Per Stromgren wrote in message

And what does it tell you? It tells me that the Smith Chart may be a
clever way to solve a computational *RF* problem, at least when we had
no better alternatives than slide rules and log books. Perhaps there
are better ways nowadays, who knows?


The Smith Chart is based on standard transmission line theory. Like a
sliderule it has limited accuracy. A sliderule may tell you that 2
times 3 is: 5.99, but we know it is based on sound priciples. The
Smith Chart is slightly inaccurate also. But, just like as the
sliderule, its fundamentals are valid.



Radio frequency techniques can not automatically be applied to the
snail pace of audio frequencies.

Yes.

Right. So why do you suggest we do use this method, then? Because you
say so?


I'm saying a transmission line model of a two-wire line, will give
slightly more accurate results than a discrete component model.



OK. What do you want me to do in order to convince you?

Well, runing a physical test would be nice. Or you could prove from
basic theory, that small wavelength lines don't "work".


Citing sources
won't do, abvoiusly. Is there any experiment result that would show
you that you are wrong?

As you know, our dialog is classical. You say A. I say: A is not what
a lot of their people say. You say: prove that the others are right. Why
should I? Isn't you the one who ought to prove "the others" wrong?


I don't think they are wrong, I think you may be misunderstanding what
they said. You may be confusing textbook statements about transmission
lines at *low frequencies*, with transmission lines that have *small
wavelenghts*. They are not the same thing at all!


Your turn. (I think I know the next step.)


I have presented a theory based on well known facts and formulas. What
more do I need to do?

Of course being a totally objective person, and being a totally honest
person, and being ever *so* humble as well, I don't insist that
everyone agree that I am right. (Even if I am.)

Have an nice day.

Bob Stanton

Ron Capik wrote in message

Somehow you guys seem to keep poking sticks in each other's
cages. I don't see that any of this hand waving will get you out of
this poking match.


I think we enjoy to poking at each others cage. :-)


First I'd like to pose the question: with the thousands of components
and feet of wire that audio goes through between the recorded source
and the playback system (including room acoustic effects) why are
people so passionate about the few feet of speaker cable?

They are just plain ignorant.



Ummm, why? What's the magic about the reactance to resistance ratio
that makes "any two wire line" a transmission line? Seems to me you only
made a statement rather than an explanation.

There are two definitions of transmission lines.

1) A conductor or group of conductors, that carry electrical energy
from one point to another.

2) A correctly dimentioned conductor or pair of conductors, for
carrying RF energy from one point to another.


In my messages, I referred to:
1) as a "line" and to 2) as a "transmission line".

RF transmission lines have completely different characteristics than
low frequency lines. For example, an RF transmission line can be (all
by itself) a narrow band transformer, step up, or a step down and of
any desired tranformation ratio ("turns" ratio).

A 2.5 ft long RF cable on the ouptut of an amplifier, will look like a
dead short circuit at 100 MHz. But, if you short circuit the end of
the RF cable, it will look like a completly open circuit, at 100 MHz.

Transmission lines, connected properly, can become RF bandpass filters
or a notch filters. Two transmission lines coupled together slightly,
can become a directional coupler, that looks at the RF signal coming
down the cable but doesnt' see the RF signals coming up the cable. And
that is only the tip of the strange iceberg called RF transmission
lines.

As the frequency gets lower, and the ratio of XL/R decreases, RF
transmission lines lose their strange propertys. So, the question of
the day is: at what low frequency do two-wire pairs stop acting like
"transmission lines".

Looking at the XL/R numbers for 12 gage speaker cable, I see the
possibiliy that we *might* get more accurate results, by considering
them as "transmission lines" rather than a just as "lines". At any
rate, we are talking about *only a few tenths of a dB*, at 20 KHz.





2. Very long speaker wires MUCH longer than a wavelength, DO NOT
behave like transmission lines.


That right, if the resistance/ft is too high, it will be only a
"line".


[ see "Ummm" above... ]

[ see "There are two..." above...]


And we're still only talking about fractions of a dB difference ...at high
frequencies. Heck, opening the curtains or another person in the room
likely has more impact on the sound...


Yes.

[ see "At any rate..." above...]


[ returning to lurking mode ]


Excellent questions.

Have fun lurking.

Bob Stanton

Ron Capik wrote in message

Somehow you guys seem to keep poking sticks in each other's
cages. I don't see that any of this hand waving will get you out of
this poking match.


I think we enjoy to poking at each others cage. :-)


First I'd like to pose the question: with the thousands of components
and feet of wire that audio goes through between the recorded source
and the playback system (including room acoustic effects) why are
people so passionate about the few feet of speaker cable?

They are just plain ignorant.



Ummm, why? What's the magic about the reactance to resistance ratio
that makes "any two wire line" a transmission line? Seems to me you only
made a statement rather than an explanation.

There are two definitions of transmission lines.

1) A conductor or group of conductors, that carry electrical energy
from one point to another.

2) A correctly dimentioned conductor or pair of conductors, for
carrying RF energy from one point to another.


In my messages, I referred to:
1) as a "line" and to 2) as a "transmission line".

RF transmission lines have completely different characteristics than
low frequency lines. For example, an RF transmission line can be (all
by itself) a narrow band transformer, step up, or a step down and of
any desired tranformation ratio ("turns" ratio).

A 2.5 ft long RF cable on the ouptut of an amplifier, will look like a
dead short circuit at 100 MHz. But, if you short circuit the end of
the RF cable, it will look like a completly open circuit, at 100 MHz.

Transmission lines, connected properly, can become RF bandpass filters
or a notch filters. Two transmission lines coupled together slightly,
can become a directional coupler, that looks at the RF signal coming
down the cable but doesnt' see the RF signals coming up the cable. And
that is only the tip of the strange iceberg called RF transmission
lines.

As the frequency gets lower, and the ratio of XL/R decreases, RF
transmission lines lose their strange propertys. So, the question of
the day is: at what low frequency do two-wire pairs stop acting like
"transmission lines".

Looking at the XL/R numbers for 12 gage speaker cable, I see the
possibiliy that we *might* get more accurate results, by considering
them as "transmission lines" rather than a just as "lines". At any
rate, we are talking about *only a few tenths of a dB*, at 20 KHz.





2. Very long speaker wires MUCH longer than a wavelength, DO NOT
behave like transmission lines.


That right, if the resistance/ft is too high, it will be only a
"line".


[ see "Ummm" above... ]

[ see "There are two..." above...]


And we're still only talking about fractions of a dB difference ...at high
frequencies. Heck, opening the curtains or another person in the room
likely has more impact on the sound...


Yes.

[ see "At any rate..." above...]


[ returning to lurking mode ]


Excellent questions.

Have fun lurking.

Bob Stanton

(Bob-Stanton) wrote in message . com...

I'm saying a transmission line model of a two-wire line, will give
slightly more accurate results than a discrete component model.

How on earth would you ever know? You have admitted never once
actually measuring the beast to see if your picture of it is
accurate or not.

Well, runing a physical test would be nice.

Good idea. So have at it.

Or you could prove from
basic theory, that small wavelength lines don't "work".

No more than you could "prove" from YOUR basic theory that it does
without ANY corroborative data.

I have presented a theory based on well known facts and formulas. What
more do I need to do?

No, you have not. You have presented NO relevant facts, like
real experimental data. None. Zilch.

If you CLAIM to present a theory base don facts, how about supplying
some facts?

Of course being a totally objective person,

Objectivity simply does not exist in the absence of facts. You have
presented a hypothesis. You have presented no facts.

(Bob-Stanton) wrote in message . com...

I'm saying a transmission line model of a two-wire line, will give
slightly more accurate results than a discrete component model.

How on earth would you ever know? You have admitted never once
actually measuring the beast to see if your picture of it is
accurate or not.

Well, runing a physical test would be nice.

Good idea. So have at it.

Or you could prove from
basic theory, that small wavelength lines don't "work".

No more than you could "prove" from YOUR basic theory that it does
without ANY corroborative data.

I have presented a theory based on well known facts and formulas. What
more do I need to do?

No, you have not. You have presented NO relevant facts, like
real experimental data. None. Zilch.

If you CLAIM to present a theory base don facts, how about supplying
some facts?

Of course being a totally objective person,

Objectivity simply does not exist in the absence of facts. You have
presented a hypothesis. You have presented no facts.

(Bob-Stanton) wrote in message . com...
(Dick Pierce) wrote in message
Mr. STanton, it's not my job or anyone else's to do YOUR work
for you. YOU are the one making the claim, YOU are the one who
has utterly failed to to provide ANY evidence for your claim.

I thought, if you were interested in the subject, you might make the
effort.

So, let's see if we have this straight: you're either too lazy,
too frightened or just too arrogant to provide support for your
hypothesis.

I think they *do* apply, but I won't be dogmatic about it without
supporting physical evidence.

No, sir, "dogma" is assertion with NO evidence. You're the one
spouting dogam.

Since the Roman Catholic Church had 100% confidence in their
model of the universe with the earth at the center and all else
moving around it in harmonic spheres, why should THEY test them?


I agree with them.

And you're the one claiming other peopl spout dogma?

(Bob-Stanton) wrote in message . com...
(Dick Pierce) wrote in message
Mr. STanton, it's not my job or anyone else's to do YOUR work
for you. YOU are the one making the claim, YOU are the one who
has utterly failed to to provide ANY evidence for your claim.

I thought, if you were interested in the subject, you might make the
effort.

So, let's see if we have this straight: you're either too lazy,
too frightened or just too arrogant to provide support for your
hypothesis.

I think they *do* apply, but I won't be dogmatic about it without
supporting physical evidence.

No, sir, "dogma" is assertion with NO evidence. You're the one
spouting dogam.

Since the Roman Catholic Church had 100% confidence in their
model of the universe with the earth at the center and all else
moving around it in harmonic spheres, why should THEY test them?


I agree with them.

And you're the one claiming other peopl spout dogma?

(Dick Pierce) wrote in message



So, let's see if we have this straight: you're either too lazy,
too frightened or just too arrogant to provide support for your
hypothesis.



I'd say Uhmm, too arrogant.

Bob Stanton

(Dick Pierce) wrote in message



So, let's see if we have this straight: you're either too lazy,
too frightened or just too arrogant to provide support for your
hypothesis.



I'd say Uhmm, too arrogant.

Bob Stanton

(Bob-Stanton) wrote in message om...
(Dick Pierce) wrote in message



So, let's see if we have this straight: you're either too lazy,
too frightened or just too arrogant to provide support for your
hypothesis.

I'd say Uhmm, too arrogant.

Q.E.D.

(Bob-Stanton) wrote in message om...
(Dick Pierce) wrote in message



So, let's see if we have this straight: you're either too lazy,
too frightened or just too arrogant to provide support for your
hypothesis.

I'd say Uhmm, too arrogant.

Q.E.D.

Bob-Stanton wrote:

Ron Capik wrote in message
..snips...
Ummm, why? What's the magic about the reactance to resistance ratio
that makes "any two wire line" a transmission line? Seems to me you only
made a statement rather than an explanation.


That right, if the resistance/ft is too high, it will be only a
"line".


[ see "Ummm" above... ]

[ see "There are two..." above...]


Bob, there was only one "Ummm" above and it asked
what makes the ratios special.
As far as I know that two wire case is but one example of
TEM mode transmission lines.

If you were dealing with flat conductor ribbon cable (maybe like
some of those "under the carpet" audio cables) you might be
dealing with significant transmission line effects at audio frequencies,
depending on geometry etc. [Like say: fold the cable in half or run the
right and left speaker ribbons on top of each other ...not that I think you
might ever do such a thing. G ]

Anyway... back to lurking.


Ron Capik
--

Bob-Stanton wrote:

Ron Capik wrote in message
..snips...
Ummm, why? What's the magic about the reactance to resistance ratio
that makes "any two wire line" a transmission line? Seems to me you only
made a statement rather than an explanation.


That right, if the resistance/ft is too high, it will be only a
"line".


[ see "Ummm" above... ]

[ see "There are two..." above...]


Bob, there was only one "Ummm" above and it asked
what makes the ratios special.
As far as I know that two wire case is but one example of
TEM mode transmission lines.

If you were dealing with flat conductor ribbon cable (maybe like
some of those "under the carpet" audio cables) you might be
dealing with significant transmission line effects at audio frequencies,
depending on geometry etc. [Like say: fold the cable in half or run the
right and left speaker ribbons on top of each other ...not that I think you
might ever do such a thing. G ]

Anyway... back to lurking.


Ron Capik
--

Ron Capik wrote in message

As far as I know that two wire case is but one example of
TEM mode transmission lines.


That's right.

T.E.M. means: "transverse electric mode". A mode where the electric
field is perpendicular to the direction of propagation.

Even hollow pipes (waveguides) can have a TEM.


Bob Stanton

Ron Capik wrote in message

As far as I know that two wire case is but one example of
TEM mode transmission lines.


That's right.

T.E.M. means: "transverse electric mode". A mode where the electric
field is perpendicular to the direction of propagation.

Even hollow pipes (waveguides) can have a TEM.


Bob Stanton

Bob-Stanton wrote:

...snip..

Even hollow pipes (waveguides) can have a TEM.

Don't even need a pipe. TEM modes can be supported
in free space.

Somewhat in support of your conjecture I contend that
there are transmission line effects in any electromagnetic
interaction. Under some conditions the bulk effects overwhelm
the spatial effects but they're still there. Any time you move a
charge there's a spatial effect than can be coupled to
other charges. Reactance is a spatial effect.

It's been years since I played with transmission lines but
I think your argument is on the right track. Dick has been
looking for substantiation, I threw the ratio question in as
a possible direction for investigation.

I think pulling up a Smith Chart was innovative. Were we
in class and I your professor you'd get extra credit for that. ;-)

I was having fun watching the thread 'till it hit the rocks.
....thought a few questions might nudge it along.

....not quite lurking.

Later...

Ron Capik
--
....the more you know the more you know you don't know.

Bob-Stanton wrote:

...snip..

Even hollow pipes (waveguides) can have a TEM.

Don't even need a pipe. TEM modes can be supported
in free space.

Somewhat in support of your conjecture I contend that
there are transmission line effects in any electromagnetic
interaction. Under some conditions the bulk effects overwhelm
the spatial effects but they're still there. Any time you move a
charge there's a spatial effect than can be coupled to
other charges. Reactance is a spatial effect.

It's been years since I played with transmission lines but
I think your argument is on the right track. Dick has been
looking for substantiation, I threw the ratio question in as
a possible direction for investigation.

I think pulling up a Smith Chart was innovative. Were we
in class and I your professor you'd get extra credit for that. ;-)

I was having fun watching the thread 'till it hit the rocks.
....thought a few questions might nudge it along.

....not quite lurking.

Later...

Ron Capik
--
....the more you know the more you know you don't know.

Ron Capik wrote in message

If you were dealing with flat conductor ribbon cable (maybe like
some of those "under the carpet" audio cables) you might be
dealing with significant transmission line effects at audio frequencies,
depending on geometry etc. [Like say: fold the cable in half or run the
right and left speaker ribbons on top of each other ...not that I think you
might ever do such a thing. G ]

Anyway... back to lurking.


Dunlavy Z6, flat speaker cable has a lower inductance/ft than Home
Depot 12 gage, but the same resistance /ft. I would not expect Z6 to
act as a transmission line at audio frequencies. However, modeling it
as discrete components, it has excellent performance.

Any open two-wire cable (flat or round) will be affected by the
external environment.

Back to lurking, me to.

Bob Stanton

Ron Capik wrote in message

If you were dealing with flat conductor ribbon cable (maybe like
some of those "under the carpet" audio cables) you might be
dealing with significant transmission line effects at audio frequencies,
depending on geometry etc. [Like say: fold the cable in half or run the
right and left speaker ribbons on top of each other ...not that I think you
might ever do such a thing. G ]

Anyway... back to lurking.


Dunlavy Z6, flat speaker cable has a lower inductance/ft than Home
Depot 12 gage, but the same resistance /ft. I would not expect Z6 to
act as a transmission line at audio frequencies. However, modeling it
as discrete components, it has excellent performance.

Any open two-wire cable (flat or round) will be affected by the
external environment.

Back to lurking, me to.

Bob Stanton

On 15 Nov 2003 08:41:22 -0800, (Bob-Stanton)
wrote:

Ron Capik wrote in message

If you were dealing with flat conductor ribbon cable (maybe like
some of those "under the carpet" audio cables) you might be
dealing with significant transmission line effects at audio frequencies,
depending on geometry etc. [Like say: fold the cable in half or run the
right and left speaker ribbons on top of each other ...not that I think you
might ever do such a thing. G ]

Anyway... back to lurking.


Dunlavy Z6, flat speaker cable has a lower inductance/ft than Home
Depot 12 gage, but the same resistance /ft. I would not expect Z6 to
act as a transmission line at audio frequencies. However, modeling it
as discrete components, it has excellent performance.

Any open two-wire cable (flat or round) will be affected by the
external environment.

Back to lurking, me to.

Bob Stanton

Why would you not expect the Z6 to act as a transmission line? It
really has no choice in the matter since it is one, and it has no
preconceptions about audio frequencies. And of course its performance
lies in what it actually is - not how you model it.

As for open two-wire systems interacting with their environment, well,
certainly there is some interaction, but it is vastly lower than the
interaction between the two conductors. More specifically, how the
wire is laid out - folded, bunched or straight - has no effect
whatever, since the effect is only present in the common mode, not the
differential (signal-carrying) mode.

d

_____________________________

http://www.pearce.uk.com

On 15 Nov 2003 08:41:22 -0800, (Bob-Stanton)
wrote:

Ron Capik wrote in message

If you were dealing with flat conductor ribbon cable (maybe like
some of those "under the carpet" audio cables) you might be
dealing with significant transmission line effects at audio frequencies,
depending on geometry etc. [Like say: fold the cable in half or run the
right and left speaker ribbons on top of each other ...not that I think you
might ever do such a thing. G ]

Anyway... back to lurking.


Dunlavy Z6, flat speaker cable has a lower inductance/ft than Home
Depot 12 gage, but the same resistance /ft. I would not expect Z6 to
act as a transmission line at audio frequencies. However, modeling it
as discrete components, it has excellent performance.

Any open two-wire cable (flat or round) will be affected by the
external environment.

Back to lurking, me to.

Bob Stanton

Why would you not expect the Z6 to act as a transmission line? It
really has no choice in the matter since it is one, and it has no
preconceptions about audio frequencies. And of course its performance
lies in what it actually is - not how you model it.

As for open two-wire systems interacting with their environment, well,
certainly there is some interaction, but it is vastly lower than the
interaction between the two conductors. More specifically, how the
wire is laid out - folded, bunched or straight - has no effect
whatever, since the effect is only present in the common mode, not the
differential (signal-carrying) mode.

d

_____________________________

http://www.pearce.uk.com

Don Pearce wrote:

...snip..

As for open two-wire systems interacting with their environment, well,
certainly there is some interaction, but it is vastly lower than the
interaction between the two conductors. More specifically, how the
wire is laid out - folded, bunched or straight - has no effect
whatever, since the effect is only present in the common mode, not the
differential (signal-carrying) mode.


Think capacitive rather than inductive coupling; as in slab waveguide.
The systems have a common ground. The interaction would be in the form
of cross talk if the right and left cables were overlaid, like if the amp were
in the back of the room. Depends a lot on geometry, we're still talking
fractions of a dB ...and any good tech would never run the wires on top
of each other.
Darn, now you have me poking about with quasi-academic sticks... ;-)

Carry on...

Ron Capik cynic in training
--

Don Pearce wrote:

...snip..

As for open two-wire systems interacting with their environment, well,
certainly there is some interaction, but it is vastly lower than the
interaction between the two conductors. More specifically, how the
wire is laid out - folded, bunched or straight - has no effect
whatever, since the effect is only present in the common mode, not the
differential (signal-carrying) mode.


Think capacitive rather than inductive coupling; as in slab waveguide.
The systems have a common ground. The interaction would be in the form
of cross talk if the right and left cables were overlaid, like if the amp were
in the back of the room. Depends a lot on geometry, we're still talking
fractions of a dB ...and any good tech would never run the wires on top
of each other.
Darn, now you have me poking about with quasi-academic sticks... ;-)

Carry on...

Ron Capik cynic in training
--

Don Pearce wrote in message


Why would you not expect the Z6 to act as a transmission line? It
really has no choice in the matter since it is one, and it has no
preconceptions about audio frequencies.

There are two definitions of "transmission lines". (Transmission
lines, and RF transmission lines) Z6 is always a transmission line, at
any frequency. But, it won't act as a RF transmission line below a
certain frequency. For example, if you tried to make it into a 1/4
wave transformer (at 1000 Hz), it wouldn't transform.


And of course its performance
lies in what it actually is - not how you model it.


What we want to be able to do is to model the way it actually is, from
simple R, L, and C measurements.

Bob Stanton

Don Pearce wrote in message


Why would you not expect the Z6 to act as a transmission line? It
really has no choice in the matter since it is one, and it has no
preconceptions about audio frequencies.

There are two definitions of "transmission lines". (Transmission
lines, and RF transmission lines) Z6 is always a transmission line, at
any frequency. But, it won't act as a RF transmission line below a
certain frequency. For example, if you tried to make it into a 1/4
wave transformer (at 1000 Hz), it wouldn't transform.


And of course its performance
lies in what it actually is - not how you model it.


What we want to be able to do is to model the way it actually is, from
simple R, L, and C measurements.

Bob Stanton

On 15 Nov 2003 17:42:45 -0800, (Bob-Stanton)
wrote:

Don Pearce wrote in message


Why would you not expect the Z6 to act as a transmission line? It
really has no choice in the matter since it is one, and it has no
preconceptions about audio frequencies.

There are two definitions of "transmission lines". (Transmission
lines, and RF transmission lines) Z6 is always a transmission line, at
any frequency. But, it won't act as a RF transmission line below a
certain frequency. For example, if you tried to make it into a 1/4
wave transformer (at 1000 Hz), it wouldn't transform.

It acts as a transmission line at every frequency. The question of how
you choose to model it is quite different.

And of course its performance
lies in what it actually is - not how you model it.


What we want to be able to do is to model the way it actually is, from
simple R, L, and C measurements.

Bob Stanton

No, you aren't modelling it the way it is, but as an approximate
abstraction - more than good enough to give you the results you want.
That is of course the nature of all models, but some are further
abstracted than others.

d

_____________________________

http://www.pearce.uk.com

On 15 Nov 2003 17:42:45 -0800, (Bob-Stanton)
wrote:

Don Pearce wrote in message


Why would you not expect the Z6 to act as a transmission line? It
really has no choice in the matter since it is one, and it has no
preconceptions about audio frequencies.

There are two definitions of "transmission lines". (Transmission
lines, and RF transmission lines) Z6 is always a transmission line, at
any frequency. But, it won't act as a RF transmission line below a
certain frequency. For example, if you tried to make it into a 1/4
wave transformer (at 1000 Hz), it wouldn't transform.

It acts as a transmission line at every frequency. The question of how
you choose to model it is quite different.

And of course its performance
lies in what it actually is - not how you model it.


What we want to be able to do is to model the way it actually is, from
simple R, L, and C measurements.

Bob Stanton

No, you aren't modelling it the way it is, but as an approximate
abstraction - more than good enough to give you the results you want.
That is of course the nature of all models, but some are further
abstracted than others.

d

_____________________________

http://www.pearce.uk.com

Don Pearce wrote in message


It acts as a transmission line at every frequency. The question of how
you choose to model it is quite different.


No, you aren't modelling it the way it is, but as an approximate
abstraction - more than good enough to give you the results you want.
That is of course the nature of all models, but some are further
abstracted than others.


I agree, if we are making a standard model from R, L, C, and/or even
RF transmission lines. There is one model type, however, that is as
accurate as the best test equipment. That would be a two-port,
S-parameter, data file. A speaker cable's S-parameters can be measured
by an HP Network Analyzer, (down to the lowest RF frequencies). Then
below RF, Y-parameters can be used down to the lowest audio
frequencies. (The Y-parameters can then be converted to S-parameters.)
Now, you have an S-parameter, two-port data file, that goes from audio
to RF. A circuit analysis program can use this file to simulate the
speaker cable. The two-port data file is treated, as a *component*.
The output of the program will be exactly the same as the data the
network analyzer measured.

The nice thing about this two-port data component model is: it will
also work in low frequency AC circuit analysis programs, with *any
source and any load impedance*. Using a voltage source and a typical
*loudspeaker load*, it will give the response of that cable into that
load, even though the speaker cable was originally measured using
equal source and load impedance.

Bob Stanton

Don Pearce wrote in message


It acts as a transmission line at every frequency. The question of how
you choose to model it is quite different.


No, you aren't modelling it the way it is, but as an approximate
abstraction - more than good enough to give you the results you want.
That is of course the nature of all models, but some are further
abstracted than others.


I agree, if we are making a standard model from R, L, C, and/or even
RF transmission lines. There is one model type, however, that is as
accurate as the best test equipment. That would be a two-port,
S-parameter, data file. A speaker cable's S-parameters can be measured
by an HP Network Analyzer, (down to the lowest RF frequencies). Then
below RF, Y-parameters can be used down to the lowest audio
frequencies. (The Y-parameters can then be converted to S-parameters.)
Now, you have an S-parameter, two-port data file, that goes from audio
to RF. A circuit analysis program can use this file to simulate the
speaker cable. The two-port data file is treated, as a *component*.
The output of the program will be exactly the same as the data the
network analyzer measured.

The nice thing about this two-port data component model is: it will
also work in low frequency AC circuit analysis programs, with *any
source and any load impedance*. Using a voltage source and a typical
*loudspeaker load*, it will give the response of that cable into that
load, even though the speaker cable was originally measured using
equal source and load impedance.

Bob Stanton