# How did we find Vin in this CMOS?

Why did the lecturer decided that Vin is vGSn - vGSp + vDD , Why did he not go through the drain path and used vGDn and vGDp ?

• ... Probably because vGDn is equal to vGDp... – Ignacio Vazquez-Abrams Apr 9 '18 at 7:01
• Probably because Vgs is the voltage that controls the channel. – mkeith Apr 9 '18 at 7:06

$$V_{in} = V_{GDn}+V_{DpG}+V_{GSn}$$ But Dn and Dp are equal. They both are same potential point. $$\implies V_{in}= V_{GDn} +V_{DpG}+V_{GSn}$$ $$= V_{GDn} - V_{GDn}+V_{GSn}$$ $$=V_{GSn}$$
$V_{in} = V_{gs,n} = V_{gs,p} + V_{DD}$
Remember that $V_{gs,p}$ is negative!