Chapter 5, Problem 52P

Figure P5.33 shows a noninverting operational amplifier.

FIGURE P5.33 a. Noninverting amplifier; b. block diagram
Assuming the operational amplifier is ideal,
a. Verify that the system can be described by the following two equations:

$\begin{array}{l}{v}_o=A\left(v_i-v_o\right)\\ v_1=\frac{R_i}{R_i+R_f}{v}_o\end{array}$

b. Check that these equations can be described by the block diagram of Figure P5.33(b).

c. Use Mason's rule to obtain the closed-loop system transfer function $\frac{V_o\left(s\right)}{V_i\left(s\right)}$ .

d. Show that when $A\to \infty ,\frac{V_o\left(s\right)}{V_i\left(s\right)}=1+\frac{R_f}{R_i}$ .