handbook of modern sensors

5.7 Bridge Circuits 197
Fig. 5.39. General circuit of a bridge temperature
compensation.
Taking the derivative with respect to temperature, we get
[
(
∂V e
∂T = E 1 ∂R B
R B + R t ∂T − R B ∂RB
(R B + R t ) 2 ∂T
+ ∂R )]
t
, (5.55)
∂T
and substituting Eq. (5.54) into Eq. (5.55), we arrive at the compensation condition:
1 ∂V e
V e ∂T = 1
(
∂R B
R B ∂T − 1 ∂RB
R B + R t ∂T
+ ∂R )
t
. (5.56)
∂T
Because for a bridge with four sensitive arms, R B = R, and (1/R)(∂R/∂T ) = γ which
is a temperature coefficient of bridge arm resistance, R (TCR), Eq. (5.56) according
to Eq. (5.53) must be equal to a negative TCS:
−β = γ − 1 ( ∂R
R + R t ∂T + ∂R t
∂T
)
. (5.57)
This states that such a compensation is useful over a broad range of excitation voltages
because E is not a part of the equation. 5 To make it work, the resistive network
R t must incorporate a temperature-sensitive resistor, (e.g., a thermistor). When R, β
and ∂R/∂T are known, Eq. (5.57) can be solved to select R t . This method requires
a trimming of the compensating network to compensate not only for TCS and TCR,
but for V e as well. The method, although somewhat complex, allows for a broad
range of temperature compensation from −20 to +70 ◦ C and with somewhat reduced
performance or with a more complex compensating network, from −40 to 100 ◦ C.
Figure 5.40A shows an example of the compensating network which incorporates
an NTC thermistor R ◦ and several trimming resistors. An example of such a compensation
is a Motorola pressure sensor, PMX2010, which contains a diffused into
silicon temperature-compensating resistors which calibrate offset and compensate for
temperature variations. The resistors are laser trimmed on-chip during the calibrating
process to assure high stability over a broad temperature range.
5 This demands that the compensation network contain no active components, such as diodes,
transistors, and so forth.