Common source MOSFET amplifier: voltage gain

In summary, the conversation discusses finding the voltage gain in a specific electronic circuit and the steps to calculate the current 'id' needed to do so. The conversation also mentions using node analysis and understanding ohms and Kirchhoff's law to solve similar problems. The conversation ends with the original poster successfully figuring out the solution and passing a test related to the topic.
  • #1
YeeHaa
28
4
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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  • #2
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.
 
  • #3
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.
 
  • #4
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:
  • #5
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.
 
  • #6
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.
 

FAQ: Common source MOSFET amplifier: voltage gain

1. What is a common source MOSFET amplifier?

A common source MOSFET amplifier is a type of electronic circuit that uses a MOSFET (metal-oxide-semiconductor field-effect transistor) as its amplifying device. It is commonly used in audio amplifiers, voltage regulators, and other applications where high voltage gain is required.

2. How does a common source MOSFET amplifier work?

The amplifier works by using the MOSFET in a common source configuration, where the input signal is applied to the gate terminal and the output is taken from the drain terminal. The voltage gain is achieved by varying the amount of current flowing through the MOSFET, which is controlled by the input voltage.

3. What is the voltage gain of a common source MOSFET amplifier?

The voltage gain of a common source MOSFET amplifier is typically determined by the load resistor connected to the drain terminal. It can be calculated using the formula Av = -gm * Rd, where gm is the transconductance of the MOSFET and Rd is the load resistor. The maximum voltage gain is achieved when the load resistor is equal to the output resistance of the amplifier.

4. What are the advantages of a common source MOSFET amplifier?

Some advantages of a common source MOSFET amplifier include high input impedance, low output impedance, and high voltage gain. It also has a simple circuit design and can be easily biased for linear operation. Additionally, MOSFETs are less prone to thermal runaway compared to other types of amplifiers.

5. What are the limitations of a common source MOSFET amplifier?

One limitation of a common source MOSFET amplifier is its limited bandwidth, as it may not be suitable for high-frequency applications. It also requires careful biasing to ensure stable and linear operation. Additionally, MOSFETs have a low output current compared to other amplifiers, which may limit its use in certain applications.

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