[SI-LIST] Can L12 ever exceed L1 or L2 ??

Ray-
I completely agree with Steve Weir's comment that it is not
physically possible for L12 > L11, whether we use these
terms as loop inductance elements or partial inductance
elements.

The self inductance is the number of loops of magnetic field
lines that surround one conductor per amp of its current.
The mutual inductance is the number of loops of magnetic
field lines that surrounds both conductor, per amp of
current in one. All the mutual field lines from one
conductor must also, by definition surround its own
conductor and be part of its self inductance. This is true
for loop inductance or partial inductance.

The real question is why your vendor supplied you with
matrix elements where you got L21 = 3 x L11. I've gotten
similar comments from other end users. The answer is that
when the vendor ran their field solver, they did not use a
fine enough mesh. If you have radically different conductor
geometries, like a short, wide conductor and a long,
meandering trace, you will often see on the first pass
calculation of the field solver that the partial self
inductance of the short trace is less than the partial
mutual between them. 

Your vendor needs to refine their mesh. When the mesh is
refined so that the matrix elements do not change by more
than about 1% for a 10-20% increase in mesh elements in the
high field regions, the mesh is refined enough.

Perhaps if your vendor were to read chapter 6 in my book
Signal Integrity-Simplified, they would have a better chance
of providing you more accurate and meaningful models.

Hope this helps.

--eric

***************************************
Eric Bogatin
Bogatin Enterprises
OnLine Lectures on Signal Integrity
26235 w 110th terr
Olathe, KS 66061
v:913-393-1305
cell: 913-424-4333
f:913-393-0929
e:eric@xxxxxxxxxxxxxxx
www.BeTheSignal.com <http://www.BogEnt.com> 

Signal Integrity- Simplified
published by Prentice Hall
*****************************************

Msg: #7 in digest
Subject: [SI-LIST] Can L12 ever exceed L1 or L2 ??
Date: Fri, 28 Oct 2005 12:21:06 -0700
From: "Ray Anderson" <ray.anderson@xxxxxxxxxx>

A question for the E&M gurus on the list:
 

Are there any conditions (pathological or not) that the
mutual inductance between two conductors can be greater than
the self inductance of either one?

 

Since L12 = k * sqrt(L1*L2) and the coupling factor k must
be -1 < k < 1 then  this would seem to imply that L12  must
be less than or equal to geometric mean of the self
inductances. However this leaves open the possibility the Lm
could be > than one or the other which flies in the face of
the commonly made assertion that Lm must be less than
either. It seems that there must be other qualifying
statements to made regarding the relationship to the self
and mutual inductances.

 

Going back to some of the basic fundamental relationships
(such as Grover's formulas) I can convince myself that for
circular conductors
L12 must be less than or equal to either L1 or L2, but how
about the mutual coupling between some other structures say
a signal trace and large planar structure that isn't
intended to be be a signal return path but very well may be
?

 

I've got a field solver reporting Lm being 2 to 3 times
Lself  on one particular problem. I'm trying to determine if
the solver is having a difficult time dealing with the
particular geometries involved or if it is indeed possible
despite the common  wisdom to the contrary.

 

Any comments  one way or the other are appreciated.

 

Regards,

 

-Ray

 

 

Raymond Anderson

Senior Signal Integrity Staff Engineer

Product Technology Department

Advanced Package R&D

Xilinx Inc.



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