Finding Voltage Gain: Help with Homework

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Discussion Overview

The discussion revolves around a homework problem related to finding voltage gain in a circuit involving a dependent source and various resistances. Participants explore the relationships between different voltages in the circuit and attempt to derive expressions for voltage gain.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant expresses confusion about the relationship between Vs, Vgs, and the voltage across R1, questioning how Vs could equal the sum of these voltages.
  • Another participant argues against the notion of Rs being a short circuit, emphasizing that the voltages are in series between Vs and ground.
  • Several participants reiterate the principle that the total potential between two points must be equal, indicating a shared understanding of this concept.
  • One participant suggests expressing VR1 in terms of the current through R1, indicating a need for a clearer relationship between current and voltage in the circuit.
  • A later reply advises relating the internal voltage Vgs to component values and independent sources, suggesting a method to derive the transfer function Vo/Vs.
  • Another participant notes the importance of the small signal model for a type of transistor, specifically a MOSFET, in understanding the circuit's behavior.

Areas of Agreement / Disagreement

Participants generally agree on the principle that total potential is equal between two points, but there remains uncertainty regarding the specific relationships and transformations needed to solve the problem. The discussion does not reach a consensus on the correct approach or solution.

Contextual Notes

Participants express confusion regarding the circuit transformation and the relationships between voltages, indicating potential limitations in their understanding of the circuit's components and dependencies.

CoolDude420
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Homework Statement



ee9b9a382f.png

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
a5e972b8b2.png


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

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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)
 
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NascentOxygen said:
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

ea42108fbd.png


Arrow doesn't mean current.
 

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

I take that statement back. I'm stil stuck :(
b551abc9b3.png


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

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Express VR1 in terms of the current through R1.
 
NascentOxygen said:
Express VR1 in terms of the current through it.
c39867768b.png
 

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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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