Homework Help: Finding Voltage Gain

1. Dec 9, 2017

CoolDude420

1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

I can't seem to figure out the answer. Apparently, the right method involves saying that Vs is actually equal to the voltage Vgs + voltage across R1. I don't understand how Vs could be voltage across R1?
This is what I have so far

I think the first two bullet points that I wrote are correct but 99% sure that the circuit transformation I did is completely wrong.

2. Dec 9, 2017

Staff: Mentor

I wouldn't call Rs a short circuit just because there is no current through it!

Vs = voltage across Rs + Vgs + voltage across R1
because these voltages are in series between the point where the potential is Vs and the point where the potential is zero volts (ground)

3. Dec 9, 2017

CoolDude420

Oh. I see. So you're sort of looking at it like this. And that's how u found out what Vs breaks down into

Arrow doesn't mean current.

4. Dec 9, 2017

Staff: Mentor

Yes. For every path traced between 2 nominated points, the total potential will be equal.

5. Dec 9, 2017

CoolDude420

Great! Thank you very much. I think I should be able to get it from here.

6. Dec 9, 2017

CoolDude420

I take that statement back. I'm stil stuck :(

I just went in a full circle back to the equation I started with...

7. Dec 9, 2017

Staff: Mentor

Express VR1 in terms of the current through R1.

8. Dec 10, 2017

CoolDude420

9. Dec 15, 2017

donpacino

I suggest you go back just one step.

You have a dependent source (gmVgs) that relies on an internal voltage (vgs). you need to relate that internal voltage to component values and independent sources.

Write out the expression as Vgs =? as a function of Vs, gm, R1, and constants.

Once you get that expresion, you already stated that the output is -gmVgsR2, you should be able to solve for your transfer function Vo/Vs. You're very close

Also just a note, pay attention to this model, it will become more important as you learn more about circuitry. It is the small signal model for a type of transistor, a MOSFET

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