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Resonant frequency of a coaxial cable

  1. May 14, 2014 #1
    What is the equation (and derivation of equation) to work out the resonant frequency of a coaxial cable? Given that the cable has a resistance, capacitance and inductance per meter which are known.

    Links and explanations are much appreciated


    Thanks :smile:
     
  2. jcsd
  3. May 14, 2014 #2

    Simon Bridge

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    Welcome to PF;
    ... the cable, then, can be modeled as the RCL part of an RCL circuit ... have you tried looking that up?
    ... context is important though.
     
  4. May 14, 2014 #3
    Hi, thanks. I've looked at LCR circuits and found an equation for the resonant frequency being 1/√LC for a series LCR circuit, but a coaxial cable is neither a series nor parallel LCR circuit since the inductance and resistance are in series, but the capacitance occurs between the main core of the cable and the shielding.

    I've found something similar but unsure if this is correct: http://en.wikipedia.org/wiki/RLC_circuit#Other_configurations
    Fig:7
     
  5. May 14, 2014 #4

    Simon Bridge

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    There are different kinds of LRC circuit.
    Remember to draw the equivalent circuit or network secton for the situation you have.
     
  6. May 14, 2014 #5
    Picture (sorry it's not good) attached.
     

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  7. May 14, 2014 #6

    Simon Bridge

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  8. May 14, 2014 #7
    Thanks for the links.
    One end is driven by a Source (with a source impedance) and the other end is connected to a Load (with a load impedance). The shielding is connected to ground at both ends.

    If there is a mismatch between the characteristic impedance of the cable and the load/source impedances then a partial reflection will occur and a standing wave will be set up. At certain frequencies, the nodes and antinodes of standing waves will correlate with the ends of a transmission line, resulting in resonance. I'm wanting to find the frequency at which this resonance occurs using previously determined parameters such as resistance, capacitance, inductance and length.
     
  9. May 14, 2014 #8

    Simon Bridge

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    Those links should help then ;)

    Note: the length is important if you have resistance etc as a function of length.
     
  10. May 15, 2014 #9

    meBigGuy

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    A terminated coaxial cable has no resonant frequency. A mismatched cable has standing waves. The standing waves have nothing to do with the C,L,R other than C,L,R determine the cable's characteristic impedance.

    If you put in 100MHz, there will be no frequencies other than 100MHz.

    The standing wave patterns are based on the length and the frequency you are driving with. The magnitude and polarity of the reflections (which create the standing waves) are based on the source and load impedance relative to the cable's characteristic impedance. For a given termination and cable, varying the length or frequency varies the standing wave pattern.
     
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