[SI-LIST] Re: Help Explaining Microstrip
- From: Peter Csapo <peter@xxxxxxxxxx>
- To: si-list@xxxxxxxxxxxxx
- Date: Thu, 25 Oct 2007 19:04:51 -0700
Hi Paul and si-listers,
I've been following this thread with interest, but I've been a little
disappointed with the unsatisfactory answers so far, so let me give it a
try.
First of all, let's realize here that a microstrip is not a
"transmission line" at DC, its just a wire conductor over a plane
conductor. A steady current through the wire will generate a B field,
which will influence currents going through the plane conductor
according to the observations of Oersted and Ampere as you have
described. A current in the opposite direction in the plane will be
forced away from the wire. The force opposing the spreading out of the
charge carriers in the plane would be the induced static electric field,
ie. the Hall effect.
Those effects should be easily demonstrable as a steady state, but you
are interested in dynamic conditions. So we consider accelerating
charges through the wire, which will result in induced current in the
plane (a direct consequence of Maxwell's equations). By Lenz's law, the
induced current's B field will tend to oppose the change in B field of
the wire. The induced current can best oppose the B field of the wire if
it is close to the wire and in the opposing direction, ie. the path of
least inductance. The resultant magnetic field is a sum of the mutual B
fields. In the case of a microstrip, the wire is reasonably well coupled
to the plane and the resultant B field is small. In the excellent
symmetric case of coaxial conductors, the coupling is ideal and will
result in a zero B field (idealising conductor properties, of course).
The physical model is the superposition of these effects, where the
first dominates under small charge accelerations and high currents, but
the second dominates under large charge accelerations and low currents.
So, there is no paradox. If one wants to talk about transmission lines,
you can and should just ignore the first case, because it isn't
significant: an ideal transmission line doesn't generate a B field.
PC
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