[SI-LIST] Re: Internal Inductance

  • From: Ege Engin <engin@xxxxxxxxxx>
  • To: steve weir <weirsp@xxxxxxxxxx>
  • Date: Fri, 06 Aug 2004 15:16:09 +0200

Steve, the paper cited by Jayaprakesh also demonstrates that there is a 
non-zero internal inductance, which decreases with frequency, associated 
with an infinite ground plane. Actually the given equation also suggests 
that the internal inductance tends to infinity at dc. However, the 
ground plane is assumed to be also infinitely thick, which makes the 
obtained expression less and less reliable at low frequencies. I think 
for an infinitely wide plane having a finite thickness your statement 
might be true though. It might be that the divergent behavior I observed 
is due to the fact that the total loop inductance tends to infinity at 
dc (since the current loops get larger and larger), and not the internal 
inductance of the plane.

Ege

steve weir schrieb:

> Ege, for infinite planes, I think you mean the inductance tends to 
> zero.  Since the current distributes over an infinite area, the flux 
> density tends towards zero as does any current impeding counter-EMF.
>
> Steve.
> At 11:10 AM 8/6/2004 +0200, Ege Engin wrote:
>
>> Craig,
>>
>> The internal inductance is frequency dependent, and simulations at
>> multiple frequency points are necessary as Scott explained. L.J.
>> Giacoletto; "Frequency- and Time-Domain Analysis of Skin Effects", IEEE
>> Tran. Mag., Jan. 1996, gives some analytical formulas for rectangular
>> conductors.
>>
>> I assume you want to obtain the internal inductance at dc. The method
>> that we apply to extract the dc internal inductance of conductors is to
>> simulate at a very high and a very low frequency (if you have an
>> eddy-current solver such as Ansoft Maxwell 2D). The difference in the
>> inductances gives the dc internal inductance. Though, I think it is
>> difficult to obtain a definite internal inductance value for conductors
>> in the presence of planes. The reason is that if the planes are assumed
>> to be infinite in extent,  the current should distribute itself
>> uniformly in the planes at dc. But this should also mean that the
>> inductance goes to infinity! Although I could not find a supporting
>> statement in the literature, it seems obvious, and simulations have also
>> shown this divergent behavior. As a result, this method gives a definite
>> internal inductance value only if the planes have a finite (and known)
>> width.
>>
>> Regards,
>> Ege
>>
>> Scott McMorrow schrieb:
>>
>> >Craig,
>> >
>> >I don't believe there is a straightforward analytical formula for
>> >non-round conductors.  When you start getting into internal inductance
>> >for trace geometries in the presence of a plane, then it will 
>> definitely
>> >depend on the shape and proximity to the other conductors.  However,
>> >this problem is easily solved by several different field solvers.
>> >
>> >Commercially, Ansoft Maxwell 2D does a very good job of extracting
>> >inductance at multiple frequency points.  You just have to be sure to
>> >use the impedance matrix.
>> >
>> >Academic codes such as FastHenry from MIT and Simian from Dean Neikirk
>> >at the University of Texas can correctly solve for frequency dependent
>> >inductance and resistance of arbitrary shapes.  Links to these can be
>> >found at http://www.fastfieldsolvers.com/links.htm
>> >
>> >Or, if you are dealing with stripline traces, you can use a boundary
>> >element method or method of moments field solver to run two problems.
>> >
>> >Problem 1) your rectangular trace at the normal thickness centered
>> >between the planes.
>> >
>> >Problem 2) a very very thin trace centered between the planes.
>> >
>> >
>> >
>> >regards,
>> >
>> >scott
>> >
>> >
>> >Craig Clewell wrote:
>> >
>> >
>> >
>> >>Greetings,
>> >>
>> >>Does anybody out there have an equation handy to calculate the 
>> internal
>> >>inductance of a square, rectangle, or any other object that is not
>> >>round?  I already know that the internal L of a round wire is 
>> (u*length)
>> >>/ (8*pi), but I'm not looking at using a round wire.  I've read 
>> that it
>> >>should be about 20% of the external inductance, however I want to dial
>> >>it in better than that.  I'm so used to neglecting this, that I know
>> >>find myself at a "loss".....ok...that wasn't funny :>)
>> >>
>> >>Thanks for sharing....
>> >>
>> >>Craig
>> >>
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>> >
>> >
>> >
>>
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>
>
>

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