For the circuit shown in Figure P7.12, the parameters are \(R_{1}=10 \mathrm{k} \Omega\), \(R_{2}=10 \mathrm{k} \Omega, R_{3}=40 \mathrm{k} \Omega\), and \(C=10 \mu \mathrm{F}\).

(a) What is the value of the voltage transfer function \(V_{o} / V_{i}\) at very low frequencies?

(b) Determine the value of the voltage transfer function at very high frequencies.

(c) Derive the expression for the voltage transfer function \(T(s)=V_{o}(s) / V_{i}(s)\). Put the expression in the form \(T(s)=K\left(1+s \tau_{A}\right) /\left(1+s \tau_{B}\right)\). What are the values of \(K, \tau_{A}\), and \(\tau_{B}\) ?

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+ R ww www R + Vi R3 C Figure P7.12