Question

In the following OP-AMP circuit, 𝑣_𝑖𝑛 and 𝑣_𝑜𝑢𝑡 represent the input and output signals, respectively.

Choose the correct statement(s):

• A. 𝑣_𝑜𝑢𝑡 is out-of-phase with 𝑣_𝑖𝑛
• B. Gain is unity when R₁ = R₂
• C. 𝑣_𝑜𝑢𝑡 is in-phase with 𝑣_𝑖n
• D. 𝑣_𝑜𝑢𝑡 is zero

Answer 1

The Correct Option is A, B

1. Circuit Analysis 

The circuit consists of two OP-AMP stages. The first stage is a non-inverting amplifier, while the second stage is an inverting amplifier.

Let v₁ be the output of the first stage, and v_out be the final output of the second stage.

2. First Stage (Non-Inverting Amplifier)

The gain of the first stage is given by:

A₁ = 1 + R₂ / R₁

The output of the first stage is:

v₁ = A₁ · v_in = (1 + R₂ / R₁) · v_in

Since it is a non-inverting amplifier, v₁ is in-phase with v_in.

3. Second Stage (Inverting Amplifier)

The gain of the second stage is given by:

A₂ = −R₃ / R₂

The final output is:

v_out = A₂ · v₁ = (−R₃ / R₂) · v₁

4. Phase Relationship

Since the second stage is an inverting amplifier, the final output v_out is out-of-phase with v_in.

5. Check Gain Conditions

The gain of the overall circuit is:

A_total = A₁ · A₂ = (1 + R₂ / R₁) · (−R₃ / R₂)

For R₁ = R₂, the total gain is:

A_total = (1 + 1) · (−R₃ / R₂) = −2 · (R₃ / R₂)

The gain is not unity under this condition.

6. Conclusions

• The final output v_out is out-of-phase with v_in.
• The gain is not unity when R₁ = R₂.
• v_out is not zero unless v_in = 0.
• v_out cannot be in-phase with v_in due to the inverting nature of the second stage.