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Re: [femm] Re: inductance - revised axisymmetric model


You are right, I'm sorry I didn't model the multi-turn coil correctly. I assumed as long as the turns are much closer together than the radius of the coil, the actual turn spacing was not critical. This is incorrect. For a multi-turn coil, the turn spacing is very important and the radius of the wire used is less important.

The equation for a single turn coil can be applied to multi-turns only if the turns are closely packed. This would be the case if the coil is made with several turns of small wire that occupy the same volume as a single turn of larger wire. My FEMM model didn't take this into account, so it was a coincidence that the results appeared to be in agreement.

Today I ran FEMM for several single-turn coils with the following results:

Let F1=formula 1: L=R*u0*Ln(R/r) , R=coil radius, r=wire radius

For all the single turn coils:
Coil radius=0.4cm
J=1 MA/m^2

(a) wire radius=0.025 cm, L(femm)=15.4nH, L(F1)=13.9nH, ratio[L(femm)/L(f1)]=1.11
(b) wire radius=0.05 cm , L(femm)=12.1nH, L(F1)=10.4nH, ratio[L(femm)/L(f1)]=1.16
(c) wire radius=0.075 cm, L(femm)=10.1nH, L(F1)= 8.4nH, ratio[L(femm)/L(f1)]=1.21

The last coil (c) is shown in the attached file: singleturn1.fem.

It appears that as the wire radius becomes smaller, the ratio of the FEMM calculation to the inductance calculated by formula 1 gets closer to unity. I repeated the femm simulations with different mesh sizes and that has only a small effect on the results. (I expected the results of these two methods to agree more closely. Does anyone have an idea why the difference is this much?)

I made another coil using 4 turns of wire with a diameter of 0.06cm and configured it so the 4 turns fit in the same space as the single wire in coil (c) above which has a wire diameter of 0.15cm. This is file: four_turns.fem
The inductance of this coil calculated by FEMM is 167.8nH. This is close to 16X the inductance of the single turn coil (c) above (16*10.1=161.6nH).

Therefore, if you have a multi-turn coil with the turns closely packed, then formula 1 gives fairly accurate results is you use the outer radius of the wire bundle as the "wire_radius" term in the equation and then multiply by N^2.

During the past year I've compared the FEMM inductance value for a variety of long solenoids with the value calculated using Wheeler's formula and the difference is typically less than two or three percent.

-- Jim



From: tborzic@xxxxxxxxx
Reply-To: femm@xxxxxxxxxxxxxxx
To: femm@xxxxxxxxxxxxxxx
Subject: [femm] Re: inductance - axisymmetric model
Date: Tue, 13 Nov 2001 22:50:40 -0000

--- In femm@xxxx, "Jim in_Dallas" <jim271@xxxx> wrote:

> >
> If we use the axisymmetric model for the coil, the FEMM results is
very
> close to the value calculated using the formula for a current loop.
>
> Example:
>
> current loop: L=N^2*R*mu0*Ln(R/r)
> where R=radius of loop
> r=radius of wire

Jim,in Your smallcoil femm file r is not 0.0005cm it is d,(d=2r)
so r=0.000025
so this formula works only for ....Ln(R/d)?
because you draw d=0.0005 not r (r is a half of diameter)

>
> Using your dimensions:
> R=4cm
> r=0.0005cm
> 4 turns
> then L = 167.2nH
>
> An alternative formula found in some references is: L=N^2*r*mu0*[Ln
(8*R/r)
> -2]
>
> Since the Ln(8) approx = 2, these formulae give similar results.
>
> Using FEMM:
> Let J=1.0 then
> integral(A.J)=6.236e-9
> I = 0.1954 Amps/turn
>
> L=163.4nH which differs by less than 3 percent. I've attached my
fem file.
>

when i changed gap between wires to something smaller result is 167.x
nH. Only thing that bothers me is that radius in formula..
So, now i will bite my nails all night (it is night in Croatia,
actually midnight) hoping that r in formula is actually d.
Or I made mistake when mesuring dimensions in smaillcoil file?
Hope You will soon read this:)))
Thanks again
tomislav





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