Circuit Analysis with VCCS and VCVS

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Discussion Overview

The discussion revolves around a circuit analysis problem involving a Voltage Controlled Current Source (VCCS) and a Voltage Controlled Voltage Source (VCVS). Participants are attempting to determine resistor values that satisfy a specific gain condition (Gv = Vout/Vin = 1000) based on given relationships between resistors R1, R2, and R3.

Discussion Character

  • Homework-related, Technical explanation, Debate/contested

Main Points Raised

  • One participant states that R3 = 500 ohms, while the book indicates R3 = 5 k ohms.
  • Another participant suggests that Vout = 5V2, which they claim is independent of R3.
  • A participant expresses uncertainty about the relationship R3 = 2R2 and questions the accuracy of the book's values.
  • Some participants propose that combining equations for V2 and Vout can yield an expression for Vout/Vin as a function of R2 only.
  • There is a suggestion that the book may be off by a factor of ten regarding the resistor values.
  • A later reply confirms that the book's stated value was incorrect, indicating it should have been 0.5 k Ω instead of 5 k Ω.

Areas of Agreement / Disagreement

Participants express disagreement regarding the correct value of R3 and the implications of its relationship with R2. There is no consensus on the correct resistor values, and the discussion reflects competing interpretations of the problem.

Contextual Notes

Participants rely on specific assumptions about the relationships between the resistors, and there are unresolved questions about the accuracy of the book's problem statement.

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Homework Statement


For the circuit in Figure P1.42, suppose R3 = 2*R2, and R2 = 10 * R1. Find the resistor values so that Gv = Vout/Vin = 1000.

question42-1.jpg


Homework Equations



V = IR

for Voltage Controlled Current Source - i(t) = gm * vx
for Voltage Controlled Voltage Source - v(t) = μ * vx



The Attempt at a Solution



Everytime I try to figure out the resistor values I get R3 = 500. The answer is R3 = 5 k ohms which the book gives us.
 
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Unless I'm losing my mind, it looks like Vout = 5V2, which is independent of the value of R3.

How do you come up with your answer?
 
lewando said:
Unless I'm losing my mind, it looks like Vout = 5V2, which is independent of the value of R3.

How do you come up with your answer?

I said that
Vin = Iin*R1

V2 = .8*Vin * R2
= .8 (Iin*R1) * R2

Vout = 5*V2
= 5 * (.8 (Iin*R1) * R2)
 
I think R3 is only needed to calculate Iout not Vout.

Rest deleted as I made a mistake.
 
Those look fine. If you combine

V2 = .8*Vin * R2

and

Vout = 5*V2

you can get an expression for Vout/Vin as a function of R2 only.

Using your stated constraint for R3 = 2R2, I also come up with R3 = 500 ohms.
 
lewando said:
Those look fine. If you combine

V2 = .8*Vin * R2

and

Vout = 5*V2

you can get an expression for Vout/Vin as a function of R2 only.

Using your stated constraint for R3 = 2R2, I also come up with R3 = 500 ohms.

Is it possible that we are a factor of ten off?
 
I think it is more likely that your book is off by a factor of 10. Are you sure that R3 = 2*R2? Maybe an additional set of eyes on this problem might build the case against your book.
 
lewando said:
I think it is more likely that your book is off by a factor of 10. Are you sure that R3 = 2*R2? Maybe an additional set of eyes on this problem might build the case against your book.

This is the question from the book:

2012-08-26200101.jpg
 
As it turns out, the book was off. It was supposed to say .5 k Ω and not 5.
 
  • #10
That's great! Thanks for the closure.
 

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