Resonant frequency of a coaxial cable

[Benthemen]

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

 

[Simon Bridge]

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.

 

[Benthemen]

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.

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

 

[Simon Bridge]

There are different kinds of LRC circuit.
Remember to draw the equivalent circuit or network secton for the situation you have.

 

[Benthemen]

There are different kinds of LRC circuit.
Remember to draw the equivalent circuit or network secton for the situation you have.

Picture (sorry it's not good) attached.

 

[Simon Bridge]

No worries - you have pictured is a 2-terminal network.
You can draw up an equivalent circuit as a singe reactance and a resistor.

Which end are you driving?
Is the other end open circuit as you've drawn?
Or are you more looking for a transmission coefficient?

http://www.allaboutcircuits.com/vol_2/chpt_14/6.html
http://www.phy.davidson.edu/stuhome/phstewart/IL/speed/Standing.html

 

[Benthemen]

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.

 

[Simon Bridge]

Those links should help then ;)

Note: the length is important if you have resistance etc as a function of length.

 

[meBigGuy]

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.