resonance in rlc circuits

Discussion in 'General Electronics Chat' started by joshpig, Jan 26, 2016.

  1. joshpig

    Thread Starter New Member

    Jan 26, 2016
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    Hi!
    If you want to find the resonant frequency for the voltage and current in a load (load is a combination of resistor, capacitor, inductor), in a circuit which has another capacitor and inductor. Would you use just the components outside the load, or include those in the load in the equation 1/(2pi)(LC^1/2).?

    I'm not sure if I've explained this very well but we shall see :))
    cirucit.JPG
    Thanks
     
    Last edited: Jan 26, 2016
  2. Dodgydave

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    Jun 22, 2012
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    The resonant frequency is when Xc = Xl,
     
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  3. ErnieM

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    Apr 24, 2011
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    You need to work out an equivalent circuit where there is but a single resistor, capacitor, and inductor.

    Then Dave's doggy formula works perfectly.
     
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  4. SLK001

    Well-Known Member

    Nov 29, 2011
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    Resonance is like what Dodgy said. The frequency of the resonance is derived as follows:

    RESONANCE.jpg
     
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  5. The Electrician

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    Oct 9, 2007
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    It all depends on your definition of resonance. For example, see this page for the three common definitions of resonance: http://hyperphysics.phy-astr.gsu.edu/hbase/electric/parres.html

    Your circuit is not exactly like that one, but the given definitions of resonance will give different results when applied to your problem.

    Which definition of resonance will you use?
     
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  6. joshpig

    Thread Starter New Member

    Jan 26, 2016
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    Thank you for the fast responses :)
    I am just trying to find the frequency at which current flowing through the load and the voltage across it to be in phase, now i was guessing that this is the resonant frequency as that is when the circuit is purely resistive? is that correct?

    And is Xi/Xc referring to the impedance ?
     
  7. Dodgydave

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    Jun 22, 2012
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    Xl and Xc are the reactances(AC resistance) of the inductor and capacitor,your circuit has a v+ symbol, is it a dc supply?
     
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  8. The Electrician

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    You said that your "load is a combination of resistor, capacitor, inductor". Show the circuit of the load in detail. Together with the additional L and C you showed in post #1, the expression for the frequency at which the load current is in phase with the load voltage can be determined.
     
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  9. joshpig

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    Jan 26, 2016
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  10. Brownout

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    Jan 10, 2012
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    You have to consider all reactances. However, you can simplify things a little by considering only the circuit to the left (initially) and making a thevinen equivalent.
     
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  11. The Electrician

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    Oct 9, 2007
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    If you derive an expression for the imaginary part of the impedance seen by the source, and plot it vs. frequency, there are 3 frequencies in the vicinity of ω = 20k for which the imaginary part is zero. Those could be considered resonance frequencies.

    Resonance1.png
     
    Last edited: Jan 27, 2016
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  12. joshpig

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    Jan 26, 2016
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    Wow brilliant thanks! I would love to see how you did that, if you have that derivation to hand it would be great to see it?
     
  13. The Electrician

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    Here you go:
    Resonance2.png

    Resonance3.png

    Resonance4.png

    Here's a zoomed in view of the crossing at ω = 21778.3

    Resonance5.png
     
    Last edited: Jan 27, 2016
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  14. The Electrician

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    To get some more insight into the behavior around resonance, let's plot both the real part (blue) and the imaginary part (red) of the impedance:

    Resonance6.png

    The real part becomes very small at the lowest and highest resonance frequencies. At the middle resonance, ω = 21778.5, the real part is 8.46 ohms, a more reasonable value. The resonance there is the useful one. It's a fairly high Q resonance but the external inductance was treated as ideal.

    Here's the calculation of the value of the real part at the 3 resonances:

    Resonance7.png
     
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