I have copied your post and am interjecting comments in "" "" marks, it gets less confusing that way. I wish I could color my inserts red, but such is life..
First however, one clarification on a comment you made earlier, that a vacuum dielectric would have no capacitance. Totally wrong. Capacitance is proportional to epsilon free space times epsilon relative. For a vacuum, epsilon relative is 1, and epsilon free space is 8.854 times 10e-12 farads/meter. I DO NOT UNDERSTAND HOW AN ENGINEER COULD MAKE THIS MISTAKE.
How are you calculating impedance at audio to such low levels?
""As I've stated prior, hf impedance is 1/sqr(L/C) At lower frequencies inductive reactance is very small, and the conductor resistivity starts raising the impedance. The full form is of the style "(R +L)/(C+G)". Unfortunately there is no equation editor on this site..sorry.""
The impedance rises rapidly at audio frequencies and is tremendously non linear. A cable can very easily be 600-ohms at 100 Hz, and drop to 50-ohms at 20 Khz with the open short method.
""I've stated that as well If you wish a general feel, the Belden website illustrates this for a general 75 ohm cable. For audio use, I recommend a value 2 to 6 times the hf value""
In don't see any liberties being taken to reduce an engineer's work load when it isn't even working as a transmission line. Oh it's "transmitting" all right, but not voltage.
""Do yourself a favor. Get an HP 8721A reflection bridge and look at the reflections which occur in the audio bandwidth. You will learn something new.""
As short as these cables are, open - short method is used to derive "impedance" even though there is no real impedance as the cable are far too short to manage such LONG audio wavelength. To be a factor, the cable length has to be at least 10X or more the quarter wave length of the frequency of interest. This relates to the fact that a voltage change has to happen BEFORE it gets to the end of the cable and audio speaker cables transit times are too fast for this to happen.
"" you are repeating generalizations and approximations which were simplified for engineering use. This discussion is beyond that. You need to ask more questions and make fewer incorrect generalizations.""
I'll jump to one other erroneous statement of yours for brevity. You've provided quite a bit of erroneous statements, but I believe everybody's time is better served by you asking questions on this topic. I am happy to teach you if you wish.""
The skin effect calculation is "wrong"? Well, All I see is you have a different opinion right now. Multiple credible sites use the most common methods and all arrive at about 18-mils at 20 KHz. Where is your documentation on your method? I agree that "approximations" can boil stuff down too far. Saying so is one thing, showing us is another. We're all tired of sayings.
Documentation?? On Bessels?? Really?
Do yourself a favor, google Bessel functions, google skin effect approximation, look it up in a good E/M textbook, something. I gave you an exact engineering statement on how time varying rate of change Lenz effect current exclusion occurs within a cylindrical conductor, and you come back with that???
You need better sites. Just because it's on the internet doesn't mean it is correct.
Please pay attention: The exponential equation is the solution for an E/M PLANAR WAVE driving into a conductive surface NORMAL to the boundary. It is NOT THE EQUATION FOR CURRENT REDISTRIBUTION IN A CYLINDRICAL CONDUCTOR WHERE THE CURRENT IS AXIAL. Skin effect in a cylindrical conductor is a consequence of Faraday's law of induction within the conductive material due to the internal magnetic field caused by the axial current. The exponential equation is an APPROXIMATION EQUATION used so that engineers do not have to get mired into the bessels. ""
I still see the yearning to be like the RF guys. Why?
""If this question is intended for me, you are barking up the wrong tree. What I speak of here is a very small subset of what I do for a living.""
I have thick skin so getting some good heads to knock me around is actually fun. Learning is NOT a spectator sport.
""It is good you have a thick skin, you are going to need it. You are not in Kansas anymore, Toto.. (no offense intended, I just HAD to use that statement..)""
I have been told you are an engineer. What I have seen posted by you is a mixed bag of engineering facts, incorrect statements, typical internet factoids. Are you an engineer, and if so, what kind?
Me, I am an electrical engineer. I design, build, and test superconducting magnets for particle accelerators, medical synchrotrons, antimatter confinement bottles, and MRI's....in addition to my other responsibilities which are more esoteric.
I appreciate and share your desire to maintain some semblence of scientific reasoning in all this. I just have a rather more advanced understanding of the problem, and find it is always necessary to teach others what they need to know. Your need to learn this is by no means unique in this regard. As I stated initially, "we" are going in 300 or more directions because so many people, you included, continue to promote somewhat erroneous engineering and physics concepts. Promotion of erroneous beliefs is part of the problem, not part of the solution.
jn
First however, one clarification on a comment you made earlier, that a vacuum dielectric would have no capacitance. Totally wrong. Capacitance is proportional to epsilon free space times epsilon relative. For a vacuum, epsilon relative is 1, and epsilon free space is 8.854 times 10e-12 farads/meter. I DO NOT UNDERSTAND HOW AN ENGINEER COULD MAKE THIS MISTAKE.
How are you calculating impedance at audio to such low levels?
""As I've stated prior, hf impedance is 1/sqr(L/C) At lower frequencies inductive reactance is very small, and the conductor resistivity starts raising the impedance. The full form is of the style "(R +L)/(C+G)". Unfortunately there is no equation editor on this site..sorry.""
The impedance rises rapidly at audio frequencies and is tremendously non linear. A cable can very easily be 600-ohms at 100 Hz, and drop to 50-ohms at 20 Khz with the open short method.
""I've stated that as well If you wish a general feel, the Belden website illustrates this for a general 75 ohm cable. For audio use, I recommend a value 2 to 6 times the hf value""
In don't see any liberties being taken to reduce an engineer's work load when it isn't even working as a transmission line. Oh it's "transmitting" all right, but not voltage.
""Do yourself a favor. Get an HP 8721A reflection bridge and look at the reflections which occur in the audio bandwidth. You will learn something new.""
As short as these cables are, open - short method is used to derive "impedance" even though there is no real impedance as the cable are far too short to manage such LONG audio wavelength. To be a factor, the cable length has to be at least 10X or more the quarter wave length of the frequency of interest. This relates to the fact that a voltage change has to happen BEFORE it gets to the end of the cable and audio speaker cables transit times are too fast for this to happen.
"" you are repeating generalizations and approximations which were simplified for engineering use. This discussion is beyond that. You need to ask more questions and make fewer incorrect generalizations.""
I'll jump to one other erroneous statement of yours for brevity. You've provided quite a bit of erroneous statements, but I believe everybody's time is better served by you asking questions on this topic. I am happy to teach you if you wish.""
The skin effect calculation is "wrong"? Well, All I see is you have a different opinion right now. Multiple credible sites use the most common methods and all arrive at about 18-mils at 20 KHz. Where is your documentation on your method? I agree that "approximations" can boil stuff down too far. Saying so is one thing, showing us is another. We're all tired of sayings.
Documentation?? On Bessels?? Really?
Do yourself a favor, google Bessel functions, google skin effect approximation, look it up in a good E/M textbook, something. I gave you an exact engineering statement on how time varying rate of change Lenz effect current exclusion occurs within a cylindrical conductor, and you come back with that???
You need better sites. Just because it's on the internet doesn't mean it is correct.
Please pay attention: The exponential equation is the solution for an E/M PLANAR WAVE driving into a conductive surface NORMAL to the boundary. It is NOT THE EQUATION FOR CURRENT REDISTRIBUTION IN A CYLINDRICAL CONDUCTOR WHERE THE CURRENT IS AXIAL. Skin effect in a cylindrical conductor is a consequence of Faraday's law of induction within the conductive material due to the internal magnetic field caused by the axial current. The exponential equation is an APPROXIMATION EQUATION used so that engineers do not have to get mired into the bessels. ""
I still see the yearning to be like the RF guys. Why?
""If this question is intended for me, you are barking up the wrong tree. What I speak of here is a very small subset of what I do for a living.""
I have thick skin so getting some good heads to knock me around is actually fun. Learning is NOT a spectator sport.
""It is good you have a thick skin, you are going to need it. You are not in Kansas anymore, Toto.. (no offense intended, I just HAD to use that statement..)""
I have been told you are an engineer. What I have seen posted by you is a mixed bag of engineering facts, incorrect statements, typical internet factoids. Are you an engineer, and if so, what kind?
Me, I am an electrical engineer. I design, build, and test superconducting magnets for particle accelerators, medical synchrotrons, antimatter confinement bottles, and MRI's....in addition to my other responsibilities which are more esoteric.
I appreciate and share your desire to maintain some semblence of scientific reasoning in all this. I just have a rather more advanced understanding of the problem, and find it is always necessary to teach others what they need to know. Your need to learn this is by no means unique in this regard. As I stated initially, "we" are going in 300 or more directions because so many people, you included, continue to promote somewhat erroneous engineering and physics concepts. Promotion of erroneous beliefs is part of the problem, not part of the solution.
jn