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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 ? enter image description here

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  • \$\begingroup\$ ... Probably because vGDn is equal to vGDp... \$\endgroup\$ – Ignacio Vazquez-Abrams Apr 9 '18 at 7:01
  • \$\begingroup\$ Probably because Vgs is the voltage that controls the channel. \$\endgroup\$ – mkeith Apr 9 '18 at 7:06
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You can if you want.

$$V_{in} = V_{GDn}+V_{DpG}+V_{GSn}$$ But Dn and Dp are equal. They both are same potential point. $$\implies V_{in}= V_{GDn} +V_{DpG}+V_{GSn}$$ $$= V_{GDn} - V_{GDn}+V_{GSn}$$ $$=V_{GSn}$$

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The statement written here is most likely:

\$V_{in} = V_{gs,n} = V_{gs,p} + V_{DD} \$

The minus should probably be an equality.

Remember that \$V_{gs,p}\$ is negative!

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