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  #281   Report Post  
Svante
 
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Default More cable questions!

Don Pearce wrote in message . ..
On 10 Jan 2004 01:33:35 -0800, (Svante)
wrote:

Nowadays, it is quicker and easier (less typing) to enter a
transmission line model, than to type in a componet (L,C) model. Use
whatever way floats your boat.


OK, in my boat there are no transmission line models, but a lot of R,
L and Cs.


You would have thought that given enough Ls and Cs (ie dividing the
lumped model very finely) you would end up with a perfect equivalent
of the transmission line model, but you don't. You just end up with an
ever steeper lowpass filter. Up to the cutoff point, this filter does
indeed behave remarkably like a true cable, though.


Yes, so the trick would be to use enough Ls and Cs then.

For much audio work a single L and C seem to do just fine, but there
are problems - like what order should you put them in? In theory you
can put the shunt C at either the start or end of the network, but if
you are modelling a very unmatched situation this won't work. For
example, if you are looking at an amplifier to a loudspeaker, the C
must be put at the speaker end - it has no effect on amplitude at the
amplifier end. In a matched scenario - equal impedances both ends, the
capacitance must be split and placed both ends if the model is to
work. So you must be careful in the application of a lumped model
cable, and understand the significance of the impedances at both ends
before you use it.


I'd think that either is OK as you increase the number of Ls and Cs.
This number will determine a highest valid frequency, and below that
frequency it does not matter much if analog starts with an L or a C.
When dealing with acoustic tubes I ususlly do it like this:

------L/2------*-----L/2-------
|
C
|
---------------*---------------

but one could also do:


-------*-----L------*----------
| |
C/2 C/2
| |
-------*------------*----------

Now, given that I have a high number of these sections, each of the
components will be small, and it will not matter much which model that
is used.


The true transmission line model has the advantage that all this is
taken care of, there is no anomalous lowpass filter effect to worry
about and it is really easy to change lengths - you just alter the
length term. It also works at any frequency. It is a sledgehammer to
crack a nut, though, and representing a cable as Ls and Cs (given the
caveats above) is perfectly proper, particularly if you are having to
hand-crank the results, or just doing a back-of-an-envelope
calculation. If you are using Spice, or something similar that
possesses native transmission line models, then why not use them? They
are easier to use, just as accurate for audio, and vastly more
accurate outside the audio band.


I can understand that this COULD be the case, but I don't understand
it (yet). I guess I'll just have to learn it.
  #282   Report Post  
Svante
 
Posts: n/a
Default More cable questions!

Don Pearce wrote in message . ..
On 10 Jan 2004 01:33:35 -0800, (Svante)
wrote:

Nowadays, it is quicker and easier (less typing) to enter a
transmission line model, than to type in a componet (L,C) model. Use
whatever way floats your boat.


OK, in my boat there are no transmission line models, but a lot of R,
L and Cs.


You would have thought that given enough Ls and Cs (ie dividing the
lumped model very finely) you would end up with a perfect equivalent
of the transmission line model, but you don't. You just end up with an
ever steeper lowpass filter. Up to the cutoff point, this filter does
indeed behave remarkably like a true cable, though.


Yes, so the trick would be to use enough Ls and Cs then.

For much audio work a single L and C seem to do just fine, but there
are problems - like what order should you put them in? In theory you
can put the shunt C at either the start or end of the network, but if
you are modelling a very unmatched situation this won't work. For
example, if you are looking at an amplifier to a loudspeaker, the C
must be put at the speaker end - it has no effect on amplitude at the
amplifier end. In a matched scenario - equal impedances both ends, the
capacitance must be split and placed both ends if the model is to
work. So you must be careful in the application of a lumped model
cable, and understand the significance of the impedances at both ends
before you use it.


I'd think that either is OK as you increase the number of Ls and Cs.
This number will determine a highest valid frequency, and below that
frequency it does not matter much if analog starts with an L or a C.
When dealing with acoustic tubes I ususlly do it like this:

------L/2------*-----L/2-------
|
C
|
---------------*---------------

but one could also do:


-------*-----L------*----------
| |
C/2 C/2
| |
-------*------------*----------

Now, given that I have a high number of these sections, each of the
components will be small, and it will not matter much which model that
is used.


The true transmission line model has the advantage that all this is
taken care of, there is no anomalous lowpass filter effect to worry
about and it is really easy to change lengths - you just alter the
length term. It also works at any frequency. It is a sledgehammer to
crack a nut, though, and representing a cable as Ls and Cs (given the
caveats above) is perfectly proper, particularly if you are having to
hand-crank the results, or just doing a back-of-an-envelope
calculation. If you are using Spice, or something similar that
possesses native transmission line models, then why not use them? They
are easier to use, just as accurate for audio, and vastly more
accurate outside the audio band.


I can understand that this COULD be the case, but I don't understand
it (yet). I guess I'll just have to learn it.
  #283   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!

(Svante) wrote in message


Thank you for the offer, but I am the (perhaps silly) type of guy that
tries to understand things and make my own computer programs. I know
it is slower, but I feel that I learn from doing this.


I do that too, and I feel the same way. The program I was refering to
was one I wrote about 20 years ago. (My, how time flys.) Write your
own program, have fun, enjoy. :-)


Well, another way would be to take an ohm-meter and measure it's
resistance. That would be another aspect, that is VERY relevant. And
at least in my mind that is an easier measurement than the delay
measurement.


No, delay is the easiest to measure. All you need is a ruler. Measure
how long the cable is. The wave in cable travels at 66% to 90% of the
velocity of light, depending on the dialectric material.



Hmmm... So what is the typical XL/R ratio for audio frequencies? :-)
If that is a prerequisite, IS the transmission line model really valid
for audio frequencies?


As a rule of thumb, the XL should be 10 times higher than R. For 12
gage cable, XL/R starts getting too low below 10 KHz.


Even in the case where the series resistance dominates, and the load
varies with frequency?


In that case, the transmission line numbers become such a small part
of the answer you can forget about them. At that point, you can use
Ohms law to calculate the cable loss.



...and this you do for one frequency at a time, right? I mean, if you
want to do this for another frequency, you go through this process
again?


That is right! As far as the computer is concerned, each frequency has
a different cable, one with it's own loss and phase shift
characteristics. Each frequency also has a different termination
impedance. The computer calculates a new cable and a new load at each
frequency. It's a lot of work to do it that way, but the the computer
never complains.



OK, but then I would argue that we are no longer talking about a
resistor, but a model of a real physical resistor, that contains other
elements as well. OK, I'm picky again.


I agree. An ideal resistor is a simpler circuit. Still the
transmission line is a fairly simpler entry into the matrix. No long
equations needed. Just convert the cable S-parameters into
Y-parameters, and pop them into the matix, at four places.



I'll have to think a bit about this to understand it. I have written
programs that reduced passive circuits down to 4-poles, but it was
some time ago.


The easiest way to program a computer to do circuit analysis, is to
write the circuit conductances into a large matrix. The conductance
(y-parameter) is entered at the row and column that correspond to the
circuit node the conductance is across. This is much easier than
trying to use different equations for every different circuit
topology. The matrix is reduced to one number, and that number is the
voltage at the output node.


There were four types, G, Y, H and Z, was it? The H one
is often used to describe transistors, and the Y would be one of those
that you describe, right?


H, Y, Z, G, and S parameters can be converted from one to the other.
You can measure a two-port device using whatever parameters suit your
test equipment the best, then convert them to any other type of
parameters.

Y, Z and H parameters require open or short circuits on the port
during measurement. A lot of devices object of having their inputs or
outputs short circuited, so S-parameters have become very popular.(
S-parameters are measure with a load on the output.)

Bob Stanton
  #284   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!

(Svante) wrote in message


Thank you for the offer, but I am the (perhaps silly) type of guy that
tries to understand things and make my own computer programs. I know
it is slower, but I feel that I learn from doing this.


I do that too, and I feel the same way. The program I was refering to
was one I wrote about 20 years ago. (My, how time flys.) Write your
own program, have fun, enjoy. :-)


Well, another way would be to take an ohm-meter and measure it's
resistance. That would be another aspect, that is VERY relevant. And
at least in my mind that is an easier measurement than the delay
measurement.


No, delay is the easiest to measure. All you need is a ruler. Measure
how long the cable is. The wave in cable travels at 66% to 90% of the
velocity of light, depending on the dialectric material.



Hmmm... So what is the typical XL/R ratio for audio frequencies? :-)
If that is a prerequisite, IS the transmission line model really valid
for audio frequencies?


As a rule of thumb, the XL should be 10 times higher than R. For 12
gage cable, XL/R starts getting too low below 10 KHz.


Even in the case where the series resistance dominates, and the load
varies with frequency?


In that case, the transmission line numbers become such a small part
of the answer you can forget about them. At that point, you can use
Ohms law to calculate the cable loss.



...and this you do for one frequency at a time, right? I mean, if you
want to do this for another frequency, you go through this process
again?


That is right! As far as the computer is concerned, each frequency has
a different cable, one with it's own loss and phase shift
characteristics. Each frequency also has a different termination
impedance. The computer calculates a new cable and a new load at each
frequency. It's a lot of work to do it that way, but the the computer
never complains.



OK, but then I would argue that we are no longer talking about a
resistor, but a model of a real physical resistor, that contains other
elements as well. OK, I'm picky again.


I agree. An ideal resistor is a simpler circuit. Still the
transmission line is a fairly simpler entry into the matrix. No long
equations needed. Just convert the cable S-parameters into
Y-parameters, and pop them into the matix, at four places.



I'll have to think a bit about this to understand it. I have written
programs that reduced passive circuits down to 4-poles, but it was
some time ago.


The easiest way to program a computer to do circuit analysis, is to
write the circuit conductances into a large matrix. The conductance
(y-parameter) is entered at the row and column that correspond to the
circuit node the conductance is across. This is much easier than
trying to use different equations for every different circuit
topology. The matrix is reduced to one number, and that number is the
voltage at the output node.


There were four types, G, Y, H and Z, was it? The H one
is often used to describe transistors, and the Y would be one of those
that you describe, right?


H, Y, Z, G, and S parameters can be converted from one to the other.
You can measure a two-port device using whatever parameters suit your
test equipment the best, then convert them to any other type of
parameters.

Y, Z and H parameters require open or short circuits on the port
during measurement. A lot of devices object of having their inputs or
outputs short circuited, so S-parameters have become very popular.(
S-parameters are measure with a load on the output.)

Bob Stanton
  #285   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!

(Svante) wrote in message


Thank you for the offer, but I am the (perhaps silly) type of guy that
tries to understand things and make my own computer programs. I know
it is slower, but I feel that I learn from doing this.


I do that too, and I feel the same way. The program I was refering to
was one I wrote about 20 years ago. (My, how time flys.) Write your
own program, have fun, enjoy. :-)


Well, another way would be to take an ohm-meter and measure it's
resistance. That would be another aspect, that is VERY relevant. And
at least in my mind that is an easier measurement than the delay
measurement.


No, delay is the easiest to measure. All you need is a ruler. Measure
how long the cable is. The wave in cable travels at 66% to 90% of the
velocity of light, depending on the dialectric material.



Hmmm... So what is the typical XL/R ratio for audio frequencies? :-)
If that is a prerequisite, IS the transmission line model really valid
for audio frequencies?


As a rule of thumb, the XL should be 10 times higher than R. For 12
gage cable, XL/R starts getting too low below 10 KHz.


Even in the case where the series resistance dominates, and the load
varies with frequency?


In that case, the transmission line numbers become such a small part
of the answer you can forget about them. At that point, you can use
Ohms law to calculate the cable loss.



...and this you do for one frequency at a time, right? I mean, if you
want to do this for another frequency, you go through this process
again?


That is right! As far as the computer is concerned, each frequency has
a different cable, one with it's own loss and phase shift
characteristics. Each frequency also has a different termination
impedance. The computer calculates a new cable and a new load at each
frequency. It's a lot of work to do it that way, but the the computer
never complains.



OK, but then I would argue that we are no longer talking about a
resistor, but a model of a real physical resistor, that contains other
elements as well. OK, I'm picky again.


I agree. An ideal resistor is a simpler circuit. Still the
transmission line is a fairly simpler entry into the matrix. No long
equations needed. Just convert the cable S-parameters into
Y-parameters, and pop them into the matix, at four places.



I'll have to think a bit about this to understand it. I have written
programs that reduced passive circuits down to 4-poles, but it was
some time ago.


The easiest way to program a computer to do circuit analysis, is to
write the circuit conductances into a large matrix. The conductance
(y-parameter) is entered at the row and column that correspond to the
circuit node the conductance is across. This is much easier than
trying to use different equations for every different circuit
topology. The matrix is reduced to one number, and that number is the
voltage at the output node.


There were four types, G, Y, H and Z, was it? The H one
is often used to describe transistors, and the Y would be one of those
that you describe, right?


H, Y, Z, G, and S parameters can be converted from one to the other.
You can measure a two-port device using whatever parameters suit your
test equipment the best, then convert them to any other type of
parameters.

Y, Z and H parameters require open or short circuits on the port
during measurement. A lot of devices object of having their inputs or
outputs short circuited, so S-parameters have become very popular.(
S-parameters are measure with a load on the output.)

Bob Stanton


  #286   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!

(Svante) wrote in message


Thank you for the offer, but I am the (perhaps silly) type of guy that
tries to understand things and make my own computer programs. I know
it is slower, but I feel that I learn from doing this.


I do that too, and I feel the same way. The program I was refering to
was one I wrote about 20 years ago. (My, how time flys.) Write your
own program, have fun, enjoy. :-)


Well, another way would be to take an ohm-meter and measure it's
resistance. That would be another aspect, that is VERY relevant. And
at least in my mind that is an easier measurement than the delay
measurement.


No, delay is the easiest to measure. All you need is a ruler. Measure
how long the cable is. The wave in cable travels at 66% to 90% of the
velocity of light, depending on the dialectric material.



Hmmm... So what is the typical XL/R ratio for audio frequencies? :-)
If that is a prerequisite, IS the transmission line model really valid
for audio frequencies?


As a rule of thumb, the XL should be 10 times higher than R. For 12
gage cable, XL/R starts getting too low below 10 KHz.


Even in the case where the series resistance dominates, and the load
varies with frequency?


In that case, the transmission line numbers become such a small part
of the answer you can forget about them. At that point, you can use
Ohms law to calculate the cable loss.



...and this you do for one frequency at a time, right? I mean, if you
want to do this for another frequency, you go through this process
again?


That is right! As far as the computer is concerned, each frequency has
a different cable, one with it's own loss and phase shift
characteristics. Each frequency also has a different termination
impedance. The computer calculates a new cable and a new load at each
frequency. It's a lot of work to do it that way, but the the computer
never complains.



OK, but then I would argue that we are no longer talking about a
resistor, but a model of a real physical resistor, that contains other
elements as well. OK, I'm picky again.


I agree. An ideal resistor is a simpler circuit. Still the
transmission line is a fairly simpler entry into the matrix. No long
equations needed. Just convert the cable S-parameters into
Y-parameters, and pop them into the matix, at four places.



I'll have to think a bit about this to understand it. I have written
programs that reduced passive circuits down to 4-poles, but it was
some time ago.


The easiest way to program a computer to do circuit analysis, is to
write the circuit conductances into a large matrix. The conductance
(y-parameter) is entered at the row and column that correspond to the
circuit node the conductance is across. This is much easier than
trying to use different equations for every different circuit
topology. The matrix is reduced to one number, and that number is the
voltage at the output node.


There were four types, G, Y, H and Z, was it? The H one
is often used to describe transistors, and the Y would be one of those
that you describe, right?


H, Y, Z, G, and S parameters can be converted from one to the other.
You can measure a two-port device using whatever parameters suit your
test equipment the best, then convert them to any other type of
parameters.

Y, Z and H parameters require open or short circuits on the port
during measurement. A lot of devices object of having their inputs or
outputs short circuited, so S-parameters have become very popular.(
S-parameters are measure with a load on the output.)

Bob Stanton
  #287   Report Post  
Svante
 
Posts: n/a
Default More cable questions!

(Bob-Stanton) wrote in message (Svante) wrote in message

Well, another way would be to take an ohm-meter and measure it's
resistance. That would be another aspect, that is VERY relevant. And
at least in my mind that is an easier measurement than the delay
measurement.


No, delay is the easiest to measure. All you need is a ruler. Measure
how long the cable is. The wave in cable travels at 66% to 90% of the
velocity of light, depending on the dialectric material.


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... :-)

Hmmm... So what is the typical XL/R ratio for audio frequencies? :-)
If that is a prerequisite, IS the transmission line model really valid
for audio frequencies?


As a rule of thumb, the XL should be 10 times higher than R. For 12
gage cable, XL/R starts getting too low below 10 KHz.


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

Even in the case where the series resistance dominates, and the load
varies with frequency?


In that case, the transmission line numbers become such a small part
of the answer you can forget about them. At that point, you can use
Ohms law to calculate the cable loss.


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

...and this you do for one frequency at a time, right? I mean, if you
want to do this for another frequency, you go through this process
again?


That is right! As far as the computer is concerned, each frequency has
a different cable, one with it's own loss and phase shift
characteristics. Each frequency also has a different termination
impedance. The computer calculates a new cable and a new load at each
frequency. It's a lot of work to do it that way, but the the computer
never complains.


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

OK, but then I would argue that we are no longer talking about a
resistor, but a model of a real physical resistor, that contains other
elements as well. OK, I'm picky again.


I agree. An ideal resistor is a simpler circuit. Still the
transmission line is a fairly simpler entry into the matrix. No long
equations needed. Just convert the cable S-parameters into
Y-parameters, and pop them into the matix, at four places.

I'll have to think a bit about this to understand it. I have written
programs that reduced passive circuits down to 4-poles, but it was
some time ago.


The easiest way to program a computer to do circuit analysis, is to
write the circuit conductances into a large matrix. The conductance
(y-parameter) is entered at the row and column that correspond to the
circuit node the conductance is across. This is much easier than
trying to use different equations for every different circuit
topology. The matrix is reduced to one number, and that number is the
voltage at the output node.


Yes, I do that a lot, and it is indeed very flexible. Mostly I use it
for (electric analogies of) acoustic circuits. I just never thought of
a cable as a 4-pole, but I guess that is what transmission line theory
would be all about.

There were four types, G, Y, H and Z, was it? The H one
is often used to describe transistors, and the Y would be one of those
that you describe, right?


H, Y, Z, G, and S parameters can be converted from one to the other.
You can measure a two-port device using whatever parameters suit your
test equipment the best, then convert them to any other type of
parameters.

Y, Z and H parameters require open or short circuits on the port
during measurement. A lot of devices object of having their inputs or
outputs short circuited, so S-parameters have become very popular.(
S-parameters are measure with a load on the output.)


So, the S-parameters would be more of a practical eqivalent circuit,
while the other ones would be more theoretically "clean"?
  #288   Report Post  
Svante
 
Posts: n/a
Default More cable questions!

(Bob-Stanton) wrote in message (Svante) wrote in message

Well, another way would be to take an ohm-meter and measure it's
resistance. That would be another aspect, that is VERY relevant. And
at least in my mind that is an easier measurement than the delay
measurement.


No, delay is the easiest to measure. All you need is a ruler. Measure
how long the cable is. The wave in cable travels at 66% to 90% of the
velocity of light, depending on the dialectric material.


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... :-)

Hmmm... So what is the typical XL/R ratio for audio frequencies? :-)
If that is a prerequisite, IS the transmission line model really valid
for audio frequencies?


As a rule of thumb, the XL should be 10 times higher than R. For 12
gage cable, XL/R starts getting too low below 10 KHz.


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

Even in the case where the series resistance dominates, and the load
varies with frequency?


In that case, the transmission line numbers become such a small part
of the answer you can forget about them. At that point, you can use
Ohms law to calculate the cable loss.


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

...and this you do for one frequency at a time, right? I mean, if you
want to do this for another frequency, you go through this process
again?


That is right! As far as the computer is concerned, each frequency has
a different cable, one with it's own loss and phase shift
characteristics. Each frequency also has a different termination
impedance. The computer calculates a new cable and a new load at each
frequency. It's a lot of work to do it that way, but the the computer
never complains.


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

OK, but then I would argue that we are no longer talking about a
resistor, but a model of a real physical resistor, that contains other
elements as well. OK, I'm picky again.


I agree. An ideal resistor is a simpler circuit. Still the
transmission line is a fairly simpler entry into the matrix. No long
equations needed. Just convert the cable S-parameters into
Y-parameters, and pop them into the matix, at four places.

I'll have to think a bit about this to understand it. I have written
programs that reduced passive circuits down to 4-poles, but it was
some time ago.


The easiest way to program a computer to do circuit analysis, is to
write the circuit conductances into a large matrix. The conductance
(y-parameter) is entered at the row and column that correspond to the
circuit node the conductance is across. This is much easier than
trying to use different equations for every different circuit
topology. The matrix is reduced to one number, and that number is the
voltage at the output node.


Yes, I do that a lot, and it is indeed very flexible. Mostly I use it
for (electric analogies of) acoustic circuits. I just never thought of
a cable as a 4-pole, but I guess that is what transmission line theory
would be all about.

There were four types, G, Y, H and Z, was it? The H one
is often used to describe transistors, and the Y would be one of those
that you describe, right?


H, Y, Z, G, and S parameters can be converted from one to the other.
You can measure a two-port device using whatever parameters suit your
test equipment the best, then convert them to any other type of
parameters.

Y, Z and H parameters require open or short circuits on the port
during measurement. A lot of devices object of having their inputs or
outputs short circuited, so S-parameters have become very popular.(
S-parameters are measure with a load on the output.)


So, the S-parameters would be more of a practical eqivalent circuit,
while the other ones would be more theoretically "clean"?
  #289   Report Post  
Svante
 
Posts: n/a
Default More cable questions!

(Bob-Stanton) wrote in message (Svante) wrote in message

Well, another way would be to take an ohm-meter and measure it's
resistance. That would be another aspect, that is VERY relevant. And
at least in my mind that is an easier measurement than the delay
measurement.


No, delay is the easiest to measure. All you need is a ruler. Measure
how long the cable is. The wave in cable travels at 66% to 90% of the
velocity of light, depending on the dialectric material.


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... :-)

Hmmm... So what is the typical XL/R ratio for audio frequencies? :-)
If that is a prerequisite, IS the transmission line model really valid
for audio frequencies?


As a rule of thumb, the XL should be 10 times higher than R. For 12
gage cable, XL/R starts getting too low below 10 KHz.


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

Even in the case where the series resistance dominates, and the load
varies with frequency?


In that case, the transmission line numbers become such a small part
of the answer you can forget about them. At that point, you can use
Ohms law to calculate the cable loss.


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

...and this you do for one frequency at a time, right? I mean, if you
want to do this for another frequency, you go through this process
again?


That is right! As far as the computer is concerned, each frequency has
a different cable, one with it's own loss and phase shift
characteristics. Each frequency also has a different termination
impedance. The computer calculates a new cable and a new load at each
frequency. It's a lot of work to do it that way, but the the computer
never complains.


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

OK, but then I would argue that we are no longer talking about a
resistor, but a model of a real physical resistor, that contains other
elements as well. OK, I'm picky again.


I agree. An ideal resistor is a simpler circuit. Still the
transmission line is a fairly simpler entry into the matrix. No long
equations needed. Just convert the cable S-parameters into
Y-parameters, and pop them into the matix, at four places.

I'll have to think a bit about this to understand it. I have written
programs that reduced passive circuits down to 4-poles, but it was
some time ago.


The easiest way to program a computer to do circuit analysis, is to
write the circuit conductances into a large matrix. The conductance
(y-parameter) is entered at the row and column that correspond to the
circuit node the conductance is across. This is much easier than
trying to use different equations for every different circuit
topology. The matrix is reduced to one number, and that number is the
voltage at the output node.


Yes, I do that a lot, and it is indeed very flexible. Mostly I use it
for (electric analogies of) acoustic circuits. I just never thought of
a cable as a 4-pole, but I guess that is what transmission line theory
would be all about.

There were four types, G, Y, H and Z, was it? The H one
is often used to describe transistors, and the Y would be one of those
that you describe, right?


H, Y, Z, G, and S parameters can be converted from one to the other.
You can measure a two-port device using whatever parameters suit your
test equipment the best, then convert them to any other type of
parameters.

Y, Z and H parameters require open or short circuits on the port
during measurement. A lot of devices object of having their inputs or
outputs short circuited, so S-parameters have become very popular.(
S-parameters are measure with a load on the output.)


So, the S-parameters would be more of a practical eqivalent circuit,
while the other ones would be more theoretically "clean"?
  #290   Report Post  
Svante
 
Posts: n/a
Default More cable questions!

(Bob-Stanton) wrote in message (Svante) wrote in message

Well, another way would be to take an ohm-meter and measure it's
resistance. That would be another aspect, that is VERY relevant. And
at least in my mind that is an easier measurement than the delay
measurement.


No, delay is the easiest to measure. All you need is a ruler. Measure
how long the cable is. The wave in cable travels at 66% to 90% of the
velocity of light, depending on the dialectric material.


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... :-)

Hmmm... So what is the typical XL/R ratio for audio frequencies? :-)
If that is a prerequisite, IS the transmission line model really valid
for audio frequencies?


As a rule of thumb, the XL should be 10 times higher than R. For 12
gage cable, XL/R starts getting too low below 10 KHz.


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

Even in the case where the series resistance dominates, and the load
varies with frequency?


In that case, the transmission line numbers become such a small part
of the answer you can forget about them. At that point, you can use
Ohms law to calculate the cable loss.


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

...and this you do for one frequency at a time, right? I mean, if you
want to do this for another frequency, you go through this process
again?


That is right! As far as the computer is concerned, each frequency has
a different cable, one with it's own loss and phase shift
characteristics. Each frequency also has a different termination
impedance. The computer calculates a new cable and a new load at each
frequency. It's a lot of work to do it that way, but the the computer
never complains.


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

OK, but then I would argue that we are no longer talking about a
resistor, but a model of a real physical resistor, that contains other
elements as well. OK, I'm picky again.


I agree. An ideal resistor is a simpler circuit. Still the
transmission line is a fairly simpler entry into the matrix. No long
equations needed. Just convert the cable S-parameters into
Y-parameters, and pop them into the matix, at four places.

I'll have to think a bit about this to understand it. I have written
programs that reduced passive circuits down to 4-poles, but it was
some time ago.


The easiest way to program a computer to do circuit analysis, is to
write the circuit conductances into a large matrix. The conductance
(y-parameter) is entered at the row and column that correspond to the
circuit node the conductance is across. This is much easier than
trying to use different equations for every different circuit
topology. The matrix is reduced to one number, and that number is the
voltage at the output node.


Yes, I do that a lot, and it is indeed very flexible. Mostly I use it
for (electric analogies of) acoustic circuits. I just never thought of
a cable as a 4-pole, but I guess that is what transmission line theory
would be all about.

There were four types, G, Y, H and Z, was it? The H one
is often used to describe transistors, and the Y would be one of those
that you describe, right?


H, Y, Z, G, and S parameters can be converted from one to the other.
You can measure a two-port device using whatever parameters suit your
test equipment the best, then convert them to any other type of
parameters.

Y, Z and H parameters require open or short circuits on the port
during measurement. A lot of devices object of having their inputs or
outputs short circuited, so S-parameters have become very popular.(
S-parameters are measure with a load on the output.)


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


  #291   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!





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
  #292   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!





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
  #293   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!





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
  #294   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!





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
  #295   Report Post  
Svante
 
Posts: n/a
Default More cable questions!

(Bob-Stanton) wrote in message
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%.


Yes, I probably would have thought that was the case. Anyway, my
multimeter is still easier to find than my ruler (I wonder what that
says about me... :-) ).
Also, the multimeter will tell me directly how many ohms there is in
the cable. My ruler tells me how many centimeters there are, not how
many (nano-)seconds.
So to get the delay I need a ruler AND a calculator. But let's not
argue about this... :-)

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.


Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?
Another clarification, the S-parameters above are they given as
magnitude/phase pairs? I assume that the two numbers that appear for
each S-parameter in some sense describe real and imaginary parts, or
amplitude/phase if you wish, is that correct?


  #296   Report Post  
Svante
 
Posts: n/a
Default More cable questions!

(Bob-Stanton) wrote in message
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%.


Yes, I probably would have thought that was the case. Anyway, my
multimeter is still easier to find than my ruler (I wonder what that
says about me... :-) ).
Also, the multimeter will tell me directly how many ohms there is in
the cable. My ruler tells me how many centimeters there are, not how
many (nano-)seconds.
So to get the delay I need a ruler AND a calculator. But let's not
argue about this... :-)

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.


Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?
Another clarification, the S-parameters above are they given as
magnitude/phase pairs? I assume that the two numbers that appear for
each S-parameter in some sense describe real and imaginary parts, or
amplitude/phase if you wish, is that correct?
  #297   Report Post  
Svante
 
Posts: n/a
Default More cable questions!

(Bob-Stanton) wrote in message
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%.


Yes, I probably would have thought that was the case. Anyway, my
multimeter is still easier to find than my ruler (I wonder what that
says about me... :-) ).
Also, the multimeter will tell me directly how many ohms there is in
the cable. My ruler tells me how many centimeters there are, not how
many (nano-)seconds.
So to get the delay I need a ruler AND a calculator. But let's not
argue about this... :-)

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.


Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?
Another clarification, the S-parameters above are they given as
magnitude/phase pairs? I assume that the two numbers that appear for
each S-parameter in some sense describe real and imaginary parts, or
amplitude/phase if you wish, is that correct?
  #298   Report Post  
Svante
 
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(Bob-Stanton) wrote in message
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%.


Yes, I probably would have thought that was the case. Anyway, my
multimeter is still easier to find than my ruler (I wonder what that
says about me... :-) ).
Also, the multimeter will tell me directly how many ohms there is in
the cable. My ruler tells me how many centimeters there are, not how
many (nano-)seconds.
So to get the delay I need a ruler AND a calculator. But let's not
argue about this... :-)

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.


Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?
Another clarification, the S-parameters above are they given as
magnitude/phase pairs? I assume that the two numbers that appear for
each S-parameter in some sense describe real and imaginary parts, or
amplitude/phase if you wish, is that correct?
  #299   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!

(Svante) wrote in message


Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?
Another clarification, the S-parameters above are they given as
magnitude/phase pairs?


Yes.

I assume that the two numbers that appear for
each S-parameter in some sense describe real and imaginary parts, or
amplitude/phase if you wish, is that correct?


Yes.


A circuit analysis program wouldn't use a two-port data file for simulating
a cable. That was just to show that transmission line theory works even at
small wavelenghts.

A circuit analysis program will have a set of rules that define the cable's
performance, at all frequencies.

The user would call up the type of cable, and specify a length for that cable.
The program would then look up the rules for that cable and calculate the
S-parameters (at each frequency) based on the cable's length, and the set of
loss rules the programer gave.

The way the program comes up with the S-parameters (for each frequency) is simple:

S21 and S12 are the loss (and angle) for that length of cable. This loss
is calculated based on the measured performance of a real cable, (when terminated
by a resistor of the characteristic impedance.)

S11 and S22 are set to -120 dB , 0.0 deg. S11 and S22 should be infinity if
the cable is terminated in it's characteristic impedance. My old computer doesn't
have an "infinity key", so I just use -120 dB at 0 degs.





My previous message was getting too long. I but wanted to show proof that a
two port, S-parameter file can simulate speaker cable accurately at 20 Hz.


A 40 ft length of line was choosen because that is slightly less
than 1 / 1,000,000 of a wavelength, at 20 Hz. People continue to believe
that transmission line theory can not accuratly produce a model of less than
1/100 W.L. I thought it would be good to show that transmission line theory can
model a cable that is less than one-millionth of a W.L.


Below is a two-port S-parameter data file, that will simulate 40 ft of
12 gage, speaker cable, at 20 Hz:


! 12 gage "speaker cable

# HZ DB S R 100

! Hz S11 deg, S21 deg, S12 deg, S22 deg

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



Two-port file

--------------
| |
------------|o o|----------
| | | |
Gen | | 4 Ohms
| | | |
------------|o o|----------
| |
--------------

The file was based on a cable resistance of 0.002 Ohms / ft, and a
characteristic impedance of 100 Ohms.




Running the analysis gave the following results:

20 Hz. Loss: 0.9804 (-0.17 dB) Z(in): 4.08 + j 0.0005




Now let us now check the results by using simple dc calculations.
We can use dc calculations to find the cable loss, at 20 Hz, because the
speaker cable's XL is so small it can be almost neglected.

R = 0.002 Ohms * 40 ft = 0.08 Ohms


-----0.08 Ohms-----
| |
Gen 4 Ohms
| |
------------------


Z(in) = 4.00 + 0.08 = 4.08 Ohms

Loss = 4/(4 + 0.08) = 0.9804 (-0.17 dB)


So, transmission line theory agrees with dc calculations.

Bob Stanton
  #300   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!

(Svante) wrote in message


Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?
Another clarification, the S-parameters above are they given as
magnitude/phase pairs?


Yes.

I assume that the two numbers that appear for
each S-parameter in some sense describe real and imaginary parts, or
amplitude/phase if you wish, is that correct?


Yes.


A circuit analysis program wouldn't use a two-port data file for simulating
a cable. That was just to show that transmission line theory works even at
small wavelenghts.

A circuit analysis program will have a set of rules that define the cable's
performance, at all frequencies.

The user would call up the type of cable, and specify a length for that cable.
The program would then look up the rules for that cable and calculate the
S-parameters (at each frequency) based on the cable's length, and the set of
loss rules the programer gave.

The way the program comes up with the S-parameters (for each frequency) is simple:

S21 and S12 are the loss (and angle) for that length of cable. This loss
is calculated based on the measured performance of a real cable, (when terminated
by a resistor of the characteristic impedance.)

S11 and S22 are set to -120 dB , 0.0 deg. S11 and S22 should be infinity if
the cable is terminated in it's characteristic impedance. My old computer doesn't
have an "infinity key", so I just use -120 dB at 0 degs.





My previous message was getting too long. I but wanted to show proof that a
two port, S-parameter file can simulate speaker cable accurately at 20 Hz.


A 40 ft length of line was choosen because that is slightly less
than 1 / 1,000,000 of a wavelength, at 20 Hz. People continue to believe
that transmission line theory can not accuratly produce a model of less than
1/100 W.L. I thought it would be good to show that transmission line theory can
model a cable that is less than one-millionth of a W.L.


Below is a two-port S-parameter data file, that will simulate 40 ft of
12 gage, speaker cable, at 20 Hz:


! 12 gage "speaker cable

# HZ DB S R 100

! Hz S11 deg, S21 deg, S12 deg, S22 deg

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



Two-port file

--------------
| |
------------|o o|----------
| | | |
Gen | | 4 Ohms
| | | |
------------|o o|----------
| |
--------------

The file was based on a cable resistance of 0.002 Ohms / ft, and a
characteristic impedance of 100 Ohms.




Running the analysis gave the following results:

20 Hz. Loss: 0.9804 (-0.17 dB) Z(in): 4.08 + j 0.0005




Now let us now check the results by using simple dc calculations.
We can use dc calculations to find the cable loss, at 20 Hz, because the
speaker cable's XL is so small it can be almost neglected.

R = 0.002 Ohms * 40 ft = 0.08 Ohms


-----0.08 Ohms-----
| |
Gen 4 Ohms
| |
------------------


Z(in) = 4.00 + 0.08 = 4.08 Ohms

Loss = 4/(4 + 0.08) = 0.9804 (-0.17 dB)


So, transmission line theory agrees with dc calculations.

Bob Stanton


  #301   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!

(Svante) wrote in message


Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?
Another clarification, the S-parameters above are they given as
magnitude/phase pairs?


Yes.

I assume that the two numbers that appear for
each S-parameter in some sense describe real and imaginary parts, or
amplitude/phase if you wish, is that correct?


Yes.


A circuit analysis program wouldn't use a two-port data file for simulating
a cable. That was just to show that transmission line theory works even at
small wavelenghts.

A circuit analysis program will have a set of rules that define the cable's
performance, at all frequencies.

The user would call up the type of cable, and specify a length for that cable.
The program would then look up the rules for that cable and calculate the
S-parameters (at each frequency) based on the cable's length, and the set of
loss rules the programer gave.

The way the program comes up with the S-parameters (for each frequency) is simple:

S21 and S12 are the loss (and angle) for that length of cable. This loss
is calculated based on the measured performance of a real cable, (when terminated
by a resistor of the characteristic impedance.)

S11 and S22 are set to -120 dB , 0.0 deg. S11 and S22 should be infinity if
the cable is terminated in it's characteristic impedance. My old computer doesn't
have an "infinity key", so I just use -120 dB at 0 degs.





My previous message was getting too long. I but wanted to show proof that a
two port, S-parameter file can simulate speaker cable accurately at 20 Hz.


A 40 ft length of line was choosen because that is slightly less
than 1 / 1,000,000 of a wavelength, at 20 Hz. People continue to believe
that transmission line theory can not accuratly produce a model of less than
1/100 W.L. I thought it would be good to show that transmission line theory can
model a cable that is less than one-millionth of a W.L.


Below is a two-port S-parameter data file, that will simulate 40 ft of
12 gage, speaker cable, at 20 Hz:


! 12 gage "speaker cable

# HZ DB S R 100

! Hz S11 deg, S21 deg, S12 deg, S22 deg

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



Two-port file

--------------
| |
------------|o o|----------
| | | |
Gen | | 4 Ohms
| | | |
------------|o o|----------
| |
--------------

The file was based on a cable resistance of 0.002 Ohms / ft, and a
characteristic impedance of 100 Ohms.




Running the analysis gave the following results:

20 Hz. Loss: 0.9804 (-0.17 dB) Z(in): 4.08 + j 0.0005




Now let us now check the results by using simple dc calculations.
We can use dc calculations to find the cable loss, at 20 Hz, because the
speaker cable's XL is so small it can be almost neglected.

R = 0.002 Ohms * 40 ft = 0.08 Ohms


-----0.08 Ohms-----
| |
Gen 4 Ohms
| |
------------------


Z(in) = 4.00 + 0.08 = 4.08 Ohms

Loss = 4/(4 + 0.08) = 0.9804 (-0.17 dB)


So, transmission line theory agrees with dc calculations.

Bob Stanton
  #302   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!

(Svante) wrote in message


Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?
Another clarification, the S-parameters above are they given as
magnitude/phase pairs?


Yes.

I assume that the two numbers that appear for
each S-parameter in some sense describe real and imaginary parts, or
amplitude/phase if you wish, is that correct?


Yes.


A circuit analysis program wouldn't use a two-port data file for simulating
a cable. That was just to show that transmission line theory works even at
small wavelenghts.

A circuit analysis program will have a set of rules that define the cable's
performance, at all frequencies.

The user would call up the type of cable, and specify a length for that cable.
The program would then look up the rules for that cable and calculate the
S-parameters (at each frequency) based on the cable's length, and the set of
loss rules the programer gave.

The way the program comes up with the S-parameters (for each frequency) is simple:

S21 and S12 are the loss (and angle) for that length of cable. This loss
is calculated based on the measured performance of a real cable, (when terminated
by a resistor of the characteristic impedance.)

S11 and S22 are set to -120 dB , 0.0 deg. S11 and S22 should be infinity if
the cable is terminated in it's characteristic impedance. My old computer doesn't
have an "infinity key", so I just use -120 dB at 0 degs.





My previous message was getting too long. I but wanted to show proof that a
two port, S-parameter file can simulate speaker cable accurately at 20 Hz.


A 40 ft length of line was choosen because that is slightly less
than 1 / 1,000,000 of a wavelength, at 20 Hz. People continue to believe
that transmission line theory can not accuratly produce a model of less than
1/100 W.L. I thought it would be good to show that transmission line theory can
model a cable that is less than one-millionth of a W.L.


Below is a two-port S-parameter data file, that will simulate 40 ft of
12 gage, speaker cable, at 20 Hz:


! 12 gage "speaker cable

# HZ DB S R 100

! Hz S11 deg, S21 deg, S12 deg, S22 deg

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



Two-port file

--------------
| |
------------|o o|----------
| | | |
Gen | | 4 Ohms
| | | |
------------|o o|----------
| |
--------------

The file was based on a cable resistance of 0.002 Ohms / ft, and a
characteristic impedance of 100 Ohms.




Running the analysis gave the following results:

20 Hz. Loss: 0.9804 (-0.17 dB) Z(in): 4.08 + j 0.0005




Now let us now check the results by using simple dc calculations.
We can use dc calculations to find the cable loss, at 20 Hz, because the
speaker cable's XL is so small it can be almost neglected.

R = 0.002 Ohms * 40 ft = 0.08 Ohms


-----0.08 Ohms-----
| |
Gen 4 Ohms
| |
------------------


Z(in) = 4.00 + 0.08 = 4.08 Ohms

Loss = 4/(4 + 0.08) = 0.9804 (-0.17 dB)


So, transmission line theory agrees with dc calculations.

Bob Stanton
  #307   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!

(Svante) wrote in message




Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?


I'd still like an answer here... :-)





In a sense, you don't have to calculate the S-parameters. What you
have to calculate is the *loss of the cable*. For example, suppose
you had 2000 ft of 12 gage cable and wanted to know the S-parameters
at the frequency of 100 Hz.

What we would have is this:

Cable

-------4 Ohms--------
|
100 Ohms (The line must be terminated
| in it's characteristic
--------------------- impedance.)



Calculated Loss = 0.9615 (-0.34 dB)



Knowing that the loss is -0.34 dB we could write the S-parameters:


! Hz. S11 deg S21 deg S12 deg S22 deg

100 -120 0 -0.34 -0.0732 -0.34 -0.0732 -120 0



We don't need rules for writing S-parameters, what we need is rules
for finding cable loss.

Cable loss is caused by: the resistance of the center conductor, the
conductance of the dialectric, and any deviation from the
characteristic impedance. A general rule is: cable loss(in dB)
increases with the sqrt(F). If the frequency doubles, the cable
loss(in dB) increases by 1.41 times. This rule works well above 1 MHz.

Cable loss at audio frequenices? I wouldn't comment on that. Not
unless I first had a opportunity to verify my comments, by actual
measurements.



A circuit analysis program will have a set of rules that define the cable's performance, at all frequencies.


What would these rules look like? They wouldn't be a table?



Using a table of actual measurments, would be the most accurate basis
for calculating cable loss.

I once used an HP Network Analyzer to automatically do this. I
programed the analyzer to measure the S-parameters from 5 Mhz to 1
GHz, at 500 frequecnies. The analyzer would then write out a file to a
floppy disk, in the ".S2P" format. All I had to do was connect the HP
Analyzer to a cable, and in a couple of minutes I had a perfect, 500
point, two-port model of that cable.

Using this method, I made two-port models 10 different RF directional
couplers and a length of 0.5 in coax. (From 5 Mhz to 1 GHz). I
cascaded the 10 two-port couplers and 10 two-port cables in the
computer.

The computer results agreed *closely* with the actual measurements of
a real asacade of cables and couplers. I saw that two-port modeling
was pretty damn accurate!


Bob Stanton
  #308   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!

(Svante) wrote in message




Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?


I'd still like an answer here... :-)





In a sense, you don't have to calculate the S-parameters. What you
have to calculate is the *loss of the cable*. For example, suppose
you had 2000 ft of 12 gage cable and wanted to know the S-parameters
at the frequency of 100 Hz.

What we would have is this:

Cable

-------4 Ohms--------
|
100 Ohms (The line must be terminated
| in it's characteristic
--------------------- impedance.)



Calculated Loss = 0.9615 (-0.34 dB)



Knowing that the loss is -0.34 dB we could write the S-parameters:


! Hz. S11 deg S21 deg S12 deg S22 deg

100 -120 0 -0.34 -0.0732 -0.34 -0.0732 -120 0



We don't need rules for writing S-parameters, what we need is rules
for finding cable loss.

Cable loss is caused by: the resistance of the center conductor, the
conductance of the dialectric, and any deviation from the
characteristic impedance. A general rule is: cable loss(in dB)
increases with the sqrt(F). If the frequency doubles, the cable
loss(in dB) increases by 1.41 times. This rule works well above 1 MHz.

Cable loss at audio frequenices? I wouldn't comment on that. Not
unless I first had a opportunity to verify my comments, by actual
measurements.



A circuit analysis program will have a set of rules that define the cable's performance, at all frequencies.


What would these rules look like? They wouldn't be a table?



Using a table of actual measurments, would be the most accurate basis
for calculating cable loss.

I once used an HP Network Analyzer to automatically do this. I
programed the analyzer to measure the S-parameters from 5 Mhz to 1
GHz, at 500 frequecnies. The analyzer would then write out a file to a
floppy disk, in the ".S2P" format. All I had to do was connect the HP
Analyzer to a cable, and in a couple of minutes I had a perfect, 500
point, two-port model of that cable.

Using this method, I made two-port models 10 different RF directional
couplers and a length of 0.5 in coax. (From 5 Mhz to 1 GHz). I
cascaded the 10 two-port couplers and 10 two-port cables in the
computer.

The computer results agreed *closely* with the actual measurements of
a real asacade of cables and couplers. I saw that two-port modeling
was pretty damn accurate!


Bob Stanton
  #309   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!

(Svante) wrote in message




Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?


I'd still like an answer here... :-)





In a sense, you don't have to calculate the S-parameters. What you
have to calculate is the *loss of the cable*. For example, suppose
you had 2000 ft of 12 gage cable and wanted to know the S-parameters
at the frequency of 100 Hz.

What we would have is this:

Cable

-------4 Ohms--------
|
100 Ohms (The line must be terminated
| in it's characteristic
--------------------- impedance.)



Calculated Loss = 0.9615 (-0.34 dB)



Knowing that the loss is -0.34 dB we could write the S-parameters:


! Hz. S11 deg S21 deg S12 deg S22 deg

100 -120 0 -0.34 -0.0732 -0.34 -0.0732 -120 0



We don't need rules for writing S-parameters, what we need is rules
for finding cable loss.

Cable loss is caused by: the resistance of the center conductor, the
conductance of the dialectric, and any deviation from the
characteristic impedance. A general rule is: cable loss(in dB)
increases with the sqrt(F). If the frequency doubles, the cable
loss(in dB) increases by 1.41 times. This rule works well above 1 MHz.

Cable loss at audio frequenices? I wouldn't comment on that. Not
unless I first had a opportunity to verify my comments, by actual
measurements.



A circuit analysis program will have a set of rules that define the cable's performance, at all frequencies.


What would these rules look like? They wouldn't be a table?



Using a table of actual measurments, would be the most accurate basis
for calculating cable loss.

I once used an HP Network Analyzer to automatically do this. I
programed the analyzer to measure the S-parameters from 5 Mhz to 1
GHz, at 500 frequecnies. The analyzer would then write out a file to a
floppy disk, in the ".S2P" format. All I had to do was connect the HP
Analyzer to a cable, and in a couple of minutes I had a perfect, 500
point, two-port model of that cable.

Using this method, I made two-port models 10 different RF directional
couplers and a length of 0.5 in coax. (From 5 Mhz to 1 GHz). I
cascaded the 10 two-port couplers and 10 two-port cables in the
computer.

The computer results agreed *closely* with the actual measurements of
a real asacade of cables and couplers. I saw that two-port modeling
was pretty damn accurate!


Bob Stanton
  #310   Report Post  
Bob-Stanton
 
Posts: n/a
Default More cable questions!

(Svante) wrote in message




Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?


I'd still like an answer here... :-)





In a sense, you don't have to calculate the S-parameters. What you
have to calculate is the *loss of the cable*. For example, suppose
you had 2000 ft of 12 gage cable and wanted to know the S-parameters
at the frequency of 100 Hz.

What we would have is this:

Cable

-------4 Ohms--------
|
100 Ohms (The line must be terminated
| in it's characteristic
--------------------- impedance.)



Calculated Loss = 0.9615 (-0.34 dB)



Knowing that the loss is -0.34 dB we could write the S-parameters:


! Hz. S11 deg S21 deg S12 deg S22 deg

100 -120 0 -0.34 -0.0732 -0.34 -0.0732 -120 0



We don't need rules for writing S-parameters, what we need is rules
for finding cable loss.

Cable loss is caused by: the resistance of the center conductor, the
conductance of the dialectric, and any deviation from the
characteristic impedance. A general rule is: cable loss(in dB)
increases with the sqrt(F). If the frequency doubles, the cable
loss(in dB) increases by 1.41 times. This rule works well above 1 MHz.

Cable loss at audio frequenices? I wouldn't comment on that. Not
unless I first had a opportunity to verify my comments, by actual
measurements.



A circuit analysis program will have a set of rules that define the cable's performance, at all frequencies.


What would these rules look like? They wouldn't be a table?



Using a table of actual measurments, would be the most accurate basis
for calculating cable loss.

I once used an HP Network Analyzer to automatically do this. I
programed the analyzer to measure the S-parameters from 5 Mhz to 1
GHz, at 500 frequecnies. The analyzer would then write out a file to a
floppy disk, in the ".S2P" format. All I had to do was connect the HP
Analyzer to a cable, and in a couple of minutes I had a perfect, 500
point, two-port model of that cable.

Using this method, I made two-port models 10 different RF directional
couplers and a length of 0.5 in coax. (From 5 Mhz to 1 GHz). I
cascaded the 10 two-port couplers and 10 two-port cables in the
computer.

The computer results agreed *closely* with the actual measurements of
a real asacade of cables and couplers. I saw that two-port modeling
was pretty damn accurate!


Bob Stanton


  #311   Report Post  
Svante
 
Posts: n/a
Default More cable questions!

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




Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?


I'd still like an answer here... :-)





In a sense, you don't have to calculate the S-parameters. What you
have to calculate is the *loss of the cable*. For example, suppose
you had 2000 ft of 12 gage cable and wanted to know the S-parameters
at the frequency of 100 Hz.

What we would have is this:

Cable

-------4 Ohms--------
|
100 Ohms (The line must be terminated
| in it's characteristic
--------------------- impedance.)



Calculated Loss = 0.9615 (-0.34 dB)



Knowing that the loss is -0.34 dB we could write the S-parameters:


! Hz. S11 deg S21 deg S12 deg S22 deg

100 -120 0 -0.34 -0.0732 -0.34 -0.0732 -120 0



We don't need rules for writing S-parameters, what we need is rules
for finding cable loss.

Cable loss is caused by: the resistance of the center conductor, the
conductance of the dialectric, and any deviation from the
characteristic impedance. A general rule is: cable loss(in dB)
increases with the sqrt(F). If the frequency doubles, the cable
loss(in dB) increases by 1.41 times. This rule works well above 1 MHz.

Cable loss at audio frequenices? I wouldn't comment on that. Not
unless I first had a opportunity to verify my comments, by actual
measurements.



A circuit analysis program will have a set of rules that define the cable's performance, at all frequencies.


What would these rules look like? They wouldn't be a table?



Using a table of actual measurments, would be the most accurate basis
for calculating cable loss.

I once used an HP Network Analyzer to automatically do this. I
programed the analyzer to measure the S-parameters from 5 Mhz to 1
GHz, at 500 frequecnies. The analyzer would then write out a file to a
floppy disk, in the ".S2P" format. All I had to do was connect the HP
Analyzer to a cable, and in a couple of minutes I had a perfect, 500
point, two-port model of that cable.

Using this method, I made two-port models 10 different RF directional
couplers and a length of 0.5 in coax. (From 5 Mhz to 1 GHz). I
cascaded the 10 two-port couplers and 10 two-port cables in the
computer.

The computer results agreed *closely* with the actual measurements of
a real asacade of cables and couplers. I saw that two-port modeling
was pretty damn accurate!


OK, I think I got it now. And the "deg" of -0.0732 would correspond to
the delay of the cable (in this case you assumed propagation speed of
299 Mm/s which would be the about 100% of the speed of light in
vacuum, right?)
I'll just have to work out the S-to-Y conversion, but you already
wrote about that so I think I can figure it out.

Thanks a lot for your time.
  #312   Report Post  
Svante
 
Posts: n/a
Default More cable questions!

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




Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?


I'd still like an answer here... :-)





In a sense, you don't have to calculate the S-parameters. What you
have to calculate is the *loss of the cable*. For example, suppose
you had 2000 ft of 12 gage cable and wanted to know the S-parameters
at the frequency of 100 Hz.

What we would have is this:

Cable

-------4 Ohms--------
|
100 Ohms (The line must be terminated
| in it's characteristic
--------------------- impedance.)



Calculated Loss = 0.9615 (-0.34 dB)



Knowing that the loss is -0.34 dB we could write the S-parameters:


! Hz. S11 deg S21 deg S12 deg S22 deg

100 -120 0 -0.34 -0.0732 -0.34 -0.0732 -120 0



We don't need rules for writing S-parameters, what we need is rules
for finding cable loss.

Cable loss is caused by: the resistance of the center conductor, the
conductance of the dialectric, and any deviation from the
characteristic impedance. A general rule is: cable loss(in dB)
increases with the sqrt(F). If the frequency doubles, the cable
loss(in dB) increases by 1.41 times. This rule works well above 1 MHz.

Cable loss at audio frequenices? I wouldn't comment on that. Not
unless I first had a opportunity to verify my comments, by actual
measurements.



A circuit analysis program will have a set of rules that define the cable's performance, at all frequencies.


What would these rules look like? They wouldn't be a table?



Using a table of actual measurments, would be the most accurate basis
for calculating cable loss.

I once used an HP Network Analyzer to automatically do this. I
programed the analyzer to measure the S-parameters from 5 Mhz to 1
GHz, at 500 frequecnies. The analyzer would then write out a file to a
floppy disk, in the ".S2P" format. All I had to do was connect the HP
Analyzer to a cable, and in a couple of minutes I had a perfect, 500
point, two-port model of that cable.

Using this method, I made two-port models 10 different RF directional
couplers and a length of 0.5 in coax. (From 5 Mhz to 1 GHz). I
cascaded the 10 two-port couplers and 10 two-port cables in the
computer.

The computer results agreed *closely* with the actual measurements of
a real asacade of cables and couplers. I saw that two-port modeling
was pretty damn accurate!


OK, I think I got it now. And the "deg" of -0.0732 would correspond to
the delay of the cable (in this case you assumed propagation speed of
299 Mm/s which would be the about 100% of the speed of light in
vacuum, right?)
I'll just have to work out the S-to-Y conversion, but you already
wrote about that so I think I can figure it out.

Thanks a lot for your time.
  #313   Report Post  
Svante
 
Posts: n/a
Default More cable questions!

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




Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?


I'd still like an answer here... :-)





In a sense, you don't have to calculate the S-parameters. What you
have to calculate is the *loss of the cable*. For example, suppose
you had 2000 ft of 12 gage cable and wanted to know the S-parameters
at the frequency of 100 Hz.

What we would have is this:

Cable

-------4 Ohms--------
|
100 Ohms (The line must be terminated
| in it's characteristic
--------------------- impedance.)



Calculated Loss = 0.9615 (-0.34 dB)



Knowing that the loss is -0.34 dB we could write the S-parameters:


! Hz. S11 deg S21 deg S12 deg S22 deg

100 -120 0 -0.34 -0.0732 -0.34 -0.0732 -120 0



We don't need rules for writing S-parameters, what we need is rules
for finding cable loss.

Cable loss is caused by: the resistance of the center conductor, the
conductance of the dialectric, and any deviation from the
characteristic impedance. A general rule is: cable loss(in dB)
increases with the sqrt(F). If the frequency doubles, the cable
loss(in dB) increases by 1.41 times. This rule works well above 1 MHz.

Cable loss at audio frequenices? I wouldn't comment on that. Not
unless I first had a opportunity to verify my comments, by actual
measurements.



A circuit analysis program will have a set of rules that define the cable's performance, at all frequencies.


What would these rules look like? They wouldn't be a table?



Using a table of actual measurments, would be the most accurate basis
for calculating cable loss.

I once used an HP Network Analyzer to automatically do this. I
programed the analyzer to measure the S-parameters from 5 Mhz to 1
GHz, at 500 frequecnies. The analyzer would then write out a file to a
floppy disk, in the ".S2P" format. All I had to do was connect the HP
Analyzer to a cable, and in a couple of minutes I had a perfect, 500
point, two-port model of that cable.

Using this method, I made two-port models 10 different RF directional
couplers and a length of 0.5 in coax. (From 5 Mhz to 1 GHz). I
cascaded the 10 two-port couplers and 10 two-port cables in the
computer.

The computer results agreed *closely* with the actual measurements of
a real asacade of cables and couplers. I saw that two-port modeling
was pretty damn accurate!


OK, I think I got it now. And the "deg" of -0.0732 would correspond to
the delay of the cable (in this case you assumed propagation speed of
299 Mm/s which would be the about 100% of the speed of light in
vacuum, right?)
I'll just have to work out the S-to-Y conversion, but you already
wrote about that so I think I can figure it out.

Thanks a lot for your time.
  #314   Report Post  
Svante
 
Posts: n/a
Default More cable questions!

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




Now we're talking, these were the nuts and bolts I wanted to see. I
don't know if I think that this is easier than the RLC implementation,
but I guess that would depend on the computer implementation that is
available. One thing in the above explanation that seems akward is
that it seems like you have to have a TABLE of the s-parameters for
each and every frequency? In the RLC model it is easy to calculate the
impedances for ANY frequency. Is there any method to CALCULATE the
S-parameters, rather than having a large table?


I'd still like an answer here... :-)





In a sense, you don't have to calculate the S-parameters. What you
have to calculate is the *loss of the cable*. For example, suppose
you had 2000 ft of 12 gage cable and wanted to know the S-parameters
at the frequency of 100 Hz.

What we would have is this:

Cable

-------4 Ohms--------
|
100 Ohms (The line must be terminated
| in it's characteristic
--------------------- impedance.)



Calculated Loss = 0.9615 (-0.34 dB)



Knowing that the loss is -0.34 dB we could write the S-parameters:


! Hz. S11 deg S21 deg S12 deg S22 deg

100 -120 0 -0.34 -0.0732 -0.34 -0.0732 -120 0



We don't need rules for writing S-parameters, what we need is rules
for finding cable loss.

Cable loss is caused by: the resistance of the center conductor, the
conductance of the dialectric, and any deviation from the
characteristic impedance. A general rule is: cable loss(in dB)
increases with the sqrt(F). If the frequency doubles, the cable
loss(in dB) increases by 1.41 times. This rule works well above 1 MHz.

Cable loss at audio frequenices? I wouldn't comment on that. Not
unless I first had a opportunity to verify my comments, by actual
measurements.



A circuit analysis program will have a set of rules that define the cable's performance, at all frequencies.


What would these rules look like? They wouldn't be a table?



Using a table of actual measurments, would be the most accurate basis
for calculating cable loss.

I once used an HP Network Analyzer to automatically do this. I
programed the analyzer to measure the S-parameters from 5 Mhz to 1
GHz, at 500 frequecnies. The analyzer would then write out a file to a
floppy disk, in the ".S2P" format. All I had to do was connect the HP
Analyzer to a cable, and in a couple of minutes I had a perfect, 500
point, two-port model of that cable.

Using this method, I made two-port models 10 different RF directional
couplers and a length of 0.5 in coax. (From 5 Mhz to 1 GHz). I
cascaded the 10 two-port couplers and 10 two-port cables in the
computer.

The computer results agreed *closely* with the actual measurements of
a real asacade of cables and couplers. I saw that two-port modeling
was pretty damn accurate!


OK, I think I got it now. And the "deg" of -0.0732 would correspond to
the delay of the cable (in this case you assumed propagation speed of
299 Mm/s which would be the about 100% of the speed of light in
vacuum, right?)
I'll just have to work out the S-to-Y conversion, but you already
wrote about that so I think I can figure it out.

Thanks a lot for your time.
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