GATE 2016 EC (EC3) – Question 29

For the feedback block diagram shown, the overall closed-loop gain G is

Show answer and explanation

Correct answer: (B) $G_1G_2/(1+G_1G_2+G_1H_1)$

Explanation

The first summing node gives X−Y. After G2, the second node subtracts H1Y, so the input to G1 is $G_2(X-Y)-H_1Y$.

Thus $Y=G_1G_2X-G_1G_2Y-G_1H_1Y$. Collect output terms and divide by X:
$$G=\frac{G_1G_2}{1+G_1G_2+G_1H_1}.$$
This is **B**.

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