# CS amplifiers cascade problem

1. Oct 19, 2014

### asdf12312

1. The problem statement, all variables and given/known data
two identical CS amplifiers connected in cascade. 1st stage fed with vsigand Rsig=100k ohm. load RL= 10k ohm connected to drain of 2nd stage. each MOSFET biased at ID = 0.25mA and VOV=0.25V. assume VA is very large. Each stage has RD=10k ohm.

a) sketch equivalent circuit of two-stage amplifier
b) find overall voltage gain Gv

2. Relevant equations
ID = (1/2)*kn*(VOV)2 <-- sat.
gm = knVOV
ro = |VA|/ID
GV=AV=-gm*RD || RL = -gm*RO
Vo = -(gmvgs)(RD||ro)

3. The attempt at a solution
i sketched the small signal circuit on paper but I'll probably show it later. solving for kn i get 8mA/V2. and gm=2mA/V. If VA is infinite then ro is infinite, and RO=ro||RD=RD. I get for 1st stage AVo1=GVo1=-20V.

To find the relationship for 2nd stage I did Vo1=Vi2=-(gmVi1)(RO) and Vo2=-(gmVi2)(RO)=(gm)2(RD||ro)2Vi2 then GVo2=Vo2/Vi2=400V. but is that right? I get a positive gain so I think i did it wrong.

2. Oct 20, 2014

### rude man

Need circuit diagram.

3. Oct 21, 2014

### asdf12312

I wasn't thinking, and i did it wrong xD
the gain for 2nd cascade stage, would actually be -gm* RD|| RL = -2 * 10||10 = -10 V/V. what I don't get though, how they get an answer of total gain of -20 V/V (1st stage) * -10 V/V = 200 V/V. are you allowed to multiply them like that?

sorry, here's the image for 2 stage cascade CS amplifiers
http://postimg.org/image/cnqur1y6h/ [Broken]

Last edited by a moderator: May 7, 2017
4. Oct 22, 2014

### rude man

I guess from what you wrote that gm = 2 mA/V.
If I have two amplifier in cascade as you have, why should you not be able to multiply their gains? The input to the 2nd stage is the output of the 1st stage.
The answer they give is correct.