Question

A push-pull capacitive displacement transducer is interfaced to a differential amplifier and an ADC as shown in the figure below.

Note that the bridge supply and the analog reference input for the ADC are derived from the same 10 V DC source.

The change in capacitance for full scale displacement is ±5% for the capacitors. The gain of the differential amplifier for utilization of the full range of the ADC (which is ±10 V) is

• A. 10
• B. 20
• C. 30
• D. 40

Answer 1

The correct option is D 40


Let gain of amplifier is $A_D$ then,

$A_D=\frac{V_0}{V_{BA}}$

Given,

$V_0=10V$

Also,

$V_{BA}=V_B-V_A$

From network,

$V_A=\frac{10R}{R+R}=5V$

$V_B=\frac{10\cdot \frac{1}{C-\Delta C}}{\frac{1}{C-\Delta C}+\frac{1}{C+\Delta C}}$

$=\frac{10\cdot \frac{1}{0.95}}{\frac{1}{0.95}+\frac{1}{1.05}}=5.25V...\left(V\right)$

Using (iii) ,(iv) and (v),

$V_{BA}=5.25-5=0.25V$

using (i), (ii) and (iv)

$A_D=\frac{10}{0.25}=40$