C O M P E N S A T I O N OF THE Z E R O D R I F T

M I C R O W A T T M E T E R S

V. I , P r o n e n k o , V. N, U s o r i s , a n d S. D. S h u l i k a

IN T H E R M I S T O R

UDC 621.317.784,029.6

Thermistor microwattmeters which consist of a bridge and a thermistor head are the most widely used power meters at ultrahigh frequencies. Their sensitivity is of the order of 10 "7 W. It is l imi ted by spontaneous thermistor heater power variations due to the drift and instabil i ty during measurements of the thermistor head temperature and of the supply voltage. Direct methods for raising the sensitivity of thermistor microwattmeters consist of thermosta- t ic control of the thermistor head, s tabi l izat ion of the supply voltage, and reduction of the duration of measurements, In addition to them there also exist compensation methods for counteracting the e lec t r i ca l zero drift. The best re-

sults can be obtained by using al l or several of the existing methods for counteracting the microwat tmeter ' s zero drift.

One of the most effect ive zero-dr i f t compensation methods which is based on using two s imilar thermistors has been applied for a long t ime in our widely ut i l ized microwattmeters type M4-1 [1]. Owing m the difference between the working and thermocompensating thermistor characterist ics the eff iciency of this compensat ion was very low (the zero drift rate was reduced by a factor of 3-5). The striving to raise the zero-dr i f t compensat ion eff iciency led to the development of another method [2] based on the appl icat ion of a disc thermistor (for instance, of the MMT-9 type) for producing a drift in the reference s tabi l ized voltage supply in order to compensate the power drift in the basic thermistor heating. This method is used in microwat tmeter type M4-3 [3]. The s imi lar - thermis tor method has not been improved since the development of microwat tmeter M4-1 in 1958, despite the fact that its appl icat ion for temperature compensation also compensates the instabiIity and zero drift due to deficiencies in the instrument sup- ply source. Below we examine the possibili ty of raising substantially the eff iciency of this method. We shall show that the method of s imilar thermistors can be used in any microwat tmeter whose readings depend on the heating pow-

ers of the working and reference thermistors in the following manner:

P = KP~ - - P l

or

A P = K,XP~ ~ AP1, (1)

where P is the microwat tmeter reading, Pl and P2 are the working and the thermocompensating thermistors' heating powers produced by the microwat tmeter currents, K is the coeff ic ient of proportionali ty ca lcu la ted to provide a zero reading at the instant when the microwat tmeter is set to zero, zXP are the microwat tmeter reading variations, z3P 1 and

zXP 2 are the working and thermocompens~ting thermistors' heating power variations.

Formula (1) corresponds to the measuring ci rcui t of microwat tmeter M4-1, which uses an e lectrodynamic in- strument with two stationary coils and a moving coi l [1]. The stationary coi l currents Ikl and Ikz are proportional to the currents in the working and reference thermistors (Ikl = KII1 and Ik2 = KzI~). The current in the moving coi l is proportional to the difference of currents in the stationary coils (K2I~-K1K1). The torque applied to the moving coi l , and, therefore, the reading on scale P is proportional to the difference of the squares of stationary coi l currents:

p = K a ( K ~ I ~ - - K ~ I~ ) . (2)

The setting of the "e lec t r i ca l zero" consists of shunting the bridge with the thermocompensating thermistor (selection of coeff ic ient Kz). We then obtain

= o .

Translated from Izmer i t e l ' naya Tekhnika, No. 7, pp. 28-31, July, 1968. Original ar t ic le submitted June 1, 1967.

888

Here and henceforth subscript "0" denotes currents at the instant when the rnlcrowattmeter is set to zero. A

microwat tmeter c i rcui t is designed so that

t(~ Ka = R~, (4)

where R T is the operating resistance of both thermistors.

By combining (3) and (4) with (2) we obtain an expressior s imilar to (1) in which

(2) K = K~ "

Formula (1) wil l also hold for the measuring c i rcui t of microwat tmeter M4-3, provided that its current is sup- plied from a vol tage s tabi l izer with a reference balanced thermistor bridge one of whose arms consists ff a thermo- compensating thermistor which is, ident ica l to the working thermistor and has the same resistance as the lat ter ,

The power produced by heating thermistors with the microwat tmeter currents in a general case is equal to

P1 = P r t - - PT.uhf ' P~ = Pr~, (6)

where PT1 and PT2 are the total dissipation powers of thermistors, 'PT.uh f is the uhf power in a thermistor.

It is possible to consider for the thermistor microwat tmeter ambient temperature range that the leakage coef- f ic ien t of thermistors does not depend on temperature and, therefore,

Pc1- . l ( r x l - - r) , Pc, = H= r ) , (7)

where Tel and Tcz are the thermistors' character is t ic temperatures, i .e . , the ambient temperatures for which the ther- mistors, without being heated by a current, have a resistance equal to their operating resistance under normal condi-

tions (RT); HI and H 2 are the thermistors' l eakage coefficients in watts per degree of temperature difference between

the working body and the surrounding medium; T is the temperature of the thermistor head.

]By substituting in (1) for Pl and P2 their values from (6) and (7) we find after transformations that

P = K H 2 ( T c ~ - - T ) - - H I ( T e l - - T)-~- PT.uhf" (8)

Variations in the microwat tmeter readings due to the thermistor head temperature changes are equal to

OP AP -~ A T = (Hx - - KHz) A T . (9)

O T

It has a l ready been noted that coeff ic ient K is determined from the zero setting condit ion (P = 0) at a temper-

ature T = To without supplying uhf power (PT.uhf = 0).

By substituting the above values for the corresponding quantities in (8), we obtain

H i ( T e l - - To) K = , ( lo )

H2( Tc'2 - - To)

and, therefore, we find from (9) that

where

H1 AT k P -- , (11)

M

r E 2 ~ T o M = - - - (12)

Te~-- T e l '

H 1 AT is the microwat tmeter ' s zero drift without temperature compensation, M is the temperature compensation ef- f iciency.

Expression (12) can be used for arriving at several conclusions which are important for designing microwatt- meters with zero-dr i f t thermal compensat ion by means of the ident ica l - thermis tor method.

1. The microwat tmeter reading variations due to the thermistor head temperature changes are the same with or without the supply of uhf power.

889

2. The characteristic temperatures of the operating and thermocompensating thermistors should be identical or as close as possible. Other characteristics (heating power, leakage coefficient) can differ.

3. If the thermistor head, in a meter which is thermally compensated by means of identical thermistors, is pro- vided with a thermostat, its temperature should be set as low as possible.

4. The use of measuring circuits with combined heating is undesirable. Dc heating of a thermistor in an ac c i rcui tor , vice versa, ac heating in a dc circuit,is equivalent to a corresponding rise in the ambient temperature at which the thermistor, without the heating effect on the measuring circuit, has a normal operating resistance, i.e., the above is equivalent to lowering the thermistor's characteristic temperature and producing, with the remaining conditions being equal, a higher frequency drift rate.

Combined supplies can be used for equalizing the thermistors' temperature characteristics in order to raise tem- perature compensation efficiency. It is then necessary to account for it in (6) by additional terms.

However, this problem can be solved in a simpler manner by utilizing the relationship of the characteristic tem- perature to the working resistance.

It follows from the well-known thermistor relationship

B R---- R~e Y

that

1 Tc2 - 7c~ %, -~P'2 (13)

1 + I n ~ B RT2

where Tc2 and T'cz are the temperature characteristics of thermally compensated thermistors at their operating re- sistances equal to RTZ and R'.I~ respectively.

It can be shown that the characteristic temperature variation ATc~ is related to the change in the characteris- tic resistance by the following expression:

92 ARt, ATe * == - - (14)

B RT~

If the thermocompensating thermistor is replaced by a thermistor with a series connected resistor, the charac- teristic resistance df a thermistor equivalent to the latter combination will be higher than that of a single thermistor, since the latter will work at a lower operating temperature. It is obvious that other characteristics of the equivalent thermistor will also change, but it has already been shown that this will not affect the temperature compensation ef- ficiency. If a thermocompensating thermistor is used with a shunting resistor, it will work with a higher operating resistance and, according to (13), the characteristic temperature of the equivalent thermistor will be lowered. Series or shunting resistances for thermocornpensating thermistors are selected for permanent operation and can be mounted in the thermistor head casing.

The required values of series or shunting resistances are related through ART2 to the desired variation of the temperature characteristic by the following expressions:

BATe2 ATc, > 0; Rsr = ARt2 = R~,2 7,2 (15)

(i T5 ). + 8Are (16)

A thermistor head with such a resistance connected to any thermistor bridge which meets expression (1) will provide without readjustment or regulation an effective temperature compensation of the zero drift for any ambient temperature.

890

The microwattmeter 's zero drift is due mainly to the heat exchange which occurs between the thermistor head

and the ambient medium and tends to equalize their temperatures. For an ambient temperature jump of ATam b, the

temperature of the head changes according to the following taw:

t

T = Tambq-5Tamb(1--e ~ ), (17)

where v is the heat constant of the head.

The temperature of the head varies for the duration At of a measurement by an amount

AT =- - - OT Aq~ ,A~

Ot T

(18)

By substituting in (11) for AT its value from (18) we obtain an expression for a microwattmeter 's relative zero

drift rate N, i .e. , for a jump of onedegree in the ambient temperature

t hP H1 Hi (19)

N - - -- e x , . < _ _ . At ATam b M'r M~r

The effectiveness of thermal compensation, i .e. , the accurate selection of a thermocompensating thermistor can be judged from the microwattmeter 's maximum relative zero drift rate measured after a temperature jump

(Nma x = H I / M r ) .

The method described above for obtaining a maximum effective temperature compensation was applied to a

thermistor microwattmeter consisting of bridge M4-1 and thermistor heads M5-40-M5-45, M5-49, and M5-50.

In practice it is possible to obtain by means of these heads an effective improvement of the order of 100-200.

With the thermocompensating thermistor selection methods used by the thermistor manufacturing plant an effective

improvement of 20 can be obtained for an ini t ia l temperature of +20~ When it is necessary to raise the effective- ness of thermocompensation it is possible to connect to the reference thermistor of these heads a series or shunting

resistance in order to correct the thermistor's characteristic temperature.

The heat constants r which represent the heat exchange process between the head and the ambient medium amount to about 15 rain for thermistor head types M5-40-M5-45 and about 40 rain for M5-49 and M5-50 types. For

these heads H I _<500 gW/~ and the duration of measuring with bridge M4-1 does not exceed 0.5 rain; therefore, ac-

cording to (19), the microwattmeter 's zero drift for a 1~ ambient temperature jump during a measurement will not exceed 0.85 pW and 0.17 pW for effective improvements of 20 and 100 respectively in the case of Mg-40-M5-45

heads. The corresponding figures for M5-49 and M5-50 heads amount to 0.31 #W and 0.06 pW respectively. After

a lapse of t = 4 r (1 h for the M5-40-M5-45 heads andapproximately 2.5 h for the M5-49 and M5-50 heads) the effect

of a jump is reduced still further by a factor of 57. The microwattmeter 's zero drift then no longer depends on the

temperature jump, but on other reasons (for instance, the instability of the bridge supply source).

The above evaluations completely correspond to the results obtained in experiments with tens of heads whose

temperature jump of 20-30~ was obtained by placing the heat in a thermostat and whose rate of drifting was calcu- lated at various instants after the temperature jump by dividing the observed microwattmeter 's rate of drifting by the value of the temperature jump.

It is obvious that for very slow ambient temperature variations the rate of the thermistor-head temperature changes is equal to that of the ambient medium, and the zero drift rate of a microwattmeter with heads which have ident ical thermistors is reduced by a factor of M (where M is the effective improvement in temperature compensation).

The advantage of applying identical thermistors consists of an effective microwattmeter 's zero drift compen- sation due not only to the thermistor-head temperature drift, but also to the supply voltage drift. If both bridges are supplied from the same source of voltage V, then

AP1 AP~ AV . . . . 2 (20)

Plo P2o V

By substituting in (1) for zXP 1 and AP~ their values from (20) we find for the case when K = Pl0/P20 that zSP = 0, i .e. , that the microwattmeter 's zero drift due to the supply voltage drift does not occur at all. In microwattmeters type M4-1 this outstanding property of the identical- thermistor method is only partly realized, since the supply cir-

891

cuits of each of itsbridges have dc to ac converters (~ 00 kHz generators) which are not covered by the automatic reg- ulation circuits. The instability of their conversion factors produces asynchronous variations of the supply voltage (equation (20) no longer holds). Thus, the instability of the microwattmeter M4-1 supplies contributes an important component to the instrument's zero instability. Experiments have shown that the precision in measuring small powers by means of heads with identical thermistors hardly raised above the precision guaranteed for the M4-1 bridges. An important practical result obtained by using such heads in M4-1 bridges consists only of the possibility of measuring small powers with the former error, but in the presence of much larger ambient temperature variations.

However, the above evaluations indicate that there exist prerequisites for developing a new microwattmeter for measuring small powers with a substantially higher sensitivity and precision. It seems advisable in a new micro- wattmeter to utilize all the advantages of the identical-thermistor method and to control thermostatically the ther-

mistor head (even with an error of ~- 1~

Let us note in conclusion that the apparent possibility of raising indefinitely the effectiveness o f temperature compensation over the entire temperature operating range without any adjustments (for Tct = Tc2) cannot be attained in practice, since two of the prerequisites upon which the derived relationships are based are met only approximately. One of them consists of the leakage coefficients H 1 and H z being independent of temperature, and the other of the thermistor head components which surround the operating and thermocompensating thermistors being at the same temperature.

L I T E R A T U R E C I T E D

1. L.M. Zaks, Transactions of the Institutes of the Committee of Standards, Standartgiz, No. 48 (108), Moscow (1960).

2. L.M. Zaks, V. M. Petrov, and E. N. Belikov, Izmeritel. Tekh., No. 2 (1962). 3. L.M. Zaks, V. M. Petrov, and E. N. Belikov, Izmeritel. Tekh., No. 6 (1965).

892