Figure 981
the Two-Stage CMOS Op Amp Shown in Fig $Q_{1}$

Figure 9.8.1
The two-stage CMOS op amp shown in Fig. 9.8.1 utilizes eight transistors, $Q_{1}$ to $Q_{8}$ , all having the same channel length $L$ . Transistors $Q_{1}$ and $Q_{2}$ are matched and $Q_{3}$ and $Q_{4}$ are matched. For the process technology utilized, $\mu_{n}=4 \mu_{p}$ . All transistors have the same Early voltage, $\left|V_{A}\right|$ .
(a) If the width of each of $Q_{1}$ and $Q_{2}$ is denoted $W$ , find the width of each of $Q_{3}$ to $Q_{8}$ in terms of $W$ so that all transistors operate at equal overdrive voltages, and that $Q_{6}$ conducts a de bias current equal to that supplied by $Q_{7}$ . Neglect the Early effect for this part.
(b) Derive an expression for the overall voltage gain in terms of $\left|V_{A}\right|$ and $\left|V_{O V}\right|$ . Hence, determine the required value of $\left|V_{O V}\right|$ for the case $\left|V_{A}\right|=10$ $\mathrm{V}$ and the voltage gain required is $2500 \mathrm{~V} / \mathrm{V}$ .