Re: FW: reactance of 0805 and smaller SMT resistors

J. Eric Bracken (bracken@ansoft.com)
Mon, 16 Jun 1997 09:44:43 -0400

>>>>> "Greg" == Edlund, Greg <Edlund@EXCHANGE.eng.pko.dec.com> writes:

Greg> I have to confess I am one of those who has experienced a
Greg> great deal of confusion over the concept of "partial
Greg> inductance." Would anyone care to take a stab at a physical
Greg> definition of this quantity? I've seen equations that
Greg> involve some pretty complicated line integrals, but perhaps
Greg> there is a more down-to-earth definition that gets at the
Greg> heart of the matter without getting bogged down in
Greg> three-dimensional calculus. (Then again, perhaps there
Greg> isn't...)

OK, I'll give it a shot:

Partial inductance is the voltage drop measured across a piece
of conductor due to time-varying magnetic fields. You can imagine
sticking an AC voltmeter across that piece of conductor and observing
the drop.

That wasn't so bad, was it? :-) Actually, to be precise, the
magnitude of the voltage drop is L * omega, so you need to divide
V by omega to get L.

Usually the major source of confusion with partial inductance
is the distinction between it and "loop inductance." Herewith,
another definition:

Loop inductance is the total voltage drop, measured around a
closed conductor loop, due to time-varying magnetic fields. It's
a bit harder to envision how you measure this... you need to insert
a small gap in the loop, place a 1-Amp AC current source across it,
and then measure the voltage across the gap.

We should probably talk about the sources of the magnetic fields: if
the source is the current in the _same_ conductor/conductor loop where
you're making the measurement of voltage drop, you have a loop or
partial "self-inductance." If the source is a current in a
_different_ conductor, you have "mutual" loop or partial inductance.

Another point of confusion in the definition of partial inductance
is the current continuity problem. If I have an open conductor
segment, where does the current flowing in it come from/go to? With a
conductor loop, there's no such problem--the current just chases its
tail in a closed circuit.

The answer is that, for partial inductances, charges are piling up
at both ends of the conductor... positive charges on the - terminal,
negative charges on the + terminal. An odd situation, admittedly,
but one that will be resolved later when you actually connect the
conductor up with other conductors to form a circuit and enforce
KCL. When this is done, the piling-up charges cancel one another out
and vanish.

If you don't hook the conductor up in a circuit (that is, you leave
its terminals open), then its current is forced to zero and the
charges at both ends again vanish. But you can still observe a
voltage drop across it, due to EMF's induced by surrounding
time-varying magnetic fields. People sometimes intensely dislike
the thought of seeing voltage drops on a conductor carrying no current,
but it is in fact physically reasonable. (No power is dissipated, after
all, since p = v * i = v * 0.)

I'll cease my ramblings now. I hope this helped someone, somewhere.

--Eric

--
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