Small signal analysis of a cascode amplifier

[mulothecook]

Hello there.

I am stuck trying to figure out the voltage gain of a cascode amplifier from a small signal analysis. The circuit seems to be under-determined for reasons I do not understand or maybe I am missing the perfectly obvious.

Here's my small signal model:

The only relation I can deduce without using further unknown quantities is the KCL for the v_x node:

However, I need another relation to eliminate v_x in order to solve for v_out/v_in. The small signal analysis without the cascode works just fine. May I kindly ask somebody to clarify this?M

 

[The Electrician]

Since you have a current source supplying the M2 FET, you can eliminate M2 and the voltage gain is the same as it would be without M2, namely Vout/Vin = -gm1*Rds1.

The small signal at Vx is the same as it is at Vout as long as the load on Vout is infinite, which is the impedance of the current source feeding the drain of M2. With a finite load on Vout, this will not be the result.

 

[mulothecook]

Since you have a current source supplying the M2 FET, you can eliminate M2 and the voltage gain is the same as it would be without M2, namely Vout/Vin = -gm1*Rds1.

Could you explain why this is the case?

 

[The Electrician]

Sorry, I was considering the gate of M2 as though it were connected to the source of M2 via a gate resistor, rather than having that gate grounded.

The correct gain expression is Av = -gm1*Rds1*(1+gm2*Rds2)

See slide 4: http://aries.ucsd.edu/NAJMABADI/CLASS/ECE102/12-F/NOTES/ECE102_F12-LecSet-6.pdf