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From: "Christopher R. Carlen"
Subject: Transmission line question
Date: Fri, 13 Sep 2002 14:25:02 -0700
Organization: Sandia National Laboratories, Albuquerque, NM USA
NNTP-Posting-Date: Fri, 13 Sep 2002 16:44:24 +0000 (UTC)
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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
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.
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.
Christopher R. Carlen
Principal Laser/Optical Technologist
Sandia National Laboratories CA USA
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