Numerical 5: Scaling

For w_p = 1 rad/sec, modify the circuit so that it becomes a low pass filter with a passband of 1000 rad/sec and load resistance of 75Ω.

fig: LPF

{For Inductor:}

\[
L_{\text{new}} = L_{\text{old}} \times \frac{K_m}{K_f}
\]

For \( L = 1.5\,H \),

\[
L_{\text{new}} = 1.5 \times \frac{75}{1000} = 0.1125\,H
\]

For \( L = 0.5\,H \),

\[
L_{\text{new}} = 0.5 \times \frac{75}{1000} = 0.0375\,H
\]

---

{For Capacitor:}

\[
C_{\text{new}} = C_{\text{old}} \times \frac{1}{K_f \times K_m}
\]

For \( C = 1.3\,F \),

\[
C_{\text{new}} = 1.3 \times \frac{1}{75 \times 1000} = 17.3\,\mu F
\]

For \( C = 1.2\,F \),

\[
C_{\text{new}} = 1.2 \times \frac{1}{75 \times 1000} = 16\,\mu F
\]

The new circuit becomes

fig: Scaled