MOSFET small signal analysis

[movinghoon96]

Hello, this problem is from (Razavi's Design of Analog CMOS Integrated Circuit, p.79, problem 3.31)

Before asking, I'd like to tell you i've tried and couldn't find answer yet.
1) tried 2 solution : KCL, Superposition
2) find solution on internet : it include only problem ~3.28

addition : using 1), I wanted to simplify answer, so I set some conditions. yes,it didn't work.

both of mine included 3 numerator, but answer has only 2.
Its ok not solving problem, just want to know how to solve it. - already spent almost 40m over...

Thank you.

 

[Dominik Przyborowski]

What are the rules of small signal estimation?

 

[movinghoon96]

What are the rules of small signal estimation?

What do you mean?
Small signal circuit is shown textbook previously, this problem just has changed +Vin location.
I used it, so i guess my circuit is correct

 

[Akanimo]

Did you set your DC source, VDD, to zero?

 

[movinghoon96]

Did you set your DC source, VDD, to zero?

of course, when I used Superposition
1) Gm2V2 only : Gm1V1 open, VDD short
2) Gm1V1 only : Gm2V2 Open, VDD Short
3) VDD Only : all current open

Sum of Vout = 1) + 2) + 3)

 

[Dominik Przyborowski]

"all DC sources are replaced by it internal impedances. It means voltage sources are shorted to ground, while current sources are open"

In your case VB has to be shorted to ground and VDD is the only AC sources used in calculations. This mean gm1 is removed, while gm2 is driven by VDD.
Do you see the answer now?

 

[movinghoon96]

"all DC sources are replaced by it internal impedances. It means voltage sources are shorted to ground, while current sources are open"

In your case VB has to be shorted to ground and VDD is the only AC sources used in calculations. This mean gm1 is removed, while gm2 is driven by VDD.
Do you see the answer now?

Damn you are genious!
it finished within very short time :O

 

[Akanimo]

Did you set your DC source, VDD, to zero?

I'm sorry about this. I was thinking the small signal gain was for Vout/VB.