**From:** Jan Vercammen (*jvercamm@roam.agfa.be*)

**Date:** Tue Aug 22 2000 - 03:42:11 PDT

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heiko,

Maxwell's equations describing a multiconductor system (which is actually a wave guide system)

are solved by separating them into two parts, a tranverse part (the cross sectional part) and

a longitutidinal part. It is the longitudinal part that describes the propagation of the wave in

the multiconductor system. The tranvers part describes the coupling details.

The (partial) differential equations describing the propagation in the wave can be cast into an

electrical equivalent transmission line model that uses voltages and currents, which

is more useful for connecting them to other circuits and for simulating them using circuit solvers.

It is possible to demonstrate that under the pseudo-TEM approximation one can use electrostatic parameters

(capacitance, inductance --> L,C matrices) to very good approximation. The equivalent voltages and

currents are but certain line integrals of the electric and magnetic field in the tranverse plane,

respectively. For very high frequencies there is some ambiguity in selecting the proper path for

the line integrals, but for our discussion this is not important.

So it is possible to define to good approximation an equivalent circuit model for the waveguide problem. In

that respect your discussion is correct. The circuit model describes all the aspects of multiconductor lines:

dispersion, saturation, reflections, ... Otherwise it would not be useful as a model. As a

matter of fact one can analyse the circuit model and derive equivalent electrical modes, which correspond

to the modes of the wave guide. So one can think of a multiconductor system as a linear superposition

of electrical modes. The modes allow one to study the properties of multiconductor lines in more depth than

your qualitative discussion.

Anyway, what you and I describe is equivalent. Which is the more simpler is actually not relevant.

A last remark. There is both inductive and capacitive coupling and it depends on their relative contributions

which mode(s) propagate faster. In homogeneous systems this coupling balances and therefor there is no

difference in mode velocities (this is a small error in your discussion). You can find a discussion in

J.R Blood's MECL System Design Handbook, 4ed, (Motorola), page 83.

regards,

Jan vercammen

Agfa-Gevaert NV

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