Calculating inductance of a loop

[dmorris619]

I am designing a loop antenna and would like to calculate the inductance. The radius of the loop is 6.67 centimeters, the radius of the wire is .42mm (#26 awg) and has 57 turns.

Using the following formula
L =N^2*R*mu_o*mu_r*(ln(8R/r)-2)
where N=turns, R=loop radius and r=wire radius. From this and assuming copper wire is roughky the same as air in terms of permeability I get a result of 1.4 mH.

To mee that seems like it is
orders of magnitude too large. Can some please verify that my calculations are correct or if theu are not provide me with the correct equation?

 

[vk6kro]

I used this site:

http://www.coilgun.info/mark2/inductorsim.htm

and got an inductance of 1.475 mH, which agrees almost exactly with the answer you got.

Note that this site uses Wheeler's formula and you need Java to use the program.

For larger diameter coils, like this one, you click on the 500 mm maximum diameter choice.

This program calculates inductance using Wheeler's Formula:

Equation for Wheeler's Formula

where N = number of turns, A = average coil radius, B = coil length, and C = coil thickness. All dimensions are in inches and the result is microhenries.

 

[vk6kro]

Calculating the inductance with Wheeler's formula, I get 2.537 mH which is quite a bit higher than the program predicted.
However, I did have to make some assumptions about the thickness of the coil.
I had A = 6.563 B = 0.25 C = 0.25 N = 57

You can put the coil in series with a 0.1 uF capacitor to ground and feed a sinewave signal to the series combination, then observe the voltage across the capacitor on an oscilloscope.

There should be a sharp peak at the resonant frequency. With the following circuit, the resonance would be about 10 KHz for a 2.5 mH coil.

[PLAIN]http://dl.dropbox.com/u/4222062/series%20cct.PNG

From this, you could calculate the actual coil inductance.