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So... The precision would be +/- 15%. My ohm meter is within the
percent, I think, and I know where it is. I always have to look for
the ruler... :-)

Velocity factor of a given cable can be known to within a small
fraction
of one percent. When I said 66% to 90% I was refering to different
types of
cable. For example, 300 twin lead has a velocity factor of 66%, while
coax
such as RG59 has a velocity factor of 80%.

So the transmission line model isn't valid under 10 kHz, is that what
you are saying?

No. A transmission line (speakercable) can be accuately modeled even
if
the line's resistance is much higher than it's XL.

A transmission line model that was designed for RF ignors the dc
resistance of cable. This makes it somewhat inaccurate below 10 KHz.
If one were to incorporate the dc resistance into the model, then one
would
have a model that worked accurately down to 20 Hz and lower.

So, what you are saying is that the lumped element model is better for
audio frequencies and a real loudspeaker load?

No. A transmission line type model, will always be more accurate than
a lumped
element model.

:-). So, how do the equations look, how do I get from delay & loss to
Y-parameters?

Here is a model for 40 feet of 12 gage speaker wi

! 12 gage "speaker cable

# HZ DB S R 100

! S11 S21 S12 S22

19 -120 0 -6.95e-3 278.2e-6 -6.95e-3 278.2e-6 -120 0
20 -120 0 -6.95e-3 292.8e-6 -6.95e-3 292.8e-6 -120 0
21 -120 0 -6.95e-3 307.2e-6 -6.95e-3 307.5e-6 -120 0

The file above is an S-parameter, two-port file.

The first line is a comment.
The second line discribes the file: Frequency = "HZ", mag in "dB",
parameter type "S", reference impedance 100 Ohms.

The third line is a comment.

The 20 Hz line, completely models 12 gage cable (at 20 Hz).

It is much simpler to model a cable with one line of code, than with a
bunch
of resistors, capacitors and inductors.

Now, you need to convert line 20, into Y-parameters.

In the book "Solid State Radio Engineering" by Herbert L. Krauss and
Charles W. Bostian, on page 110 is a conversion formula:

dS =(S11*S22)-(S21*S12)

Yin = (S22-S11-dS/S22+S11) * (1/Z)
Yf = (-2*S21/S22+S11+dS) * (1/Z)
Yr = (-2*S12/S22+S11+dS) * (1/Z)
Yo = (S11-S22-dS/S22+S11+ds)* (1/Z)

From the Y-paramerters, you can find: delay, loss, impedance,
inductance, resistance/capacitance and phase shift of the cable. This
model will work with *any* source impedance, and with *any* load.

So, the S-parameters would be more of a practical eqivalent circuit,
while the other ones would be more theoretically "clean"?

All the parameters are equally accurate (clean). You might say they
are
five different sides of the same coin. :-)

Bob Stanton