# Common source MOSFET amplifier: voltage gain

Hi everyone,

I need to find the voltage gain for the following scheme: My book says I need to calculate 'id' first, which is:

id = gm.ro.vin/(Rs+RL+ro+(gm.ro.Rs))

Then with the help of vout = -RL.id you get:

Av = -gm.ro.RL/(Rs+RL+ro+(gm.ro.Rs))

So I get the last part, but I really have no clue how I get to 'id'...

Could anyone help me with this? Give me some more steps.. (my book only shows the above formulas).

Thanks!

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If you want to solve questions like this I really urge you to look at node analysis. When you understand that and have an understanding of ohms and kirchoffs law you will manage all of these questions.

Well, I do have a basic knowledge of node analysis, but I just can't seem to get to the form of 'ib' as displayed above.., I tried about a hundred times. Sometimes you need a little help to get further.

uart
Well, I do have a basic knowledge of node analysis, but I just can't seem to get to the form of 'ib' as displayed above.., I tried about a hundred times. Sometimes you need a little help to get further.
No replies? Probably because the algebra is a bit tedious. Let me just skim through it really briefly for you and I'll let you fill in the details. Also I'll give latex a miss to make this quick.

Firstly it's a much easier problem if you don't have to include ro, so let me review that simple case first (just to get you up to speed if you're not already there).

vgs = vin - gm vgs Rs

Here we have vgs on both sides of the equals sign so we have to rearrange the equation to group all the vgs terms together.

vgs(1+gm Rs) = vin

vgs = vin/(1 + gm Rs)

hence id = (gm vin) /(1 + gm Rs)

Now to repeat but including ro (fair bit harder). btw I'll use the notation go=1/ro to make things easier.

vs = (vo - vs) go Rs + gm vgs Rs

vs = (vo - vs) go Rs + gm (vin - vs) Rs

(Now rearrange to group vs on LHS)

vs (1 + go RS + gm Rs) = go Rs vo + gm Rs vin

vs = (go Rs vo + gm Rs vin) / (1 + go RS + gm Rs)

id = (go vo + gm vin) / (1 + go RS + gm Rs)

id = (gm vin - go RL id) / (1 + go RS + gm Rs)

Now we just have to rearrange to get all the "id" terms on the LHS. I'll leave that as an exercise for you.

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I guessing (?) the confusion is the gm and Ro - these are "constants" you either:

1. are given
2. use as algebraic parameters for your final solution
3. get from a linearization of a nonlinear device model
4. get from empirical measurement

Assuming these are constants, it should be pretty straight forward to write the loop equations for this.