Circuit Analysis with VCCS and VCVS

[Mootix1313]

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.

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.

 

[lewando]

Unless I'm losing my mind, it looks like V_out = 5V₂, which is independent of the value of R₃.

How do you come up with your answer?

 

[Mootix1313]

Unless I'm losing my mind, it looks like V_out = 5V₂, which is independent of the value of R₃.

How do you come up with your answer?

I said that
V_in = I_in*R₁

V₂ = .8*V_in * R₂
= .8 (I_in*R₁) * R₂

V_out = 5*V₂
= 5 * (.8 (I_in*R₁) * R₂)

 

[CWatters]

I think R3 is only needed to calculate I_out not V_out.

Rest deleted as I made a mistake.

 

[lewando]

Those look fine. If you combine

V₂ = .8*V_in * R₂

and

V_out = 5*V₂

you can get an expression for V_out/V_in as a function of R₂ only.

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

 

[Mootix1313]

Those look fine. If you combine

V₂ = .8*V_in * R₂

and

V_out = 5*V₂

you can get an expression for V_out/V_in 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?

 

[lewando]

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.

 

[Mootix1313]

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:

 

[Mootix1313]

As it turns out, the book was off. It was supposed to say .5 k Ω and not 5.

 

[lewando]

That's great! Thanks for the closure.