GATE 2022 EC – Question 51
Consider an FM broadcast that employs the pre-emphasis filter with frequency response
$$H_{pe}(\omega)=1+\frac{j\omega}{\omega_0},$$
where $\omega_0=10^4$ rad/sec.
For the network shown in the figure to act as a corresponding de-emphasis filter, the appropriate pair(s) of $(R,C)$ values is/are ________.
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Show answer and explanation
Correct answer: (A) $R=1\ \text{k}\Omega,\ C=0.1\ \mu\text{F}$
Explanation
The de-emphasis filter must be the inverse of the pre-emphasis filter, $H_{de}=\frac{1}{1+j\omega/\omega_0}$. The RC network with the output across the capacitor has $\frac{1}{1+j\omega RC}$, so $RC=\frac1{\omega_0}=10^{-4}$ s. Only $1\ \text{k}\Omega\times0.1\ \mu\text{F}=10^{-4}$ s satisfies this.