608 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL 42, NO 2, APRIL 1993

High Precision Automated Measuring System for ac-dc Current Transfer Standards

Karl-Erik Rydler

Abstract-An automated measuring system for ac-dc current transfer standards has been developed at the Swedish National Testing and Research Institute (SP). The use of a guard makes intercomparisons with ppm precision possible at frequencies up to 100 kHz. Two multijunction thermal converters are used for evaluating the uncertainty of the system.

I. INTRODUCTION HE intercomparison of two thermal current convert- T ers (TCC's) is made by connecting them in series and

measure the output response when either ac- or dc-current is applied. The difference of the output voltages are usu- ally measured by a bridge method.

The current ac-dc transfer difference of a TCC is de- pendent on the leakage current from the input to the hous- ing and the output. It has been shown by Klonz [l] that in order to have a well defined ac-dc transfer difference of a multijunction thermal converter (MJTC) one of the thermocouple output leads and the housing must be con- nected to the low terminal of the input connector.

Different methods for the connection and grounding of the case, the input of the current converters and the dif- ference measuring bridge has been described by Williams [2] and Hermach [3]. At lower frequencies high accuracy is achieved by these methods. The error of the measured ac-dc difference will increase at higher frequencies due to leakage currents.

A measuring system with high accuracy also at high frequencies is described by Klonz [ 11. An inductive volt- age divider is used for Wagner grounding. The potential of the low terminal of the difference measuring bridge and the point between the low-input terminals of the current converters is at each frequency manually adjusted to vir- tual ground.

Fig. 1. SP automated measuring system for ac-dc current transfer standards.

The ac-dc transfer difference is computed by a digital 'bridge' [4], [5]. Thirteen measurements are made in a sequence ac, dc', ac, dc-, ac, dc', etc. The measured output voltages are divided by the sensitivity and 13 dif- ferences Ai are calculated as:

(1) where Es and ET are the output voltages of the standard and the test object. Ks and KT are the sensitivity of the standard and the test object and i is 1-13.

Three polynomials of the third degree are fitted by the least-square method to the differences corresponding to ac, dc', and dc- respectively, Ai = Ai + Bi + Ci2 + Di3 where Ai is equal to A,, for i = 1, 3, 5, 7,9, 11, and 13 and equal to A&+ for i = 2, 6 and 10 and equal to Adc- for i = 4, 8, and 12. The shape is the same for all three polynomials, only the constant terms differ. From the constant terms the ac-dc transfer difference (a, - as) is computed as

Ai = Esi/Ks - E,/KT

d T - as = A,, - (A&+ + & - ) / 2 (2)

Errors in the measured value due to drift of the output voltages, back-off voltages or thermal EMF'S are mini- mized in this way. 11. MEASURING SYSTEM

Before a measurement starts, the current level and the At sp the intercomParison Of converters is made in an automated measuring system, Fig. ' * The difference between the Output Of the current converters and the back-off voltages are measured by nanovoltmeters.

measuring frequencies are selected and the back-off volt- ages are manually adjusted to a value approximately equal to the output voltages of the current converters. The sys- tem then starts a measuring cycle by determining the sen- sitivity of the current converters. The change of the output

rent is applied. Before the measurement Of the ac-dc dif- ference begins at each selected frequency, the system ad- justs the ac current to give the same output voltage as the dc current within k 100 ppm.

Manuscript received June IO, 1992; revised October 4, 1992. The de- velopment of the automated measuring system for ac-dc current transfer standards was supported in part by the Swedish Board for Technical AC- creditation (SWEDAC).

The author is with the Swedish National Testing and Research Institute, S-501 15 Bods, Sweden.

IEEE Log Number 9207007.

are measured when a known shift Of the dc "'-

0018-9456/93$03.00 0 1993 IEEE

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RY DLER: AUTOMATED MEASURING SYSTEM

The nanovoltmeter used on the guarded side is con- nected to the IEEE bus via an opt0 interface. To minimize the leakage current through the net transformer of this na- novoltmeter it is connected to the net via a surge trans- former. For currents 5 30 mA, the current generators are replaced by voltage generators. This eliminates the re- maining errors due to leakage current from the guarded nanovoltmeter.

111. GUARDING To eliminate errors due to different potentials the sys-

tem is made symmetric by using a guard, see Fig. 2. In Williams’ method, the housing of the TCC on high po- tential side is guarded. The digital “bridge” also allows the low terminal of the output voltage, the screen of the back-off voltage source, and the nanovoltmeter case to be guarded to the same potential as the low input terminal of the TCC.

A comparison is made in Appendix A between the two methods where the thermocouple output of the TCC on high potential is either connected to guard or to ground. It is found that the error cTs in the measured ac-dc differ- ence, if the output of the current converter on high poten- tial is connected to ground, is

E T S = (RT + R.dYS/2 (3)

I where Rs and RT are the input resistances of the TCC’s on high potential and on ground potential respectively. Ys is the leakage admittance of the TCC on the high potential side.

(This error can be used for measuring the leakage con- ductance of a MJTC. The error eTS can be determined by subtracting the ac-dc difference measured with guard from ac-dc difference measured without guard.)

IV. T-CONNECTOR On low current ranges the admittances in the T-con-

nector can cause errors in the measured ac-dc difference. The current through the two TCC’s will be equal only if the currents through the admittances Y , and Y2 are equal or negligible, see Fig. 3. It can be shown that the error cTS in the measured ac-dc difference will be

= ZTY’ - zsY1 (4)

where ZT and Zs are the input impedance of the TCC’s and Y, and Y2 are the admittances of the T-connector. With Y = G + jwC and approximating Z by R , (4) can be writ- ten as

ETS = R T G ~ - RsGl + W 2 [ ( R ~ C 2 ) * - R & ’ 1 ) 2 ] / 2 ( 5 )

where RT and Rs are the input resistances of the TCC’s. G, and G2 are the conductances and C, and C, are the capacitances of the T-connector.

If RT = Rs the error of the mean value eTSm of two mea- surements where the TCC’s are interchanged will be zero. For intercomparisons of TCC’s with different input impedances the admittances must be known as they will cause measurement errors.

l l

Ground penrial current sources Guard potential

Fig. 2. Circuit diagram of the guard arrangement.

Fig. 3 . T-connector admittances.

The capacitances C and C 2 can easily be measured and a correction made by using ( 5 ) . They can also be made negligibly small and equal if the lead interconnecting the two TCC’s is guarded by a screen at the same potential as the high input terminals. The guard voltage is supplied by a high impedance capacitive divider, Fig. 2.

The measuring system can be used to measure the con- ductance in the T-connector. If C , = C, = C and RT = Rs = R the errors in the measured ac-dc difference are

cTs and cST can be determined by two measurements where the two TCC’s are interchanged in between. If cTS and EST

= 0 this implies that G2 = GI = G. This is very likely as the T-connector is made with two connectors of the same type (GR874). In the same way more connectors, e.g., four, can be determined to have equal conductance G. Again, two measurements are made where the two TCC’s are interchanged but now the four connectors, i.e., 4G, are added on the high potential side. The measured ac-dc differences dTs and dsT will be

dn = aT - as + R ( G - 5G) + cc (7)

where aT and as are the ac-dc differences of the two TCC’s. As it is not possible to add the four connectors without adding some capacitance, this will also cause an error e C . However, this capacitance can be measured and the error corrected for by using (5). The mean value mTs of the two measurements is

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610 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 42, NO. 2. APRIL 1993

Thus the conductance of the T-connector can be deter- mined as

G = (mn - dn + cC)/4R

By this method the conductances G1 and G2 of the T-con- nector of SP have been determined to be less than 0.7 nS at 100 kHz.

V. UNCERTAINTIES For accurate intercomparisons the use of guarding is

important at low current, in particular when MJTC’s are used. Uncertainty budgets are therefore made for inter- comparison of two MJTC’s, Table I , and for the inter- comparison of a single-junction thermal converter (SJTC) and a MJTC, Table 11.

The main sources of error in the measuring system are nonlinearity of the nanovoltmeters, remaining nonsym- metry between the guarded and the grounded sides and leakage admittances in the T-connector.

The nonlinearity of the nanovoltmeters is measured to be less than 5 nV. The uncertainty due to admittances is calculated from (5 ) with C, = C2 = 2 pF, 1 C, - C, 1 I 1 pF and G, = G2 < 0.7 nS. The input resistances are 185 Q for MJTC and 45 Q for SJTC. The capacitances are measured by a commercial impedance meter and the con- ductances are determined by the above-described method. The resistances are measured by a dc-current ohmmeter. For frequencies up to 100 kHz, the change in the input resistances are negligible.

The uncertainty due to remaining nonsymmetry be- tween the guarded and the grounded sides are estimated by comparing two measurements where the position of the two converters has been interchanged and the same mea- surements when an error has been introduced in the guard potential by using a capacitive divider.

Other sources of uncertainty are the measurement of the sensitivities of the TCC’s, the difference between the ac- current and dc-current, reversal error of the TCC’s and switching of relays. The uncertainty budgets are valid if the measured ac-dc transfer difference is within k 100 ppm and the reversal errors are less than 50 ppm. The time constants of the two TCC’s should be of the same order.

VI. CONCLUSION A high precision automated measuring system for in-

tercomparison of ac-dc current transfer standards has been developed by using a guard. For currents up to 30 mA and frequencies to 100 kHz the uncertainty of the ac-dc current transfer difference of intercomparison of thermal current converters is estimated to be within f 1 part in lo6 (14.

APPENDIX A A comparison is made between the two methods where

the thermocouple output of the TCC on high potential is either connected to guard or to ground.

TABLE I UNCERTAINTY BUDGET FOR INTERCOMPARISON OF TWO MULTIJUNCTION

THERMAL CONVERTERS

Uncertainty (lu) in 1 O P at the frequency

Source of Uncertainty 1 kHz 100 kHz

0.1 0.1 Nonsymmetry of guarding 0.1 0.1 T-connector admittances 0.1 0.1 Other 0.1 0.1

Type B Nonlinearity of nV-meter

0 .3 0.4

Type A Standard deviation of mean

Total uncertainty, 0 .3 0.4

TABLE I1

CONVERTER AND A MULTIJUNCTION THERMAL CONVERTER

Uncertainty (IO) in

UNCERTAINTY BUDGET FOR INTERCOMPARISON A SINGLE JUNCTION THERMAL

at the frequency

Source of Uncertainty 1 kHz 100 kHz

0.5 0.5 0.1 0.2 0.1 0.1

Other 0.1 0.1

Type B Nonlinearity of nV-meter Nonsymmetry of guarding T-connector admittances

0.5 0.5

Total uncertainty, 0.8 0.8

Type A Standard deviation of mean

The analysis of the error in the measured ac-dc differ- ence due to leakage currents in the TCC’s is made using an equivalent circuit model of a TCC where the leakage admittance of a TCC is represented by two lumped leak- age admittances of equal value. The leakage admittances are connected between the thermocouple and the input high terminal and the input low terminal respectively. In Fig. 4 the leakage admittance between the thermocouple and the input low terminal of the TCC’s are omitted as they are either short circuited or connected in parallel with the current source.

In this simple equivalent circuit model, the output (thermocouple) resistance of the TCC’s are assumed to be zero. This assumption is valid of the dc leakage is inde- pendent of polarity and for ac leakage at frequencies where the normal mode rejection of the nanovolt meter are high. (A dc leakage current will produce a voltage drop in the output resistance of each TCC, and will affect the read- ings in the nanovolt meters. If the dc leakage is inde- pendent of polarity its effect will cancel. However, this is not always the case. Due to ac leakage currents in the output resistance, an ac voltage will appear in the output of the TCC’s. Its effect will depend on the normal mode rejection of the nanovolt meters.)

When the output of the standard TCC on high potential is connected to the guard, the current through the leakage admittance is ZsRsYs/2. By this leakage current, the ac-

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RYDLER: AUTOMATED MEASURING SYSTEM 61 I

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I + Fig. 4. Leakage currents in thermal current converters.

dc difference of the TCC is defined. However, if the out- put of the standard TCC on high potential is connected to the ground the current through the leakage admittance will be - Z T R T Y S / ~ . Hence the measured ac-dc difference will depend on the voltage drop over the test TCC at ground potential. The error eTS (the first index indicate TCC on ground potential and the second index indicate TCC on high potential) of the measured ac-dc difference when the output of the standard TCC on high potential is connected to ground can be determined by

(All The error of the mean value eTsm of the measurements where the TCC’s are interchanged is

CTS = (RT + RS) y S / 2

where Rs and R T are the input resistances of the standard

TCC and the test TCC respectively. Ys and YT are the leakage admittance between the heater and the thermo- couple of the standard TCC and the test TCC respec- tively.

From ( A l ) and ( A 2 ) the following conclusions can be made. With the method where the thermocouple output of the TCC on high potential is connected to ground, accu- rate intercomparison of two MJTC’s are only possible if their leakage admittances are equal. Intercomparison of a SJTC and a MJTC should be made with the SJTC on the high potential as the leakage admittance in SJTC’s nor- mally are small.

REFERENCES

[l] M. Klonz, “Entwicklung von Vielfachthermo-konvertem zur genauen Riickfiihrung von WechelgriiSen auf aquivalente GleichgroBen,” PTE- Eericht E-29, Fakultat f i r Maschinenbau und Elektrotechnik, Tech- nische Universit5t Carolo-Wilhelmina, Braunschweig, Germany, 1987.

[2] E. S . Williams, “Thermal current converters for accurate ac current measurements,” IEEE Trans. Instrum. Meas., vol. IM-25, pp. 519- 523, 1976.

[3] F. L. Hermach and D. R. Flach, ”An investigation of multijunction thermal converters,” IEEE Trans. Instrum. Meas., vol. IM-25, pp.

[4] P. Martin and R. B. D. Knight, “Components and systems for ac-dc transfer at the ppm level,” IEEE Trans. Instrum. Meas., vol. IM-32,

[5] R. B. D. Knight, D. J . Legg, and P. Martin, “Digital ‘bridge’ for comparison of ac-dc transfer instruments,” IEE h o c . - A , vol. 138, no.

524-528, 1976.

pp. 63-72, 1983.

3, pp. 169-175, 1991.