Small signal analysis of MOSFET. Calculating Gain

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Hauzron

Newbie level 1
I can do DC analysis and draw the small signal equivalent circuit just fine. I generally have trouble calculating gain. I'm having trouble understanding the answer to this question.

This is the question. Question 4.36: "]

This is my working. I hope it is clear:

According to the solution manual this is the wrong answer. The correct answer is Av = Vo / Vo + 1:

I don't understand. Vi is in parallel with Vsg therefore it Vi must equal Vsg right? Where did I make a mistake?

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BigBoss

I can do DC analysis and draw the small signal equivalent circuit just fine. I generally have trouble calculating gain. I'm having trouble understanding the answer to this question.

This is the question. Question 4.36: View attachment 118065"]

This is my working. I hope it is clear: View attachment 118066

According to the solution manual this is the wrong answer. The correct answer is Av = Vo / Vo + 1: View attachment 118067

I don't understand. Vi is in parallel with Vsg therefore it Vi must equal Vsg right? Where did I make a mistake?
Vi has not to be equal to Vgs because coupling is capacitive and Vi signal will be on the Vgs so the input signal at the gate of the MOS will be;

Vgs+Vi=Vgs+Vi*cos(wt+Theta)

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