From: Roy McCammon
Subject: Re: Transmission line question
Date: Fri, 13 Sep 2002 13:31:59 -0500
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"Christopher R. Carlen" wrote:
> This question resulted from another guy's post about grounding ribbon
> cables at both ends or just one end.
> Let's say we have the following transmission line arrangement:
> +--Zg--+===============+---+ <--+ cond.#1
> | | |
> Vg Zo1 | |
> | | |
> +------+===============+ | Zo2 cond.#2
> | | |
> | Zl |
> | | |
> +------+===================+ <--+ cond.#3
> Where Vg is an AC voltage generator,
> Zg is the generator impedance,
> Zl is the load impedance,
> Zo1 is the characteristic impedance of the transmission line formed by
> the top two conductors (1 and 2), ie the conductor from the hot end of
> the generator and the conductor that is grounded at one end but open at
> the other end.
> Zo2 is the characteristic impedance of the transmission line formed by
> the top (hot) conductor 1 and the bottom conductor 3, the one grounding
> the load.
> We assume that Zo1 << Zo2, which is likely to be the case if Zo1 is
> formed by two adjacent ribbon cable conductors, and Zo2 is formed by the
> hot ribbon conductor in relation to a ground wire far away.
> What happens?
> It seems to me that a wave propagates forward on the line with Zo1,
> since that is a lower characteristic impedance than Zo2. But some
> proportion will also propagate on the Zo2 line. What happens when the
> wave reaches the end of the line? Hmm. It could be said that since the
> Zo1 line is effectively unterminated, that there is total reflection of
> the proportion of the energy that is propagating in the wave on the Zo1
> line. Thus, only the energy carried by the Zo2 line would bear on the
> load, which depending on how it is matched to Zo2 will produce a
> reflected wave related to the reflection coefficient for that Zl, Zo2
> What happens when the two reflected waves get back to the generator?
> Obviously they will react with the Zg and absorb in Zg or reflect
> according to the reflection coefficient formed there between Zg and the
> two Zo values. But the proportioning also happens again.
> Well, I have formed a picture in my head of what is going on here, and
> it is quite complicated. The end result though is that it has conviced
> me that it is likely to be the best choice to ground the ribbon cable at
> both ends, and send any signals with reasonably fast components over a
> ribbon with interspersed ground conductors.
I have a good paper on this subject, but I can't find it.
Anyway one of the authors was Harrington and the word
multiconductor was in the title and it was either an IEEE
or IEE publication.
It may be this one or another with a similar title.
W. Cao, R. Harrington, J. Mantz, and T. Sarkar,
"Multiconductor transmission lines in
multilayered dielectric media," IEEE Tran. on MTT, vol.
MTT-32, pp. 439-450, April 1984.
Upshot is you have to find the eigen solutions to
the multiconductor cable and then express the input
as a blend of those eigen solutions. In certain
symmetric cases, those eigen solutions become
the common and differential modes.
I'll look for the paper. Seems that whenever I am at
work, it is at home and vice versa.
> Comments appreciated.
> Christopher R. Carlen
> Principal Laser/Optical Technologist
> Sandia National Laboratories CA USA
Thank you for reading and or replying
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