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# [femm] Re: Drawing circles & Another AC analysis question

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- Subject: [femm] Re: Drawing circles & Another AC analysis question
- From: Dcm3c@aol.com
- Date: Fri, 12 Nov 1999 17:35:11 EST
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    In a message dated 11/11/99 4:50:09 PM Eastern Standard Time, Marctt2@aol.com
    writes:

    >
    > << Now, inductance is:
    > L=4*E/abs(i)^2
    > The 4 gets in there (rather than a 2, like in the mstatic case) because
    we
    > are working in terms of amplitude, rather than rms quantities. Likewise,
    > resistance is: >>
    >
    > I'm assuming that E is calculated over the whole problem area (i.e. over
    the
    > whole FEA region ?

    Yes, it is calculated over the whole problem area.

    > Also, when I do the integral over my coil volume to get total current, I
    get
    > Total = Real + j(Imag) since there is a phase shift and amplitude change.
    > I'm assuming that abs(i)^2 = Real^2 + Imag^2, or the amplitude^2 of the
    > current. ?

    Yes, that's right: abs(i)^2 = Real^2 + Imag^2

    > Now, let's take the problem to one more level of difficulty:
    >
    > I have a multi-turn coil .... I would like to measure AC inductance and
    > resistance of the coil.
    >
    > Is there a way to insure that the individual loops have the same net
    current
    > in them ? If not, how do you calculate the inductance given that the
    > different loops will have different net currents (due to proximity
    effect)?
    >
    > Is there a smart way to add up the individual Em = 0.5LI^2 terms ?
    >
    > In the problem that I'm working on, I have a 28 turn inductor that I would
    > like to figure out the AC resistance and the AC inductance in the DC-1 MHz
    > range. I'm thinking that perhaps I need to work out a
    > including self and mutual inductances .... perhaps there's an easier way.

    Like I was saying before, I've been working on adding the options of applying
    this sort of constraints on harmonic problems, but you can't really solve
    this problem directly now. I wonder if there is a continuum way to model a
    coil with skin and proximity effects, perhaps by solving a second
    differential equation for the voltage gradient that is required to enforce
    constant current in the coils in the presence of skin and proximity effects.
    Anyone know of a reference?

    I'd have to think about the about the 28x28 matrix approach. It seems like
    the current distribution that you induce via proximity effects is different
    than that induced by the self-inductance part, so this approach might only be
    approximate.

    Dave.
    --
    http://members.aol.com/dcm3c

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