In the following OP-AMP circuit, 𝑣𝑖𝑛 and 𝑣𝑜𝑢𝑡 represent the input and output signals, respectively.
Choose the correct statement(s):
Choose the correct statement(s):
- 𝑣𝑜𝑢𝑡 is out-of-phase with 𝑣𝑖𝑛
- Gain is unity when R1 = R2
- 𝑣𝑜𝑢𝑡 is in-phase with 𝑣𝑖n
- 𝑣𝑜𝑢𝑡 is zero
The Correct Option is A, B
Solution and Explanation
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 vout 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 · vin = (1 + R2 / R1) · vin
Since it is a non-inverting amplifier, v1 is in-phase with vin.
3. Second Stage (Inverting Amplifier)
The gain of the second stage is given by:
A2 = −R3 / R2
The final output is:
vout = A2 · v1 = (−R3 / R2) · v1
4. Phase Relationship
Since the second stage is an inverting amplifier, the final output vout is out-of-phase with vin.
5. Check Gain Conditions
The gain of the overall circuit is:
Atotal = A1 · A2 = (1 + R2 / R1) · (−R3 / R2)
For R1 = R2, the total gain is:
Atotal = (1 + 1) · (−R3 / R2) = −2 · (R3 / R2)
The gain is not unity under this condition.
6. Conclusions
- The final output vout is out-of-phase with vin.
- The gain is not unity when R1 = R2.
- vout is not zero unless vin = 0.
- vout cannot be in-phase with vin due to the inverting nature of the second stage.
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