Ele591I E-Testing II
Final Exam

Figure 3

3. Derive an expression for the gain,

   

   of the circuit shown in Figure 3.

First Stage Gain

The same current flows in R1 and R2.

I = (V1-V2)/R2 = (Va-Vb)/(2R1+R2)

(Va-Vb)/V1-V2) = 1 + 2R1/R2

Second Stage Gain

Using superposition, let Vb =0

Then,

Vo1 = -(R4/R2)Va

If Va = 0, the second stage is a non-inverting amplifier

Vo2 = (1+R4/R3)V⁺
Vo2 = (1+R4/R3)R4/(R4+R3)Vb = (R4/R3)Vb

Super imposing these 2 Vos Vo = Vo1+Vo2 = -(Va-Vb)R4/R3

The gain is the product of the first and second stage gains

A_v = -(1+2R1/R2)R4/R3