# Re: [SI-LIST] : Re: approximations for partial self inductance - WHY

From: jrbarnes@lexmark.com
Date: Tue Mar 20 2001 - 06:49:03 PST

Doug,
A simpler viewpoint is to treat the signal and its return as two inductors wired
in anti-parallel:

! L1 o !
!---------UUU---------!
! ! (left and right endplates contribute no inductance in
this model)
! M12,M21 !
! !
! o L2 !
!---------UUU---------!
! !

L1 is the signal path's inductance assuming a return path very far away;
L2 is the return path's inductance assuming the signal path very far away;
M12 = M21 is the mutual inductance between L1 and L2.

Loop inductance L = L1 + L2 - M12 - M21
and M12 = M21 <= (L1 + L2) / 2

The energy stored in the system is proportional to L. Since nature always tries
to minimize total energy in a system, if given a choice the return current will
choose a path that minimizes
L1 + L2 - M12 - M21 -- if we have perfect coupling between L1 and L2, L1 + L2
= M12 + M21 and the loop inductance is zero. To maximize M12 we minimize the
number of field lines from L1 that are between L1, L2, and the endplates; and
similarly for M21. So if we have a ground (return) plane under the signal,
overall the return current will track the signal current as closely as it can.

If we take a microscopic view of the signal trace and return plane, there is
also energy stored between the filaments of current going in one direction (this
is related to skin effect) which adds to the total energy. So we get some
spreading of the current filaments. The instantaneous current density in a
trace and its groundplane (microstrip) might look something like this:

!\ /!
! \------/ !
==============

=========================================================
-----\ /------\ /-----
\/ \/