Finding Voltage Gain: Help with Homework

[CoolDude420]

Homework Statement

Homework Equations

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.

 

[NascentOxygen]

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)

 

[CoolDude420]

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)

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.

 

[NascentOxygen]

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

 

[CoolDude420]

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

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

 

[CoolDude420]

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

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

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

 

[NascentOxygen]

Express V_R1 in terms of the current through R_1.

 

[CoolDude420]

Express V_R1 in terms of the current through it.

 

[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