Peter O. Brackett wrote:
A widely applied practical example is the transmission of bi-directional
broad band digital subscriber loop (DSL) signals over telephone twisted
pair.
Peter K1PO
Indialantic By-the-Sea, FL.

As Peter notes,
telephone transmission line impedance is always complex.
The parameters R, L, G & C per unit length
(series resistance, series inductance, shunt conductance,
shunt capacitance) are NOT CONSTANT with frequency,
or temperature. So the cable impedance is not
constant either.
Signal spectra extend from nearly DC (a few kHz)
up to 12MHz or more - many octaves.
Even over voiceband, 400Hz to 2800 Hz,
the cable impedance changes a _lot_.

Lengths vary from several feet to 10s of kft.
There are often/usually open-ended shunt cable sections,
a.k.a. bridged taps, along the cable.
Other things, like series lumped loading coils (inductors),
may appear if not removed from longer cables.
Signals at the DSL receiver ends are umpteen dB below
the transmitter signal levels on the same pair of wires,
and can be in the same band if separate to-the-customer
and to-the-network bands are not used.

Smith Charts, as much as I like them for ham purposes,
are of no help.

This subject is addressed in T1.417-2001, Issue 1
"Spectrum Management For Loop Transmission Systems"
January, 2001
Developed by Sub-Committee T1E1.4
which develops the xDSL standards (DSL, HDSL,
ADSL, VDSL,...) for North America.

Annex B of T11.417 deals with the modeling
of cables for such cases: formulas, RLCG vs. freq.
and other data for common AWG and metric cables...

Software packages are available offline and online.

http://net3.argreenhouse.com:8080/dsl-test/index.htm
(A free registration is needed.)

(The other 200+ pages are left for the reader.)

The latest working draft of Issue 2 is available free*
as document T1E1.4/2003-002R3 from

http://www.t1.org/filemgr/filesearch.taf

Do a "Simple Search" for filename 3e140023

When the "Results of Simple Search" page appears,
click on the blue full name T1E1.4/2003-002R3
under the Contributions column.

When the next page appears,
click on the blue 3e140023 after "File Prefix"
to finally download the document. (2.1MB)

I just tried this procedure to be sure it works.

* The official Issue 1 is over US$300.

In 1995 I was the first editor and wrote the first draft
of what became T1.417. Much of what I wrote is intact
word-for-word as the first half of Annex B
(to my amazment) - the general descriptive part
before the nitty-gritty models and numbers.

Have fun.

There will be an exam.

Cheers, 73,

Ron McConnell
Retired Secretary T1E1.4


N 40º 46' 57.9" W 74º 41' 21.9"
FN20ps77GU46 [FN20ps77GV75]

http://home.earthlink.net/~rcmcc