work consists of one or more cylindrical metal-film re- sistors in a coaxial metal cylinder. The resistors can

be connected in series with one of two 5 mA TEs

mounted in separate cylinders so that the output EMF

is then a measure of the input voltage. Like an earlier

set developed at NBS [3], the effect of the reactance on the frequency response can be computed at least roughly from the simple geometry. Adjacent ranges of these TVCs may be compared with greater certainty

than those of the older design, which had integrally

mounted TEs.

As shown in Fig. 1, a single two-watt resistor is used

for each range below 200 V. The higher-voltage resistor units have two or more resistors in larger cylinders, with

two adjustable inner shields to control capacitance currents, as shown in Fig. 1, and have ports and baffles to permit the controlled flow of cooling air from the laboratory compressed-air supply.

Pertinent data on the TVCs, and the ac-dc differences

assigned to each range are given in Table II. The TVCs

are shown in Fig. 2.

IV. EMF Comparator

The ac-dc differences of a transfer instrument may be

defined as d= (X,- Xi)/Xi

where Xa and Xi are the magnitudes of the ac and dc

quantities that are required to give the same response

(such as deflection or output EMF) of the instrument.

(Normally, the average for the two directions of the dc

quantity gives the best measure of the dc reference.)

This is a useful definition, for the ac quantity for a

given response is then simply Xa = Xd{i + 8). As is well known, the instrument may be used as an ac-dc transfer

standard simply by observing the response with the ac quantity applied, then measuring (with external stan- dards) the average for the two dc quantities required to obtain the same response, thus avoiding many of the

limitations of an ordinary instrument.

At the National Bureau of Standards, TEs are evaluated in pairs with the EMF comparator shown in Fig. 3, to determine the differences in their ac-dc transfer

performance, i.e., 81 — 62 as defined previously. TVCs are connected in parallel and evaluated in the same way.

With the desired current or voltage applied, Ri and K2

are adjusted in a preliminary balance to obtain a near

null on the detector Di. Then, in regular succession,

alternating-, direct-, reversed direct-, and alternating- currents are applied to the TEs at nearly equal time

intervals and without changing Ri or R2. In each case, the current is adjusted to obtain the same output EM F, El of TEi, as indicated by an auxiliary Lindeck potentiometer {P with its detector D2), and the resulting deflections of Di are observed. Then, as shown in Appendix

1, the relative ac-dc difference is

61 — 82 = s{Da — Dj)

where Da and Dd are the averages of Di with alternating

and direct currents applied, respectively, fhe sensitivity factor s can be determined in one of several ways, as indicated in the Appendix, such as by changing tin- . ur rent in the heater of TE2 by a small known amount aiui observing the resulting deflection of D\.

The scciuence of readings, nearly ef|ually s|).n . d m

time, greatly reduces errors from drifts, temper,it lire changes, etc., in either TE and from either lonstant < i slowly changing thermal EMI's in the rompar.itor Tlie comparator accommodates any reasonable r.uig< oi thermocouple ICMFs, which need not be equal, .uul tiie small currents (up to 20 ^A) in the thermrx oujih- ( iri uit do not affect the measured values. With this circuit, small lluctu.itions in the suppl.

(heater) current do not appreciably rh.inge tin- d« il. tion if the two I’lCs have reason.ilily equ.il pro|K«rii »n il changes in EMF (AE/K), with .1 given < h.mge m h»'itrr current and reasonably erjual time const.ints .Milv
262 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT DECEMBER

c

Fig. 1. Essentials of thermal voltage converters (construction details not shown).

A Thermoelement unit, with 5 mA 100 Cl TE, for 0.5 V, in brass

cylinder, 4 cm long and 5.1 cm diameter, with brass end

plate D. B Low-voltage resistor unit (1 to 100 V) with one 2-watt metal

film resistor R in brass cylinder 11 cm long and 5.1 cm di- ameter. C High-voltage resistor unit (200-500 V) with multiple 2-watt

metal-film resistors, in brass cylinder 18 cm long and 6.4 cm

diameter with brass end plate D. Air inlet at I, outlet holes

at other end (not shown).

Si, S2 Inner brass shields 5.5 cm long, 5.1 cm diameter, connected

as shown, with no end plates. 52 can be moved parallel to

axis and locked in place. P Non-conducting air-baffle plate with holes. E Coaxial connector GR874. F Two-pin output connector AN lOSL.

it would be difficult to calculate the resultant “stabilization factor” of the circuit, in practice, fluctuations are much less than those observed when the output EMF

of each TE is balanced against a constant voltage

source, as in earlier comparators [4]. Thus, with this circuit and technique, TEs may be intercompared with an imprecision which is much less than the fluctuations

of the supplies used.

Ri consists of ten 100 Q resistors mounted on an en- closed-contact silver-alloy switch whose thermal EMFs

are much less than 0.1 when the wiper is stationary.

Rt is a 100 S2, 10-turn helical resistor of manganin,

with a manganin wiper to minimize thermal EMFs.

Detector Di consists of a commercially available primary galvanometer, incorporating photocells in an adjustable negative-feedback circuit, which serves as a current amplifier to a secondary galvanometer. The

scale factor of the combination is about 10 pA/mm,

and the input resistance (which is dependent on the

negative feedback) ranges from 200 to 3000 f2. The

primary galvanometer is liquid filled to reduce disturbances from mechanical shocks and vibrations and, with

its period of two seconds, is an excellent mechanical lowpass filter. A similar pair of galvanometers is used for D^. Both secondary light beams appear on one scale so that

the observer may quickly read the deflection of D\ if it

is stationary and if D7. is in the desired range. (Residual

TABLE II NBS “Model F” Thermal Voltage Converters

Range V

Resistors Total

«r (ppm)t

No.

kci (each) 2 kHz 20 kHz 50 kHz

0.5-A* none 0.1 + 1 + 1 + 15 0.5-B* none 0.1 -4 -2 + 11

1 1 0.1 0.2 -2 0 + 11 2 1 0.3 0.4 -3 -2 + 3

3 1 0.5 0.6 -1 0 + 3

5 1 0.9 1.0 -1 0 - 1 10 1 1.9 2.0 0 + 1 - 1 20 1 3.9 4.0 0 +1 - 1 30 1 6 6.1 + 1 +1 - 2 50 1 10 10 +1 0 - 4

100 1 20 20 + 1 0 - 7 200 4 40 40 + 1 0 - 7 300 6 90 60 + 1 0 - 3 500 8 200 100 + 1 -6 + 13

* TEs A and B as TVCs, without series resistors,

t Including 0.5 V TE. Re.sistors connected in series-parallel for higher ranges.

1 5r is the impedance error only (see text) computed from Table

III with either TE of pair #1. A similar table with the #2 pair differs from it by not more than 1 ppm at 2 and 20 kHz except at 0.5 V' range.

Fig. 2. Thermal voltage converters.

I

Fig. 3. Essentials of EMF comparator.
1966 HERMACH AND WILLIAMS: THERMAL CONVERTERS FOR AF VOLTAGE MEASUREMENTS 263

deriections of are less critical if the TEs are well

matched.)

All of the components of the comparator except the

detectors are mounted in a metal box behind a metal

panel to provide electrostatic shielding, and the box is lined with foamed plastic to reduce temperature fluctuations. The metal cases of the primary galvanometers are connected to this box by the shields of two-conductor

cables. With li\, and Ri at their midpoints and each of the

thermocouple inputs to the EMF comparator shortcircuited, peak-to-peak fluctuations in the secondary

galvanometer of D\ in periods of 10 seconds amount to 1 mm at the gain setting normally used. With 7 mV at

eacli thermocouple input, this corresponds to a value of

5i — 62 of 2 ppm. This is only about four times the calculated Johnson-noise value for this circuit. A comparison of two TEs (or TVCs) usually consists

of four or more determinations of 5i — 52by the method

described. Three times the standard error (standard deviation of the average) computed from a number of

typical series of such measurements is about 2 ppm.

This is a reasonable measure of the uncertainty in the

comparator. Comparisons of various pairs taken from

three TEs, with the TEs interchanged in the comparator

and with the EMF of first one TE and then the other

held constant in each sequence, have disclosed no systematic error as large as 1 ppm.^ These measurements were made with commercially available dc and ac voltage

sources, having peak-to-peak instabilities, observed with

a TVC in 10-second intervals, of about 10 and 20 ppm,

respectively, at 2 kHz.

A TVC can be used for ac measurements with appropriate dc standards by balancing its output EMF

against an adjustable stable voltage source such as the

potentiometer P. To reduce errors from drifts, a similar

sequence of ac and dc readings can be used, with the

setting of P fixed, and the direct voltage Vd preset and

accurately known. Then

Va = Vd[l + 8 + s(Da - Dd)]

where s, the sensitivity factor, is determined as before.

V. Comparisons of TEs

The fourteen reference TEs were compared, using

sinusoidal currents at frequencies of 20 Hz, and 2 and

20 kHz. All of these measurements (as well as the comparisons of TVCs) were made in a shielded room to reduce electromagnetic interference, which is particularly troublesome with TEs because of their high sensi- tivity and very wide frequency range. The step down

from one current to the next was made by connecting

’ If the net dc reversal difference of the two TKs is more than 300 ppm, an error is introduced by nonlinearities in Di. This can be mini- mized by taking determinations with first one and then the other TE

EMI' held coi\stant.

the heaters of two low-current TEs, a and h, in parallel

and their thermocouples in series aiding, and considering the combination as a single TE connected in the TEi

position of Fig. 3.^ As shown in Appendix II, if the

TEs are reasonably well matched, the ac-dc difference

of the parallel combination is simply 5p = (5a + 56)/2 to better than 1 ppm. From the test, 8p — 8i = Ki where

82 is the ac-dc difference of the high range TE in position

2, and Ki = s{Da — Dd). The two low-current TEs are then connected in series and compared to determine

K.2 — 8a — 8b- Thus, 8a~

K

i-\- 82~\~K2/2, and 8b = Ki-\-8i

-K2/2.

The network of comparisons at 2 kHz and the results are shown in Fig. 4. Here the circles identify individual

TEs and the rectangles represent a pair in parallel. The

arrows indicate comparisons, and the numbers on them

are the values of the relative ac-dc differences in ppm ;

i.e., the ac-dc difference of the TE at the point of the arrow is greater or less than that at the tail by the

amount shown. These tests have extended over a period

of three years during the development of this project;

in many cases, each number is the average of two or more tests, each consisting of four or more sequences

of ac-dc readings already described.®

As indicated by Wilkins, the ac-dc difference of the

two NPL TEs should, theoretically, be less than 1 ppm.

In tests at NBS at 20 mA, the two agreed to better than

0.2 ppm with a 3<r imprecision of 0.3 ppm.* Thus, it is reasonable as well as convenient to start with an assignment of zero ppm to the ac-dc differences of each. Then,

following principles given by Youden [S] in weighting

the various paths in a network, it is possible to calculate

the ac-dc differences of the other TEs. The resulting

values are given to the nearest ppm in each circle and

in Table I. The average for all of the conventional TEs is only — 0.3 ppm. Thus, these simple TEs agree with the more

complicated multijunction converters very closely, and

essentially the same values would have been obtained

for each TE on the alternative basis of assigning zero to the average of the entire group.

A complete but less redundant chain of measure- ments was carried out at 20 Hz to evaluate low-frequency errors of each 'FE. The precision was less at th.it frequency because of much larger instability in the .ic source. The results of the values assigned on the basis

of zero error for the NFL TICs are given in Fable I Not enough TEs were intercomjiarcd at 20 kH/ ti> assign independent values to each, l>craiis<- .i< d( <li(

* To minimi/.e certain alK-rratimis discus^-d m S*-. iion IX, rr 1 tors of at least five limes the heater re'>ist.iiuc were .aided i" r.n h •( the heaters before pjirallelini; them.

^ Beaiuse mejisurement-. were m.ide over .in i-xii iidnl iimr o' develoniii}; program, the network is not svmmelrii.il

* The I'bME was higher anri .1 highc-r <li-ic-< tor 'ensitivit-. > ..uid lo- used than with other 1 I-.s sinrx; the two I I'.s m-ie well m.ii< hr-,1. that an extraordinarily high precision w.is .itt.iinrsl
264 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT DECEMBER

Fig. 4. Intercomparisons of NBS TEs, and assigned ac-dc

differences in ppm at 2 kHz.

ferences from all known sources [3] should be the same

as at 2 kHz within 1 ppm. No measured values at the

two frequencies differed by more than 2 ppm. Thus, the same values were assigned to each TE at the higher fre- quency.

VI. Comparisons of TVCs

The TVCs were designed so that adjacent ranges

could be compared to step up and down the voltage

scale. Their nearly identical 5 mA TEs were each first compared with one of the reference group of TEs as current converters, i.e., with the heaters connected in series.They were then paralleled through a“T” connector

and compared with each other as voltage converters

(basic range 0.5 V). The lowest resistor (see Table 2) was then connected in series with one TE, say TEo,

to make a one-volt TVC. This was connected in parallel

with the other, TEt, and compared at 0.5 volt. A twovolt TVC was then formed with the next resistor and

TEb, and compared with the one-volt TVC at 1 V. This

process was continued until the highest range was

reached. If the ac-dc difference of each combination is independent of the voltage level, the ac-dc difference of any range may be found in terms of one as a reference.

This requirement is easily met if the TEs have no significant errors, for the reactance errors of each resistor unit

should be independent of voltage. The validity of this assumption itself can easily be verified by making each

comparison at two voltage levels.

If we define Z«= E,7/„ for a TVC, where 7,- is the

magnitude of the applied voltage and lo 'is the magnitude

of the current through the TE, then, from the definition

for ac-dc difference, applied to a TVC,

where the subscripts a and d refer to alternating and

direct current (or voltage). Since ha and hd produce

equal output EMFs, Ioa = hdil +h)- If we let we get, if second-order terms are negligible, = Thus, 6, can be determined if dr can be deduced from the comparisons of adjacent ranges, since

do can be evaluated in terms of the reference group of TEs.

Two complete sets of adjacent-range comparisons

from 0.5 to 500 V were carried out at frequencies of 2, 20, and 50 kHz, with two different pairs of 5 mA TEs.

These TEs had 80Ni20Cr heaters but were otherwise

similar to those in the reference group. Measured values

of d as current converters were — 1 or —2 ppm, except at 20 Hz where they ranged from —6 to —9 ppm.^ The

results of the adjacent-range tests given in Table III showed excellent precision. In addition, the inter-range

differences were less than 2 ppm through 20 kHz, except

for the lowest and highest ranges. The differences of a few ppm observed on the lowest ranges were rather

puzzling and will be discussed in Section IX. They

were essentially independent of frequency through 20

kHz but were negligible above the 1 volt range.

TABLE III Comparisons of Thermal Voltage Converters

TVC 1 TVC 2 Voltage

V

5i — Sj in ppm

2 kHz 20 kHz 50 kHz

#1* m #1 *2 n #2 A B 0.5 +2

B A 0.5 -3 -3 -4 -3 -4 -4

1-B A 0.5 +2 0 -2

1-A B 0.5 +2 +2 + 1 0 +3

2-B 1-A 1 -1 -2 -1 -8 -4

3-A 2-B 2 +2 +2 + 1 0 -1

5-B 3-A 3 0 0 0 -4 0 10-A 5-B 5 + 1 + 1 + 1 0 0 -2

20-B 10-A 10 0 0 -H 0 -1

30-A 20-B 20 -fl 0 0 -1 0 50-B 30-A 30 0 -1 0 -2 0 100-A SO-B 50 0 0 0 -3 -2

200-B 100-A 100 0 + 1 0 -1 0 +4

300-A 200-B 200 0 0 0 +4 +6

500-B 300-A 300 0 -6 -5 + 16 +8

* Test #1 —With one pair of .5 mA, 100 ohm TEs.

t Test §2—With another pair of 5 mA, 100 ohm TEs. These tests were made three months after those with pair #1.

Except for this, the results of the comparisons are in excellent agreement with computed values (see Section

VHI), which show that 5, should be less than 1 ppm

through the 100 V range. It is extremely unlikely that

any single source or combination of sources of ac-dc

difference should produce the same 5r in each of these

ranges. Thus, the authors believe that, from the con- cordance of theory and experiment, it is safe to assign zero ppm to the average of the values of dr from the 2 V

Via - Via

Vi,

ha^l hd^l

IodJ^l

’’ 'I'liese Tl'2s, which were the only ones available at the time with

the correct heater resistaiic-e, will be repl.iced by others.
1966 HERMACH AND WILLIAMS: THERMAL CONVERTERS FOR AF VOLTAGE MEASUREMENTS 265

through the 100 V ranges in establishing the values given

in Table II from the comparisons of Table III. The comparisons at 50 kHz (which were less precise) were made to verify that ac-dc differences were not

sharply dependent on frequency at 20 kHz. They indi- cate that excellent accuracy should be expected for most

ranges at even higher frequencies.

A complete set of measurements at 75 percent of rated voltage was also made at 2 kHz with TE pair

§\ in order to investigate voltage coefficients. These

results agreed with the rated-voltage measurements to

1 ppm, with no systematic difference.

A completely independent verification of the accuracy

of these reference TVCs has come from some careful

comparisons by Flach and Marzetta [S] of a “time-gate”

peak ac-to-dc voltage comparator (designed by Marzetta) with an rms comparator which incorporated a TV’C that had been calibrated with the reference set. In a long series of tests at 400 and 1000 Hz, where the

error in the comparison introduced by distortion of the

ac source was less than 10 ppm, the two comparators

agreed on the average to 4 and 8 ppm, respectively, at

the two frequencies.

VII. Thermoelectric Errors

Hermach’s treatment of the ac-dc errors arising from

Thomson effects in the heater of a conventional TE [4]

has been extended by Widdis [6] to include the effects

of Peltier heating, and to correct for the heat abstracted

by the thermocouple. Widdis’ expression for the Thomson ac-dc difference, dt^ocW/llpk, is the same as that

found by Hermach for high-range TEs, where a, p, and

k are, respectively, the Thomson coefficient, electrical

resistivity, and thermal conductivity of the heater

alloy, and B is the midpoint temperature rise (100°C to 150°C in a conventional TE). The error can thus be

computed reasonably well if a. can be determined. The

Thomson heating of copper is reasonably well known

[7], and is not much affected by moderate temperature

elevations or by the cold working of ordinary handling.

Thus, this metal can serve as a practical reference. The

authors have calculated the Seebeck and the absolute

Thomson coefficients of a number of pertinent alloys

from careful measurements of the EMF vs. temperature

of thermocouples formed from each of these alloys and

copper. The results are shown in Table IV, along with

the calculated ac-dc difference (using Widdis’ for- mula) in a TE having midpoint heater temperature rise of 150°C (giving a 10 mV output with a typical NiCrconstantan thermocouple). With Evanohm or Karma,

bt should not exceed 1 ppm. At an output of 5 mV it should be less than 1 ppm, since both B and a are

smaller.

Additional measurements indicated that the thermoelectric coefficients may be sensitive to cold working

and may be changed by exposure to high temperature.

For Evanohm and Karma significant changes were obTABLE IV

Thermoelectric Data and Errors

Metal

or Alloy

a, AiV/°C*

at 400°K

5

/xvrc

Calculated E Dc

reversal** A///, ppm

,rrorinaTE||

Ac-dc

difference

&i, ppm

Copper -2.0 — —

Evanohm -1.5 -1-0. 3t 200 -1

Karma -1.0 -H.8 150 <1

Manganin -3.0J -1.8t 400 -4

80Ni20Cr -3.9 -F4.4 500 -7

60Nil6Cr24Fe -2.3 -1-0.8 300 -2

* a (Thomson coefficient) is proportional to the absolute temperature.

t 5 is Seebeck coefficient vs. copper.

j This was quite dependent on heat treatment.

II From Thomson heating, with 0 = 15O°C and pk = 25 X

10-6 yi/°c at^K)0°K, the weighted average temperature of the heater.

** With the bead off center (see text).

served at 800°C, but not at 400°C. Thus, care must be

taken in controlling the temperature of the wire near welded joints and when out-gassing during the construction of TEs. Here the use of TEs in the reference group

by four different manufacturers having differing techniques provided powerful assurance against unknown

errors. As indicated by Wilkins, the thermoelectric errors are greatly reduced in the NPL TEs because of the bifilar heater and the low temperature rise (about 10°C at 20

mA in the present TEs). The resulting error should be

much less than 1 ppm, even with nickel-chromium

heaters.

Rather unfortunately, commercial TEs have lead-in

wires (see Fig. 1), through the glass bulb to the heater,

of a copper-coated nickel alloy to match the thermal

expansion coefficient of the glass. The combination has

a rather uncertain but fairly large Seebeck coefficient

vs. the heater alloys used. With direct current applied,

Peltier heating and cooling of the junctions of these leadin wires and the heater can cause a temperature differ- ence (-f- at one junction and — at the other). Most of this heat is conducted by the lead-in to the thick glass press or disk which forms the base of the glass bulb. This can be considered as a “heat sink” so that the first-ordi-r junction temperature change is AB=TIS/K, where /'

is the absolute temperature, I is the current, .S’ is the

Seebeck coefficient, and K is the thermal condiu t-me

of the lead-in. Widdis showed that this leads to an m- d. difference term d,p = oM/ where a is the Thom-.;

coefficient and Vh is the heater voltage. 'I here m . . n addition, be a second-order term at the mi(l|>oint cause the Peltier heat itself depends on the jam in •' temperature. This can be calculated by rarr\ ing out t .<• second-order approximation mentioned by Hern. ,. !>, Appendix 2 of reference [4] to give, with re4,<,nMr

accuracy, 5p= +A6^/T(fi, where To is the he.it sink tr. perature. Of course, AB can he ralrnl.ited onl v<

- roughly, but this is sufficient. I'or a tyjiii al 10 n \ I

*
266 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT DECEMBER

it is less than 0.01°C, and the Peltier errors, Btp and 8p

(independent of frequency), are less than 1 ppm. This

has been verified by comparisons with Evanohm-heater

TEs which had copper lead-in wires butt-welded to the

nickel alloy wires at the glass press. However, 8p in particular could be significant in higher-range TEs.

VIII. Low- AND High-Frequency Errors

As the frequency is lowered, the temperature of a TE begins to follow the cyclic fluctuations of the square

of the heater current. If the TE is not a linear device,

the average temperature rise may no longer be the same

as at higher frequencies. Hermach’s solution of the re- sulting nonlinear differential equation for the temperature rise has been verified experimentally [4], at least

for high-range TEs having large heaters in which the

heat abstracted by the thermocouple is negligible. However, for the low range TEs we are concerned with now,

these formulas may not apply. The solutions for such

cases would be even more difficult, and have not been

attempted, particularly since the thermal mass of the

bead should then also be considered. In the simpler

case, Hermach showed that the ac-dc difference is

8i = hdd^/o}H*, where d is the diffusivity of the heater

alloy, 21 is the heater length, co = 27t/, where / is the fre- quency, and h IS 3. factor expressing the nonlinearities.

The same relationship might be expected for the more

complicated case, but with a different numerical factor. Thus, the agreement to better than 10 ppm among the

TEs at 20 Hz, shown in Table I, with their varying

lengths, gives strong verification to the absence of significant low-frequency errors down to this frequency.

These reference TEs have heaters less than 1 by 10~®

cm in diameter, with resistivities of 120 /xft cm. The

computed errors from skin effect are much less than 1 ppm even at 50 kHz. The ac and dc conductances and

the capacitance between binding posts on the phenolic

top of the box in which the TEs are mounted are much

less than the limiting values of 0.01 nA/V and 100 pF,

respectively, which might cause 1 ppm errors at audio

frequencies.

Reactance and skin-effect errors in the resistor units

of the TVCs, computed according to formulas developed

by the authors [3], are also less than 1 ppm through 50

kHz up through the 100 volt range, and the comparisons

verify this. They cannot easily be calculated for the

higher ranges, which have several resistors and adjustable inner shields. Additional reactance errors can arise from the lumped capacitance C of the connector between the resistor and the TE. This shunts the heater,

which at these frequencies can be considered as a lumped

resistor R in series with an equivalent lumped in- ductance L. It can be shown that the resultant effect of

this capacitance on the magnitude of the heater current approaches cv^/2— a/3 as the series resistance (voltage

range) is increased, where a = wCR and & = wL/R

(a and /3«1). The computed error of less than 1 ppm at 50 kllz has been verified by deliberately doiil)ling the

capacitance.

IX. Other Errors

Peltier effects at the heater and lead-in junctions can

also cause a second-order change in the effective dc re- sistance of a TE. The calculation is difficult and the re- sults uncertain, but the change should be much less than one ppm for the 5 to 20 mA TEs in the NBS reference

group. Thus, this cannot account for the somewhat

larger changes in effective dc resistance implied by the

voltage comparisons of the TEs alone (without series

resistors) in the TVCs. Even larger and more puzzling

changes have been observed in some other TEs. There is good evidence that they may be caused by rectification at oxide films, which may persist in spite of the welded

joints, but there is as yet no direct proof of this. Dc reversal errors (A/// for the same EMF) provide a good clue in studying these secondary effects. As shown

in Table IV, A/// calculated by Widdis’ formulas

should not exceed, perhaps, 200 ppm with Evanohm or Karma, and 500 ppm with nickel-chromium heaters, even if the thermocouple is mounted off the midpoint by

5 percent of the length of the heater (which is easily

noticeable). Larger differences are, thus, a sign of other

difficulties. As Hermach showed [4], the current from the heater

to ground through the bead of an ungrounded TE can

cause heating of the bead and, thus, an error. This is difficult to compute because power dissipated in the

bead is somewhat more effective in raising the thermocouple temperature than that in the heater, and the cur- rents in the two halves of the heater are no longer identical. However, rough calculations indicate that with one

volt across the bead of TE2 in the circuit of Fig. 3, the

bead resistance of a 10 mA TE must be greater than 500

megohms if the error is to be less than 1 ppm. For the

bead materials commonly used, the resistance is a sharp

function of temperature and is much less at audio fre- quencies than with direct current. At NBS, bead re- sistances are normally measured with a 2 kHz ac bridge

with rated direct current through the heater of a TE.

The results have been verified (within a factor of 2) by

ac-dc comparisons of pairs of TEs with added resistance

between the two heaters to significantly increase the

bead voltage.

X. Conclusions

A reference group of two very different kinds of TEs

has been established. The authors believe that it is very

unlikely that the average ac-dc difference of the group

differs from zero by more than 2 ppm at audio fre- quencies. This is based on the agreement to better than

0.5 ppm of the averages of the two kinds of TEs, and on

allowance of 1 ppm for the uncertainly of the average

in the network of comparisons. The results are in excel- lent agreement with calculations, which show that the

ac-dc differences should not exceed 1 ppm. W ith the

precise techniques that have been developed, pairs ot TEs of the groiq) ma\' be compared with a 3cr uncer- tainty of about 2 ppm without any evidence to date

(in over three ye.irs of measurements) of significant
1966 HER MACH AND WILLIAMS. THERMAL CONVERTERS FOR AF VOLTAGE MEASUREMENTS 267

systematic errors. This is somewhat remarkable, since

fluctuations in the best available wide-range ac and dc

sources greatly exceed this, and most of these TEs have

rather large residual thermal EMFs and have temperature coefficients of EMF exceeding 1000 ppm/°C.

Adjacent ranges of the TVCs may also be compared

with the same precision to step up and down the voltage

scale, fheir ac-dc differences can be determined to better than 10 ppm when used with TEs of known ac-dc

differences, again without evidence of systematic error. .Alternating voltage measurements can be made to 20

ppm or better by using the TVCs or ac-dc transfer

standards with appropriate dc standards.

'I'his accuracy and precision in the ac-dc transfer, more than ten times better than heretofore available, are good indications of the virtue of simplicity in refer- ence standards. Properly designed and constructed TEs

are rather simple devices that correspond to the desired

idealized mathematical models remarkably closely, thus

providing the agreement between theory and experiment which is so desirable in a development such as this. The agreement to better than 1 ppm between the conventional TEs and the new very different multijunction

NPL TEs (which should theoretically have smaller errors), in addition to providing semi-independent verifi- cation of the accuracy of both, indicates that even

higher accuracy may be possible in the future with these new designs. Conventional single-j unction TEs could

be improved by the use of bifilar heaters and closely

spaced lead-in wires with good thermal conductance

between the two halves of the heater and between the

two lead-ins. In this way, other heater alloys could be

used.

Well-designed and well-constructed ac-dc transfer

standards can be remarkably stable over most of their

frequency range. Most factors which may change the

response, such as temperature and dimensional changes,

have little or no effect on the ac-dc difference. There is already some evidence that long-time stabilities of a few

ppm can be attained in properly designed and constructed TEs and TVCs. However, we have noted an

apparently abrupt change of -f 5 ppm in one TE, ac- companied by a change of over 100 ppm in its dc reversal

difference. Thus, TEs should be compared frequently if the highest accuracy is desired.

Comparisons of adjacent ranges, with a step-up pro- cedure such as the one described, can be used to guard

against unexpected changes in TVCs. This has already

been verified in the design and construction of two some- what similar sets of TVCs by W. Scott, K. Ballard, and

D. Bailey of the NBS Electronic Calibration Center,

Boulder, Colo. These units incorporate large wirewound resistors of controllable reactances and low temperature coefficients, so that they do not require trouble- some forced-air cooling. They will be described else- where.

The step-up procedure is also feasible with simpler

sets of TVCs incorporating fewer plug-in resistor units

and two TEs of different current ranges. Two such sets have been built but have yet to be completely evaluated.

Appendix I EMF Comparator

If the thermocouple resistance Rn of TEi (Fig. 3) is much less than Ri-\-R2, the EMF Ei is substantially the same with alternating and direct currents applied during

the test (the procedure involves holding the voltage at the output terminals of TEi constant). Then, from the

definition of ac-dc difference, {Ia — h)/Id = h- Similarly,

for TE2 {la — Id) /Id = hi, where Id is the direct current

that would be required to produce the same EMF of

TE2 as la- The change Da —Rd in detector D\ which

occurs when I is changed from to Id {Id being adjusted to keep El constant) results from the change in El- Da — Dd may then be interpreted as a measure of the

departure of Id from the value Id which would have

produced the same Ei as would E- Thus, combining the

above two equations and neglecting second-order terms, we have {Id —Id)/Id = 8i — 8i. The sensitivity of the detector to small current dif- ferences in TE2 can be determined by shunting its heater Rh with a resistor R.'^Rh to cause a small change

in its heater current A/, noting the change in deflection

AD of Di and computing s = AI/IAD {AI/I = Rh/R, if the heater current of TEi is unchanged). Then, if 5 is constant over the range of deflections involved, we have

8i — 8i = s{Da —Dd), as in the text. Similarly, in the comparison of two voltage converters, a resistor can be added in series with TVC2 to give proportional change

in applied voltage A F/ F = where Rm is the T\’C

resistance. Then s = AV/VAD.

These two calibration methods must leave the current

in TEi unchanged. The change AI can often be introduced and measured more conveniently in some wa\'

(as by changing the supply voltage) that changes the current in both TEs by a small known amount. We have

found it convenient to disconnect Ei, set the voltage of P to the same value, short Di, observe the resulting AD

when I is changed, and compute 5 as before.

If only a few TEs are ordinarily used in the “stan- dard” position (TE2 in Fig. 3), it is convenient to make

use of the approximate output-input relation (at a fi.\>-d frequency) for a TE, AE/E = nAI/I, where n is depcn

dent on I but not AI if A/«/, and is close to 2. I'or eai h such TE, n can be determined in advance at m-vit d

values of E and plotted vs. E, since it is (piite st.ihU- Then the sensitivity of the detector in the circ uit . .111 b. determined by inserting a small known voltauc Ah „

/• (with a Lindeck potentiometer, not shown in 1 ly, ' n: series with and opposing Ei, observing tin- rli.m.- A ‘

in Di and computing the factor k=AD/AE„. rh< n, Ir- this and the previous equations 61 hi !! h

= {Ed' — Ed)/niEi = {D„ — Dd)/kniEi. hi is sured with potentiometer P.

If Rti is not negligible, E\ is not lonst.mt di, nr.. test, since the currents in Ri and Ri depend •n t >t and El. The corresponding equations for detei-;

hi — 81 by means of deflections of D\ then tiiiit m. k|<:

tional correction terms involving the n sistan<i 'd t several parts of the EMF comparator, and .»r*- i. . .
268 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT

plex to be useful for routine measurements. They show,

however, that if (i^i+-R2 )/ 100 , the simplified equations already derived are valid to a few percent of the

computed di — 82 . They show that Rt2 is not critical. For

our comparator, i?x+i?2 = 1100 Q and i?ti<10 for the

usual TEs.

For each NPL converter, i?t«1000 Q. It is always

placed in the TE2 position, except when the two NPL

converters are intercompared, requiring the use of the more complicated formula.

Appendix II T^Es IN Parallel

By using the definitions for n and 5 of a TE (see

Appendix I) we have, closely enough for small changes

in E,

Ea — Ed la — Id = 5. nEd Id

In the ac-dc test, nominally equal resistors are con- nected in series with TE„ and TE^, and the two branches

are connected in parallel. The sum of the two EMFs,

Ea-\-Eb, is held constant. Then, with second subscripts

to identity the two TEs, we have

Eaa + Eab ~ Eda ~ Edb = 0

If the reactances of the two paths are not equal, additional terms will be introduced which are difficult to

calculate. However, they are zero if n<,m = ni,(l — w),

i.e., if the TEs are matched in response. Then Bp = {Ba+Bb)/2. Even if the reactances are unequal, the

added terms are essentially eliminated if a second test

is made with the two resistors interchanged and the

results averaged.

Acknowledgment

The authors express their appreciation and thanks to

F. J. Wilkins for the two multijunction TEs, to L. Julie

of the Julie Research Laboratories for suggesting the

basic idea of the EMF comparator, and to the following

for their cooperation in the manufacture of other TEs

used in this group: the Levy brothers of the American

Thermoelectric Company, L. R. Graham of Graham

Associates, F. Gay of the Best Products Company,

M. Rosenfield of the former Field Electrical Instrument

Company, and L. W. Pignolet of Weston Instruments

Incorporated.

The use of these particular TEs with heaters of Evanohm and Karma should not in any way be construed as constituting an exclusive endorsement by NBS of these

products or alloys. Other TEs, made to the same specifications with the same or other alloys of equally low

thermoelectric effects, should be equally suitable.

and References

/1aa Ida\ (lab Idb\ “ \~ir~) )= HaEaSa "f" HbEbBb

If the reactances of the two paths are equal

laa Ida lab Idb

Ida Idb

where la and Id are the sums of the alternating and

direct currents in the two branches.

If Ea = mE and Eb = {\—m)E,

[woW + Wb(l — m)] = natnba + « 6(1 — m)hb.

[1] “American standard requirements for electrical indicating instru- ments.” New York: American Standards Association, C.39.1,

1964.

[2] F. J. Wilkins et al., “Multijunction thermal converter,” Proc. lEE {London), vol. 112, pp. 794-806, April 1965.

[3] F. L. Hermach and E. S. Williams, “Thermal voltage converters

for accurate voltage measurements to 30 megacycles per second,”

Trans. AIEE (Communication and Electronics), vol. 79, pt. I, pp. 200-206, July 1960.

[4] F. L. Hermach, “Thermal converters as ac-dc transfer standards

for current and voltage measurements at audio frequencies,”

J, Res. NBS, vol. 48, pp. 121-138, February 1952.

[5] W. J. Youden, “Measurement agreement comparisons,” Proc. 1962 Standards Laboratories Conf. Washington, D. C.: NBS,

Mi.sc. Pub. 248, August 16, 1963, pp. 147-152.

[6] F. C. Widdis, “The theory of Peltier and Thomson effects in thermal ac-dc transfer devices,” Proc. lEE (London), Monograph

497M, January 1962.

[7] Landolt-Bornstein, “Zahlenwerte und Funktionen aus Physik,

Chemie, Astronomic, Geophysik und Technik,” 6. Auf., Band II/6, (6th ed. vol. 2, pt. 6). Berlin: Springer-Verlag, 1959.

[8] D. Flach and L. A. Marzetta, “Calibration of peak a-c to d-c comparators,” Proc. 1965 ISA Conf., pt. 1, vol. 20, paper 14.
JOURNAL OF RESEARCH of the National Bureau of Standards — C. Engineering and Instrumentation

Vol. 75C, Nos. 3 and 4, July-December 1971 Thermal Voltage Converters and Comparator for Very

Accurate AC Voltage Measurements

E. S. Williams

Institute for Basic Standords, National Bureau of Standards, Washington, D.C. 20234

(July 22, 1971)

A new fourteen-range set of thermal voltage converters and a thermoelement comparator are used

to measure ac-dc difference, and a-c voltages relative to etctemal d-c standards, with 20 ppm (parts- per-miUion) accuracy at audio frequencies. The imprecision is less than 2 ppm. Corrections relative to the very stable middle ranges can be redetermined for every range by a seven-step intercomparison of certain adjacent ranges.

Key words: AC-DC difference; comparator; thermoelement; transfer voltmeter; voltage measurements.

1. Introduction

An a-c' voltage at audio frequencies is measured

most accurately at the present time by using a thermal

voltage converter (TVC) to compare it with a stable

and accurately measured d-c voltage, which is nominally equal to it. The basic d-c standards are then,

in effect, “transferred” to the a-c measurement. The

TVC may be simply a thermoelement (TE) in series

with an appropriate multiplier resistor. The output

emf of the TE is ordinarily monitored with a null detector and a balancing circuit, which may be a Lindeck potentiometer. A balancing circuit and a null detector are included in most commercial multirange models.

Before the TVC is used for a-c voltage measurements

it must be tested for ac-dc difference or frequency in- fluence so that corrections may be applied. The set of TVCs and the new TE comparator described in

this paper were developed primarily for making these

tests. However they may also be used for a-c voltage

measurements as explained in section 9. For ac-dc

difference measurements the TE comparator, whose

read out instrument may be either a nanovoltmeter or a galvanometer, provides a considerable advantage over

other methods in overcoming the difficulties caused

by power supply instability and inexact voltage control. The 14-range set of TVCs (designated No. 7) consists

of six resistor units and two TEs, and extends from 1 to 1000 V. The TEs are rated at 2.5 and 5.0 mA, and each

one may be attached to any one of the resistors by a

coaxial connector (see fig. 1). This permits each resistor

to be used for two voltage ranges, as shown in table

1. Certain adjacent ranges of the set can be inter- compared, and the ac-dc differences of all the ranges

can be determined relative to any one range. This

set is otherwise similar to an earlier set [IJ^, which

consisted of two 5-mA TEs and 12 series resistors,

and covered a range from 0.5 to 5(X) V. The earlier set, designated No. 1, has been extended to KXX) V with one additional resistor as part of the present project.

It is evaluated in a 14-step intercomparison in which

each range is compared, at reduced voltage, with the next lower one. In a well designed TVC the ac-dc difference is not affected by changes in the applied voltage. Therefore, an ac-dc difference determined for the 100-V range at 60 V can be applied as a correction when this resistor

is used at 200 V to test the nominal 3(X)-V range of the next higher resistor. Experience has shown this stepup procedure to be feasible. However if the higher volt- age ranges are not carefully built the ac-dc differences can change due to self-heating effects to be described

later.

2. Design and Construction

The two TEs are mounted in 2-in brass tubes

(see figs. 1 and 2, upper right) with coaxial connectors

for attaching to a resistor. The 2.5 mA-TE has a 400 fl heater and is used alone as the 1-V range. The 5 mA-TE

has a 125 fi heater and a 275 fi resistor is added inside

its enclosure to make a 400 fi, 2-V range. The middle ranges (six ranges, 3 to 60 \ ) make ii>e of three resistors — 0.8 kfi, 3.6 kli, and 12 kli (see table 1). Each of these is a 2W metal-film resistor mounted coaxially in a 3-in brass cylinder 4 1/2 in long with coaxial connectors at each end.

' Figures in brackets indicate the literature references on p«ge |.V\

145
Figure 1. New set ofthermal voltage converters. The simple symmetrical geometry of these units

permits approximate calculations of their reactances

[2]. The calculations are inexact because of the nec- essary assumptions as to end-effects, and they neglect

any small residual reactances of the resistors themselves. They do indicate however, that the frequency

error of each resistor unit (without the TE) should be

less tharr 1 ppm at 50 kHz, even for tubes smaller than

2 in in diameter. (The 3-in tube was chosen for the

higher ranges where more space is necessary and was

therefore used for the middle ranges also.) The higher voltage ranges have larger resistor as- semblies to avoid excessive temperature rise. The

100-200 V unit has a 40 kfl spiraled metal-film resistor

five inches long.* The 300-600 and 500-1000 V units

have resistors of tin oxide deposited on a 0.81-in glass

tube 6 in long. A small voltage coefficient was antici- pated in these resistors, but measurements have shown

it to be negligible.

‘This experimental resistor is not ordinarily available commercially. Four 40 kO metal

film resistors in series-parallel can also be satisfactory.

Table 1. NBS thermal voltage converter set No. 7

Fourteen voltage ranges (column 2) are formed with six series

resistors and two TEs (F 1 and F 2).

Series

resistor Voltage range TE Total resistance m mA kCl

1 2.5 (FI) 0.4 2 5.0 (F 2) 0.4 3 2.5 1.2 0.8 6 5.0 1.2 10 2.5 4.0

3.6 20 5.0 4.0 30 2.5 12.4 12 60 5.0 12.4 100 2.5 40.4 40 200 5.0 40.4 300 2.5 120.4 120 600 5.0 120.4

,300 2.5 200.4 200 1000 5.0 200.4

Errors in these ranges are caused mainly by capacitance between the resistor assembly and the outer

casing, which permits alternating current to bypass

the TE to ground. Therefore more a-c than d-c voltage

is required for a given TE output. Frequency compensation could be provided by placing relatively small

capacitors in paraUel with part of the resistance.

However, such capacitors probably would not be suf- ficiently stable over a long period of time and might

be affected by temperature changes which occur in the

resistor enclosure.

Compensation was therefore provided (as in the

earlier set No. 1) with an inner shield which is con- nected to the input and surrounds the high- or inputend of the resistor (see “S” in fig. 2). The shield is positioned, relative to the resistor, to control the capacitance currents and provide optimum high-frequency

Figure 2. Essentials of thermal voltage converters.

Thermoelement (TE) enclosure, low voltage unit with resistor (R), and high voltage

unit (100 to 1000 V) with resistor (R) and frequency compensation shield (S). 146
rnmpensation; perfect compensation is possible only

at one frequency.

3. 1000-VTVC

As slated earlier the corrections for the high and low

voltage ranges are determined relative to the middle

range by intercomparison tests. It is necessary theref*>re that the ac-dc difference of all ranges be unaffected by voltage level. The voltage effect is rare in low

and middle ranges, but it can be troublesome at higher

ranges where the heat generated by the resistor is appreciable. All intercomparison tests were initially

made at two voltage levels in order to evaluate this effect— or to prove its absence. If, for example, the

nominal 600-V range is compared with the 1000-V

range at both 400 and 600 V, and the same results are obtained, it is unlikely that the 600-V range is affected

by the voltage increase (the 1000-V range is very

probably unaffected at these voltages). However both

ranges are in question until we are assured that the

1000-V range is also free of this effect. The highest range, then presents a special problem.

It is more likely to change due to increased voltage

(heating) and there is no higher range to compare it with. If it is compared with another 1000-V TVC at two or more voltages and no change is observed it is possible lhat both have the same voltage effect. However this is unlikely if TVCs are of somewhat

different design. If intercomparisons of several units

of difference design show no change between rated

voltage and a lower voltage we may safely assume

this effect is negligible in each one. Five 1000-V TVCs (table 2) have therefore been

built, each with differing components, and a network

of intercomparison tests was made as described in the

next section. The original set of TVCs [1] was included

in these tests. Table 2. Five 1000-V TVCs

Unit Resistance Voltage range with TE Resistor assembly

FI F2

A

kCl 400 1000 Four 100 wire- wound resistors in series, each 1 3/8 in long.

B 400 1000 Four 100 kQ, wire- wound resistors in series, each 1 3/8 in long. C 200 500 1000 Four 200 kCl metalfilm resistors in series-parallel, each

2 in long. D 200 500 1000 One 200 tin oxide

resistor 6 in long.

E 400 1000 Four 400 kil metalfilm resistors in series-parallel, each

2 in long.

The five 1000-V TVCs are designated alphabetically

(A through E)® and all except “A” have the inner shield, as described below, for frequency compensation. The

resistor in unit “A” is mounted concentrically in a set of six brass rings whose potentials are maintained by a capacitance divider. The whole assembly is mounted in a 4-in brass cylinder 7 in long.

Self-heating of a TVC may affect either the fre- quency compensation or the resistor itself. Apparently

the dielectric losses in the insulation between con- ductors can be affected by heating and change the

impedance of the resistor. This change occurred within

a few minutes eifter a voltage increase or decrease in several resistor types, which were therefore discarded.

The frequency compensating shield may be moved,

relative to the resistor, by thermal expansion of mounting parts and cause a change in ac-dc difference. This

occurred in some of our early units and the change was slow, taking up to an hour. Later shields were

therefore mounted very rigidly since a small displacement will have a large effect on the frequency influence.

The shield now in use is in two parts. A brass

cylinder, with one end closed, is mounted firmly

against the outer end piece (input end) with a polystyrene insulator one-half inch thick (fig. 3). A movable

tube fits tightly inside this cylinder and the shield

length adjustment is made by pushing this piece for- ward with a smaU rod inserted through the end piece

and the insulator. The rod is removed after each

adjustment.

The shield is most effective at the leading edge

where the voltage difference is greatest between the

resistor and the shield. Therefore the movable part of

the shield is cut at an angle, so that only part of it (see fig. 3) extends outside the fixed cylinder. Thereby

the effect of small position changes is reduced. Even

so, the compensation is affected by approximately 0.01 percent per millimeter of position change in some

typical units. The shield length adjustment is made in small steps,

and tests are made after each adjustment. When

optimum compensation is achieved, the unit is opened

and the shield parts are locked together with three screws through their overlapping portions.

4. TE and TVC Tests

As stated earlier the middle ranges are the most

accurate, and they are the base from which higher

and lower ranges are tested. However they are no more accurate than the TE used with them. Before

being instedled in a TVC the TEs are therefore compared with one of a group of carefully selected TE standards which were made according to NBS specifications.

This group contains twelve elements made by four

manufacturers, and are rated from 5 to 20 mA. ( 1 1 Thev

have either Karma or Evanohm * heaters to reduce

® Unil “D” is assigned lo this set (No. 7). ^Certain commerciai products and instrumrnis are tdeniifird in <hi» tn i- specify adequately the experimeniaJ procedure. In no rase does turh »deniih< impl< recommendation or endorsement by the National Bureau of Standards. rw>r >• impt*

that the products or equipment identihrd are necessarily the best sssilsbie for iKe 147
Figure 3. Cross section ofhigh voltage TVC,

Input end le it the left. Fixed and idjuitable thield parti are lupported by a polyityrene Iniulitor one-half inch

thick,

thermoelectric effects in the heaters. They also have

small reverse d-c differences (less than 200 ppm),

high bead resistances (over 1000 Mfl), and small ac-dc

differences. An additional two are multi-junction

elements of different design. All of these TEs have

been intercompared as current converters with agree- ment to better than 3 ppm. Theoretical calculations,

taking into consideration all known sources of error, also indicate that the error should not exceed a few

ppm at audio frequencies. Because of this and because

of the excellent agreement between these thermoelements of different design and construction, we may safely assume that the average ac-dc difference

of the group is 0 to ± 2 ppm.

The low-frequency performance of a TVC depends

on the TE since the reactance of the resistor is entirely

negligible even at a few kilohertz. The accuracy of

a TE at low frequency is mainly dependent on the

length of the heater. A very short heater permits heat

to flow more readily to the support stems and cooling

to occur between current peaks. However most commercial TEs have errors less than 10 ppm at 20 Hz

and some have errors less than 10 ppm even at 5 Hz.

In testing selected commercial TEs for the TVCs

at audio frequencies we often And a small ac-dc

difference (up to 4 ppm) which is independent of

frequency but dependent on heater current. It or- dinarily decreases at lower heater currents. When

these TEs are used in a TVC the ac-dc difference

will therefore be slightly voltage dependent. In the

step-up test process, where the TVC is alternately

used at 50 and 100 percent of rated current, this rela- tively small thermoelement error is introduced at every step of the process. If the process is a long one,

as in the 12-resistor set, there could be a significant

accumulation of error. TVCs in the new set are inter- compared by testing each resistor once with one TE

at reduced current (60 or 67%), and again with rated current on the other TE. If these TEs differ in ac-dc

difference at these currents, there will again be an accumulation of error. This is one of the advantages of the set with only

six resistors. If the 20-V range is the starting point

(it is probably the most stable), we have only four

steps up to the 1000-V range, and three steps down

to the 1-V range. The other advantages are that less time is required for the intercomparisons and there

are fewer units to construct.

Intercomparison data for this set of TVCs are listed

in table 3 as well as determinations made using TVC

set No. 1. (Test methods are discussed in later sections

of the paper). The middle ranges differ by 2 ppm or less even though the resistance varies from 1200 to 12000 II. Since the resistance enters into the theoretical calculation of ac-dc difference, this agreement is an additional indication of accuracy. Step-down tests show that the two lowest voltage

ranges usually have a positive correction (i.e., more

a-c than d-c voltage is required for a given TE output)

of 5 ppm or less at 50 kHz. Ther^ is no resistor in series with the TE at the 1 V range, and at the 2-V

range the TE is a large part of the total impedance.

These ranges are therefore affected more by the small reactance of the TE. The corrections for these ranges

are more likely to change if a TE is replaced than for the higher ranges. A step-down test from the middle

range is therefore advisable when TE replacements

are made.

The five 1000-V TVCs were compared with the

300- and 500-V ranges of TVC set No. 1 and the 600-V

range of the new set No. 7. The corrections are listed

in table 4 for 20 and 50 kHz and all values are averaged.

Table 3. AC-DC difference

TVC-a TVC-b

Applied

voltage

AC-DC difference (ppm)

20 kHz 50 kHz

S,-8„ 6, 6 h,-h„ 6, 6

FI 1 -3 -3 + 1 -3

F2 FI 1 -i-1 0 F2 2 -2 -2 + 1 -2

Fl-3 F2 2 + 1 -1

FI -3 3 -1 -f 1 0 -2

F2-6 6 -1 0 0 -3

Fl-10 F2-6 6 + 1 + 1 Fl-10 10 0 + 1 + 1 + 1 F2-20 20 0 0 + 1 + 1 FI -30 F2-20 20 -1 -2

FI -30 30 -1 + 1 -1 +2

F2-60 60 -1 0 -1 0 Fl-lOO F2-60 60 -1 -4

Fl-lOO 100 -2 0 -5 -2

F2-200' 200 -2 -1 -5 -6

FI -300 F2-200 200 -2 + 6 FI -300 300 -4 -3 + 1 +4

F2-600 600 -4 -4 + 1 + 1 FI -500 F2-600 500 -2 + 26

FI -500 500 -6 -3 +27 +30

F2-1000 1000 -6 +27

148
Table 5 lists intercomparison data for the same fre- quencies for seven pairings of the five 1000-V TVCs.

Values for 600 and 1000 V do not differ significantly and

so they are all averaged together.

Corrections (S) for each range of the new TVC set are listed as determined in comparison with TVC Set

No. 1. Intercomparison data(6a — 8/,) are also listed and

a computed correction (8*) based on the intercomparison, starting with the average of the measured ac-dc

differences of the 10- and 20-V ranges. The TVCs are

identified as the combination of a TE (FI or F2) with

the appropriate resistor; i.e., F2-600 forms the 600-V

range. -Averages of the corrections for the five 10(K)-V

TV Cs listed in table 4 are shown in the circles in figure

4, and the connecting lines show the intercomparison

values from table 5. The agreement between the vari- ous units is illustrated by this figure.

Each of the values listed in tables 4 and 5 is the

average of at least four separate determinations.

An analysis of the data taken in a series of 26 inter- comparison tests (an average of 5 determinations

with each one), involving aU ranges at two frequencies and usually two voltages, showed an imprecision

(3 (T„, where era is the standard deviation of the aver- age of five determinations) of only 1.4 ppm.

Table 4. Ac-dc difference corrections for five 1000-volt TVC (A-E)

Thr tlandard instniments are the 300- and 500-V units of Set No. 1 and the 600-V range of Set No. 7.

Standard Volts A B C D E AC-DC difference at 20 kHz (ppm)

.500-1 500 -20 -9 -4 -12

.500-1 300 -4 -10

600-7 600 -3 -22 -2 -12,-10

-8 -3 -10

Ave. -6 -21 -9 -3 -11

AC-DC difference at 50 kHz (ppm)

500-1 500 + 21 -6 + 11 + 30 -3

300-1 300 + 30 -4

600-7 600 + 30 -9 + 30 -6

+ 23 + 32 -6

Ave. + 25 -7 + 11 + 30 -5

Table 5. Relative ac-dc differences for seven pairings of members of

the five lOOO-V TVCs

Volts Sa Sg Sb Sc Sc 6d Se Sa Sa Sc Sa Sd AC-DC difference at 20 kHz (ppm)

600 -11 + 14 + 2 -7 + 7 + 3 0

1000 -17 + 13 0 -6 0 + 9 + 5 600 -16 + 17 -10 -2

1000 -17 + 5 Ave. -15 + 15 + 1 -7 + 4 + 6 + 2 AC-DC difference at 50 kHz (ppm)

600 -20 + 14 + 10 -33 + 28 -15 + 3 1000 -22 + 6 + 2 -33 + 35 -14 + 4 600 -25 -37 -15 + 2 1000 -24 + 1 Ave. -23 + 10 + 6 -34 + 32 -15 + 2

5. Thermal Compensation

The coaxial connector between the TE and the series

resistor provides a low-reactance connection for minimum frequency error. Tests and calculations show the

error is less than 1 ppm at 50 kHz. However, it also permits heat to flow freely from the resistor, which

dissipates up to five watts on the 1000-V range, to the

TE which has a temperature coefficient of emf of ap- proximately 0,2 percent/® C (at constant input current).

Heat conduction through the center conductor of

this connector was reduced, at 300 V and higher, by

replacing the two polystyrene insulators in the coajdal connectors (one in the resistor output and one

in the TE input) with two made of boron nitride. This

material is a good electrical insulator and yet it con- ducts heat well enough to provide an effective heat

sink for this conductor. It is used in both ends of the

high voltage resistors to improve the heat flow from the

resistor to the relatively heavy brass casing. This also helps to reduce the temperature rise in the resistor. Heat flow through the outer part of these connectors

will gradually raise the temperature of the TE casing,

and this also causes a heating drift. The increase in temperature of the TE bulb is slowed by mounting it in a short section of brass tubing to increase the

thermal mass and this tube is thermally insulated from

the TE casing. Thermal compensation is also added by

attaching a 10-0 thermistor to the tube containing

the TE and connecting it in series with the TE output.

A resistor appropriately chosen to complete the compensation circuit (see Fig. 7 and appendix I) will draw current through the thermistor sufficient to compensate for the temperature increase.

This resistor Vcilue may be computed for TEs with

average temperature coefficients as in appendix I. However, temperature coefficients differ considerably

and, for best results, it is usually necessary to match

the resistor to the TE and thermistor combination. A

suitable value can be found by substituting a variable

resistor outside the TE casing and adjusting it for minimum warmup drift on a 1000-V range. However, if the

TVC is to be used with a TE comparator similar to the one to be described, it will frequently be connected

aOkHi 50 kHz

Figure 4. Intercomparisons of 1000-volt TVCs.

Ac-dc dilTerence corrections (ppm) from ublr 4 for |(X)0-\ T\ ( • arr «h>-«n m

the circles and the relative difTerences from table S are shown on iKe mierr iiof

line,s. The algebraic difference between any pair should be equal lo the figure <>r, iKe connecting line within experimental error. 149
across a 1000-0 divider, and this will affect the compensation by about 20 percent. A value about 10 per- cent higher than the one chosen experimentally should

provide a satisfactory compromise and reduce the

drift by a factor of five or more. With the compensation

and the large thermal time constant of the TE in its casing, the drift can be reduced to less than 5 ppm/

minute under typical laboratory condition. The error from this is almost completely eliminated by taking a sequence of readings with a-c, d-c, reversed d-c, and a-c voltage applied, as described in the next section.

6. TVC Test Methods

A brief review of other comparison methods may be

useful before describing the TE comparator. Figure 5 shows two TVCs connected in parallel. The separate

balancing circuits (or Lindeck Potentiometers) (B) and

null detectors (D) may or may not be built in. Stable a-c and d-c voltage supplies are connected to the two TVCs

by the ac-dc switch. The switching arrangement shown

is typical and convenient, although others, such as re- versing the d-c supply by a separate switch, are satis- factory. The d-c supply must have an ungrounded

output and it should be possible to ground either ter- minal as the voltage is reversed. The reversed d-c dif- ferences.of the TVC can rarely, if ever, be neglected

in these tests. For convenience and clarity, we shall call one TVC

the “standard” and the other the “test.” Normally the one with known ac-dc difference corrections is the

standard, and the test TVC is usually treated differ- ently in the test procedures, as explained below.

There are two procedures for this intercomparison.

One might be called a null-balancing method. With a-c voltage applied to both TVCs, the balancing circuits of

the test and standard instruments are adjusted to null the detectors. The d-c supply is then switched to the

TVCs, and the voltage is adjusted to obtain a null bal- ance first on the detector of the test instrument and

then on the standard. Each d-c voltage is carefully

measured, and the small difference between the two

should equal the difference between the a-c voltage and

Figure 5. Two-Potentiometer method for TVC comparisons.

one direction of d-c voltage. The measurement is then

repeated with reversed d-c voltage, and an average is taken.

This method is tedious and time consuming, an ac- curate d-c voltage standard is required, and if there is any drift in either instrument output due to warmup or other reasons, as there very often is, the data may lack

both accuracy and precision.

A more satisfactory procedure and one that will minimize the effect of drift may be called a deflection

method. Both balancing circuits are adjusted to near

null, and then a-c and d-c voltages are applied in the

succession indicated in figure 5 (AC, DC+, DC—, AC).

For each input the power supply is adjusted to set the

test instrument detector to null. The deflection of the

standard TVC detector is read for each setting, and the

difference between the average reading on a-c voltage

and d-c voltage is an indication of relative ac-dc differ- ence. If the readings are made at nearly equal time

intervals, and if the drift rate is reasonably constant

(even though fairly large), the determinations can be

made with satisfactory precision.

If the detector of the standard TVC is a galvanometer

the reading may be in divisions or millimeters, but they can be converted to volts or percent ac-dc differences

by calibrating the detector scale in one of several ways.

A calibration factor can be determined simply and di- rectly by making a small measured change in the d-c input and observing the detector response.

If the detector is a microvoltmeter and if the balancing circuit is a Lindeck potentiometer indicating the

millivolt output of the thermoelement, the calibration

step can be eliminated. With the four deflection readings on the detector the difference between the average

reading on a-c voltage {E„) and those on d-c voltage

{Ed) is computed from the differences of the corresponding readings of the microvoltmeter. The ac-dc differ- ence of the test instrument is

where the subscript s indicates that these values come

from the standard instrument, and 6* is the ac-dc differ- ence correction for the standard.®

The factor n relates small changes in thermoelement

heater current (A/) (at a fixed frequency) to corresponding changes in output eml (A£'/£'= nA//7 approximately). For a TVC we may substitute raAF/F for the right

hand expression, so that n=FA£'/EAF. The value of n is 2 if the thermoelement has a square law response,

possibly at very low heater currents, but it is usually

1.7 to 1.9 at rated current. Determinations of n should

therefore be made in a d-c test at five or more current

levels by measuring the values indicated. A plot of n

against E can be made so that values corresponding to any emf can be found for substitution in the equation

above (see sec. 8).

‘ See eq 3 of appendix II. This general formula is applicable here also. 150
7. TE Comparator

There are several variations of basic comparator

circuits which are used to minimize the difficulty

caused by power supply instability [1, 3]. They employ

a voltage divider circuit to which two emfs are connected. The divider is adjusted to null a detector,

and at this point the divider setting corresponds to the ratio of the emfs. If one emf (Et) is held constant

as a-c and then d-c voltage is applied to the TVCs,

the other emf (f,,) will change if there is a relative

ac-dc difference in the TVCs at the frequency (8< 9

^

8*). The resulting unbalance in the divider will produce a change in the detector deflection proportional to the

ac-dc difference. However, small fluctuations in the

power supply will produce nearly equal proportional

changes in the emfs and therefore the detector will not be affected appreciably. The stabilizing effect depends on how well matched the time constants and response characteristics of the TEs are, but the

effect usually affords a significant advantage. Also,

the monitored emf need not be held constant so

exactly as with a simple balancing circuit. In the new comparator (fig. 6) the higher of the

two emfs is connected across a 1000-fi Kelvin-Varley

divider, and the lower one is connected to the variable

tap. The .detector is brought to nuU by adjusting the

divider. A Lindeck potentiometer and the same de- tector (with key ^i) is used to monitor the test TVC

output (El). The detector is labeled “N” in the dia- gram because the use of a nanovoltmeter is suggested.

The test procedure is similar to that already mentioned. Preliminary settings of the potentiometer

and divider are first made so the readings of the

nanovoltmeter wiU fall near mid-scale. Then with a-c voltage applied, the key ki (labeled “SET” on the

instrument, figs. 8 and 9) is depressed and the appro-

+DC DC

Figure 6. New TE comparator.

priate power supply is adjusted for a null on the

detector. Key k2 (READ) is then depressed and the

detector indication is read. The two-step procedure

is repeated for two directions of d-c voltage and for a second a-c input. The average indication in nanovolts ® (No) for a-c input and the average for d-c input

(Nd) is computed and the ac-dc difference of the

test instrument is

8t = ds+ (appendix II eq 5)

Tls

Figure 6 shows the test TVC output (Et) connected

to the high emf terminal (Eh in fig. 8). If Et is smaller

than Eg it will be necessary to interchange them, but

this is a minor inconvenience. If Et is connected to the El, terminal the potentiometer is switched to that input with switch S2 (fig. 8) and Et is monitored as

before. The same switch also reverses the polarity

of the detector, and therefore the sign of the indication. The slightly modified equation for 81 is eq 11 in appendix II. A galvanometer may also be used as a detector but

since the circuit resistance is relatively high a photoelectric amplifier is necessary for sufficient sensitivity.

The sceile must be linear over the portion to be used

and a scale calibration is eilso necessary to relate the

readings in divisions or millimeters to a voltage change.

The calibration can be made quite easily however by

moving switch Si from READ to CAL with lc2 closed

and observing the resulting deflection change. This

increases the resistance of the IGOO-H divider by 0.5 O

and changes the divider current by 0.05 percent. The

CAL

Figure 8. New TE comparator

*61 — 6, is conveniently in p«rts-per-mi)lion if f., is in millivolt* N • N, •

151
Figure 9. Photograph of TE comparator.

voltage applied to the galvanometer circuit is changed

by the same amount and the deflection change D\

is used in eq 10 and 12 in appendix 2 to determine

8j. A measurement of Es is made only to find the cor- responding value of rig from a plot as before.

8.

n Tests

Measurements of n are conveniently made with the

comparator. The thermoelement to be tested is con- nected to the El input and the Eh input is unused. A

key labeled “n TEST” (fig. 6) is locked down and

switch S2 is moved to Eh connecting the potentiometer

voltage across the divider. The divider is set arbitrarily but preferably near fuU range and the potentiometer is adjusted to nuU the detector. The input

voltage is then changed by a small measured amount

AV/V, and the resulting change in TE output (AE)

is measured by observing the change in indication of

the detector (nanovolts or microvolts).^ Switch S2 is then moved to El and a measurement of TE output

(E) is made with the potentiometer. The values for each factor of the equation given above (n = VAEI

EAV) are then known and n is calculated from this equation.

If a galvanometer is used as the detector a measure- ment of D\ is made as described above, and the deflection change resulting from the measured change in input voltage (AV) is designated D2 . Then n = 0.05

D2 lqDi, where q is the percentage change in input

voltage (100 AVIV).

Determinations of n need be accurate only to a few

percent, and, since they are quite stable, retesting is not usually necessary.

9.

AC Voltage Measurements

As suggested earlier, the comparator may be used

with one TVC to measure an a-c voltage such as the

^ A small change in the input to a TVC can be measured with a volt box and potenti- ometer or by a setting with a calibrated d-c voltage supply. It is also convenient to use a

resistor with a shorting switch in series with a TVC to introduce a small current change

(A/) in the thermoelement heater (i.e., 20 n with a 40-kn, 200-V TVC will give 100 A/// =

0.05 percent which is equivalent to 100 AK/K).

input to a digital voltmeter or the output of a cahbrated

a-c voltage supply. Switch Si has a third position

marked “POT’R” which disconnects the divider from

the Eh input. If a TVC output is connected to Eh, and

switch S2 is moved to that input, the potentiometer and

detector can be used to measure the TVC output and

changes in it. The circuit is as figure 5 without the test TVC. The d-c voltage is accurately measured and nominally equal to the a-c voltage.

It is suggested that d-c voltage be applied to the TVC

first and a detector reading taken. Then, at nearly equal

time intervals, a second reading is taken with a-c volt- age and a third with reversed d-c voltage. The differ- ence between the average of the readings with a d-c voltage {Ed) and the one with a-c voltage (Ea) is related

to the input voltage difference very much as before.

With a nanovoltmeter the emfs are read directly, but

if the detector is a galvanometer a scale sensitivity

factor must be determined.

10.

Design Details

The case of the TE comparator has thermal insulation and electrostatic shielding, and the comparator is carefully built to minimize thermal emfs and contact

resistances. The switch decks of the Kelvin-Varley

divider and Si and S2 have enclosed silver contacts and

the keys ki and k2 are of a low-thermal type. The back

contacts on these keys connect a 100-fi shunt across

the detector to reduce sensitivity and noise until one key or the other is depressed. The fine control for the

divider is a ten-turn helical resistor with a special lowthermal sliding contact. The resolution of the uncali- brated divider is not quite sufficient for setting an exact

null on the detector, but setting within a few divisions

is adequate in the ordinary use of the instrument.

152
1 1

.

Conclusion

The use of one resistor unit for two TVC voltage

ranges has reduced by about half the time required, over previous TVC sets, to make a complete intercomparison test. Changes in any member of the set are

readily detected since frequent intercomparison tests are more feasible. The TE comparator combines the stabilizing fea- ture of other comparators with much of the simplicity

of the single Lindeck potentiometer or balancing

circuit. It is relatively inexpensive to build and calculations are simplified and direct, especially where the

detector is a nanovoltmeter. Repeated tests have shown

that the imprecision is less than 2 ppm and ac-dc transfer accuracies, with the TVC set, are 10 ppm at audio

frequencies and 20 ppm up to 50 kHz.

This work was supported in part by the Army Metrology and Cahbration Center, Redstone, Alabama.

Their encouragement and support are gratefully

acknowledged. The author also acknowledges the

help of C. B. Childers and A. G. Perrey who made

many of the exacting measurements described here.

1

2.

References

(1) Hermach, F. L. and Williams, E. S., Thermal converters for audiofrequency voltage measurements of high accuracy, IEEE

1'ransactions on Instrumentation and Measurement, IM-15,

No. 4, 260-268, (Dec. 1966).

[2J Hermach, F. L. and Williams, E. S., Thermal voltage converters

for accurate voltage measurements to 30 megacycles per second,

Trans. AIEE (Communication and Electronics), 79, Pt. I, 200-206, (July 1960).

(31 Turgel, Raymond S., A comparator for thermal ac-dc transfer standards, ISA Transactions, 6, No. 4, 286-292, (1967).

13.

Appendix I

The temperature coefficient of emf, /8, of the

average TE is about —0.2 percent/® C, with constant

input current. Thus a corresponding decrease in the

resistance, R = Rc + Rt + Rs (see fig. 7) is required

to maintain a constant voltage across the resistor

Rf For a 1 degree increase in temperature, the

Figure 7. Thermal compensation for TE.

Rc TE output resistance (about lOH). Rf Thermistor resistance (about lOH). R, Series resistor to complete compensation circuit. {jRe and R» have negligible temperature coefficients.)

change in thermistor resistance, A/?t= o/?(/100

where a is the temperature coefficient of the thermistor

in percent/® C — typically about — 4 percent/® C. Therefore, for thermal compensation,

^=\Wi^Rt|R = aRt|R

and R = (xRtlfi

With the typical values listed we find R — 200 fi, and, subtracting Rc and Rt, the value for Rs is 180 Cl.

14.

Appendix II

Development of Equations"

The ac-dc difference of a TVC is defined as

where Va is the a-c voltage and Va the average of the

two directions of dc-voltage required to produce the same output emf. In the circuit of figure 6 the a-c and d-c voltages are adjusted to give the same emf

Et, of the TVC under test, as indicated by a null on

the detector N with ki closed. The same voltages are applied to the standard TVC. Then,

F„=Fd(l + 8,) = F;,(l + 8,) (2)

where V'^ is the d-c voltage required to produce the same output emf of the standard as Va, and the subscripts, t and s, refer to the test and standard instru- ments respectively. If V^— Vg « 1, then, closely

enough

From the definition of n given in the paper = (3)

Tight sd With the polarities as shown in figure 6,

N= mE,—E, (4)

where N is the detector voltage with k2 closed and

ki open, and m is the divider ratio (with the detector

resistance Rd »Ri).

Thus.

Tightgii

where the subscript a and d have the same meaning

as before.

* These equations were developed by F. L. Hermach 153
If a galvanometer is used as the detector, the current through it with lc 2 closed is, by Thevenin’s Theorem, _ mEt — Eg

R.

( 6 )

where Re is the resistance of the galvanometer circuit with Et and £* = 0. With Et and Eg held constant and

pRi inserted by means of Si,

Igc —

mEtl ( 1 + p) —Es

R'e (7)

held constant, with the detector and potentiometer con- nected as shown in the figure, a similar analysis leads

to the following equations;

8t = 8» +

Nd-Na

and — 8, +

rigEt

p{Dd-Dg)

rigDi

The characteristic n is determined from

( 11 )

( 12)

where R'g is the resistance of the galvanometer circuit. Since mEt — Eg «Eg and p << 1, we have to a

sufficient degree of approximation,

, ^

Egp ^

(Dft — Dc) _ Di

Re S S

(8)

where Di, and are the resulting galvanometer deflec- tions and S is the galvanometer current sensitivity. In the ac-dc test, with mEi constant.

(9)

Thus, from (3), (8) and (9),

8t = 8g + ^-^- ^J.-^ ( 10 ) figUi

The test and standard TVCs may be interchanged

if Et < Eg. If Et is applied to the El input of figure 8 and

^^EIE

byIV

(13)

by applying known changes in input voltage and

observing the changes in output emf with a high resist- ance voltmeter, as described in the text. If a galvanometer is used as the detector instead of the voltmeter

its sensitivity is determined by inserting pR\ as de- scribed. From equations similar to (8) and (9)

bkEg_pM>

Eg Di

(14)

If the thermocouple resistance of the test TVC,

Rtc, is significant, p in equation (7) should be replaced

by p', the fraction of Rt + Ru inserted by Si.*Similarly

if the potentiometer resistance Rp is significant, p

in equation (14) should be replaced by p", the fraction

of Ri + Rp inserted by Si.

(Paper 75C3&4-321)

* with a high impedance detector. With

a galvanometer the formula for 6. is

too complicated to be useful.

154
524 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-25, NO. 4, DECEMBER 1976 An Investigation of Multijunction Thermal Converters

FRANCIS L. HERMACH, fellow, ieee, and DONALD R. FLACH

Abstract—The relative ac-dc differencea of a group of multi*

junction thermal converters (MJTC’s) have been determined over

the frequency range 30 Hz-10 kHz. These MJTC’s are of different ranges and were obtained from several sources. Differences were

observed at low frequencies when converters of various ranges were intercompared. For voltage measurements, the use of matched

resistors in series with the MJTC heater resistors greatly reduced

these errors and contributed to the reduction of other errors as

well. It is believed that the average ac-dc difference of this group

is less than 0.3 ppm at 160 Hz and 0.5 ppm up to 10 kHz.

Introduction

Measurements of rms current and voltage have been based on a technique which converts

electrical energy into heat and compares this with the heat

produced by a dc signal. Single-junction thermal converters, each consisting of a wire heated by an electric current with a thermocouple to sense the temperature-rise,

have been in use for almost 3 decades at NBS for accurate rms ac-dc transfer measurements. Recently, a potentially more accurate form of the resistor-thermocouple combination, the multijunction thermal converter (MJTC), was

developed at NPL by Wilkins [1|. Verification of these

MJTC’s, to 0.5 ppm at 9 V and 159 Hz, was initially needed

at NBS for an absolute volt experiment, now well underway. Later, a goal of 1 ppm from 30 Hz to 10 kHz wets es- tablished as a marked and useful advance over the present

10 ppm.

^ch MJTC has a bifilar heater wire with from 50 to 200

series-connected thermocouples to sense the heater current, overcoming fundamental limitations in single-junction thermal converters [2]. Since actual converters may

depart from the ideal values, experimental comparisons

of converters of different construction, range, etc are desirable to buttress the theoretical accuracy. Unfortunately

there are at present no other suitable kinds of ac-dc

transfer standards to provide additional verification [3]. MJTC’s with heaters ranging from 5 to 25 mA and with

rated output EMF’s of 30 to 120 mV were obtained from

commercial manufacturers for this investigation, and

50-mA MJTC’s were donated by NPL. Techniques were

developed for intercomparing MJTC’s with high precision,

and a number of ac-dc errors were uncovered and over- come, to attain the desired goals.

EMF Comparator

The ac-dc difference is defined as 6 = (Qa — QdVQd

where Qa and Qd are the ac and dc inputs which produce

Manuscript received June 29, 1976. The authors are with the Electricity Division, National Bureau of Standards, Washington, DC 20234.

the same output of a thermal converter. A modified Williams EMF comparator [4] was used with a commercial

chopper-type nanovoltmeter to determine A = 8 i~ 62, for two MJTC’s whose heaters were connected either in series as thermal current converters (TCC’s) or in parallel as thermal voltage converters (TVC’s). A simplified schematic of the measuring circuit is shown in Fig. 1. The 11-kJl three-stage divider D, (adjustable to 1 ppm) and the Lindeck potentiometer P, were first adjusted to bring the

nanovoltmeter N, near zero for both positions of the key

K with dc applied, and were thereafter not disturbed

during an ac-dc determination. S was switched to ac, dc-D

(direct), dc-R (reversed), and AC in succession. In each

case the supply voltage was adjusted to bring N to zero^

in the A position of K and the reading of N in the B position was recorded. As shown in [4], A = 5i — 62 = (Nd —

Na)/ri2E2, where and Nd are the average voltage

readings with ac and the two directions of dc applied, re- spectively, and ri 2 is 2 for these square-law MJTC’s.

When the dc reversal difference was larger than the

range of N, the reversal compensator (RC) was used. It consisted of an adjustable, 0-13-/iV dc source, with negligible change on reversal. It was switched on for one direction of the applied dc current and reversed for the other, so that there was no net change in the average. Carefully timed sequences of ac-dc readings, with 30-s

intervals and less than 10-ms off times were necessary to overcome serious limitations from drifts and fluctuations

in the MJTC’s as well as the power supplies. In some cases Johnson noise was 0.3 ppm, and detector noise was 0.6 ppm, peak to peak, in the pass band of the detector. The

MJTC’s were placed in a 0.02 m^ passive oil bath in a temperature controlled room. Even so, some had to be

discarded because of excessive drifts or large switching

transients.

The detector had a 20-dB narrow-band rejection filter centered at 60 Hz, and was sensitive to common-mode

voltage at and near harmonics of its chopper frequency of

94 Hz. Significant ac outputs at twice the input frequency'^ were observed in MJTC’s below 100 Hz (approximately

proportional to 1//*-^), and at the input frequency above

1 kHz. Errors from these were reduced by modifying the

filter and connecting a 2-^F capacitor across the instrument.

To verify the accuracy of the nanovoltmeter, a number

of ac-dc difference measurements were also made with 8

' Close settings were not neces.sary for square law M-ITC's I.ikr the prototype the potentiometer could be connected across Ej. but thi» •*»'• rarely done, except to measure Ej.

^ Peak-to-peak ac outputs of up to 0..*) percent, over 1000 time* the normally used 0.3-*jV range of the detector, were observed at an input

frequency of 30 Hz.

Copyright © 1977 by The Institute of Electrical and Electronics Engineers. Inc Printed in U.S. A. Annals No. 612IM056
HKRMACH AND FLACH: MULTIJUNC'TION THERMAL CONVERTERS

30 50 100 200 300 500 1000 FREQUENCY IN Hz

Fig. 2. Ac -dc differences of TCC’s.

photocell galvanometer amplifier as a null detector, in- serting small known voltages in the detector circuit with

the reversal compensator. The results with the two detectors were in agreement to 0.2 ppm or better.

Low-Frequency Errors

Initial tests were made from 30 to 1000 Hz (a range near

5/1 about 160 Hz). Stepupicomparisons as thermal current

converters (TCC’s) were made by connecting, for example,

two 5-mA MJTC’s in parallel (outputs in series) and connecting the pair in series with a 10-mA MJTC. The two

5-mA MJTC’s were also compared, with their heaters in

series. These tests disclosed alarming differences between

ranges, roughly inversely proportional to frequency, as shown (at rated currents) in Fig. 2, with the 50 mA MJTC’s

taken as a base. The cause of these differences is as yet

unknown. The error was affected by shunting the heater

and was opposite in sign for TVC’s. Thus it weis caused by

a change in the effective resistance of the heater at low

frequencies.

525

As the frequency of the applied current decreases, the

heater temperature of a thermal converter begins to follow

the double-frequency variation of the instantaneous input

power. This can cause low-frequency errors if the resis- tance is dependent on the temperature. However, the

MJTC heaters are quaternary alloys of mainly NiCr, which

have low temperature coefficients (0 ± 20 ppm/®C). One

pair of MJTC’s of the same range had nearly equal lowfrequency errors but opposite temperature coefficients. The error was generally opposite in sign from that deduced

mathematically by treating all of the heater as a mass at uniform temperature, with all of the heat lost by temperature-independent lateral cooling. The thermal situation

must be much more complex than this, as evidenced by the

measured 1//^ ® variation of ac output with heater fre- quency, instead of 1// as predicted by this and other simple

models when the ratio of ac to dc outputs is small. A prototype MJTC with a NiCr heater from a third

manufacturer had much larger ac dc differences; about

—100 ppm as a TCC and -1-120 ppm as a TVC at 30 Hz.

This shows rather strikingly the necessity for experimentally verifying new designs. These errors agreed with the

sign predicted by the model, but varied roughly as 1// in- stead of 1//2 as predicted for low ac outputs.

Ac bridge measurements showed that the low-frequency

insulation resistance between the halves of a heater that

had been cut in the middle was too high to account for the

low-frequency error. Thus the low-frequency error is ap- parently not caused by the temperature coefficient of re- sistance of the heater or dielectric loss between the halves

of the heater.

A well-known theorem states that the power in a resistor

i?i fed by a constant voltage source having a fixed internal

resistance R^isa maximum when R\ = /? 2 - From this, as shown in the appendix, the power in the heater of an MJTC used to measure voltage would to the first order be

independent of small changes in the heater resistance if a matched (equal) fixed resistor were connected in series with the heater. Analogously, for measuring current the

power would be independent of small changes with a matched resistor across the heater. Since the thermocouples respond to the power dissipated in the heater, these

interesting applications of the maximum-power-transfer

theorem make possible compensated MJTC’s, in which the

first-order errors from changes in effective resistance are eliminated, at the cost of doubling the current and voltage

ranges. Calculations and tests showed that matching to 10

percent is adequate for the desired accuracy. Other Errors

Other errors in voltage measurements arise from Peltier

effects at the junctions between the heater and its lead-in

wires, and skin effect in magnetic leads used in some MJTC’s [1], [2]. For a given construction the errors from

Peltier effects are independent of frequency (except at low

frequencies) and current level, and are inversely proportional to the resistance, so that they could in principle be
52fi IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, DECEMBER 1976

TABLE I TVC Comparisons

[ MJTC

fl MJTC#2 V 30 Hz

A - 6, -

160 Hz

62 (ppm)

1 kHz 10 kHz

B10*2 B5*2 9 +0.4 -O.Z -0.2 -0.4

B10*44 B5*2 9 +0.6 -0.1 0.0 - 0.2

B10*2 B10*44 6 -K).l - 0.0 +0.1

" "

9 0.0 0.0 -0.2 +0.2

C10*2 "

6 +0.4 +0.1 +0.1 +0.2

cio'i " 6 40.4 +0.1 +0.1 +0.6

C10*2 B10*45 6 +0.4 -0.1 -0.3 -0.1

cio'i " 6 +0.3 0.0 +0.3 +0.2

B10*2 6 +0.1 +0.2 0.0 +0.4

" A50*14 6 +0.4 0.0 -0.2 - A5o'l4 A50*15 8 +0.2 o.p -0.1 - A50*15 B10*2 9 0.0 -0.1 +0.2 -

NOTE: B10*2 signifies a 10 mA HJTC, serial number 2, of manufacturer B.

1 N B5 2 and BIO 2 were mounted In unevacuated glass tubes at NBS.

A50*14 and 15 were in evacuated glass tubes with magnetic leads.

All others were in evacuated copper containers

.

evaluated by making TVC tests with different series resistors. However the low-frequency variation can be

complicated, and the evaluation is difficult in the presence

of other errors. Instead these and skin-effect errors were

eliminated by specifying MJTC’s with copper leads, which

have low thermal emfs against the quaternary heater al- loys.

At higher frequencies (up to 10 kHz), tests disclosed

errors in some of the MJTC’s from dielectric losses between the heater and the thermocouples.^ For example,

differences of up to several ppm at 10 kHz could be obtained by changing the ground from one line to the other

in tests of two 5-mA TCC’s in series. Dielectric errors were

also greatly reduced by the matched resistors. (See Appendix.)

TVC Tests

Since the needs were for voltage measurements, a group

of 8 MJTC’s of 4 different constructions and 3 current

ranges, and with copper leads, were compensated with

matched series resistors of quaternary alloys wound on thin

mica cards.^ Each MJTC with its resistor was mounted in an aluminum box (through which oil could circulate), with

input binding posts and a 2-pin output connector of low

thermal EMF’s. They were compared as TVC’s at 6 to 9 V,

at 30, 160, 1000, and 10 000 Hz. The results are shown in Table I. At the important frequency of 160 Hz the results are shown more vividly in Fig. 3. The circles identify the

MJTC’s and the number adjacent to each arrow gives dh — 5t in ppm, where dh and dt are, respectively, the ac-dc

•* Dielectric losses in the oil were negligible. Two MJTC’s, with 50-mA ranges, have magnetic leads and were not used above 1 kHz. A series resistor of 200 fi was used with each, to give a 10-V range. Tests with other resistors showed that resistance-dependent

low-frequency errors of these MJTC’s were less than 0.5 ppm. Series

resistors for the other MJTC’s were within 10 percent of the heater re- sistances.

TABLE II Assigned AC-DC Differences

differences of the MJTC’s at the head and tail of the arrow. In the absence of systematic errors the arrows around the

loops should sum to zero within the limits imposed by the

random errors of the comparisons. Alternatively failure to close properly is an indication of systematic errors. Techniques described by Youden [5] can be used to eval- uate networks such as this. The values of d assigned in this way to each MJTC at 160

Hz are shown in each circle, on the assumption that the

average of all is zero. Each value is less than 0.2 ppm, and

the closure errors are very small.

Similar analyses were carried out for the measurements

at other frequencies. The assigned ac-dc differences are shown in the columns marked in Table II. The dis- crepancies are somewhat larger than at 160 Hz but there

is no evidence of systematic error, or of significant residual

low-frequency errors in these compensated MJT(”s.

The standard error s (standard deviation of the average

of 4 determinations) in a comparison of 2 MJTC’s was 0. 1

2

ppm. Because of the network of comparisons the standard

deviation of an MJTC with respect to the average should

be somewhat less than this.

Series Rh>5i.sTOH.s

The high-quality wire-wound series resistors uwd with

these MJTC’s have excellent ac-dc characteristics at audio

frequencies. The phase angles are small and cause only a
llp^p^|p^#it^ 'vpmuli

.... ^

jl ^f^ff ^ j ^iWKi mmlm'.S0

:»|{»li|^iE»f#a*Wli«PiWfW ^ IL.* \J..aL..iJ;: ”"

jNftSi II AI Hiiff liiiilli im^^sm mmw^^

&-±&>as^!ieiiSss£ tsmtmamuitm

'•«
.j' .i'’ ir.4^ a'.*'.". , . m
HKHMACH AND Fl.ACH: MULTIJUNCTION THERMAL CONVERTERS

second-order effect on impedance magnitude. However

there is a possibility of dielectric loss in the insulation at the higher audio frequencies. (The maximum powertransfer theorem does not help here.) To determine this,

the 1/1 inductive-voltage-divider bridge shown in Fig. 4 was set up to compare two nearly equal resistors and i?2. A balance was made for each switch position of this “re- versing bridge” by adjusting m and n with the detector lead

d, as shown, after adjusting the Wagner arms with d

grounded. Most of the bridge errors were eliminated in this way, leaving as the difference equations, (/?2 ~ Ri)/Ri =

2(Ua ~ ^b) and aa — «i = y{m.a — mb) where R and a are

the resistive components and the phase angle, respectively,

of the parallel equivalent circuit for each resistor, y =

itjCsR, and the subscripts a and b refer to the switch positions shown. These simple equations hold to 0.1 ppm if the

phase angles of C3 and m are each less than 0.1 mrad and

(02 “ «i) is less than 1 mrad.®

A 1-kfl resistor of the same type as those used with the

MJTC’s was mounted in a metal box, for four-terminalpair ac-dc measurements on Cutkosky’s bridges [6] from

160 to 16 000 Hz. This served as a standeu’d for evaluating

two 1-kQ unmounted resistors. These were paralleled to evaluate a 5-section 500-fl card. The 5 sections were in- tercompared and then used to evaluate the 300, 400, and

500-fi cards for the MJTC’s. The 1300-fl card for the 5-mA

MJTC was compared with the l-kl2 card in series with 3

100-fi sections.

An upper limit of 10 kHz was imposed by the effects of

lead inductance and of stray capacitance from the cards

to the grounded aluminum boxes in which they were tested

and used. Below this, changes in the parallel resistances were less than 0.1 ppm for drastic changes in the positions

of the resistors. The cases of the inductive voltage dividers

and the shields of all leads of the reversing bridge were

grounded. C3 was a low-loss 3-terminal air capacitor, and

D was a tuned null detector. All bridge components were

commercially available.

Measurements were made at 0.1, 1, and 10 kHz with 8

V applied. The results are shown in Table III as dg and a, where 5g = {Rf — Rp)/Rp and a is the phase angle. Rf and

Rp are the parallel-equivalent-circuit resistances at the

frequency f and the base frequency (0.1 kHz), respectively.

For each resistor, a was closely proportional to /, and so is not shown at 1 kHz in the table.

® The dividers were rated up to 10 kHz. Only the lower dials were changed on reversal, with only moderate accuracy required.

527 TABLE III Resistance Measurements

MJTC n

1 kHz 10 kHz

6e

6 e a 6 r

6 c Bi0*44 500 -0.1 -0.7 -0.55 -0.5 +0.3

B10*A5 " +0.1 +0.3 -0.41 +0.1 -0.1

C10*l 300 0.0 +0.5 -0.60 +0.1 +0.2

C10*2 " 0.0 0.0 -0.41 -0.1 +0.1

B10*2 400 0.0 +0.4 -0.4 7 +0.1 -0.3

B5*2 1300 0.0 0.0 -0.26 0.0 +0.1

NOTE: All values of 6 in ppm a in mrad. See text

.

The effect of these small errors on the magnitude of the current through the MJTC is approximately hr = bel2-

3aV8. This was negligible at 1 kHz and, except for one

resistor, even at 10 kHz. The average for all of the resistors was less than 0.1 ppm at each frequency, so that no cor- rections need be applied to Table II. The ac-dc differences of a TVC is = 6^ + bg [2] where

be is the ac-dc difference of the thermal converter. Since

ba and br were evaluated as indicated above, be could be

determined for each MJTC. As shown in Table III, each was 0.3 ppm or less at 10-kHz.

Conclusions

This work reaffirms the value of both experimental and

theoretical investigations to evaluate ac-dc differences in 8m absolute sense, and to determine how well 4ctu8il ac-dc

transfer standards meet the theoretical ideals. A number

of sources of ac-dc differences were uncovered, and were

eliminated by changes in design, or were compensated for. The agreement between a group of 8 MJTCs which met

these requirements W8is excellent. Because of this, because

of the significant differences in construction and ranges

of these MJTC’s, emd because of our long investigation, we

believe it is very unlikely that the average ac-dc difference

of this group exceeds 0.3 ppm at 160 Hz or 0.5 ppm at 30

and 10 000 Hz. This belief is supported by an analysis

based on estimates of the limits of error from such factors as mismatch of series resistors, Peltier-heat exchanges,

ac-dc differences of resistors, systematic errors in the

comparator, and random errors. For the latter we took as the 95 percent confidence limit 2s/Vn, where n is the

number of MJTC’s in the group.

A few measurements over several months indicate a repeatability of 0.3 ppm or better. The long-term stability

of ac-dc difference is as yet unknown, but there is no rca son to expect drifts greater than this. Extensions to higher voltages and frequencies seem

feasible. Small ac-dc differences in the effective heater

resistance could be compensated with combined shunt and

series resistors, as indicated in the Appendix. A wide range

of film resistors could be mounted in a geometry that

would allow the reactance to be calculated, so that the

powerful comparison technique of (2| could then he ap

plied.
528 IEEE TRANSACTIONS ON, INSTRUMENTATION AND MEASUREMENT, DECEMBER 1976

Appendix

Compensation for Changes in Resistance

When a resistoi: mR is in series with MJTC heater, i?(l + a), a « 1, the current (with no reactance) is

(m + 1)R{1 + a/(m + 1)) ~

^

(l

° \

(m + l)i? \ m + 1/

neglecting higher order terms in a. The power in the heater

is

V/2 / Off \ P = PR{l + a)^- 1-—

+ a).

For a fixed V and m, the power is independent of a if m

= 1 (neglecting higher order terms). Thus since the thermocouples respond to the power dissipated in the heater, a small difference between the effective dc and ac heater

resistances will cause no first-order ac-dc difference in a TVC with a matched series resistor. Matching to 10 per- cent will reduce a 2 ppm ac-dc difference (from this cause)

to 0.1 ppm.

Similarly for a TCC with mR in parallel with R(1 + a)

the power in the heater is independent of a if m = 1, so that

there will be no first-order ac-dc difference with a matched

shunt.

This compensation will be effective, however, only if the

heater is a two-terminal resistor in the measuring circuit,

and if the thermocouples are insensitive to any change in the distribution of the power. For example, an error would

occur with dielectric leakage from the heater to the thermocouple of an MJTC unless the thermocouple, output and

one end of the heater were connected together, and the

thermocouple resistance was much less than the insulation

resistance.

Matching provides only a single compensated voltage

or current range. However, for higher voltage ranges a

similar analysis shows that if a resistor nR is connected

across the heater and mR in series with the combination,

compensation is achieved if n = m/{m — 1). Acknowledgment

The authors are very grateful to F. Wilkins for the NPL

MJTC’s, to R. Cutkosky for the ac-dc measurements of the

mounted resistor, and to J. Sutcliffe and I. Malcolm of

Guildline Instruments Ltd. for their extended cooperation. References

[1] F. J. Wilkins, “Theoretical analysis of the ac/dc transfer differences of the NPL thermal converter over the frequency range dc—100 kHz,” IEEE Trans. Instrum. Meas., vol. IM-21, pp. 334-340,

1972.

[2] F. L. Hermach and E. S. Williams, “Thermal converters for audio- frequency voltage measurements of high-accuracy,” IEEE Trans. Instrum. Meas., vol. IM-15, pp. 260-268, 1966.

[3] F. L. Hermach, “Ac-dc comparators for audio-frequency current and

voltage measurements,” to be published.

[4] E. S. Williams, “Thermal voltage converters and comparators for very accurate ac voltage measurements,” J. Res. Nat. Bur. Stand., 75C,

pp. 145-154, July-Dee. 1971.

[5] W. J. Youden, “Measurement agreement comparisons,” in Proc. 1962 Standards Lab. Conf., NBS Misc. Publ. 248, pp. 147-152, Aug.

1963.

[6] R. Cutkosky, “New NBS measurements of the absolute Farad and Ohm,” IEEE Trans. Instrum. Meas., vol. IM-23, pp. 305-309,

1974.
i.n4A (REV. 2-80) U.S. DEPT. OF COMM.

BIBLIOGRAPHIC DATA

1. PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

SHEET (See Instructions) NBSIR84-2903 April 1985

4. TITLE AND SUBTITLE

An Investigation of the Uncertainties of the NBS Thermal Voltage and Current

Converters

5. AUTHOR(S)

F. L. Hermach

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

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

7. Contract/Grant No.

8. Type of Report & Period Covered

9.

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

National Bureau of Standards

10.

SUPPLEMENTARY NOTES

I I Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11.

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

bibliography or iiterature survey, mention it here)

The uncertainties of the NBS reference and working standards for ac-dc current

and voltage transfer measurements have been redetermined, to 50 and 100 kHz,

respectively, by means of a set of mul ti junction thermal converters (MJTCs), an improved emf comparator, and extensive series of intercomparisons. Numerous

supporting investigations have also been performed. As a result of this work the

accuracy of the NBS standards and the output of its calibration service for ac-dc

current and voltage transfer are considered to be on a much firmer and better

documented basis than heretofore. Improvement by factors of two to five in the

calibration accuracy for high-quality, single-range thermoelements and thermal

voltage converters is possible for certain ranges of current, voltage, and frequency,

For very special tests, such as international comparisons, accuracies approaching

1 ppm are within reach. (Nineteen references)

12.

KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolon

accuracy of ac measurements; ac-dc transfer standards; calibration accuracy; current

measurements; measurement accuracy; mul ti junction thermaTconverters ; thermal current

converters; thermal voltage convertenr,- uncertainties of measurements; voltage measuremenis

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Order From National Technical Information Service (NTIS), Springfield, VA. 22161

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