Calculating capacitive reactance


by voidnoise
Tags: capacitance, capacitive reactance, impedance, transformer
voidnoise
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#1
Feb7-13, 05:39 AM
P: 4
Hi,

Apologies if this has been posted/answered else where but I could not find it.

I am trying to develop a model in matlab for a simple (short cylindrical coil) air cored transformer. So far I am capable of defining the coil such as core diameter, turns, length etc.., calculate the coil resistance, input current, magnetic field produced, flux density at a given distance along the central axis, and potential emf for the secondary coil.

The next thing I need to work out is the impedance Z.

Z = sqrt(R^2 + X^2)

where X = XL - XC

I can calculate XL because I have found an equation to work out the inductance of the coil, L.

L = (r^2 * N^2)/(9r + 10l)
*from the wiki inductor page

so XL = 2πfL.

I run in to problems with capacitive reactance XC. I cannot find anywhere online explaining how to work out the capacitance of a coil so I can calculate the capacitive reactance XC.

XC = 1/(2πFC)

Does anyone here know how to calculate the capacitance of a coil, or even if my understanding is completely off?
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jim hardy
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#2
Feb7-13, 06:49 AM
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Here's a fellow experimenter who gives a formula for self-resonant frequency, and some references:
http://www.pupman.com/listarchives/1.../msg00227.html


If you are just interested in computing self-resonant frequencies
there is another method which I have found useful and generally accurate
to about 10% for all coil sizes - space wound or not. Its limitation is that
it probably shouldn't be used for aspect ratios (Height/Diameter)<1 due
to the assumptions of the original derivation.

The formula is:
F = (29.85 x (H/D)^(1/5))/(N X D)
(hope the ascii came out) <---it didn't - i transcribed from link jh
where
F= self resonant frequency in Mhz of an 'isolated' coil
H= coil height in meters
D= coil diameter in meters
N= total number of turns

Make sure the top line reads " (H/D) to the 1/5 power"<--- numerator jh
Note that the frequency is a very weak function of the
aspect ratio (H/D), but a fairly strong function of the number of turns
and the diameter.
more at the link

maybe you could back into capacitance...
voidnoise
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#3
Feb13-13, 11:05 AM
P: 4
Thanks for a reply, its been useful, but seems to be for coils greater in length than I am dealing with. I tried using the suggestions anyway but they maths doesnt seem very dependable. I think I am best off just measuring it from a physical coil, then compare it back to the maths.

sophiecentaur
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#4
Feb13-13, 04:42 PM
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Calculating capacitive reactance


Quote Quote by voidnoise View Post
Thanks for a reply, its been useful, but seems to be for coils greater in length than I am dealing with. I tried using the suggestions anyway but they maths doesnt seem very dependable. I think I am best off just measuring it from a physical coil, then compare it back to the maths.
If you have one available then that is certainly worth doing. Just find the self resonant frequency and the inductance at a very low frequency. That will give you the self capacitance more accurately than you are likely to be able to calculate it. You can alter things a lot by squashing or stretching the coil just a bit.


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