Register to reply

Calculating capacitive reactance

Share this thread:
voidnoise
#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?
Phys.Org News Partner Engineering news on Phys.org
Hoverbike drone project for air transport takes off
Student develops filter for clean water around the world
Developing the next evolution in underwater communication
jim hardy
#2
Feb7-13, 06:49 AM
Sci Advisor
PF Gold
jim hardy's Avatar
P: 3,505
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
#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
#4
Feb13-13, 04:42 PM
Sci Advisor
PF Gold
sophiecentaur's Avatar
P: 11,899
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.


Register to reply

Related Discussions
Calculating Impedance Using Capacitive Reactance Introductory Physics Homework 11
Capacitive reactance Introductory Physics Homework 3
RC Circuit, what does it imply when resistance = capacitive reactance (R=Xc)? Introductory Physics Homework 2
How can capacitive reactance be zero for no capacitor? Introductory Physics Homework 4
DC and capacitive reactance Advanced Physics Homework 1