Circuit Gain Q, will take you 2s to answer

Discussion in 'Homework Help' started by ferrishthefish, May 1, 2012.

1. ferrishthefish Thread Starter New Member

May 1, 2012
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Suppose I have Vin = V1 + V2*sin(wt) and Vout = V3 + V4*sin(wt). How do I calculate gain? I know it's Vout/Vin, but my lab handout tells me it's a constant (the lab handouts are garbage, tho, so it could be wrong). I have zero background in circuits, I'd already spent 40+ hours on this lab before I even got to the circuit gain part, it took me hours figure out what the "Z" in my handout stood for and I've spent even more hours running in circles around Google trying to figure out how to calculate it, I just need to finish this lab report before tomorrow morning or else I will lose my scholarship AND have to spend an extra year in college (= -\$60,000), please help me!

2. Jony130 AAC Fanatic!

Feb 17, 2009
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Show as the circuit diagram

3. ferrishthefish Thread Starter New Member

May 1, 2012
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Is that even necessary? All the V's are constant ...
I just don't know how to handle the sine waves. Is there just some special trick to it? I tried using the root-mean-square of the AC component, but then the whole thing was dominated by the DC component which is 2 orders of magnitude bigger, and we calculate the DC gain separately.

Last edited: May 1, 2012
4. Jony130 AAC Fanatic!

Feb 17, 2009
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1,378
The gain is equal to

Vout/Vin = (s*L + r) / ( R + (s*L + r ).

and the gain will be frequency dependent.

For DC current the gain

Vdc = r/(R + r)

5. ferrishthefish Thread Starter New Member

May 1, 2012
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Is there any way to calculate it when L and r are unknown or changing? I'm sorry, I was literally in tears when I made my first post and I wasn't very clear.

I am studying superconductivity. The circuit was set up to discover r and X = w*L at the same time because r and L will be changing with temperature. I have all the data I need, and I can find r = (Vdc/(1-Vdc))*R, but I can't decipher what comes after that in the lab handout. It tells me to calculate total gain g = |Vout|/|Vin|, then tells me to calculate |Z| = (g/(1-g))*R, then tells me to calculate impedance X = Z*sqrt(1-r^2/Z^2), and I just don't know how to start.

Thanks for your help, tho, I really appreciate it.

6. Jony130 AAC Fanatic!

Feb 17, 2009
4,901
1,378
To find L you need to measures measured or calculated the AC current.
I_Ac = ( Vin_ac - Vout_ac) / R
So the impedance off a circuit is equal to
$Z = \frac {Vin_{ac}} {I_{ac}}$

And also

$Z = sqrt{XL^2 + (R +r)^2}$

So if we know Z, R and r also the sin wave frequency you can solve for XL.
And finally solve for L

$XL = 2 *\pi * f *L$

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7. ferrishthefish Thread Starter New Member

May 1, 2012
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Thank you! This is exactly what I need!