Figure 961
in the Circuit of Fig $k_{n}=k_{p}=2 \mathrm{~mA} / \mathrm{V}^{2},\left|V_{t}\right|=0.4 \mathrm{~V}$

Figure 9.6.1
In the circuit of Fig. 9.6.1, all transistors are matched with $k_{n}=k_{p}=2 \mathrm{~mA} / \mathrm{V}^{2},\left|V_{t}\right|=0.4 \mathrm{~V}$ , and $\left|V_{A}\right|=10 \mathrm{~V}$ .
(a) If $v_{G 1}=v_{G 2}=0 \mathrm{~V}$ , find the dc bias current in each of the four transistors $Q_{1}, Q_{2}, Q_{3}$ , and $Q_{4}$ , as well as the overdrive voltage $\left|V_{O V}\right|$ for each. Ignore the Early effect. Also, find the de voltage at the sources of $Q_{1}$ and $Q_{2}$ , as well as the de voltage at the gates of $Q_{3}$ and $Q_{4}$ .
(b) Find $g_{m}$ of each of $Q_{1}$ and $Q_{2}$ , and determine $r_{o}$ of each of $Q_{2}$ and $Q_{4}$ .
(c) If $v_{G 1}=+v_{i d} / 2$ and $v_{G 2}=-v_{i d} / 2$ , find the differential gain $A_{d}=v_{o} / v_{i d}$ .
(d) Find the output resistance $R_{S S}$ of the biascurrent source $Q_{5}$ and use it to determine the common mode gain $A_{c m}$ in the case $v_{G 1}=v_{G 2}=$ $v_{i \mathrm{~cm}}$ . Also, find the CMRR in $\mathrm{dB}$ .
(e) If it is required to increase the CMRR by $6 \mathrm{~dB}$ , by what factor should the channel length of $Q_{5}$ be changed?