# Calculating the self resonance frequency of coil

If I have a coil of diameter D (in mm), using wire that is d mm in diameter, having N turns over a total height of L mm, assuming that it is just a single layer, and has an air core, is it possible to calculate what the self resonance frequency should be (approximately) of such a coil? If so, what would the formula for the frequency be? If not, what additional information needs to be known?

To dispel any concerns about doing someone's homework for them in advance, be assured that this is not a homework question. I'm just curious how this kind of thing can be calculated. Thanks.

So... for clarification purposes I have the following parameters:

1) Diameter of the coil (D) in mm
2) Diameter of the wire (d) in mm
3) Overall height of the coil (L) in mm
4) Number of turns (N)


I also know the material in the conductor of the wire, although I do not think that would be relevant to solving the problem unless the material was not a good conductor.

One thing we categorically cannot assume is that I will have any way to measure any properties of the coil with tools such as a meter or scope... I am asking how to calculate this on paper only.

• The short answer is yes. First you calculate the self inductance which is dependent on the physical parameters as you just described. Then there will be a self resistance too which is basically the resistance of the wire. Then there is all the stray capacitance because of the coil turns and the dielectric used as insulation. Put it all together and you have a LRC circuit model of one component! Resonance will be $\sqrt{L/C}$ or something like that. Forgive me its early! Its not trival though to calculate because the capacitance is hard to measure let alone calculate. – crowie Oct 29 '16 at 4:17
• Single layer air-core coil, sounds like a Tesla coil secondary. Look for online calculators (javatc) for resonant frequency, and then have a look at the equations they use, and dig into the references they quote. In the limit, you can break the coil down into elements of wire and simulate the whole thing, but that's intractable. So approximations have been created (for example by Wheeler) over the decades that approximate, within certain ranges of width/height, what the inductance and capacitance is for a given geometry and number of turns. Whether application of that formula is calculating??? – Neil_UK Oct 29 '16 at 4:29
• Do you know of any online calculators for resonant frequency from the parameters I have? The only ones I've found require both inductance and capacitance as input. – Mark Oct 29 '16 at 4:31
• Sorry resonance happens when $X_{L} = X_{C}$ which is when $f_{r} = \frac{1}{2\pi\sqrt{LC}}$ – crowie Oct 29 '16 at 4:32
• i43.photobucket.com/albums/e358/gary350/003_zpszmidnli2.jpg. This is 89kHz 500W coil FYI – Sunnyskyguy EE75 Oct 29 '16 at 4:43