GATE 2022 EC – Question 57
A circuit and the characteristics of the diode (D) in it are shown. The ratio of the minimum to the maximum small signal voltage gain $\frac{\partial V_{out}}{\partial V_{in}}$ is ________ (rounded off to two decimal places).
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Correct answer: 0.74 to 0.76
Explanation
The diode is either off ($V_D<0.7$ V) or on at a fixed $0.7$ V (vertical characteristic), so the small-signal gain takes two values. With the diode off, the output sees $2\text{k}+2\text{k}=4\text{k}$ to ground, so the gain is $\frac{4}{2+4}=\frac23$. With the diode on it shorts the upper $2\ \text{k}\Omega$ (as a constant offset), leaving only the $2\ \text{k}\Omega$ to ground, so the gain is $\frac{2}{2+2}=\frac12$. The ratio of minimum to maximum is $\frac{1/2}{2/3}=0.75$.