RE: Partial Inductance

Edlund, Greg (Edlund@EXCHANGE.eng.pko.dec.com)
Tue, 17 Jun 1997 16:46:45 -0400

I myself don't have a problem with currents that don't form a loop.
After all, current is just charge moving past a point (or through a
surface, or through a volume). And if you're moving along with the
charge, it isn't a current at all, right? Witness the quarter-wave
dipole antenna. When a time-dependent magnetic field cuts the wire, a
current is induced, right? There doesn't need to be a loop for the
charge in the copper to move around.

Now about partial inductances: seems like this is kind of a
mathematical construct to let us think about inductive voltage drops in
much the same way we think about Ohmic drops, i.e. that they add up to
zero around a loop. (Most of us would rather think in terms of i and v
rather than E and B.) OK - I'll buy that. But you need to DEFINE the
rest of the current loop in order for the partial inductance to have any
meaning, don't you? After all, inductance is defined by current loops.
Otherwise you have people saying things like, "The inductance
per-unit-length of a 1 mil diameter wire in free space is blah, blah,
blah..." Antennas might not need a loop to have current, but SPICE
surely does. And I can't talk about - or accurately simulate - the
voltage on the chip-side of a 1 mil diameter bond wire unless I know
where the current is coming from and where it's going.

p.s. Wouldn't it be cool to take a short course called "Maxwell's
Equations Applied to Modeling Packages, Connectors, and Transmission
Lines?" Then those of us with a dim memory of the material could speak
with more authority!

----------
Greg Edlund , Principal Engineer
Alpha Server Signal Integrity
Digital Equipment Corp.
129 Parker St. PKO3-1/20C
Maynard, MA 01754
(508) 493-4157 voice
(508) 493-0941 FAX
edlund@eng.pko.dec.com

>----------
>From: J. Eric Bracken[SMTP:bracken@ansoft.com]
>Sent: Monday, June 16, 1997 2:58 PM
>To: si-list@silab.eng.sun.com
>Subject: Re: Partial Inductance
>
>
>The point about "piling up" of charges is not strictly necessary to
>the discussion of partial inductance (and I now regret starting this
>digression), but since it's provoked so much discussion I thought I
>would clarify what I was saying. Stop reading this *NOW* if you don't
>want to hear electromagnetics lingo.
>
>If you try to solve Maxwell's equations with a current distribution
>that just terminates in the middle of nowhere, then Maxwell's
>equations will actually pile up charges on the ends of that
>distribution for you.
>
>This is because Maxwell's equations have "charge continuity" built
>into them. Remember this one?
>
> curl H = J + epsilon * dE/dt
>
>If you take the divergence of this equation, you get
>
> div curl H = 0 = div J + d[ div( epsilon * E ) ] / dt
>
>But div( epsilon * E ) = Q (this is another of Maxwell's equations, known
>as Gauss' law), and so we get
>
> div J + dQ / dt = 0
>
>There's a big divergence to J where the current distribution abruptly
>terminates, and so there's a dQ/dt there to balance this.
>
>Fortunately, even time-varying charges don't contribute to the magnetic
>vector potential A. It's computed by integrating over all the currents
>
> A = Integral[ (Green's function) * J ]
>
>The vector potential is used in the energy definition of inductance:
>
> Wm = (1/2)*Integral[ A * J ] = 1/2 * L * I^2.
>
>So, the piling-up charges DO NOT affect the inductance calculation in
>any way. Therefore, they may safely be neglected, and indeed they are.
>
>Sorry to drag anybody through this muck, who, really, didn't give
>a damn.
>
>
>--
>J. Eric Bracken, Ph.D. Tel: 1.412.261.3200 x135
>Group Leader, Signal Integrity R&D Fax: 1.412.471.9427
>Ansoft Corp., Four Station Square, Suite 660 bracken@ansoft.com
>Pittsburgh, PA USA 15219-1119 http://www.ansoft.com
>