MEASUREMENTS

OF ELECTRICAL

AND MAGNETIC

QUANTITIES

CALIBRATING VOLTAGE SOURCE Yu. and

UDC 681.2 : 621.3.072.2 : 621.317.725

M. T u z , Y u . S. E s i k o v , A. 8. P o p o v

In order to improve the accuracy of measurements, instruments that have inadequate time stability are cali = brated before measuring with some standard instrurnent or with a built-in source of calibrating voltage. Nonlinear resistances connected in a bridge circuit are used extensively for the latter. For example, a calibrating voltage source using incandescent lamps maintains an output voltage amplitude to an accuracy of ~ (0.5 to 1)% over an input voltage change of :k10%. However, the time instability of incandescent lamps reduces the reliability of such

sources. As a rule a sinusoidally-shaped voltage is employed for graduating and calibrating instruments, we will analyze the possibility of utilizing for these purposes an alternating voltage of rectangular shape which can be obtained from simpler and more reliable calibrating voltage sources. For a curve having the form of a meander the average, effective, and peak values are equal, consequently it is possible to calibrate with a rectangular-shaped voltage the averaging, effective, and peak-reading instruments without extra calculation. A calibrating voltage source has systematic errors that are due to frequency error in the calibrated voltmeter and to the form of the calibrator's voltage, and also errors resulting from instability of circuit elements and power supplies. Systematic Errors. When calibrating effective and average-reading instruments with a rectangular-shaped voltage the error is

A= ~8 Z

'~2t:--I (2~2-1)~'

(~)

where T 2k-1 is the instrument error at a frequency (2k- l)fc and fc is the frequency of the calibratingvoltage. For instance, with a type F505 voltmeter the systematic error is 0.04% if fc = 250 IIz, and 0.28% if fc = i000 Hz. With the majority of electronic voltmeters having a frequency band from 20 Hz up to i0 kHz or higher the frequency error at a calibratingfrequency between 200 and I000 I-Iz,corresponding to the middle frequency range, is negligible when using a rectangular-shaped voltage. It can be determined from gq. (I) for each specific

case. when the symmetry of the rectangular voltage is disturbed (Fig. 1), i.e., when

8 - - - t / ( T - - t ) r l,

(2)

but U1 + U2 = const, after eliminating the dc component there are for the effective and average values of voltage the errors t

(l - V~) ~ ~e-

I+ 8

'

(3)

(I - - 8 ) 2

']av= ( ! + 6)2

(4)

Fig. i Translated from Izmeritel'naya Tekhnika, No. 9, pp. 42-44, September, 1973. 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 transmitted, in any form or by any means, electronic, mechanical, photocopying, microfilming, recording or otherwise, without written permission of the publisher. A copy of this article is available from the publisher for $15.00.

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J, g Uout

up( 1 /II 8.1~-- --/~I~ l,t

1,05

1,,0

O,f8 0,96 0,90

~up

"~JR b v

0,9

Fig. 2

Fig. 3

The errors 7e and 7av are shown as functions of the ratio of the half-periods in Fig. 2, where curve 1 is for the average values of voltage and curve 2 is for the effective values. Thus, if the effective and average values of a rectangular voltage must be maintained within an error of • the ratio of the half-periods must be kept within the limits of 1.1 > 5 > 0.91 and 1.063 > 6 > 0.94, respectively, which is quite feasible. The primary advantage of a stabilizer having a rectangular-shaped voitage which uses voltage-stabilizing diodes is that the amplitude of the alternating voltage, since it is equal to the stabilization voltage, can be accurately determined with dc. However, when there is dc on a voltage-stabilizing diode, approximately twice as much power is dissipated as with ac so that the temperature is approximately twice as high. The resulting transfer error, i.e., the error of the ac amplitude relative to the amplitude determined with dc, is given by .~t = O,45at

IUrev Sa

(5)

where c~t is the stabilization temperature coefficient, S is the cooling surface of the diode, p is the heat-transfer coefficient, and I is the current strength flowing through the diode. The transfer error can be reduced by choo~ng the minimal feasible current strength and by increasing the thermal stabilizing surface. There are currently in production the type /9818 voltage-stabilizing diodes having a small temperature coefficient with which 7t can be considerably reduced. Assuming a perrnissible transfer error of 0.05% and c~t = 0,5%/10~ the temperature difference for the diodes between dc and ac should not exceed l'C, which is easily realized. The error due to the duration of the leading edge r f of the rectangular voltage is 4

Tf

Vd=7'

T'

(6)

Consequently, with a rectangular-voltage frequency of 1 kHz (T = 10 -3 sec) the error will be less than 0.1% if r f is less than 0.75 ~see. Error Due to Parameter Variations in Circuit Elements. The best way to form a rectangular-shaped voltage is with a flip-flop having an inverting input and two voltage-stabilizing diodes as shown in Fig. 3. Output voltage error may develop because of parameter variations in the circuit elements, i.e., because of changes in the resistance of resistors, in the supply voltage, and also in the residual parameters of transistors such as the saturation voltage when-on" and leakage current when "off.- To 4mplify the calculations we will neglect the output resistance Rsu p of the power supply, the resistances of resistors shunting the ,,on- junctions of transistors, and also the voltage drop across ',on,' junctions in comparison with the power supply voltage. The relative variation of the calibrator's output voltage is AUst

Veal- wst

IstRst -

(7)

v~st wst

1343

s ,

]B

,a-60V

' tOOutput

Fig. 4 where 7ist is the relative variation in the current strength flowing through the voltage-stabilizing diode, Ist is the the current strength flowing through the diode, Rst is the dynamic resistance of the diode, and Ust is the stabilizing voltage. The relative variation in the current strength flowing through the diode can be found from the expression for the diode's current strength in the present circuit (see Fig. 8)

Ist

Reesup --

-

-

A,

Rce

(8)

where

Rc%n

Rc%

Rce= Ra-k Rstff pe--~onq- Rc_k Rb ' 1 A~

ebi-k ece 1-- ebi + ebe esup _ esup I co Rc-k Ron Re+R b - ~ e s u p

Rb

Rlq-Rz;

(9)

(10)

R a is the additional resistance, Ron is the collector-emitter resistance of an "on', transistor, ece is the voltage drop between the collector and emitter of a transistor, ebe is the voltage drop between the base and emitter of a transistor, esu p is the power supply voltage, Ico is the collector current of a transistor when cut off, Rc is the collector resistance, and R b is the base resistance. It can be shown that 7Ist = 7esupXesup-kYRc•

+?Rb•

-k ?ebe~ebe-k ?ico,~ico q- ?Ra•

]/ece>tece q,

where 7 designates the relative errors of the corresponding parameters and x designates the influence coefficients. The relative variations of the parameters are determined according to the service conditions or a handbook. From the values of the influence coefficients it is possible to choose acceptable errors for the elements such that the error of the calibrating voltage source will not exceed a prescribed value. Schematic Circuit of the Calibrator. The calibrator (see Fig. 4) is made up of a driving bloeldng oscillator T1, a shaping flip-flop T2 and T3 using type MP'26 transistors, a limiter D3 using a type D818 voltage-stabilizing diode, a thermal compensating circuit/34, a voltage divider R1 to R3, and a stabilized power supply. The output voltage from the blocking oscillator T1 is differentiated by the network C - R 4 and passed on to the inverting input D1 and D2 of the flip-flop. The rectangular-shaped voltage output of the flip-flop is fed to the diodes of the lira iter. Owing to the shaping of the flip-flop at a voltage amplitude of around 40 V and the subsequent limiting to a voltage of 8 V the leading edges of the rectangular-shaped voltage are very steep. The thermal compensation is achieved by means of a copper resistor connected in series with the dividerwhich is made up of manganin resistors. In order to provide a constant temperature field close to the resistor and the volt-

1344

age-stabilizing diodes, the latter are potted tightly in with the brass housing of the copper resistor. The voltage divider is made from manganin low-reactance resistors. Instruments fabricated in accord with this circuit were tested over a temperature range from - 3 0 to +50~ The temperature error did not exceed 20.05%/10~ It can be reduced by individually selecting circuit elements for the thermal compensation.

1345