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#281
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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
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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
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#284
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#286
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#288
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(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
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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
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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
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#292
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#293
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#294
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#296
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#297
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#298
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#299
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#301
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#302
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#303
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Great post! ...but of course I'd still have a few more questions, see below:
(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... :-) 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? snip So, transmission line theory agrees with dc calculations. Yes, that seems watertight. |
#304
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More cable questions!
Great post! ...but of course I'd still have a few more questions, see below:
(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... :-) 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? snip So, transmission line theory agrees with dc calculations. Yes, that seems watertight. |
#305
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More cable questions!
Great post! ...but of course I'd still have a few more questions, see below:
(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... :-) 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? snip So, transmission line theory agrees with dc calculations. Yes, that seems watertight. |
#306
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More cable questions!
Great post! ...but of course I'd still have a few more questions, see below:
(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... :-) 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? snip So, transmission line theory agrees with dc calculations. Yes, that seems watertight. |
#307
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#308
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#309
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#311
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(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
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(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
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(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
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(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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