Q$5.$ In the CMOS op amp shown below, all MOS devices have $|V_t|=1V,{}_n{C}_{ox}=2{}_p{C}_{ox}=200\frac{A}{V^2},$ and $||=0\mathrm{.}02V^{-1}.$ Device lengths and widths are indicated on the figure in units of $m.$

$V_{DD}=+5V(Fig5)$

$($a$)$ Design $R$ to provide a $10-A$ reference current.

$($b$)$ Assuming $v_O=0V$ with $v_{\text{I}\text{C}\text{M}}=0V,$ as established by external feedback, perform a DC bias analysis, find the voltages at nodes B and D $.$

$($c$)$ Provide in table form, $V_{GS},I_D,g_m$ and $r_o$ for all devices.

$($d$)$ Estimate the voltage gain $\frac{v_o}{v_{id}}$ of the amplifier.

$($e$)$ What is the output signal range under no load condition?