## Related questions with answers

(a) For a circuit, the parameters are $R_S=2 \mathrm{k} \Omega$ and $R_P=8 \mathrm{k} \Omega$. (i) If the corner frequency is $f_L=50 \mathrm{~Hz}$, determine the value of $C_S$. (ii) Find the magnitude of the transfer function at $f=20 \mathrm{~Hz}, 50 \mathrm{~Hz}$, and $100 \mathrm{~Hz}$. (b) Consider a circuit with parameters $R_S=4.7 \mathrm{k} \Omega$, $R_P=25 \mathrm{k} \Omega$, and $C_P=120 \mathrm{pF}$. (i) Determine the corner frequency $f_H$. (ii) Determine the magnitude of the transfer function at $f=0.2 f_H, f=f_H$, and $f=8 f_H$.

Solution

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In solving the problem, we recall the expressions for the open-circuit and short-circuit time constants as given in the textbook.

$\tau_S = (R_S +R_P)C_S$

$\tau_P= (R_S||R_P)C_P$

We also recall the Laplace equivalent impedance expressions of each circuit component from the time domain to the complex frequency domain.

For resistors:

$Z_R = R$

For capacitors:

$Z_C = \frac{1}{sC}$

For inductors:

$Z_L = sL$

This will be essential in simplifying the analysis further in the next steps.

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