In the Circuit of Fig $C_{C 1}$ And $C_{C 2}$ Are Very Large and Thus Act as Perfect Short Circuits

In the circuit of Fig. 11.7.1 (refer to Figure below), assume that coupling capacitors $C_{C 1}$ and $C_{C 2}$ are very large and thus act as perfect short circuits at


Figure 11.7.1
the frequencies of interest. Transistors $Q_{1}, Q_{2}$ , and $Q_{3}$ are identical and are operating at identical dc bias conditions so that each has $g_{m}=5 \mathrm{~mA} / \mathrm{V}$ and $r_{o}=10 \mathrm{k} \Omega$ .
(a) Replacing the signal source $V_{S}$ and $R_{S}$ with its Norton's equivalent circuit, show that this feedback amplifier utilizes the shunt-shunt feedback topology.
(b) Give the $\beta$ circuit and determine the value of $\beta$ .
(c) Give the ideal value of the closed-loop gain and hence of the voltage gain $V_{o} / V_{S}$ .
(d) Provide the $A$ circuit and determine the values of $A, R_{i}$ , and $R_{o}$ .
(e) Find the values of $A_{f}, R_{i f}$ , and $R_{o f}$ .
(f) Find the actual value of voltage gain $V_{o} / V_{S}$ realized and compare to the approximate value found in (c).
(g) Find the value of $R_{\text {in }}$ ,
(h) Find the value of $R_{\text {out }}$ .
(i) If $V_{s}$ is $100 \mathrm{mV}$ , find the magnitudes of the signals at the gates of $Q_{1}, Q_{2}$ , and $Q_{3}$ and at the output (i.e., $V_{o}$ ).