IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-16, NO. 3, SEPTEMBER 1967

Thermistor Bead Matching for TemperatureCompensated RF Power Thermistor

Mounts

EDWARD ASLAN, MEMBER, IEEE

Abstract-The temperature compensated thermistor-power meterof the dual bridge design has for many years been the most widelyused instrument for microwave power measurement. During thesemany years very little if anything has been written with regard to themanner or criteria for matching the thermistor beads. This paperattempts to fill that void.

The procedure to match thermistor beads for less than 2 ,W/°Cdrift is to be accomplished by pairing the dR/dt characteristic of eachbead and adjusting the dP/dR characteristic for a match. dR/dtof the beads may be determined from resistance data at 900C and1100C, and the expression

dR= 9.4497 [ln Ra - 1.11648 ln Rb + 0.61749]

which is derived for 200 0 operating resistance thermistors. Thethermistor beads are then paired by selecting such that dR1/dt anddR2/dt are within 1 percent of each other. The conditions necessaryfor matched dP/dR of the thermistor beads are developed and pro-cedures indicated.

The paired beads are installed in the thermistor mount and theconstant dP/dR of each bead adjusted for equality by moving theheat sink of one of the thermistors until a balance of the slave bridgeand master bridge is obtained simultaneously.

M /\tICROWAVE POWER is most commonly mea-sured utilizing bolometric techniques. Thepower to be measured is used to heat a bolom-

eter, and temperature rise is a measure of this power.There are many variations of this technique though allare dependent upon temperature and, as such, variationsof ambient temperature may cause error and drift. Inorder to minimize this temperature drift error, the dualor slave thermistor-bridge power meter has been intro-duced and has found wide acceptance in the field.The thermistor mounts used with these power meters

contain two thermistor beads. One is positioned in theRF field, and the other out of the RF field, but in closeproximity to the other.To minimize drift due to changes in ambient tem-

perature at the thermistor mounts, the dissipation con-stants of each element in microwatts per °C must bematched. This constant is dependent not only upon thecharacteristics of the thermistor bead but also uponmounting configuration and environment. Its measure-ment before mounting the beads is impractical. It ismore practical to reduce this constant to two component

Manuscript received April 10, 1967.The author is with the Narda Microwave Corporation, Plain-

view, N. Y.

constituents-one dependent upon characteristics of thebead, the other dependent upon its mounting configura-tion. It is then possible to match the former constantand make provision for adjusting the latter.The former constant may be matched by selection

and the latter matched by adjustment of its environ-ment.These characteristics are dR/dt in ohms/jC and

dP/dR a constant in microwatts per ohm. dR/dt at afixed operating resistance is dependent upon the mixand the geometry of the bead. dP/dR is dependent uponthe geometry of the bead and the manner in which andwhere it is mounted.The dissipation constant in microwatts per °C is

equal to

(dR) (dP\)dt dR

The thermistors will be matched to within 2 uW/°Cwhen they are selected and adjusted such that

dR, dP1 dR2 dP2-x --X <21LW/0C.dt dR dt dR

The expression

= Rb exp ( -4)] (1)

describes the thermistor-resistance temperature charac-teristics for limited differences in Ta and Tb.

R,=resistance at temperature T,Rb=resistance at temperature TbTa and Tb are in °K3 is a constant in °K for a limited range of tempera-

tures T and To.

Differentiating this expression yields

dR - 1 1 2-d = Rexp LM \ Toj_(T-H )

dR Rfdi T2

It is necessary to determine f and T at the thermistoroperating resistance of 200 U.

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ASLAN: BEAD MATCHING

It will be required to obtain resistance data at twotemperatures near the operating temperature of thethermistor. For the thermistors typically used, thetemperature at 200 Q is nominally 1000C or 373.16°K.These temperatures of measurement have been chosenas 90°C and 110°C (363.16 and 383.10°K). This willsatisfy the condition for A to be assumed constant.

In the expression to follow, Ra = resistance at Ta363.16, and Rb = resistance at temperature Tb = 383.16.From (1) above, we may write

Ra /1 1\

Rb \Ta Tb

InRa

Rb

1 1aTa TbJ

The specific temperature To at the operating resis-tance Ro= 200 Q is determined as follows:

Rain-

dR Rb= Ro

dt /1 1\

1n2 (&_ Ta Tb/IR

10 RQ

[TTb Ra\in2

dR 200= 0.02874

dt lIn R(aL RbJ

2 ln(Ra)Ta Rb

I

- 38.32 In R-a200/

+ 367.1 In Ra

Rb

Ta To)

Ra /1 1\ln -=O _ _

Ro Ta To/

RaIn =

Ro

1Ra)Rb

(1 1)Ta Tb

1

Neglecting the first term of the above expressionintroduces less than 0.1-percent error in dR/dt. Thisomission results in a more manageable expression.

dRdR = 9.4497[In Ra - 1.11648 In Rb + 0.61749].di

1 T

(Ta To!

I 1 1

Ta Tb)

dR/dt may now be determined using the above expres-sions for : and 1/To

dR Rofdi To2

In Ra)Rln I1T

In R-a KT Tb_Rb/

212

Ta]

Ra and Rb can be measured with an accuracy of + 0.05percent at 90°C and 1 10°C temperatures with a toler-ance of 0.003 percent using commercially availablebridge and temperature baths.

Certain precautions and procedures are necessary toinsure the high degree of accuracy. A silicon base oil isused as the medium in the bath to maintain a low tem-perature gradient and immeasurable electrical conduc-tivity of the bath.A fixture is used for holding the thermistor bead dur-

ing the measurement. This fixture provides a gap of0.080 inch between the contacts that connect to thethermistor bead wires. This closely approximates themounting configuration in the thermistor head. A sketchof a fixture is shown in Fig. 1.The resistance of the thermistor bead wires is approx-

imately 8 2 per inch and must be taken into account.The aforementioned fixture provides for this.

During the measurement of Ra and Rb each thermistoris placed in the same location in the bath. This is afurther precaution to minimize the effects of tempera-ture gradients in the bath.The bridge which is used to make the actual resis-

tance measurement must not cause any measurableheating of the thermistor bead. The bridge excitationvoltage is reduced such that less than 0.25 mA flowsthrough the thermistor bead during measurement. Thenull detector is changed from a simple galvanometer to

dR

dt

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IEEE TRANSACIIONS ON INSTRUMENTATION AND MEASUREMENT, SEPTEMBER 1967

THERMISTOR BEAD

.080'

TO BRIDGE

Fig. 1. Holding fixture for thermistor-bead resistance measurement.

and

dR2 -= C4dP2

and

R2 = C4(P2) + C5.

A dual thermistor bridge of a typical power meter isshown in Fig. 2 in simplified form.We can determine the power dissipated in the ther-

mistors as-E([ + M) - 2

P2 = _2+ -+N_* R(l + M)

a chopper-amplifier microvoltmeter to insure adequatebridge resolution.As was stated earlier, drift in

W (dRi\(dPi_ (dR2 (dP2)dt dRJ di dR2

We may define

dR2 /dRI\di dt/

and further define

dP2

dR2

dPi)(I(+Y)

then

drift = dR\\di

(dRk\dR1 / [1- (1+x)(1 +y)] = D

for x<<1 and y<<1

/dR /dP\drift = (x + y) = D.

Typically(dR (dP\dt JYIR /

is equal to 100,uW/°C. (x+y) is then equal to 2 percentfor the assigned 2 ,uW/°C drift specification.We may split this total 2 percent and assign a maxi-

mum matching specification for dR/dt of 1 percent. Yhas been defined as 1 percent maximum matching spec-ification for matching dP/dR of the paired thermistors.For limited increments of power, dR/dP is equal to aconstant, then

dR1-= C1dPI

and

R = C1(P1) + C3

E2P1=-.

4R

Then the ratio of the powers dissipated in the pairedthermistors is

P2 (1+M)4P1 (2 +M + N)2

for M<<1 and N<<1

P2 (1 + M) 1

P1 1+M+N 1 +N

For small deviations from the 200-Q thermistor op-erating resistance, the ratio of power dissipated in thethermistors is independent of the thermistor resistanceand dependent only upon the tolerance of the bridgearm resistors. R2 has been defined as equal to R1(1+ M); and P2 has been shown to be equal to P1/ (1 + N).We can substitute this information into the expres-

sion

R2 = C4P2+ C5

and obtain

C4P1

(1 + N)C4P1 C5

R, = - +(1 + N)(1 + M) (1 + M)

dR1 C4d,= = CdP, (1 + M)(1 + N)

and

Cl 1

C4 (1 + M)(1 + N)

From the definition

dP2 dP,-=-( + Y)dR2 dR,

194

ASLAN: BEAD MATCHING

BRIDGE NO.1 BRIDGE NO.2

R I+M)-R2- TEMP.

COMP.THERMISTOR

Fig. 2. Dual thermistor bridges.

THERMISTOR BEAD

Fig. 4. Slave bridge arrangement for adjustmentof dissipation constant.

-LOW THERMALCONDUCTIVITY MATERIAL

BEADS

dP ADJUSTMENT SCREW

Fig. 3. Adjustment of dissipation constant with moveable heat sink.

we can obtain

dP2 dR1 C1(1+ Y)= --=

dR2 dP1 C4

which yields

(I1+ Y)=1(I + M) (1 + C)

For small increments in power, the dP/dR of a ther-mistor bead is dependent only upon the power dissi-pated within the bead and the operating resistance ofthe thermistor bead.We have previously determined Y to be equal or less

than 0.01 as a necessary condition for the 2 ,W/°Cmaximum drift.

For the thermistor bridge with +0.05 percent toler-ance bridge resistors, N is equal to 0.001 as a worstcase.From the expression

1(1 + Y) (1 + M)(I + N)

MI| Y - N.

For the conditions previously set forth, M=(0.009,and R must equal 200 Q+± 1.8 Q.The thermistor dR/dP characteristics will be matched

to ± 1 percent when with the same power dissipated ineach thermistor, ± 0.1 percent due to the bridge resistor

COPPER

1._ ) THERMISTOR

Fig. 5. Typical mount mechanical design.

tolerance, and the thermistor operating resistances arewithin 0.9 percent of each other, or 200 Q+1.8 Q. Inpractice, this may be accomplished by using the dualself-balancing slave bridge of Fig. 2 and adjusting theposition of a heat sink further or closer to the bead.When the bead under adjustment is within 1.8 Q of200 Q, the second condition for thermally matchedbeads will be met.The ability to set dP/dR of each bead for exact equal-

ity allows for insured temperature compensation inspite of mechanical shocks to the thermistor mountwhich might move the position of the bead relative toits sink.The manner of obtaining an adjustment in dP/dR is

not limited to that mentioned in the preceding para-graphs. This adjustment may also be accomplished byapplying solder to the thermistor-bead lead wires, or bypositioning the bead closer to its supporting contacts orother suitable sink. The most popular technique is asdescribed, with an adjustable heat sink as shown inFig. 3. The heat sink may be only a screw which ismoved closer or further from the bead.

It is not the purpose of this paper to discuss the

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-16, NO. 3, SEPTEMBER 1967

mechanical or electrical design of a thermistor mount.It should be noted though that matched thermistorbeads alone do not make a drift free thermistor mount.It is equally necessary to insure that the matched beadsare so mounted that they have equal and long thermaltime constants, and that the temperature gradientsabout the beads are equal.

Typical mount designs utilize the format of a lowpassthermal filter. A large mass at the RF connector end isequivalent to a capacitance followed by a thermallyinsulating material which becomes a series resistance.The thermistor beads are mounted in the second mass

of high conductivity material forming the terminatingcapacitance and load. This is shown graphically inFig. 4.

BIBLIOGRAPHY1M1 E. Aslan, "Temperature-compensated microwatt power meter,"

IRE Trans. Instrumentation, vol. 1, pp. 291-297, September 1960.[12 R. F. Pranann, "A microwave power meter with a hundredfoldreduction of thermal drift," Hewlett-Packard J., vol. 12, pp. 1-5,June 1961.

[31 R. N. Griesheimer, "Microwave power measurements," inTechnique of Microwave Measurements, C. A. Montgomery, Ed.,M.I.T. Rad. Lab. Ser. New York: McGraw-Hill, 1947, ch. 3.

[4[ E. Aslan, "Bolometer power measurements," Narda Probe,vol. 2, pp. 1-5, December 1965.

Thse Measurement of Efective Resolution ofNonwirewound Potentiometers

ANDREW S. WILLIAMS, MEMBER, IEEE

Abstract-The measurement of the effective resolution of non-wirewound potentiometers has been simplified by the developmentof test equipment which makes use of the "resolution window" con-cept, as set forth by Schneider and Silverman.[1] This concept isbriefly described again, and a method of mechanization is con-sidered. Analytical and practical experience has shown that the sam-pling method is the most promising to date, and the development ofequipment using this approach is therefore discussed in detail. Theconcept of the "detection aperture" is introduced and its use in pre-dicting the effective sampling coverage is shown. As a result of thesedevelopments, a definite number can now be ascribed to a given non-wirewound potentiometer to describe its resolution capability. It isanticipated that the introduction of these ideas for resolution mea-surement will contribute materially to the establishment of resolutionstandards for nonwirewound potentiometers.

I. INTRODUCTIONT HE ADVENT of the conductive glass and con-

ductive plastic potentiometer has caused themethods of measurement of electrical resolution to

be reappraised. The term "effective resolution" is in-troduced here to point out the important differences inelectrical features between wirewound and nonwire-wound potentiometers. The wirewound potentiometerpossesses a relatively predictable step type outputcharacteristic. Resolution measuring equipment in thiscase can consist simply of a highpass capacitor-resistorfilter (see Fig. 1) followed by an amplifier and pen re-corder. Resolution is then determined by the pulse to

Manuscript received April 24, 1967.The author is with Industrial-Medical Instruments, Incorporated,

Newport Beach, Calif. 92660.

pulse spacing of the resultant train of impulses pro-duced by rotating the potentiometer wiper. Thus, themeasurement of resolution of the wirewound potenti-ometer is a fairly straightforward task because of thediscontinuous nature of its characteristic.The nonwirewound potentiometer, on the other hand,

has a continuous characteristic which lacks this steppattern. Examination of the fine structure shows de-viations of local slope from the mean. In fact, the outputpotential shows small positive and negative changes invalue with changing wiper position. This is depicted inFig. 2. A new principle of evaluating effective resolutionof nonwirewound potentiometers has been introducedby Schneider and Silverman,11] and has been termedthe "resolution window." Briefly, the principle takesinto account the practical limits of angular positioningof the wiper by specifying a particular angular excur-sion for a particular potential change in output.

Fig. 3 shows how this frame, or window, can bemoved along the potentiometer output characteristic toindicate whether the average slope over the chosenangular interval is within allowable limits. The refer-ence point of the window is the lower left-hand corner,and in position A it is seen that the increment Y2- Ylis less than the window height h. This implies an averageslope during the interval (width w) of less than h/w.Positions B, C, and D illustrate other possibilities. Forexample, B would be considered acceptable while Dwould not.

196