Re: [SI-LIST] : Oscillation in lumped circuits and transmi

RAY_WAUGH@HP-SanJose-om1.om.hp.com
Fri, 5 Feb 1999 09:17:14 -0800

Item Subject: Re: [SI-LIST] : Oscillation in lumped circuits and transmission l ines
Arani (and others)...

Any transmission line element can be described by a lumped circuit, if
the lumped elements are made small enough (less than a tenth
wavelength at the highest frequency of operation). An interconnect,
which is certainly smaller than lambda/ten at the highest frequency in
the Fourier series that describes your digital waveforms, can be
modeled with equal accuracy by either method (lumped or distributed
elements). You may, however, have to use a __lot__ of lumped elements
to achieve an accurate model of your interconnect.

Eric Bracken showed a lumped model for a transmission line, except
that he forgot the conductance G which represents the loss in the
line's dielectric. See below. With that addition, the model is quite
accurate.

"Ringing" and "reflection" describe the same phenomenon which we RF
guys have always dealt with. If you load the end of a transmission
line with something different from Zo (the line's characteristic
impedance), you'll get a reflection and standing waves on the line
(when you have a continuous sinusoidal source).

If you are so unfortunate as to be driving the line with a source
having an impedance other than Zo, you will indeed have a mess on your
hands. A single voltage (or current) pulse (containing a rich
spectrum of frequencies in its Fourier series representation) will
cause reflections to bounce back and forth until line losses dampen
them, something the digital guys call "ringing."

Ray

_/ Raymond W. Waugh - WSD Diode Applications
_/ E-mail: ray_waugh@hp.com
_/_/_/ _/_/_/
_/ _/ _/ _/ USPS : Wireless Semiconductor Division
_/ _/ _/_/_/ 39201 Cherry Street, MS NK20
_/ Newark, California 94560
_/


R L
0--/\/\/\---() () ()------+-----------0
Vin () () | | Vout
----- C /
----- \
| / G
V \
|
V

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