CMOS Inverter

Find out $V_{TH}$,

When $V_{in} = V_{TH}$

i.e. region c of operation of CMOS inverter

Both pmos and nmos transistors are in saturation

$I_L(sat) = I_D(sat)$

$\frac{K_P}{2}[V_{in} - V_{DD} - V_{TP}]^2 = \frac{K_n}{2}[V_{in} - V_{TD}]^2$

$V_{in}(1 - (\frac{K_P}{K_n})^{1/2}) = V_{Th} + (\frac{K_P}{K_n})^{1/2} - V_{DD} - V_{Tp}$

substitute $V_{in} …