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# Re: [femm] inductance - axisymmetric model

- To: femm@yahoogroups.com
- Subject: Re: [femm] inductance - axisymmetric model
- From: "Jim in_Dallas" <jim271@hotmail.com>
- Date: Tue, 13 Nov 2001 14:02:35 -0600
- Bcc:

``

>     From: Tomislav Borzic <tborzic@yahoo.com>
>     Reply-To: femm@yahoogroups.com
>     To: femm@yahoogroups.com
>     Subject: [femm] inductance
>     Date: Tue, 13 Nov 2001 07:12:23 -0800 (PST)

>     Hello everybody, I am (again) coming with small
>     problem.
>     It is about inductance. I am callculating inductance
>     of a coil.
>     1. one turn
>     2. four turns.

>     In case (1) I use formula L= (mi0/pi)*(1/4 + ln(D/r0)
>     where is: mi0=4*pi*e-7
>     D- diameter of coil ( like this: 0-----D----0, where 0
>     is
>     conductor and D is space between them)
>     r0= radius of conductor

>     I know this is formula for two paralell conductors and
>     inductance
>     between them but with some assumptions it can work.
>     so in this case, r0=0.05m, D=0.8m,I+ = 1A, I-=-1A,
>     my callculations give 1.2 e-6 H/m, FEMM 1.16 e-6 H/m,
>     so it is ok.
>     I used AJ block integral (A j dV/2 = energy)
>     BUT, if I take four turns of wire, inductance should
>     be 16 times
>     higher because inductance of coil rises with n^2.
>     (n = number of turns)
>     I can not achieve acceptable solution.

>     *.fem file is attached.
>     plase help
>     thanks
>     tomislav.

`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

    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.`
`HTH`

    Regards,
    Jim

``

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Attachment: `smallcoil2.FEM`
Description: Binary data

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