handbook of modern sensors

200 5 Interface Electronic Circuits
The voltage across the bridge is equal to
V e = i c R B . (5.64)
Because the current source is temperature independent and, for a bridge with four
identical arms, R B = R, then
∂V e
∂T = I ∂R
c
∂T , (5.65)
and dividing Eq. (5.65) by Eq. (5.64) we arrive at
1 ∂V e
V c ∂T = 1 ∂R
R ∂T . (5.66)
If condition (5.63) is fulfilled, we receive a provision of an ideal compensation as
defined by Eq. (5.52). Unfortunately, this method of compensation has a limitation
similar to that for Option 2—specifically, a reduced output voltage and a need for
individual sensor characterization if used in a broad temperature range. Nevertheless,
this method is acceptable when the accuracy of 1–2% of FS over 50 ◦ C is acceptable.
The above options provide a framework of the compensating techniques. While
designing a practical circuit, many variables must be accounted for: temperature range,
allowable temperature error, environmental conditions, size, cost, and so forth. Therefore,
we cannot recommend a universal solution; the choice of the most appropriate
option must be a result of a typical engineering compromise.
5.7.4 Bridge Amplifiers
The bridge amplifiers for resistive sensors are probably the most frequently used
sensor interface circuits. They may be of several configurations, depending on the
required bridge grounding and availability of either grounded or floating reference
voltages. Figure 5.41A shows the so-called active bridge, where a variable resistor
(the sensor) is floating (i.e., isolated from ground) and is connected into a feedback
of the OPAM. If a resistive sensor can be modeled by a first-order function
then, a transfer function of this circuit is
R x ≈ R 0 (1 + α), (5.67)
V out =− 1 αV. (5.68)
2
A circuit with a floating bridge and floating reference voltage source V is shown in
Fig. 5.41B. This circuit may provide gain which is determined by a feedback resistor
whose value is nR 0 :
V out = (1 + n)α V 1
4 1 + α/2 ≈ (1 + n)α V 4 . (5.69)
Abridge with the asymmetrical resistors (R ̸= R 0 ) may be used with the circuit shown
in Fig. 5.41C. It requires a floating reference voltage source V :
V out = nα V 1
4 1 + α/2 ≈ nα V 4 . (5.70)