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need help with small signal gain

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kobesitu

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the question is required to find the small signal gain, in the attached file, shown the small signal model that i have done, please someone help me to look at it, tell me it is right or wrong, and if possible , tell me the small signal gain. thank you very much.
 

Re: small signal gain

based on the small signal model i have done, i get the small signal gain as in the following attached file, please someone help me look at it , thanks a lot.
 

At first, if lambda is zero there is no channel length modulation effect, ro will be zero for all cases. Besides, gamma is zero, there is no body effect, gmb are all gone.

It looks like Common Source degerenation case.

Gain ~ -gm1*Rd/(1+gm1*Rs)~-gm1*Rd/(1+gm1*1/gm2)
 

oh, i double check the formula, if lambda is zero, ro will be infinited, and it will forms open circuit, and yup, there is no body effect. is that corrected??
 

Assuming vds1=1,

vout=-{gm1*ro1/[ro1+ro2//(1/gm2)+Rd]}*Rd
vin={gm1*ro1/[ro1+ro2//(1/gm2)+Rd]}*[ ro2//(1/gm2)]

Av=vout/vin

For ro1 and ro2 equal infinity

vout=-gm1*Rd
vin=gm1*(1/gm2)

Av=-Rd/(1/gm2).

That's it!
 

For jasmin_123,
I cannot get why vout or vin is no unit?? can you explain detail your approach? I am interested in variety ways to solve problems.

For kobesitu,
if the transistor is in diode connected (drain ties to gate), the impedance seeing from its source is (1/gm)//ro. In your case, ro->inf, pmos source impednce is 1/gm2, use degenaration, the small signal gain is close to -gm1*Rd/(1+gm1/gm2)
 

thanks i got it now, thanks all leg1234 and jasmin_123
 

leg1234 said:
For jasmin_123,
I cannot get why vout or vin is no unit?? can you explain detail your approach? I am interested in variety ways to solve problems.

For a linear circuit, the transfer function does not depend on the magnitude of signals.
You can choose any signal, set it at 1 V, or at 1 kV, and then express all the other signals through the unit signal and find their ratio.
---
It simply very convenient to set a signal at a unit and omit it in the equations.
 

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