Bridge for Thermistor Thermometers

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Constant sensitivity bridge for thermistor thermometers

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1962 J. Sci. Instrum. 39 75

(http://iopscience.iop.org/0950-7671/39/2/316)

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2/4

J. SC

INSTRUM.,

1962, VOL. 39

Constant sensitivity bridge for thermistor

thermometers*

E.

PITTS and

P. T. PRIESTLEY

Research Laboratories, Kodak Ltd., Wealdstone, Harrow, Middlesex

MS. received 21st September 1961

Desp ite the variation of the incremental tempera ture resistance sensitivity of therm istors,

temperatures c n be measured in a Wheatstone bridge circuit having constant'temperature

deflection sensitivity if the bridge is fed from a variable voltage supply.

In

the circuit

described the compensation c n be a utom atically set when the bridge is balanced, both

operations being performed simultaneously on one and the same variable resistor, which

is in series with a thermistor in one arm of a Wheatstone bridge and

is

part of

a

fixed

resistor, the remainder of which is in series with the b ridge voltage supply. s a result,

the voltage across the bridge changes with the balancing resistor, so that the rate of change

with temperature of the off-balancecurrent

is

independent of the temp erature at which the

bridge is balanced.

The resistance values of the other three bridge

rm

must be suitably

chosen to achieve

this

automatic compensation, and a method

is

described for their

evaluation. In a typical example, full-scale deflection was obtained for

a

change of

0.31 5 degc , i.e. a sensitivity of 2.45 pA-deg-', which was within 1 of the calculated

value and constant to 1 over the w orking range of 15 degc.

1 IntrodIi~on

Thermometric analysis involves the measurement of small

temperature changes during a chemical reaction, and the

thermometer used must therefore accurately measure such

differences irrespective of the initial temperature. It is very

desirable to have an instrument more convenient and of a

much smaller thermal capacity than the B e c k thermo-

meter, w hich is otherwise suitable for the purpose.

Direct-reading thermistor thermometers (McLean 1954,

Beakley 1951) in which the full-scale deflection of a galvano-

meter corresponds to a tempe rature change

of

about 25 degc,

lack sufficient linearity, require complicated setting up and

are not immediately adaptable to the abo ve use.

We here describe a simple bridge circuit in which a

full-

scale deflection always corresponds to the same small

tempe rature difference. The instrum ent has adequate sensi-

tivity which is

also

constant over a working range of about

15 degc.

As

an additiona l advantage, it is very easy to use,

adjustment being effected by varying a single resistance

without the need for complicated cyclical procedures. More-

over, if an accuracy to 1 % in the measurement of the

temp erature difference s enough, no calibration of the bridge

is necessary, the theoretically calculated sensitivity being

sufficiently accurate.

This

feature may save

a

great amount

of time.

2 The

bridge

circuit

Repeated measurements of the thermistor resistance are

inconvenient, so the thermistor is placed in one

rm

of a

Wheatstone bridge which

is

then balanced at a given

temperature, and subsequent small changes of temperature

are measured by the c urrent flowing through the galvano -

meter as the bridge departs from balance. The current

through he galvanometer is proportional to

a

small change

* Communication No. 2192 H from the Kodak Research

Laboratories.

The

subject matter

of

this

paper

is

covered

by

U.K.

Pat. Appl. No. 33420/61.

in resistance. Since the rate of chang e of therm istor

resistance with temp erature decreases with rise in tempera-

ture, the sensitivity of this simple a rrangem ent decreases as

the working tem perature increases.

To compensate for

t i s

change in ssnsitivity, a resistance

is included in the circuit outside the bridge, in series with

the applied voltage.

This

resistance is decreased as the

working temperature increases, thus increasing the voltage

applied to the bridge.

At any working temperature, when the bridge is balanced

the total resistance of the arm containing the thermistor and

the adjustable resistance must have a k e d value determined

by the k e d resistances of the other

three

arms. If the s u

of the adjustable resistance and that in the external circuit

is kept constant, then, as the resistance of the thermistor

decreases with increasing working temperature so wi l l the

resistance in the ex ternal circuit.

By suitably choosing the

resistances of the other

three rms

it is then possible to

maintain c onstant sensitivity.

3.

Theory

The figure shows the b ridge circuit and th e provision

of

a

resistance

A-Y

in the external circuit. The figure indicates

the symbols used in the following argument.

Balance

is

obtained by varying

Y.

The current is through he galva-

nometer may be found by the usual methods, and diJdT

may be derived and conditions chosen such that this ate of

change remains independent of the thermistor resistance R .

The equation for the current is

vi?,( R

Y)

L ( M + A - Y

75


3/4

CONSTANT

SENSITIVITY B R I D G E

FOR

THERMISTOR

T H E R M O M E T E R S

Thermistor bridge circuit.

V voltage of cell;

,

pre-set potentiometer;

Rb,

made up

from a

high

stability resistance and a potentiometer;

R,

resw

tance of thermistor;

G,

galvanometer resistance; iD cment

through the galvanometer;Y esistance of potentiometer in

the bridge circuit;

A-Y,

resistance

of

potentiometer in extemal

circuit; A , total resistance of the balancing potentiometer.

We now consider the expression for

di dT

in conditions

where the bridge isvery nearly balanced.

There wi l l be small

changes in Lo and O hen the bridge goes

off

balance, but

it is readily shown that the main change in

ig

will be due to

the change in (Rb R Y).

good approximation is

therefore

where we have

used

equation (2) to substitute for Y in the

denominator. Over a tempera ture range of abo ut 20 degc

the variation of thermistor resistance with temperature is

given by

where a and

b

are constants and Tis the absolute temperature.

Equation

(5)

then becomes

R

= ebiT, (9

The requirement of constant sensitivity means that thii

expression must

be

independent of

R

throughout the range.

A way of effectingths is to m ake the sensitivitiesequal at

each end of the working range; in practice this also sufEces

to keep sensitivities very nearly constant throughou t.

Suppose

R 1

and

R2

are the resistances of the thermistor a t

the ends of the working range at temperatures

l

nd

T2

respectively.

Sensitivitieswill be equal if

Thevalue of the po tentiometer resistance

A

may conveniently

be

chosen to

qual.RI R2,

and we shall put

Rb equal

to

76

R 1 .

Equation

8)

may be solved to find O nd hence

R,,

which is given by

From these results we ha ll y obtain two numerically equal

expressions for the sensitivity at temperatures

Tl

nd

T2

respectively.

The simpler equation (11) is used for calculations of the

sensitivity.

An

alternative method is based upon the observation that

over the working range the change of thermistor resistance

with temperature may be written approximately as

d R

_ -

T

(R

@,

where a and p are independent of T.

This

result can

be

easily shown graphically or theoretically.

If

this expression

is used in equation 9, here results

dip aVRa(R

k?

dT

Lo M0 +

A

b +R)'

This

expression will be independent of

R,

and hence of T,

provided

The application of this approximation obviously ensures

constant sensitivity throughout the working range.

Its use

leads in practice to the same value of R, as that found by

the first method , an d also to th e sam e value of the sensitivity.

4.

A practical example

In

order to test the validity of the foregoing approximate

theory, we calibrated an 'aged' thermistor (Stantel

F23,

S.T.C. L td.) using an N.P.L.-certiiied 0-50 c thermometer

and

a

Muirhead Wheatstone bridge.

The values R , and R2

of the thermistor resistance were 2500 Q a t 1440 c and

1463 Q at 29.62 c respectively.

The latter temperature was

chosen so that R1 R2 was equal to the value of a nominal

l m 10-turn helipot (Colvem CLR 2301/22) having an

actual resistance of 1037 Q. These results enable the values

of

a

and

b in

equation (6) to be calculated. The result is

b

=

2982 K, = 0-0775Q.

By use of equation

(9),

the

value of

R,

was found to be 749

Q.

The bridge circuit was

then constructed,

R,

and

Rb

being calibrated against the

Muirhead Wheatstone bridge.

The thermistor thermometer was then checked at various

temperatures against a Beckmann thermometer. The

experimental values of sensitivity are shown in the table.

Temp.( c)

14.8 15.2 18.0

24.0

2 7 . 2 2 8 . 2

dig

- (p~deg- ' )

2.45 2 .45 2 4 7 2.46 2 .45 2 .45

dT

Substitution of V =

1-5Ov, G

= 1308 Cl and other

quantities in equation 11) gives the theoretical result

M O

= Rb A.

= 2.43 /LA Qeg-'.

d T


4/4

CONSTANT

SENSITIVITY

BRIDGE

FOR

THERMISTOR THERMOMETERS

From these results it will be seen that the sensitivity varies

by about 1 % over the working range and

is

within about

1 of the theoretical value obtained from the approximate

theory. W ith the galvanometer used (Pye Scalamp,

0-00556

p 4

-I) a full-scale deflection corresponded to

approximately

3

degc.

5. Conclusions

The approximate theory gives results which differ from

experiment by about 1 . Greater accuracy cannot be

expected since the evaluation of the derivative di,ldT is

only approximate. Nevertheless, for many purposes this

accuracy is sa ci en t, in which case the theoretical value c n

be used without the need for time-consuming calibration.

The sensitivity does remain nearly constant over the whole

working range .

It is impo rtant that an 'aged' thermistor is used, otherwise

results will vary considerably over a period of months see,

for example, Beck 1956).

In

the present experiments, the

thermistor was immersed altemately in hot and cold water

until the resistance at

a

given tem perature remained constant.

The theory enables

a

suitable choice of galvanometer to

be

made if the sensitivity needed is

known.

The thermistor

thermometer is accurate and very convenient to use and

therefore suitable for many types of work where small

temperature differences have to be m easured. The balancing

potentiometer

A

may b e ca librated in absolute degrees if

so

desired.

The 10-turn-helipot, used for

A,

was fitted wth an

indicator dial having

lo00

divisions so

that

in the apparatus

described lo00 divisions were equivalent to 1 5 . 6 2 ~ r

1 division to 0.015

62 c.

Consequently the bridge sensitivity,

expressed as degrees

c

per full-scale deflection,

could

be

easily evaluated in the following manner, t o tak e into a ccoun t

any change in the bridge supply voltage due to battery

deterioration. The thermistor was immersed in a liquid at

constant temperature, or replaced by a 2.2 kilohm resistor,

and the bridge balanced. The balance helipot was then

rotated tw gi ve full-scale deflection of the galvanom eter.

The number of divisions,

on

he indicator

dial,

which

corre-

sponded to

ths

deflection was noted and the temperature

span of the galvanometer was evaluated.

The authors have lso made

a

thermistor thermometer

to

cover the range 56-82'

c

for use in the Heitler (1958) ebullio-

meter. This thermometer has a sensitivity of 1 e94 PA deg-*

with a galvanometer @ye Scalamp 040556 PA

mm-')

and

its

full-scale deflection corresponds to 0.4 degc.

References

BEAKLEY, . R., 1951,J. Sei. Instrum., 28,176.

BECK,

A.,

1956,

J.

Sei. Instrum.,

33,

16.

I-IEITLER

C., 1958, Analyst, 83,223.

MCLEAN,.

A.,

1954, J.

Sei.

Instrum., 31, 455.

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Bridge for Thermistor Thermometers