Consider the bandpass filter in Figure P15.15.

(a) Show that the voltage transfer function is

\[A_{v}(s)=\frac{v_{O}}{v_{I}}=\frac{-1 / R_{4}}{\left(1 / R_{1}\right)+s C+1 /\left(s C R_{2} R_{3}\right)}\]

(b) For \(C=0.1 \mu \mathrm{F}, R_{1}=85 \mathrm{k} \Omega, R_{2}=R_{3}=300 \Omega, R_{4}=3 \mathrm{k} \Omega\), and \(R_{5}=30 \mathrm{k} \Omega\), determine: (i) \(\left|A_{v}(\max )\right|\); (ii) the frequency \(f_{o}\) at which \(\left|A_{v}(\max )\right|\) occurs; and (iii) the two \(3 \mathrm{~dB}\) frequencies.

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