In comparing the lumped model to the transmission line model, I would ask
where the transmission line equations come from. I've seen textbooks that
derive the transmission line equations by considering a cascaded series of
RLC "cells" and then looking at what happens in the limit as the number of
cells becomes infinite and the RLC component values within each cell
approach zero, such that the end-to-end totals stay the same as in the
lumped model. From that perspective, the lumped model would then be just a
"reduced case" of the transmission line model -- reducing the number of
"cells" in the model to just one, on the assumption that the single-cell
model is accurate enough for the frequency range of interest.
I'm sure Dr. Howard Johnson would have a lot more to say about this than I
do. Have you looked at his book, "High-Speed Digital Design" (co-authored
with Martin Graham)?
---- Dave W. Johnson, San Jose, CA
From: Arani Sinha [mailto:firstname.lastname@example.org]
Sent: Friday, February 05, 1999 12:02 AM
Subject: [SI-LIST] : Oscillation in lumped circuits and transmission
I have the following question.
We can model an interconnect as either a lumped circuit or a
transmission line. By means of lumped modeling, we can say that
it has an oscillatory response if its damping factor is less
than 1. By means of transmission line modeling, we can say that
it has an oscillatory response if the signal reflection
co-efficients at source and load satisfy certain conditions.
My question is whether oscillation in a lumped circuit and
signal reflection in a transmission line are actually the same
phenomenon. If so, there should be a correlation between
conditions for oscillation in a lumped circuit and those for
oscillation in a transmission line.
After many discussions and much thought, I have not been able
to determine a correlation. I am also ambivalent about whether
they are the same phenomenon.
I understand that the damping factor in a lumped circuit is
equivalent to the attenuation constant in a transmission line
and that condition of no reflection is equivalent to the
maximum power transfer theorem.
I will really appreciate help in this regard.
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