Re: [SI-LIST] : Trace Impedance Selection

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From: Josh Nickel ([email protected])
Date: Sun May 07 2000 - 14:40:46 PDT

I believe the confusion here lies in a misunderstanding of the
"transmission line" concept.

A "transmission line", by definition, is a structure which is capable of
transmitting power in such a way that the wave intensity is limited to a
finite cross section (for example, not an idealized uniform plane wave
often used to model far-field radiation in practical systems), and is also
capable of guiding the wave along a curved path. This definition implies
two or more conductors at different potential carrying opposite currents.
Free space is obviously NOT a transmission line.

Now, for certain types of "open" transmission lines, (like two wires in
parallel), the fields propagated down the line are necessarily localized
to the wires but nonetheless exist in the "space" around the wires and
travel in what you are visualizing as "free space". The misunderstanding
here, I believe, is that the waves associated with these "nearby" fields
are "free space" waves.

However, there is in fact no notion of "transmission line region" vs.
"free-space region" in such a system, and therefore no notion of
"transmission line" waves vs. "free space" waves. Why? because the power
of "free space" waves must travel with some uniform intensity, like a
plane wave or cylindrical wave in the far-field. While these two waves
are TEM, the converse is not true: a purely lossless coaxial cable carries
a TEM wave yet this wave is not a plane or cylindrical wave. Therefore,
when a wave has been launched down a transmission line, its localized
component fields (even though they exist in the surrounding space) do not
constitute "free space" waves; they are part of the "transmission line"
wave configuration.

Therefore, you cannot say that "more" power travels down the transmission
line and "less" through free space, regardless of the geometry or material
in the transmission line since no "free space" wave exists in this case.
The only meaningful power quantity in this case is the integration of the
time-averaged Poynting vector over all space.

Finally, "impedance" implies only the ratio between the elctric and
magnetic fields; it generally does not account for the wave nature of the
fields themselves (plane, cylindrical, etc.). Balanis's book "Advanced
Engineering Electromagnetics" has some good points on this matter.

I hope this clarifies things.

Josh G. Nickel
Graduate Research & Teaching Assistant
Department of Electrical and Computer Engineering
University of Illinois at Urbana-Champaign

On Fri, 5 May 2000, Vinu Arumugham wrote:

> If you were able to connect a transmitter to a receiver using a 377 ohm > transmission line, this line would be in parallel to the "transmission > line" between the two formed by free space. Therefore, one half the > transmitted power would go through free space and the other half through > the line. As the line impedance is lowered, more power would be > transmitted through the line and less through space. > > What's wrong with this scenario? > > Thanks, > Vinu

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