Chapter 9, Problem 9.39P

Consider the summing amplifier in Figure 9.14(a). Assume the op-amp hasa finite open-loop differential gain $A_{od}$ . Using the principle of superposition, show that the output voltage is given by $v_O=\frac{-1}{1+\frac{\left(1+R_F/R_P\right)}{A_{od}}}\left[\frac{R_F}{R_1}{v}_{I1}+\frac{R_F}{R_2}{v}_{I2}+\frac{R_F}{R_3}{v}_{I3}\right]$ where $R_P=R_1\left|\right|R_2\left|\right|R_3$ . Demonstrate how the expression will change ifmore or fewer inputs are included.