Figure 116 $A_{1}$ Has a Differential Input Resistance Of $82 \mathrm{k} \Omega$

Figure 11.6.1 (refer to Figure below)


Figure 11.6.1
shows a feedback voltage amplifier in which the basic amplifier is composed of three cascaded stages having the following characteristics:
$A_{1}$ has a differential input resistance of $82 \mathrm{k} \Omega$ , an open-circuit differential voltage gain of $20 \mathrm{~V} / \mathrm{V}$ , and an output resistance of $3.2 \mathrm{k} \Omega$ .
$A_{2}$ has an input resistance of $5 \mathrm{k} \Omega$ , a shortcircuit tranconductance of $20 \mathrm{~mA} / \mathrm{V}$ , and an output resistance of $20 \mathrm{k} \Omega$ . $A_{3}$ has an input resistance of $20 \mathrm{k} \Omega$ , an opencircuit voltage gain of unity, and an output resistance of $1 \mathrm{k} \Omega$ .
The feedback amplifier is fed with a signal source having $R_{S}=9 \mathrm{k} \Omega$ and is connected to a load $R_{L}=1 \mathrm{k} \Omega$ . The feedback network has $R_{1}=10 \mathrm{k} \Omega$ and $R_{2}=90 \mathrm{k} \Omega$ .
(a) Give the $A$ circuit and find the value of $A$ .
(b) Find $\beta$ and the amount of feedback.
(c) Find the closed-loop gain $A_{f} \equiv V_{o} / V_{s}$ .
(d) Find the input resistance $R_{\text {in }}$ .
(e) Find the output resistance $R_{\text {out }}$ .
(f) If the high-frequency response of the openloop gain $A$ is dominated by a pole at $1 \mathrm{kHz}$ , what is the upper 3-dB frequency of the closed-loop gain?
(g) If for some reason the gain of $A_{1}$ drops to half its nominal value, what is the percentage change in $A_{f}$ ?