MEASUREMENT OF ELECTRICAL AND MAGNETIC QUANTITIES A SIMPLE

COMPARATOR

V. G. Boiehuk,

FOR T E S T I N G

N. M. Ogirko,

and

NORMAL N.

CELLS

M. Tsaryuk

UDC 621.375.024.082.52

Normal cells are checked with c o m m e r c i a l balancing systems [1, 2]. I f one has to check a precision standard cell, m a n y operations are involved in order to e l i m i n a t e the effects of contact emfs and to monitor the working current, while the method of comparison with a standard specimen requires a r i t h m e t i c calculations. These factors are important, e s p e c i a l l y in routine testing, where high productivity is required. For standard normal ceils, e m f comparison cannot be performed even with the most a c c u r a t e standard c o m m e r cial compensating systems, because these do not adequately correct for thermoelectric emfs; therefore, special systems are used [3, 4], in which the effects of these emfs are largely e l i m i n a t e d , and the e m f is read out directly. However, they resemble standard c o m m e r c i a l b a l a n c e systems in containing m a n y precision elements and therefore costly and c o m p l i c a t e d to m a k e . A large range is necessary in the eomparator [3, 4], when one is examining the parameters of normal cells, but not during standard checking. A differential method of comparison involves measuring only a s m a l l difference of emf, and provides therefore high a c c u r a c y in testing, which enables one to use a simple comparator of c o m p a r a t i v e l y low accuracy [5]. The e m f Ex of the c e l l under test is measured with the eomparator of Fig. 1 by a differential method using simultaneous comparison [4]. This comparator gives high a c c u r a c y in measurement, because the effects of t h e r m o emfs are m i n i m i z e d there. The comparator consists of the c a l i b r a t e d compensator K c and the uncallbrated one Ku with adjustable currents, the p o t e n t i a l leads of the compensating resistors being j o i n e d in series. T h e working current circuit of the calibrated compensator includes the m i l l i a m m e t e r m A, whose scale is calibrated in terms of the emf of the normal c e l l . ! I

:

Rs ,'---I

f-"!

Pbz Pb3

g

The comparator is c a l i b r a t e d before the e m f is measured. For this purpose, the standard normal c e l l EN and the accessory one Ea are conneeted via their free potential leads from the compensation resistors R via the null indicator NI and a switch; the current K c is adjusted to set the reading o f mA to correspond to EN, while the current in K u is adjusted via NI to bring about balance:

eN--Ea=+_ Ucv-~Uu,

(i)

where UcN and Uu are the voltages at the outputs of K c and K u during calibration. In measuring the emf, the cells Ex are connected in turn by a switch in opposition to the auxiliary cell, and the current K c is adjusted with the previous current Ku to bring about b a l a n c e as i n d i c a t e d by Nh Ex - - E a = + Ucx •

Uu,

(2)

where Ucx is the voltage at the output of K c. The reading of mA corresponds to Ex.

Fig. 1 Translated from i z m e r i t ' n a y a Tekhnika, No. 3, pp. 41-43, March, 1974.

9 1974 Consultants Bureau, a division of Plenum Publishing Corporation, 227 West 17th Street, New York, N. Y. 10011. No part of this publication may be reproduced, stored in a retrieval system, or trcmsmitted, in any form or by any means, electronic, mechemical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $ I5.00.

381

U OUt

R

8

o

I

;

to Rd U/ut 81 c,-

,

:1 Fig. 2

Fig. 3

As the value Ea ~ U u for any Ex can r e m a i n unchanged in 1) and (2), it can be taken as the origin for the reading of the comparator E =E a * U u. T h e value of the e m f of the normal c e l l m a y be put as e ~ = e • vex = e + Z c ~ ; Ex = E + Uc, = E +, IcxR; E a = E ~- Uu = E •

(3) R,

where IcN and Icx are the currents in K c respectively during cattbration and measurement, while R is the resistance o f the compensating resistor in the compensator and I u is the current in K u. Conditions (3) form t h e basis of the work of the comparator and are strictly obeyed in measuring the emf; they enable one to calibrate the scale of mA in terms of e m f and to read E x directly without additional calculations. From (1) and (2) we get the dependence of the ernf on the parameters whose accuracy governs the error of measurement:

Ex = eN

(4)

vex

From (3) and (4) we get with AR=6RR, ( I c x - - I e N ) R=Ex--E N, for constant Ea and U u that the absolute error in measuring Ex is

a~ = A,v 4- 6~ (E~ -- EN) ___(a& - - At,v) R,

(5)

where A N is the absolute error in the e m f of the standard normal c e l l , 5 R is the r e l a t i v e error in R in K c, and Aix and AIN are the absolute errors in the m i l l i a m m e t e r readings correspondingly during measurement and calibration. From (5) with AIx=/XIN =6iI].i and t~lli = E l we get the l i m i t i n g error in the comparison of ~the two emfs as AK ----- 6R (Ex - - E N ) q- 261 (E l - - E) ,

(6)

where 61 is the l i m i t i n g error of the m i l l i a m m e t e r , El is the l i m i t to the reading of the comparator, and Ili is the l i m i t to the reading of the m i l l i a m m e t e r . In this comparator one adjusts the current strength and polarity in the compensators, so one uses a c e n t e r - z e r o meter; the origin of reading for E coincides with the zero point. In choosing the parameters of the elements i t is convenient to use the relationships 8st

< 1

-T"

Z~K

(7)

9E/--E

Ii---+

IU ,

R= EI--E II

382

(8) )

(9)

u R~ = IU

Rp -< 0. IR'd ,

(11)

r =2ARp,

(12)

10r- Rb
(lo)

'

AR,'E < 1

Rp R'p

(13)

o.1%, }

(14)

5 EI--E

Rd+R+RA+0.5Rp=0.5RpIu-I...__.L, Iz

(15)

where I l is the l i m i t i n g working current of the compensator, which corresponds to El for K or to Ea, which for K u C is substituted into (7), (9), and (14) in p l a c e of El within the Emits Ea min--Ea max; also I u is the limirlng current from the source U, while ARp and AR'p are the resistances of one step in the potentiometers gp and R'p, RA is the resistance of the m i l l l a m m e t e r (RA = 0 for Ku), and 6st is the instability in the working current of the compensator during the t i m e between setting up and taking the reading. During c a l i b r a t i o n of the comparator, the t i m e between these operations is that necessary to obtain a b a l a n c e between the working current in K u, but the stability of the current in K e can be checked at any t i m e from the m i l l i a m m e t e r , whose reading during calibration remains unchanged 9 In measuring Ex, the operations of balancing and taking the reading follow directly one after the other, so any change in the working current of K c has hardly any effect on the result. The working current in K u needs to be monitored only in calibrating the compensator, which is not performed very often, e.g., every 100 measurements of Ex. T h e stability of the working current is dependent on the stability of the power supply voltage and in the resistances of the circuits in which I U and ~ flow. Switch Bt serves to reverse the polarity (Fig. 2) in the c a l i b r a t e d compensator, so one uses a m i l l i a r n m e t e r with center zero; the circuit of Fig. 2 increases the l i m i t of measurement by a factor 2 c o m p a r e d with Fig. 1, when the m i l l i a m m e t e r of the same class of a c c u r a c y is used. M i l l i a m m e t e r s with the zero at the start o f the scale are more a c c u r a t e than c e n t e r - z e r o meters, so the circuit of Fig. 2 enables one to increase either the l i m i t or the a c curacy of the comparator. A further advantage of this system is the scope for using standard potentiometers to adjust the working current 9 The c i r c u i t o f Fig. 2 combines the possible forms of compensator. Resistor Rk is needed only to adjust K u i f the origin for E lies outside the range of the e m f of E a, i.e., one is testing unsaturated n o r m a l cells in the c o m p a r ator, where Ea max < E. Polarity switching is not necessary in this form. The parameters of the compensator e l e ments are determined by (7)-(10) and Rp R k + Rp

Eamax - - Eamin E ~ E a rain

Rd + R 4- RA

I~i - - 1z

R k + Rp

Is

ARp -

-

Rp

(.rD (18)

ARp R-'~

(16)

As ~< E a . m x - Eamin ' 1

--< - - " 5

_ _ A~r E l -- E

(19)

One uses (17) and (19) for a c a l i b r a t e d compensator, while (16)-(18) are used for an uncalibrated one 9

A comparator with the compensators as in Fig. 3 has all the advantages of Fig. 2, while it can be rapidly assembled from instruments available in any metrological laboratory. For this purpose one needs two standard coils, two resistance boxes, two batteries of output 1.3-1.6 V, a polarity reversing switch, and a milliammeter. The parameters of the elements for such a compensator are determined by (7), (9), and ( R d + R + RA) I S = U

(20)

383

U Rp > 5 " ~ R

(9.1)

ARp

I

Ak

Rdq-R+R a

5

Ez--E

(22)

A disadvantage of this circuit by comparison with Figs. 1 and 2 is that the current adjustment is not very smooth. One can change the l i m i t in output voltage for any of the compensators by varying the compensating resistance R by means of switch B2, as shown in Fig. 3, or else by varying the supply voltage while simultaneously changing the l i m i t of the m i l i l a m m e t e r . Resistors r'd and r d are switched by means of push buttons Pb2 and Pb3 in Fig. 1, and they serve to restrict the current in the measuring circuit when checking the polarity of connection of the normal c e l l and during rough balancing. Resistor Rs provides for the c r i t i c a l state of the null indicator. Push button Pbl and resistor RR are used to determine the internal resistance of the normal c e l l by means of the internal voltage drop [1]. Only the contacts of switch B and push button Pb3 need to provide s m a l l t h e r m o - e m f s in the circuit (< 0.2 AK). T h e other thermo-emfs in the measuring circuit are compensated by K u during calibration. As the accessory normal c e l l one can use a saturated normal c e i l of ordinary design with an e m f instability < 0.2A K between calibrations. At our factory, two comparators with compensators as of Fig. 3 have been used for a year in measurements on saturated and unsaturated normal ceils with e m f instabilities o f about 1 0 / I V / y r . One o f these is used to compare the emfs of first-grade normal ceils with an error not exceeding * 0.1 /IV, and these comparators employ Ml109 class m i l t i a m m e t e r s o f a c c u r a c y 0.2, together with R321 standard coils. T h e accessory normal c e l l is an e l e m e n t whose electrode surfaces are larger than those in a normal c e l l of standard construction (diameter of the branches 35 mm) [3]. To reduce the thermo-emfs, the switch is made of sliding stud type with massive copper contacts. As the null indicator one uses an M17/3 galvanometer or a m i c r o v o l t m e t e r R325. There is also potential protection o f the null indicator from l e a k a g e currents. This comparator enables one to cheek a l l normal ceils produced in the USSR and elsewhere, and also to compare the emfs of standard normal ceils. The eomparator is simple to make and use, while providing high productivity. T h e t h e o r e t i c a l circuit of the comparator is the most convenient for designing an automatic d i g i t a l system for checking normal ceils.

LITERATURE 1o 2. 3. 4. 5.

384

CITED

G O S T 12054-66: Normal Cells (Measures of Electromotive Force), Test Methods [in Russian].

N. H. Z. V.

I. Kotel'rdkov, Izmeritel' Tekh., No. I0 (1971). B. Brooks, I. of Res., Bureau of Standards I_~I,(1933). I. Zelikovskii, T m d y VNIIM, No. 81 (81), Standartgiz, Moscow (1967). G. Boichuk, N. M. Ogirko, and N. M. Tsaryuk,Author's Certificate No. 346678, Byull. Izobr., No. 23 (1972).