The circuit in Figure P12-32 is a typical \(R L C\) filter circuit.
(a) Find the circuit's transfer function \(T(s)\) if \(C=33 \mu \mathrm{F}, L=\) \(47 \mathrm{mH}\), and \(R=10 \Omega\).
(b) Determine the filter type.
(c) Use MATLAB to plot the filter's gain characteristic.
(d) Either by hand or from the MATLAB plot, find \(Q, B, \omega_{\mathrm{C} 1}\), \(\omega_{\mathrm{C} 2}, \omega_{\mathrm{o}}\), and \(T_{\text {MAX }}(s)\)
(e) Select a value of \(R, L\), or \(C\) that would shift the center frequency to \(1 \mathrm{krad} / \mathrm{s}\) but not change \(B\).

Transcribed Image Text:

V(s)( (+1) Ls 000 1 Cs R V(S)