Exercise 8.12 A more elaborate opamp circuit schematic

a)

An answer:
The bias current in the three not-labeled NMOS transistors is $I_{\mathit{BIAS}}$
The bias current in $\mathit{mn}1$ and $n2$ is $I_{\mathit{BIAS}}∕2$
The bias current in the three PMOS transistors is $I_{\mathit{BIAS}}∕2$
The bias current in $M_{o1}$ and $M_{o2}$ is $(\frac{K_1}{K_2})I_{\mathit{BIAS}}$.

b)

An answer:
non-inverting: B inverting: A

c)

An answer:
Due to the presence of the finite $r_{\mathit{ds}}$ this yields

$$\begin{array}{rcll}& r_{\mathit{out}}& =\frac{1}{g_{m,M_{o1}}}& \end{array}$$

where

$$\begin{array}{rcll}& g_{m,M_{o1}}& =K_1\sqrt{\frac{2I_{\mathit{BIAS}}}{K_2}}& \end{array}$$

d)

An answer:

$$\begin{array}{rcll}{K}_1=\frac{1}{r_{\mathit{out}}\sqrt{\frac{2I_{\mathit{BIAS}}}{K_2}}}=\frac{1}{1000}\frac{A}{V^2}=1\frac{\mathit{mA}}{V^2}& & & \end{array}$$

e)

An answer:

$$\begin{array}{rcll}& \frac{i_x}{v_A-v_B}& =\frac{1}{2}{g}_m& \\ & & =\frac{1}{2}\sqrt{2K_2\frac{1}{2}{I}_{\mathit{BIAS}}}& \\ & & =\frac{1}{2}\sqrt{K_2{I}_{\mathit{BIAS}}}& \end{array}$$

f)

An answer:
$\frac{i_y}{i_x}=2$

g)

An answer:
$\frac{v_C}{i_y}=r_{\mathit{ds}}$

h)

An answer:
$\frac{v_{\mathit{out}}}{v_C}=1$

i)

An answer:

$$\begin{array}{llll}\hfill a_v& =\frac{v_{\mathit{out}}}{v_A-v_B}& \hfill & \\ \hfill & =\frac{1}{2}\sqrt{K_2{I}_{\mathit{BIAS}}}\cdot 2\cdot r_{\mathit{ds}}& \hfill & \\ \hfill & =r_{\mathit{ds}}\sqrt{K_2{I}_{\mathit{BIAS}}}& \hfill & \end{array}$$