expression (eq. Al) R =a exp (b/Z' ) for the resistance of a therm- 
istor, Beakley wrote an expression, using Ohm's law, for the 
current through the bridge. He then expanded this into a Taylor's 
series. This series is linear if all derivatives with respect to 7 
after the first are zero. He then showed that the second derivative 
term was the only significant one, and it was zero for the condition 
b- 27) 
so B3 
in pear aexp (2/7) (B3) 
where Es is the absolute temperature at the midpoint of the range, 
b = constant (see below), and 
r =optimum series resistor for linearity. 
The constant, 0, may be found by taking the derivative of 
the empirical expression (eq. Al) for thermistor resistance with 
respect to 7 
Oi SO 
ar. ea a exp (b/T) 
Solving for b; 
_me2 
be Se at (B4) 
I ose 
Letting g exp (b/T .) be? |, eq. (B3) may be written, 
Die 22 
eee SAS B3a 
r=>yar Ry (B3a) 
O 
Beakley finds, among other things, an expression for the extent 
of the temperature range within which the departure from linear- 
ity is less than a specified value. This will be discussed later 
(see eq. Bl16a). 
For work with thermistors, a good bridge circuit plus a 
method for obtaining optimum parameters which is easy to apply 
and involves a minimum of calculations while giving good results, 
is desirable. Since Burke's method and Kaufman's asymmetric 
half-bridge appeared to meet these requirements, they have been 
combined for our purpose. Results will be compared with those 
45 
