Chapter 12, Problem 12.22P

Consider the op-amp circuit in Figure $\text{P}\mathrm{12.22.}$ The op-amp has a finite gain, so that $i_o=A{i}_{\epsilon },$ and a zero output impedance. (a) Write the closed-loop transfer function in the form
$A_{if}=\frac{i_o}{i_s}=\frac{A_i}{\left(1+{\beta }_i{A}_i\right)}$

(b) What is the expression for ${\beta }_i?$ (c) If $A_i={10}^5$ and $A_{if}=25,$ what is the required ${\beta }_i$ and $R_F/R_3?$ (d) If $A_i$ decreases by 15 percent, what is the percent change in $A_{if}?$