1960 Aslan: Temperature-Compensated Microwatt Power Meter 291Combining these last two equations gives Substituting this value in (26), we find

2V2 RIa 2A/2 RIaB co_rR.,_ _ _ _2

- (27) RC= - (29)_--2_a2 r1+( C 82a21-I+2)B+(: J L \K(1-I2 -a2,B) and substitution in (24) gives

The quantity Rocp

~R= 4- a2- (30)_______p 412a2f32 1K(1- I2 a2) 1- (12 + a2)3 1+ W2T2

is essentially r, the time constant of the bolonmeter, from ACKNOWLEDGMENT(20). The small difference is clearly due to the presenceof the ac as well as the dc currents in the present case. The authors express their gratitude to the Hewlett-Therefore, Packard Comnpany, the Narda Microwave Corporation,

_V2RIai3 1 and Horman Associates for making available the equip-22X/2 Rla 1 (28) ment required to perform the measurements described1- (2 + a2)3 1 + w2T2 in this paper.

Temperature-Compensated Microwatt Power Meter*EDWARD E. ASLANt, MEMBER, IRE

rp HE normal way to measure RF power is by usinga thermistor or barretter whose resistance is de-pendent upon temperature. The RF power heats R2

the element and the change in resistance is a measure of R T 2the power level. Changes in ambient temperature, there- 160 R F BRIDGEfore, would have a deleterious effect on the measure- VA 200ments, particularly when measuring the lower power 2 200levels. The circuitry and special mount of the tempera- _C X E'ture compensated power meter to be described mini-mizes the effect of this ambient temperature variation. A

R4 RC200 200 TEMPERATURE

PRINCIPLE OF OPERATION COMPENSATINGBRIDGE

Referring to Fig. 1, the circuit of the power meter B tconsists of an RF bridge, an oscillator whose power out- \ 06put is controlled by the RF bridge, a temperature com- ERRORpensating bridge, and an error detector amplifier and I AMPLIFIEmeter. The RF mount consists of two identical thermis-tors, one in the RF field, and the second out of the RFfield but in the same atmosphere. The RF power meas- Fig. 1-Simplified schematic.urement is based upon the substitution of audio for RFpower.

equal to 240 ohms, an oscillator gain of approximatelyThe gain of the oscillator iS preset to such a value 10 wil mananteR hriso eitnea 0that the impedance of the RE thermistor element iSohsmaintained at 200 ohms by the output of the oscillator. Tetmeauecmestn rdeam r eThne values of the resistance arms are SUCh as to main-tain the bridge in this unbalanced condition. With Rx lected so that it is balanced with no RE power appliedto the RE bridge. Under these conditions the error de-

tector sees a zero voltage and indicates zero on the* Received by the PGI, June 24, 1960. Presented at the 1960 Con- meter

ference on Standards and Electronic Measurements as paper 6-6. eert FXR, Inc., Woodside, N. Y. When RE power is applied to the RE thermistor ele-

292 IRE TRANSACTIONS ON INSTRUMENTATION Septemberment, its impedance decreases. This change in the It is obvious then that the temperature compensationthermistor resistance decreases the feedback of the must be quite effective if the power meter is to have aoscillator, thereby lowering its output. A new steady- 0- to 10-,uw range. With the temperature compensationstate condition is quickly reached such that the 200 actually achieved, a drift of 1 ,uw on the meter scaleohms of the thermistor element is maintained by a de- accompanies approximately a 0.30°C ambient tempera-crease in the power output of the oscillator. This change ture change, or the temperature drift is 1 per cent of thein audio power is proportional to the RF power applied temperature drift without compensation (see Fig. 2).to the thermistor, and the net power dissipated in the The resistance of a thermistor at any temperatureRF thermistor element remains unchanged. may be expressed

This decrease in power output of the oscillator affects / 1the temperature compensating bridge and causes the R = Roe exp B t--) , (3)impedance of the temperature compensating thermistor T Toelement to increase, thereby unbalancing its bridge. 'IThe where B is a constant dependent upon the material ofoutput voltage of the temperature compensating bridge the thermistor expressed in 'K. Thermistors made fromis given by' the same batch will have values of B extremely close to

Vba each other.

Ev = 0 1 + OP j (1) Ro = resistance at temperature To.1600 L 400J

The variations in Ro of thermistors are determined bywhere OR/oP may be defiAed as the sensitivity of the the variations in the geometry of the thermistor and thethermistor element andcha is the increment of applied lead spacing within the thermistor. It is the largest vari-power that causes a chaogein the thermistor resistance. able encountered in the thermistor characteristics but

For small increments of power where the change in the easiest to measure and control by selection.thermistor resistance is small, the second term of the ex- Perfect temperature compensation can be had whenpression may be dropped. The voltage Vb may also be Ro, B, and the dissipation constants D expressed inconsidered a constant. In addition, it can be assumed mw/C0 for both thermistor elements are equal. Underthat thermistor will have a linear variation of resistance these conditions the RF thermistor element is main-with power, and OlROP may be replaced with a con- tained at 200 ohms by the power output of the oscillator.stant. The expression for small increments in power Since the temperature compensating thermistor ele-then becomes: ment has the same characteristics, it too will be main-

Ev = KAP, (2) tained at 200 ohms when no RF power is applied.

resulting in a meter scale which is linear and directly The temperature coefficient of resistance of a ther-

proportional to the incremental applied RF power. mstR B

TEMPERATURE COMPENSATION T = Ro - (4)

A change in ambient temperature will cause both ohms 0C.thermistors to change their resistances simultaneously. The degree of temperature compensation -q may beThe change in resistance of the RE thermistor element indicated by the ratio of the compensating bead tem-

will increase or decrease the output of the oscillator in perature change Atc, caused by a change in audio power,such a manner that its steady state value of 200 ohms to the ambient temperature changeAta.will be maintained. This change in audio power will also (DI)(RC) I DI Rcbe applied to the temperature compensating bridge. If X tta D RD (5)both thermistors are identical, then the change of audio Ata(200) D2 D2 200power in the temperature compensating bridge will be where D is the dissipation constant expressed in mw/°C.just enough to return the resistance of the thermistor to It is dependent upon the mounting configuration andits original value. Since the power sensitivity of the the geometry of the thermistor mount. The differencesthermistor is almost constant over a reasonable tem- can be closely controlled by careful positioning andperature range, both the zero and the power readings soldering of the thermistor in the mount.would then be temperature compensated.

For the thermistors and the geometry of the mount R0 200 ~ratio of audio power dissipated in the tempera-used, a change of 1 ,uw of power would change the ture compensating thermistor to the audio power dis-thermistor bead temperature approximately 0.003°C. sipated in the RE thermnistor @, RF = 200 Q.. (6)

By close matching of the Ro of the thermistors and

met,"MIT. Rad. Lab. Ser, McGraQw-eHi°l Book C.,Ic.,e Newsr-York, N. Y., pp. 85-86; 1947. pensation is possible as shown by Fig. 2.

1960 Aslan: Temperature-Compensated Microwatt Power Meter 293

OSCILLATOR GAINw For correct operation of the power meter, the oscil-

lator gain and power output must be controlled solely0

by the resistive balance of the RF bridge and should bew 1 independent of the reactive balance. The reason for

D881/this criteria is obvious since the RF energy applied to

6 7 / the thermistor will affect only the thermistor tempera-6 1 < ture and in turn its resistance. Therefore, the reactive5 / component of the error voltage must be very small com-

,Cr4 pared to the resistive component.W 31 / To help accomplish this, the gain of the oscillator is

2 made relatively small, and the RF bridge is maintainedWJ 2

in a considerably unbalanced condition with a resultantMICROWATTS DRIFT large error voltage. However, the resistors in the bridge

o 2 4 6 8 10 2 14 16 8 20 22 24 26 28 30 arms are selected so that in equilibrium the RE thermis-

(a) tor is 200 ohms. This system permits proper operation ofthe circuitry with a lesser concern over the residual re-actances in the bridge arms.

It would be desirable to make Rx such a value that

o the error voltage of the RF bridge is 1/50 of the bridgeexcitation voltage Eo/2. The required gain of the oscil-lator is then

oscillator output voltage 50 X Eo X 2=

__ __ __ _ _ _ = 1 00. (7)error voltage E

2 For the values shown in Fig. 1,

1750 + 200 ARx = (8

3A - 9.253l_

_A = 100, Rx = 237, or for simplicity, 240 ohms.

4 THERMISTOR MOUNT DESIGN

The thermistor mount as a unit contains two ther-w mistor elements Rf and Rc, and a precision resistance R4.

D 5 One thermistor element is positioned in the RF field, the- 17 | St { l | other is positioned out of the RF field, but in close prox-

imity with the thermistor element in the RE field. They6 are a selected pair, matched with regard to dissipation

constant (as determined by mounting configuration),exponential constant B (which is determined by thematerial of the thermistor), and basic resistance R0. Theprecision resistance R4, is preset to such value that itwill determine (when used with proper external cir-

cuitry) the operating conditions and resistance of thel thermistor elements.

For proper operation of the power meter the gain ofthe oscillator must be set to such a value as to maintain

9 l | l | | | | 1 the RF thermistor element at 200 ohms and at the same} .~~~~~~~~~~time balance the temperature compensating bridge. In;~~~~~~~~~ ~~addition the power meter must operate with many dif-

o10l ferent mounts which will have thermistors of slightly0 1 2 3 4 5 6 7 8 9 10 different characteristics. The means for adjustment is

ORIfT(MICROWATTS) based upon the characteristics of aged thermistors.

(b) The change in resistance of a new thermistor, held at

Fig 2-a) rifvstemertur chnge (b Drftan elevated temperature, taken over a period of tenvs time in uncontrolled ambient. years would take the shape of an exponential curve

294 IRE TRANSACTIONS ON INSTRUMENTATION SeptemberRF BY-PASS CAPACITOR

REMOVABLE TEMPERATURECOMPENSATING ASS"Y

TEMPERATURE COMPENSATINGTHERMISTOR

RF THERMISTOR

HOUSING FLANGE

WAVEGUIDE FLANGE

Fig. 3-Waveguide type thermistor mount.

asymptotically approaching a fixed change of 2 to 3 per meter null, the resistance of the RF thermistor elementcent of the entire period. Ninety per cent of the change will be maintained at 200 ohms.would take place in the first week, leaving only a 0.2 to One power meter may be used for power measure-0.3 per cent change to take place through the years of ments over the range of frequencies from 10 Mc to 40use.2 kMc. The coaxial thermistor mount of Fig. 4 covers theThe resistance of the RF thermistor element is de- 10-Mc to 10-kMc frequency range, and each high effi-

termined by the current through it. This current in ciency waveguide mount (Fig. 3) from L-band to K-turn is determined by the resistance of the temperature band covers the full recommended waveguide frequencycompensating bridge between points A and B, Fig. 1, range.Rx, R2, R3, R4 and the power output of the oscillator. The RF and temperature compensating thermistorThese resistances are fixed precise values, the power elements in the coaxial thermistor mounts each containoutput being the only variable condition. two thermistors with operating resistances of 100 ohms.The two thermistor elements Rf and Rc, and resistor The thermistors that make up the temperature com-

R4 are contained in each thermistor mount (see Fig. 3). pensating elements are connected in series to provide aEach mount is independently adjusted in the basic cir- total resistance of 200 ohms. The two thermistors com-cuit shown in Fig. 1, so that R4 = Rc (temperature com- prising the RF element are connected so that they ap-pensating bridge balanced) when Rf= 200 ohms; i.e., pear in parallel to RF power for a load resistance of 50with the gain adjusted to such value that Rf= 200 ohms, ohms and in series to audio and dc power for a resistanceR4 is adjusted to equal Rc for balance of the tempera- of 200 ohms.ture compensating bridge. It should be noted from Figs. 3 and 4 that the tem-As previously stated, the characteristics of the perature compensating thermistor in each of the mounts

thermistors and bridge elements are fixed; therefore any is contained in a separate subassembly to facilitatemount designed and adjusted as described will operate matching of the characteristics of both thermistors.with the power meter. Once the gain of the oscillator is During the development of the thermistor mount anadjusted (with no RE power applied) for an indicating interesting phenomena was noted. The thermistor

2R. S. Goodyear, "Industrial thermistor applications, " Elec. mount exhibited the characteristic of a change in theMfg., vol. 62, p. 90; October, 1956. operating temperature of the thermistor beads when

1960 Aslan: Temperature-Compensated Microwatt Power Meter 295

REMOVABLETEMPERATURE

/ \ \ \ / / / / ~~~~~~~~~~~~~~~~~~~COMPENSATINGASSYTYPE "N" COAXIAL CONNECTOR \O\E\S/I/ /S/

TEMPERATURE COMPENSATING THERMISTORS

RF THERMISTORS

COUPLING CAPACITOR

RF BY-PASS CAPACITOR

HOUSING FLANGE

Fig. 4-Coaxial thermistor mount.

the mount was rotated from a vertical to a horizontal tual full scale meter current. Additional markingsposition. This was found to be due to a change in the termed "calibration factor" may be placed in the re-path taken by the convection air currents, resulting in a maining 10 per cent of the scale. The calibration forchange in temperature gradient of the air surrounding these markings is equal to 90 per cent of full scale cur-the beads. This condition was corrected by positioning rent divided by the calibration factor.a thin walled foamed polystyrene enclosure symmetri- Calibration factor for a thermistor mount is defined ascally around the beads, thus limiting the convection cur- the ratio of substituted dc power in the thermistor ele-rents to identical paths regardless of the position of the ment to the microwave power incident upon the ther-mount. The foamed polystyrene enclosure did not af- mistor bead.fect the RF characteristics. The full-scale calibration can now be made to the

actual calibration factor for the thermistor mount. ThisFULL-SCALE CALIBRATION results in absolute power measurements that exclude

It has been indicated in the description of the opera- errors caused by the thermistor mount due to VSWR,tion of the power meter that the error voltage or meter efficiency, and dc substitution, all of which are includedreading is proportional to the amount of RF power dis- in the calibration factor.sipated in the RF thermistor. A reference must be pro- A typical X-band thermistor mount as shown in Fig.vided to enable absolute power measurements to be 3 has been certified by the National Bureau of Standardsmade. This calibration is accomplished by dissipating to have a calibration factor of 0.973, 0.982 and 0.980 atdc power of a full-scale value in the RE thermistor and frequencies of 9000 Mc, 9800 MIc, and 11,200 Mc, re-adjusting the gain of the error detector amplifier to indi- spectively. The accuracy of the measurements was 1.5cate a full scale meter reading. The source voltage for per cent at 9000 Mc and 1 per cent at 9800 and 11,200the dc power may be monitored on the indicating meter Mc.to insure precise measurements. For the commercial power meter the input of the error

detector amplifier has a 5-db-per-step attenuator pro-CALIBRATION FACTOR viding six full-scale ranges from -20 dbm to +5 dbm.

The meter indication at the full scale power indica- The position of a range selector switch simultaneouslytion can be made to correspond to 90 per cent of the ac- selects the proper setting of the attenuator and the

296 IRE TRANSACTIONS ON INSTRUMENTATION September

proper amount of dc power to be dissipated in the RF ohm resistor of +0.1 per cent tolerance appears to thethermistor for a full scale calibration. The full scale cali- dc calibrating power to be across the RF thermistor.bration may be accomplished on any position of range Algebraic analysis of the error in the full-scale dc cali-selector switch. brating power dissipated in the RF thermistor will showOnce the power meter has been properly calibrated that to a first approximation this error is independent

(first for an indicating meter null by adjusting the gain of the error in the setting of the RF thermistor to 200of the oscillator, and second for a full scale indication by ohms and is equal to twice the error of the 250-voltadjusting the gain of the error detector amplifier, with a source voltage plus twice the error in series calibratingfull-scale value of dc power being dissipated in the RF resistor added to the error in the 200-ohm bridge re-thermistor) it may be switched from range to range sistor shunting the RF thermistor. The maximum ac-without requiring any additional adjustments. cumulative error at full scale on all ranges due to theseThe indicating meter has 3 scales enabling power to contributing errors is 1.3 per cent.

be read directly in mw or in dbm, over a 6-db range. Down from full scale, the maximum error on the0.01-, 0.03-, 0.1- and 0.3-mw scales increases by a maxi-

ACCURACY mum of 0.70 per cent of full scale. This is due to theThe accuracy of the power measurements at full scale tracking accuracy of the meter, and to the error ampli-

exclusive of the calibration factor of the thermistor fier.mount is limited by the accuracy to which the full scale The error on the 1- and 3-mw scale will be slightlydc calibrating power can be held, as well as the main- higher, approaching a maximum total error on the 3-mwtenance of the RF thermistor at 200 ohms. scale of 3 per cent of full scale.The bridge and calibrating resistors have an initial The added error on the higher range scales is due to

tolerance of 0.05 per cent, and are operated far below three causes: the deviation of the thermistor from a truetheir rated power. Operating at rated power for 1000 square law (linear variation of resistance vs power)hours would contribute less than 0.05 per cent change in characteristic, variation of the excitation voltage acrosstheir resistance. The assumed tolerance of the resistors the temperature compensating bridge, and the erroris taken as +0.1 per cent. The accuracy of the differen- caused by the temperature compensating bridge beingtial type voltmeter used for calibration has a 0.05 per in an unbalanced condition. Each of these individualcent tolerance; adding an additional 0.05 per cent for errors is constant for each increment in applied powerhuman error brings the assumed tolerance to +0.1 per and occurs in such a manner that it tends to cancel, re-cent. ducing the total accumulative error.At the initial calibration of the thermistor mount, the Fig. 5 shows a plot of the actual thermistor resistance

RF thermistor can be adjusted to an accuracy of + 0.2 for values of incident RF power. The straight line drawnper cent. Allowing an additional 0.2 per cent for ther- through the curve is the assumed true square law char-mistor aging and 0.4 per cent for the interchangeability acteristic upon which the calibration of the 3-mwof the thermistor mounts brings the tolerance on the meter scale is made. The error due to the deviation fromsetting of the RF thermistor to 200 ohms to +0.8 per the true square law characteristic is given bycent.

Additional error caused by operating the power meter ARP- ARf,in an ambient temperature other than the temperature PfsX 00percent 1, (9)at which it was initially calibrated could contribute an ARf sPlRf,additional nominal 0.1 per cent error for each 10°F dif- whereference in ambient temperature. Since the total error in200-ohm setting of the RF thermistor is small, it would P = incident RE power,contribute very little change in the VSWR and calibra- Pf = full scale incident RE power,tion factor of the mount and almost imnmeasurable error ARfs= change in thermistor resistance at Pfs,due to reflection of incident power. ARp=change in thermistor resistance at P.The 250-volt calibrate voltage which is the source for This error is plotted for values of incident RF power

obtaining the full scale dc calibrating power can be on the 3-mw range on Fig. 6.maintained within +0.5 per cent. The accuracy of the It is assumed in the scale calibration of the powerinitial 250-volt setting is ±0.1lper cent. The stability of meter that the excitation voltage of the temperaturethe monitoring meter is ±0.1 per cent and the reset- compensating bridge is a constant. This assumption re-ability of the meter is to within ± 0.2 per cent. The regu- sults in an error, on the 3-mw range, N2. The variationlation of the power supply when switching between the of this excitation voltage on the 3-mw range is shown in250-volt monitoring position and the full scale calibrat- Fig. 7. The error N2 is given bying position could add an additional error of ±0.1 per V 1cent. The total of these errors is the ±0.5 per cent tol- Z2 = bVf (10)erance on the 250-volt calibrating source voltage. A 200- V1s

1960 Asian: Temperature-Compensated Microwatt Power Meter 297

ACTUAL THERMISTOR CHARACTERISTIC

200. 00 .

w w

0- 00- .5 0 1.5

I8- --

z zw -wo ~~~~~~~~~~~~~~~~~~~~~0

o4 ETRUE SQUARE LAW CHARACTERISTIC iz z

-TEMPERATURE COMPENSATING BRIDGE THERMISTOR RESISTANCE-OHMS

2002 000405060 080 300 300 2.64 266 0.70 2.76 2.800.842088

Fig.5 -Thermistor characteristics. TEMPERATURE COMPENSATING BRIDGE EXCITATION VOLTAGE-VOLTS

Fig. 7-Bridge excitation voltage variation with incident power.

IS

and is plotted in Fig. 6 for values of incident power on1 6 the 3-mw scale.H4 ERROR DUE TO Vf = bridge excitation voltage at full scale incident

THERMISTOR RESISTANCEINCREASING FROM power,

IS2 NULL RESISTANCE

Vb =bridge excitation voltage at incident RE powerID P.

ERROR DUE TOa

l EXVOLTAGE VARIATION X The third source of error occurring at large incre-6- ments in power arises out of the assumption that the

bracketed term of (1) is negligible and can be disre-4

garded in the meter scale calibration. This error is ex-Z 2 - ~ _ \ pressed as N3.01

w 0 - ~~~~~~~~~~~r ARPa II_Z T3 rRRolN--~7 S 1 + 4001

cr ~ TOTAL ERROR IN _3__-_____ercen._(O PERCENT OF FULL SCALE PR

w 1-~~~~~~~~~~~~~4-6 L ~~~~~~~~~~~~~~~~~~400]_

8 - / The terms ARp and ARj, are as previously defined. 23for values of incident RF power on the 3-mw range is10 E also shown in Fig. 6.

12 - / SQUARE LAW CHARACTERISTICS The total accumulative error from these three sourcesin terms of per cent of full scale is equal to

14 -

P16 - It = (t + l1)(I + 2) ( + 3) -1

~~~~~~~~~~~~~~~~~~~~~Pf0 (12)INCIDENT POWER-MW X 100 per cent,

20 -* * * .1.2 5 1.5 75 2U0 2. 5 2 5 2 75 3 316 and is shown in Fig. 6 for values of incident power on the

Fig. 6-Error due to large increments in RF power. 3-mw range.