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

Since the mutual inductance is a measure of magnetic flux linkage between
the two bodies it can be equal to either of the self inductance in the
limiting sense where there would be no flux leakage between the conductors.
However, this is only a theoretical case and in practice L12 will always be
smaller than the self inductances as most people already agree here.
So, what's wrong with the math? This is like a puzzle where something
obvious is delibrately held back from us. I checked an elementary EM book
for the definition of "k." It is indeed defined as k^2=k12xk21, where
k12=L12/L11 and k21=L21/L22 and either k12 or k21 cannot be greater than
one, which conforms the math to physics. Since L12=L21 we get the notorious
k=L12/sqrt( L11xL22) expression. Interesting...
Ihsan

On 10/28/05, Qazi Arif Iqbal <qazi@xxxxxxxxxx> wrote:
>
> Siddharth,
> In that case what would be L21 equal to?
> Can an inductive coil induce more inductance to a nearby coil then itself?
> Clearly highest magnetic flux goes around the coil itself.
>
> Qazi
>
> -----Original Message-----
> From: si-list-bounce@xxxxxxxxxxxxx
> [mailto:si-list-bounce@xxxxxxxxxxxxx]On Behalf Of Singh, Siddharth
> Sent: Friday, October 28, 2005 1:46 PM
> To: ray.anderson@xxxxxxxxxx; si-list@xxxxxxxxxxxxx
> Subject: [SI-LIST] Re: Can L12 ever exceed L1 or L2 ??
>
>
> 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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