A tuned Circuit

Discussion in 'Homework Help' started by conclusionof, Nov 12, 2008.

  1. conclusionof

    Thread Starter New Member

    Nov 11, 2008
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    If there is a RLC-tuned circuit designed such that an inductor and a resistor is connected to parallel each other and in series to a capacitor.
    How can we find the resonance frequency and bandwidth of this circuit ?
     
  2. KL7AJ

    AAC Fanatic!

    Nov 4, 2008
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    Regardless of any resistance, the resonant frequency of any circuit is determined by 1/2pi(sqrt(LC)). The bandwidth of a circuit is determined by the general formula : BW=f/Q. All other things being equal, the Q is the ratio of the reactance over resistance. However, your circuit is neither a pure parallel nor pure series circuit. The proper model of this is an L network, with a resistive load. There are is a special case for determining the bandwidth of loaded L networks, covered in quite a lot of detail in the ARRL Handbook. I don't have the formula on the tip of my tongue right now, for which I am highly ashamed....I should know it. But I'll look it up. Stand by!

    eric
     
  3. KL7AJ

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    Okay, this is cheating....but here's a calculator for ya. You want to use "Network 2"

    http://www.smeter.net/feeding/l-network-terminating-impedance.php


    Eric
     
  4. conclusionof

    Thread Starter New Member

    Nov 11, 2008
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    Thanks Eric for your effort to answer my question. I really appreciate for it.

    But, I m still not sure whether we have a resonance at w=1/sqrt(LC) for any combination of RLC.

    For instance, I have found out that if there is a circuit like Network-3 (in the link) have a resonance at w^2 = 1/LC - (R/L)^2.

    And that is not equal to the frequency which we have a series or parallel RLC ...
     
  5. KL7AJ

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    Hi, Conclusion:

    I located the elusive fomula: Q= sqrt( Rhigh/Rlow-1), where R high is the highest value of resistance and R low is the lower value.


    When the Q is very low, there can actually be THREE different definitions of resonance (again, illustrated thoroughly in the venerable ARRL Handbook). You can have: 1: zero phase shift
    2: Maximum voltage/minimum current
    3: XL=XC

    For very low Q tank (parallel) circuits, these three conditions do NOT coincide. There is such a thing as LOADED and UNLOADED Q.

    Eric
     
  6. steveb

    Senior Member

    Jul 3, 2008
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    Can you provide a schematic for how you are using this circuit. I just quickly wrote out an equation for this combination assuming the output voltage is taken across the capacitor.

    The transfer function is (1/RC)*(s+R/L)/(s^2+s/(RC)+1/(LC))

    this is not quite a pure bandpass unless R/L is much less than 1/sqrt(LC).

    Under that condition the 3 dB bandwidth is about 1/(2 pi RC) and the resonant frequency is 1/(2pi*sqrt(LC))
     
  7. KL7AJ

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    Nov 4, 2008
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    Indeed....you confirmed precisely my caveat about low Q circuits! It's gratifying when you get the same answer approaching from two different directions. :)
     
  8. KL7AJ

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    You'll also see how much straightforward this problem is if the resistance is simply in series with the other components. In this case, the loaded and unloaded Q are one and the same.

    eric
     
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