Figure 114 $\left(R_{1}, R_{2}\right)$ To Sample the Output Voltage $V_{o}$ Though the Bias Details Are Not Shown, It Is

Essay

Figure 11.4.1
The series-shunt feedback amplifier shown in Fig. 11.4.1 uses a feedback network $\left(R_{1}, R_{2}\right)$ to sample the output voltage $V_{o}$ . Though the bias details are not shown, it is known that each of $Q_{1}$ , $Q_{2}$ , and $Q_{3}$ is operating at a $g_{m}$ of $2 \mathrm{~mA} / \mathrm{V}$ and that their $r_{o}$ 's are very large.
(a) Give the $\beta$ circuit and find the value of $\beta$ .
(b) What do you estimate the approximate value of the closed-loop gain $A_{f}=V_{o} / V_{S}$ to be?
(c) Give the $A$ circuit and calculate the value of $A$ .
(d) Use the results of (a) and (c) to determine $A_{f}$ and compare the result to the value obtained in (b).
(e) Find the output resistance $R_{O}$ of the $A$ circuit.
(f) Find the output resistance $R_{\text {out }}$ of the closedloop amplifier.
(g) If the open-loop gain $A$ is found to have a dominant high-frequency pole at $1 \mathrm{MHz}$ , what do you expect the upper 3-dB frequency of the closed-loop gain $A_{f}$ to be?
(h) If for some reason $g_{m}$ of $Q_{2}$ decreases by $20 \%$ , what is the corresponding percentage decrease in $A_{f}$ ?