Chapter 4, Problem 4.99IP

(a)

To determine

To prove: The currents in the $2R$ legs are $i_1=\frac{V_{\text{REF}}}{2R}$ , $i_2=\frac{V_{\text{REF}}}{4R}$ , $i_3=\frac{V_{\text{REF}}}{8R}$ and $i_4=\frac{V_{\text{REF}}}{16R}$ regardless of the switch position.

(b)

To determine

To prove: The sum of the currents at the inverting input is $b_1{i}_1+b_2{i}_2+b_3{i}_3+b_4{i}_4+i_{\text{F}}=0$ .

(c)

To determine

To prove: The output voltage equation for the op-amp using results of (a) and (b) is $-V_{\text{REF}}\frac{R_{\text{F}}}{2R}\left(b_1+\frac{b_2}{2}+\frac{b_2}{4}+\frac{b_2}{8}\right)$ .