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

  • From: "Singh, Siddharth" <siddharth.singh@xxxxxxxxxxxxxxxxxxx>
  • To: <ray.anderson@xxxxxxxxxx>, <si-list@xxxxxxxxxxxxx>
  • Date: Fri, 28 Oct 2005 16:46:05 -0400

Ray,
Mathematically speaking if L1(or L2) is less than L2(orL1)by more than a
factor of k square i.e. if  L1 <(k^2*L2) then clearly L12 will be larger
than L1.
So for a conductor with small self inductance, lying in vicinity of an
inductive path can make their mutual go above self inductance.

Siddharth.


-----Original Message-----
From: si-list-bounce@xxxxxxxxxxxxx [mailto:si-list-bounce@xxxxxxxxxxxxx]
On Behalf Of Ray Anderson
Sent: Friday, October 28, 2005 3:21 PM
To: si-list@xxxxxxxxxxxxx
Cc: Ray Anderson
Subject: [SI-LIST] Can L12 ever exceed L1 or L2 ??

A question for the E&M gurus on the list:
=20

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

=20

Since L12 =3D 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.

=20

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 ?

=20

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.

=20

Any comments  one way or the other are appreciated.

=20

Regards,

=20

-Ray

=20

=20

Raymond Anderson

Senior Signal Integrity Staff Engineer

Product Technology Department

Advanced Package R&D

Xilinx Inc.

=20

=20


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