Question

The op-amps in the following circuit are ideal. The voltage gain of the circuit is ……….. . (Round off to the nearest integer) 
 

Hint:

For ideal op-amps, use the following principles:
- The voltage difference between the inputs is zero (i.e., \( v_+ = v_- \)).
- Use KCL (Kirchhoff's Current Law) and KVL (Kirchhoff's Voltage Law) to analyze circuits with feedback.

Answer 1

Step 1: Analyzing the given circuit, we have two ideal op-amps connected in a feedback configuration. We are required to find the voltage gain of the circuit using the given equations.
- The equation for the output voltage \( v_o \) in terms of \( v_x \) is: \[ v_o = 2v_2 - v_x \] Using KCL at node \( A_2 \), we get: \[ v_x - v_2 = v_2 - v_o \quad \Rightarrow \quad v_x = 2v_2 - v_o \]
- Applying the formula for the voltage at node \( A_1 \), we get: \[ v_x = (1 + \frac{10k}{10k}) v_1 \quad \Rightarrow \quad v_x = 2v_1 \]
- Substituting \( v_x = 2v_1 \) into the equation for \( v_o \): \[ v_o = 2v_2 - 2v_1 \] Thus, the voltage gain is given by: \[ \frac{v_o}{v_{\text{in}}} = 2 \]