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RLC Circuit Transfer Function (Vout NOT referencing ground; want to check solution)

  • Engineering
  • Thread starter Leomusic
  • Start date
  • #1
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Hi all,

New to the forums here, but I've got a question for you guys:

I've ran into this rather peculiar circuit. In all the circuits I've seen (as far as transfer functions go), Vout has always referenced ground (e.g. one node of Vout is ground); in this one, however Vout is across an inductor. I've attached the circuit diagram. (excuse the crudeness of the circuit diagram...quickly whipped it up on Paint :rolleyes:).


Homework Statement



Find the transfer function Vout(s)/Vi(s) of the circuit.

R=1Ω, L1=2H, L2=3H, C=0.1F

Homework Equations



Zr = R; Zl=Ls; Zc=1/Cs; KVL; KCL, etc.

The Attempt at a Solution



Since Vout wasn't referencing ground, I figured that I needed to use the mesh-current method to get equations for Vi and Vout for each loop. After some rather nasty symbolic matrix algebra, I got expressions for I1 and I2 (loop currents), plugged each of those back into the mesh-current equations, and obtained:

[itex]H(s)=\frac{V_{out}}{V_{i}}=\frac{3s^2}{6s^3+5s^2+20s+10}[/itex]

Is this correct? Also another question: is there a simpler way to do this? Forgive my idiocy but I might be missing something terribly obvious...

It's been a while since this textbook stuff! I tinker around quite a bit with circuits, but I'm no EE...I guess that's what I get for being mechanical :biggrin:

Thanks everyone!

-Leo.
 

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Answers and Replies

  • #2
gneill
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Your solution looks good. Your method is fine too.
 
  • #3
The Electrician
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Is this correct? Also another question: is there a simpler way to do this? Forgive my idiocy but I might be missing something terribly obvious...
Nodal analysis also works well for these transfer function problems. See the image.
 

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  • #4
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Sounds good! Thanks a lot guys.

-Leo.
 
  • #5
rude man
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I too can corroborate your answer as being correct. Happy days!
 

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