From: "Jim in_Dallas" <jim271@xxxxxxxxxxx> Reply-To: femm@xxxxxxxxxxxxxxx To: femm@xxxxxxxxxxxxxxx Subject: Re: [femm] Re: inductance - revised axisymmetric model Date: Wed, 14 Nov 2001 13:29:55 -0600
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 > > >
_________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp
_________________________________________________________________ Get your FREE download of MSN Explorer at http://explorer.msn.com/intl.asp
Attachment:
singleturn1.FEM
Description: Binary data
Attachment:
four_turns.FEM
Description: Binary data