Calculating capacitive reactance

[voidnoise]

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 into 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?

 

[jim hardy]

Here's a fellow experimenter who gives a formula for self-resonant frequency, and some references:
http://www.pupman.com/listarchives/1996/june/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]

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 doesn't seem very dependable. I think I am best off just measuring it from a physical coil, then compare it back to the maths.

 

[sophiecentaur]

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 doesn't 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.

 

[alphysicist]

Hi there,

Calculating the capacitance of a coil can be a bit tricky, but it is definitely possible. The capacitance of a coil depends on a few factors such as the coil geometry, the dielectric material between the coil turns, and the spacing between the turns. One way to approach this problem is to use the concept of self-capacitance, which is the capacitance between the turns of the coil. This can be calculated using the formula C = (π^2 * r^2 * N^2)/(9r + 10l), where r is the radius of the coil, N is the number of turns, and l is the length of the coil. This formula is derived from the capacitance equation for a parallel plate capacitor, where the coil turns act as the plates and the air in between acts as the dielectric material.

Once you have calculated the self-capacitance, you can then calculate the total capacitance of the coil by adding the self-capacitance to any additional external capacitance, such as the capacitance between the coil and the secondary winding. This will give you a more accurate value for the total capacitance of the coil, which can then be used to calculate the capacitive reactance XC.

I hope this helps and good luck with your model in MATLAB! Let me know if you have any further questions.