GATE EC 2017 Set 1 — Question 42
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Analog Circuits → Op-Amp Circuits → Ideal & Non-Ideal Op-Amp
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Question
The amplifier circuit shown in the figure is implemented using a compensated operational amplifier (op-amp), and has an open-loop voltage gain, and an open-loop cut-off frequency, . The voltage gain of the amplifier at , in V/V, is ________.
Correct answer
43.3 to 45.3
Solution
The circuit shown is a non-inverting amplifier configuration.1. Calculate the ideal closed-loop gain ():
For a non-inverting op-amp, the ideal closed-loop gain is given by:
From the circuit, and .
.2. Understand the op-amp frequency response:
The op-amp is compensated, meaning it behaves like a single-pole system. Its open-loop gain can be described by:
Given and .3. Calculate the gain-bandwidth product (GBW):
For a single-pole compensated op-amp, the gain-bandwidth product is constant:
.4. Calculate the closed-loop bandwidth ():
The closed-loop bandwidth of the non-inverting amplifier is approximately:
.5. Calculate the actual closed-loop gain at the given frequency:
The voltage gain of the amplifier at a frequency is given by:
We need to find the magnitude of the gain at .
Substitute the values: , , .
.The final answer is .
For a non-inverting op-amp, the ideal closed-loop gain is given by:
From the circuit, and .
.2. Understand the op-amp frequency response:
The op-amp is compensated, meaning it behaves like a single-pole system. Its open-loop gain can be described by:
Given and .3. Calculate the gain-bandwidth product (GBW):
For a single-pole compensated op-amp, the gain-bandwidth product is constant:
.4. Calculate the closed-loop bandwidth ():
The closed-loop bandwidth of the non-inverting amplifier is approximately:
.5. Calculate the actual closed-loop gain at the given frequency:
The voltage gain of the amplifier at a frequency is given by:
We need to find the magnitude of the gain at .
Substitute the values: , , .
.The final answer is .
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