**From:** *jrbarnes@lexmark.com*

**Date:** Tue Mar 20 2001 - 06:49:03 PST

**Next message:**Larry Miller: "RE: [SI-LIST] : Jitter measurement"**Previous message:**Sunil Kumar: "Re: [SI-LIST] : Jitter measurement"**Maybe in reply to:**Howard Johnson: "[SI-LIST] : Re: approximations for partial self inductance - WHY"

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:

!\ /!

! \------/ !

==============

=========================================================

-----\ /------\ /-----

\/ \/

John Barnes Advisory Engineer

Lexmark International

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**Next message:**Larry Miller: "RE: [SI-LIST] : Jitter measurement"**Previous message:**Sunil Kumar: "Re: [SI-LIST] : Jitter measurement"**Maybe in reply to:**Howard Johnson: "[SI-LIST] : Re: approximations for partial self inductance - WHY"

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