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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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
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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
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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.