Common source MOSFET amplifier: voltage gain

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Discussion Overview

The discussion revolves around calculating the voltage gain of a common source MOSFET amplifier, focusing on the derivation of the drain current 'id' and the voltage gain formula. Participants explore various methods and approaches to understand the underlying concepts, including node analysis and algebraic manipulation.

Discussion Character

  • Homework-related
  • Technical explanation
  • Exploratory

Main Points Raised

  • One participant seeks help in deriving 'id' from the given formulas, expressing confusion about the process.
  • Another participant suggests using node analysis and understanding Ohm's and Kirchhoff's laws to tackle such problems.
  • A participant shares a simplified approach to derive 'id' without including 'ro', providing a step-by-step breakdown of the algebra involved.
  • There is mention of the complexity introduced when including 'ro' in the calculations, with a participant outlining a more complicated derivation.
  • One participant speculates that confusion may arise from the constants 'gm' and 'ro', suggesting they can be treated as either given values or parameters in the solution.
  • A later reply indicates that the original poster successfully figured out the problem and passed a related test.

Areas of Agreement / Disagreement

Participants generally agree on the need for a solid understanding of node analysis and algebraic manipulation to solve the problem. However, there is no consensus on the best approach to derive 'id', as different methods are proposed and explored.

Contextual Notes

Participants express varying levels of familiarity with the concepts involved, and some steps in the algebraic derivations remain unresolved. The discussion reflects a range of assumptions about the constants involved and their implications for the calculations.

YeeHaa
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Hi everyone,

I need to find the voltage gain for the following scheme:

35i26nr.jpg


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 kirchhoffs 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.
 
YeeHaa said:
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.
 
Last edited:
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.
 
Thank you for your replies!
It took a while but I figured it out :) I also passed the test I took yesterday, so that's good news.
 

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