Consider the current-to-voltage converter circuit shown in Figure P12.30. The input resistance \(R_{i f}\) is assumed to be small, the output resistance is \(R_{o}=0\), and the op-amp gain \(A_{z}\) is large.

(a) Write the closed-loop transfer function in the form

\[A_{z f}=\frac{v_{o}}{i_{s}}=\frac{A_{z}}{\left(1+\beta_{g} A_{z}\right)}\]

(b) What is the expression for \(\beta_{g}\) ?

(c) If \(A_{z}=5 \times 10^{6} \Omega\) and \(A_{z f}=5 \times\) \(10^{4} \Omega\), what is the required \(\beta_{g}\) and \(R_{F}\) ?

(d) If \(A_{z}\) decreases by 10 percent, what is the percent change in \(A_{z f}\) ?

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Rif RF ww is 3 Figure P12.30