GATE 2023 PH – Question 34
For a transistor amplifier, the frequency response is such that the mid band voltage gain is 200. The cutoff frequencies are 20 Hz and 20 kHz. What is the ratio (rounded off to two decimal places) of the voltage gain at 10 Hz to that at 100 kHz?
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Correct answer: 2.27 to 2.29
Explanation
A single-stage amplifier with lower and upper cutoff frequencies $f_L$ and $f_H$ has a gain whose magnitude (relative to the mid-band gain $A_0$) is
- below the mid-band: $\dfrac{A}{A_0}=\dfrac{1}{\sqrt{1+(f_L/f)^2}}$,
- above the mid-band: $\dfrac{A}{A_0}=\dfrac{1}{\sqrt{1+(f/f_H)^2}}$.
**At 10 Hz** ($f_L=20$ Hz): $\dfrac{A}{A_0}=\dfrac{1}{\sqrt{1+(20/10)^2}}=\dfrac1{\sqrt5}$.
**At 100 kHz** ($f_H=20$ kHz): $\dfrac{A}{A_0}=\dfrac{1}{\sqrt{1+(100/20)^2}}=\dfrac1{\sqrt{26}}$.
**Ratio** of the gain at 10 Hz to the gain at 100 kHz:
$$\frac{1/\sqrt5}{1/\sqrt{26}}=\sqrt{\frac{26}{5}}=\sqrt{5.2}=\mathbf{2.28}.$$