Figure 911
for the Differential Cascode Amplifier in Fig $\left|V_{t}\right|=0.5 \mathrm{~V}$

Essay

Figure 9.1.1
For the differential cascode amplifier in Fig. 9.1.1, all the transistors have the same threshold voltage $\left|V_{t}\right|=0.5 \mathrm{~V}$ and are operating at the same overdrive voltage. For the purpose of calculating dc quantities, neglect the Early effect. The current source $I$ requires a minimum dc voltage $V_{C S}=0.25 \mathrm{~V}$ for its proper operation.
(a) With $v_{G 1}=v_{G 2}=0 \mathrm{~V}$ , find:
i. The bias current in each of the eight transistors.
ii. $\left|V_{O V}\right|$ for each of the eight transistors. iii. $g_{m}$ for each transistor.
iv. $r_{O}$ and $A_{0}$ for each transistor assuming $\left|V_{A}\right|=$ $5 \mathrm{~V}$ .
v. The dc voltage at the drains of $Q_{1}$ and $Q_{2}$ .
(b) Find the input common-mode range.
(c) With $v_{G 1}=v_{i d} / 2$ and $v_{G 2}=-v_{i d} / 2$ , where $v_{i d} \ll 2 V_{O V}$ , give the differential half-circuit and use it to determine the differential gain $v_{o d} / v_{i d}$ .