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Design a circuit w/1 Ohm impedance

  1. Sep 16, 2012 #1
    1. The problem statement, all variables and given/known data
    Design a suitable combination of resistors, capacitors, and/or inductors which has an equivalent impedance at ω=100 rad/s of 1Ω using at least one inductor.

    2. Relevant equations
    Zeq=ZR+ZL+ZC
    ZR=R
    ZL=jωL
    ZC=-j/ωC

    3. The attempt at a solution
    I really am not sure how to start. I can see this being a fairly simple problem, but I just can't seem to wrap my head around it. I have read through the chapter numerous times, and I don't see anything else that could help at all.
     
  2. jcsd
  3. Sep 16, 2012 #2
    maybe
    1= R + jwL +j/wC

    1= R + j(wL+1/wC)

    1= R + j(100L+1/100C)

    easy one can be R =1, L=.01, C= -0.01
    which equals 1 = 1+ j(0)
     
  4. Sep 16, 2012 #3

    gneill

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    Staff: Mentor

    What do you know about LC or RLC circuits? Any special properties come to mind?
     
  5. Sep 16, 2012 #4
    ω0=[itex]\frac{1}{\sqrt{LC}}[/itex]

    and

    [itex]\alpha[/itex]=[itex]\frac{1}{2RC}[/itex]

    Underdamped when [itex]\alpha[/itex]<ω0, which has imaginary components.
     
    Last edited: Sep 16, 2012
  6. Sep 16, 2012 #5

    gneill

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    Staff: Mentor

    What conditions exist when a series RLC circuit are at resonance (ω = ωo)?
     
  7. Sep 16, 2012 #6
    At resonance, XL=XC, but that would just make them cancel out so I'm not sure what to do.
     
    Last edited: Sep 16, 2012
  8. Sep 16, 2012 #7

    gneill

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    Staff: Mentor

    Well, if they cancel out, what remains?...
     
  9. Sep 16, 2012 #8
    R, but I'm supposed to use at least one inductor. I must be over-analyzing this (I think about these things too much lol).
     
  10. Sep 16, 2012 #9

    gneill

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    Hmm, doesn't the "L" in "LC" count as an inductor?
     
  11. Sep 16, 2012 #10
    Yes, but I'm lost as to how to find the value(s). It isn't making sense to me. I don't even know which equation(s) to use. I have looked at the equations in the book and examples, and they aren't helping at all. No matter what, they always know at least one of the impedance values.

    EDIT: Am I going anywhere with the below equation?

    Zeq=jω[itex]\frac{1}{4\pi^{2}f^{2}C}[/itex]-[itex]\frac{j}{ωC}[/itex]

    where Zeq=1.
     
    Last edited: Sep 16, 2012
  12. Sep 16, 2012 #11

    gneill

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    Staff: Mentor

    I'm not sure what's confusing you :confused: Choose any L and a corresponding C that cancels it for the given frequency of operation --- then bang in a 1 Ohm resistor and you're home free.
     
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