[SI-LIST] Re: Internal Inductance

  • From: Ege Engin <engin@xxxxxxxxxx>
  • To: George Tang <gtang@xxxxxxxx>
  • Date: Mon, 09 Aug 2004 10:23:55 +0200

George,

The surface impedance of a conductive half plane has a sqrt(j*2*pi*f) 
dependency. The imaginary part of this function increases only with 
sqrt(f) and represents the reactance due to the internal inductance 
(2*pi*f*L). As a result, the internal inductance decreases with sqrt(f), 
which means the dc internal inductance goes to infinity. In any case, 
the flux density should be integrated on a surface to calculate the 
inductance, not around a contour.

Ege

George Tang schrieb:

>I disagree with what you are suggesting.  If you have a wire above a plane
>with a finite current flowing through the loop, even with infinite plane
>size and thickness, the DC inductance cannot be infinite.  You can integrate
>the flux density out to infinity, but the total flux should add up to the
>loop current (enclosed current), which is finite, so the total flux is
>finite.  This will result in a finite inductance (internal and external).
>
>
>George
>
>
>
>-----Original Message-----
>From: si-list-bounce@xxxxxxxxxxxxx
>[mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Ege Engin
>Sent: Friday, August 06, 2004 6:16 AM
>To: steve weir
>Cc: scott@xxxxxxxxxxxxx; cclewell@xxxxxxxxx; si-list@xxxxxxxxxxxxx
>Subject: [SI-LIST] Re: Internal Inductance
>
>
>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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>  
>

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