Of course 🙂 I think the audio modelisation of a 2 conductor cable becomes more coherent when you try to figure it out in terms of propagated fields (vectors) instead of potentials and currents.
I always try to figure an electromagnetic wave, guided by the rails, propagating through the space between conductors (mostly primary dielectric & air);
we could split this wave in 2 composantes, the electrical field and the magnetic field, that should be equal in energy and at 90° angle each other (if conductivity of materials was infinite).
In a coax. type cable the electric field is radial to the conductors, and the magnetic field turns around the inner conductor.
In other cable geometry, those fields exist too, and the different cables geometries simply give different fields patterns.
Copper (or silver) is a highly conductive element, but none of the less has a defined and known finite conductivity 5.8.10e7 (6.14.10e7).
The consequence of this are losses at the interface with a different angle (no more 90°) (heat, but also a part of the electromagnetic wave) and electromagnetic energy spills out of the dielectric and comes back into the conductors, somewhat later & slower.
This is also why an audio wave experiments an attenuation in the energy field whilst carried across a conductor which diameter is greater than the skin depth.
Electrons tend to take the easiest path, e.g. trying to stay in periphery of the conductor, but given the frequency fed into the conductor and regards to the skin depth, some do sink and experience a slow down.
Current density is greater at the surface, and as the field enters the conductor the density of the flux becomes smaller, and the frequency gets a slower propagation.
Like a river, where water has a greater speed on the surface than at the bottom.
F(Hz) ---------- skin depth (mm) ------------ velocity (m/s)
50 ----------------- 9,35 ----------------------- 2,93
100 ---------------- 6,61 ----------------------- 4,15
1000 --------------- 2,09 ---------------------- 13,12
10000 -------------- 0,66 ---------------------- 41,50
20000 -------------- 0,47 ---------------------- 58,69
Hence the recommendation of using smallest AWG cable possible or even ribbons @ 0,05 or 0,07 mm thickness, that give a practical solution to get rid of the majority of time smears at audio frequencies.
And this also gives the cable some almost linear (resistive) loss, instead of complex loads Z that also produce phase shifts in the highs ... In that way the cable acts as a crossover, and phenomena is audible starting at 6 KHZ ... top of piano ...
I would say ... One Ribbon To Rule Them All !!!!
Some 30 mm large by 0,07 mm thick copper ribbons give a comfortable section (2,1 mm2) for speaker interconnects.
One can also try some nice www (30 AWG) wire as speaker cable 😱
Given you don't use Apogees and big Krells, that can be a fantastic sonic upgrade in your system, at only a few bucks ... 😎
Best,
nAr
When you say "velocity (m/s)," which velocity are you talking about? Can you define "time smear" and give some experimental data demonstrating the effect at audio frequencies for normal, non-fancy wire?
That must make circuit design slow and cumbersome! Using the full wave model (do you use an EM simulator?) when the quasi-static (i.e. circuit) model is more appropriate is daft.nar said:
Use waves to calculate conductor resistance and internal inductance, then insert these values in the circuit model.
Balanced cables can and used with a shield, the signal is still balanced, or a differential signal. The definition of a differential pair is having equal impedance with respect to the ground. Some links posted earlier go into depth on the action of drain wires on twisted pair and the impedance mismatch it causes. Cat 6 is shielded ethernet cable, 4 diff pairs running at very high speed. The diff signals being more closely coupled share both the forward and return currents.
As to velocity of signals I have always been taught it is the dialectric that effects the velocity of a signal, of the top of my head velocity factor being Vf=1/Squ rt Er and always related to air or vacuum having a factor of 1 (this facter when multiplied by the speed of light in air gives the speed of the signal. Electons only travel at approx 84mm per hour in wire, so are only part of the equation.
Co-ax cables are one of the fastest wire configurations for wave propagation, and one of the true TEM guides. On PCB's only stripline (trace burried between two gnd or pwr planes) routing is again truely TEM propagation.
Again I dont see how skin effect can have that much influence at audio frequencies, you dont realy worry about it for high speed digital.
As to velocity of signals I have always been taught it is the dialectric that effects the velocity of a signal, of the top of my head velocity factor being Vf=1/Squ rt Er and always related to air or vacuum having a factor of 1 (this facter when multiplied by the speed of light in air gives the speed of the signal. Electons only travel at approx 84mm per hour in wire, so are only part of the equation.
Co-ax cables are one of the fastest wire configurations for wave propagation, and one of the true TEM guides. On PCB's only stripline (trace burried between two gnd or pwr planes) routing is again truely TEM propagation.
Again I dont see how skin effect can have that much influence at audio frequencies, you dont realy worry about it for high speed digital.
DF96
For high speed digital layout full 3D EM field solvers and IBIS models are used extensivly, but the designs it is used on can take months to complete. Bit of overkill for Audio probably.🙂
For high speed digital layout full 3D EM field solvers and IBIS models are used extensivly, but the designs it is used on can take months to complete. Bit of overkill for Audio probably.🙂
I think he was talking about the propagation speed of waves in the conductor, as they get attenuated by the skin effect. If this created a dispersion problem for audio then high speed logic would not work either.
It's interesting to see the effect of Maxwell's equations: some people seem to understand them just well enough to confuse themselves. More or less understanding would remove the confusion, either through blissful ignorance or adequate knowledge.
It's interesting to see the effect of Maxwell's equations: some people seem to understand them just well enough to confuse themselves. More or less understanding would remove the confusion, either through blissful ignorance or adequate knowledge.
Correct 🙂 But not only attenuated 🙂 Conductor is not the only medium taking into count. Dielectric is also a (bad) conductor, and definitely has a finite ( very bad) conductivity ! 🙂
IMHO high speed logics have nothing to do with a large spectra, awfully complex mix of transcients/sines in a huge amplitude variation as found in musical signals. But I may be wrong 😀
Maxwell equations, yup 🙂 But ears are not confused; audible sonic gains are the only subjective proof I can acknowledge, the awaited "lift the curtain !!!", in the lack of proper recognized cable science/modeling linked to subjective sonics (I'm not talking about cable makers's commercial claims 🙂
But as always your mileage may vary.
Humbly,
nAr
seems like a mental mashup of electromagnetic velocities and the drift velocities of an electron on the lattice of a metal conductor?
if the point made would hold true then high speed signalling wouldnt work using that logic.
if the point made would hold true then high speed signalling wouldnt work using that logic.
High speed logic has true transients, not rounded off ones like music. Timing is more important too. Distortion is less important, but we are talking about wires so irrelevant.nar said:
What is the velocity referenced to in the figures from the Essex Echo documentation, I have read through it and do not realy understand what this velocity is, is it the speed of the wave fronts,
the electrons...I also find that text rather hard to follow unlike othe papers and information (more up to date) on signal proagation, maybe I'm just dumb.
Dielectric, an interesting and easily understandable description.
PCBDESIGN007 "Dielectric Constant 101" for the Non-Microwave Engineer
PCBDESIGN007 "Dielectric Loss 101" for the Non-Microwave Engineer, Part II
Square waves have numerous sine wave sub harmonics, the highest frequecy of these is determined by the rise time, the majority of the spectural content being determined by the knee frequency.
For the masochistic...
The Essex Echo 1995: Electrical Signal Propagation & Cable Theory | Stereophile.com
the electrons...I also find that text rather hard to follow unlike othe papers and information (more up to date) on signal proagation, maybe I'm just dumb.
Dielectric, an interesting and easily understandable description.
PCBDESIGN007 "Dielectric Constant 101" for the Non-Microwave Engineer
PCBDESIGN007 "Dielectric Loss 101" for the Non-Microwave Engineer, Part II
Square waves have numerous sine wave sub harmonics, the highest frequecy of these is determined by the rise time, the majority of the spectural content being determined by the knee frequency.
For the masochistic...
The Essex Echo 1995: Electrical Signal Propagation & Cable Theory | Stereophile.com
http://www.theaudiocritic.com/back_issues/The_Audio_Critic_24_r.pdf
Skip the overheated mouthfoaming and go directly to the second column on p76. The professor gives a very calm and clear explanation.
hahaha; did you really just explain that to me? perhaps you have trouble recognising rhetorical questions? hard to say why you felt the need.... i'm genuinely confused, but not about balanced interconnection.
i've been almost (some might argue the almost part) belligerent about NOT using the shield in RCA, or pin 1 and mostly NOT shield in XLR, but rather UTP.
i wouldnt have thought this left much to the imagination.
using wave theory to describe audio signal cables is good for flexing muscles in audiophile consumer threads, but not terribly useful for the purposes of general conversation
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I suspect that the 1995 Hawksford stuff on cables is just a long-winded way of talking about internal impedance. This can be modelled as an extra resistance and inductance, which in many cases is negligible compared with the external impedance. It is the inductance which gives rise to the energy storage he mentions. His 'smearing', as is usually the case, is just the effect of putting the signal through a filter. It looks like distortion (in the time domain) but no new frequency components are generated.
Hawksford may be ascribing too much to the Poynting vector. The Poynting conjecture says that if you do a surface integral of the Poynting vector over a closed surface, then the result is the total energy flow through that surface. It does not say that the Poynting vector is the energy flow, yet many people misunderstand this.
I suspect that John Atkinson has never read "Fields and Waves in Communication Electronics" by Ramo, Whinnery and van Duzer, where all this sort of stuff is worked out in gory detail.
Hawksford may be ascribing too much to the Poynting vector. The Poynting conjecture says that if you do a surface integral of the Poynting vector over a closed surface, then the result is the total energy flow through that surface. It does not say that the Poynting vector is the energy flow, yet many people misunderstand this.
I suspect that John Atkinson has never read "Fields and Waves in Communication Electronics" by Ramo, Whinnery and van Duzer, where all this sort of stuff is worked out in gory detail.
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genuine question coz i know you are right into the (individually sheathed stranded) litz wire Steve, doesnt it present a higher capacitance than standard stranded or solid core wire? or is the answer yes but not a meaningful amount higher for the purposes of audio where the knee presented by such a small amount occurs at a frequency far above the audio band? thus as a trade off it solves more problems than it presents
Far as I'm aware, if you've got a cable made with solid, stranded and litz of the same diameter and overall geometry, you'll end up with pretty much the same capacitance.
What gets me are the "strand wars" in the headphone cable market, where they've gone from four, to eight, to sixteen. Increasing the number of strands will increase capacitance and as a consequence, crosstalk.
se
What gets me are the "strand wars" in the headphone cable market, where they've gone from four, to eight, to sixteen. Increasing the number of strands will increase capacitance and as a consequence, crosstalk.
se
Jim Brown reports that the Velocity of Propagation for a typical co-ax cable is:
At 20 Hz about 5 000 000 Meters per Second
At 20 kHz about 100 000 000 Meters per Second
(my reading from a chart)
For more see:
http://www.audiosystemsgroup.com/TransLines-LowFreq.pdf
At 20 Hz about 5 000 000 Meters per Second
At 20 kHz about 100 000 000 Meters per Second
(my reading from a chart)
For more see:
http://www.audiosystemsgroup.com/TransLines-LowFreq.pdf
Sy,
thanks for that, an interesting and not suprising read🙂
Speedskater
Read and re-read the article, I cant see how he is calculating the velocity factor and thus Vp. As again I always though the velocity factor was related to the dielectric (be it expressed as either 1/sqr rt Er or 1/c *(squ rt LC)) I am curious as to how it can vary so greatly as shown in the graph. As L and C are a constant of the cable construction and the dielectric, i dont know how the figures in the graph are calculated.
I have a few more articles on short transmission lines (electricaly short) to plow through, but I would appreciate it if someone can point to the calcualtions used to come up with the figures shown.
thanks for that, an interesting and not suprising read🙂
Speedskater
Read and re-read the article, I cant see how he is calculating the velocity factor and thus Vp. As again I always though the velocity factor was related to the dielectric (be it expressed as either 1/sqr rt Er or 1/c *(squ rt LC)) I am curious as to how it can vary so greatly as shown in the graph. As L and C are a constant of the cable construction and the dielectric, i dont know how the figures in the graph are calculated.
I have a few more articles on short transmission lines (electricaly short) to plow through, but I would appreciate it if someone can point to the calcualtions used to come up with the figures shown.
Is he using the slight change in inductance with frequency due to the effects of skin effects and Vf=1/c*(SQRT LC)?
Quite fun and interesting this but some of the reading matter gets a bit heavy. Though I wonder how much actual effect on the audio signal this will have.
Quite fun and interesting this but some of the reading matter gets a bit heavy. Though I wonder how much actual effect on the audio signal this will have.
Quick tutorial on non-ideal transmissions lines (i.e. almost all audio cables).
w= 2 pi f, j=sqrt(-1), R=resistance of conductor, G=conductance of dielectric
Characteristic impedance Z = sqrt((R+jwL)/(G+jwC))
At sufficiently high frequencies that wL dominates over R, and wC dominates over G, this simplifies to Z = sqrt(L/C) which is the formula you will often see quoted but without the necessary conditions attached. At audio frequencies we can assume that wC will dominate over G, but R and wL may be of similar size so you have to use the full formula. At sufficiently low frequencies you can use Z = sqrt(R/jwC) - so you can see that Z is complex, no longer a pure resistance.
Propagation speed is done in a similar way. The propagation constant 'g' is given by g = sqrt((R+jwL)(G+jwC)). Then the real part of g gives the attenuation, and the imaginary part of g gives the propagation speed. For an ideal line (no R or G) this just becomes g=jw sqrt(LC), and you will recognise sqrt(LC) as the speed.
However, for a general line it gets more complicated because the line is dispersive: speed depends on frequency so you have to start thinking about the difference between group and phase velocity. I guess you can get a rough idea of the speed from v=Im(sqrt((R+jwL)(G+jwC)))/w. If the line is not too lossy (i.e. mid frequency audio) then an approximation is v=sqrt(LC)[1-((RG/4LC)+(G^2/8C^2)+(R^2/8L^2))/(w^2)].
Information obtained from standard textbook by Ramo, Whinnery and van Duzer.
w= 2 pi f, j=sqrt(-1), R=resistance of conductor, G=conductance of dielectric
Characteristic impedance Z = sqrt((R+jwL)/(G+jwC))
At sufficiently high frequencies that wL dominates over R, and wC dominates over G, this simplifies to Z = sqrt(L/C) which is the formula you will often see quoted but without the necessary conditions attached. At audio frequencies we can assume that wC will dominate over G, but R and wL may be of similar size so you have to use the full formula. At sufficiently low frequencies you can use Z = sqrt(R/jwC) - so you can see that Z is complex, no longer a pure resistance.
Propagation speed is done in a similar way. The propagation constant 'g' is given by g = sqrt((R+jwL)(G+jwC)). Then the real part of g gives the attenuation, and the imaginary part of g gives the propagation speed. For an ideal line (no R or G) this just becomes g=jw sqrt(LC), and you will recognise sqrt(LC) as the speed.
However, for a general line it gets more complicated because the line is dispersive: speed depends on frequency so you have to start thinking about the difference between group and phase velocity. I guess you can get a rough idea of the speed from v=Im(sqrt((R+jwL)(G+jwC)))/w. If the line is not too lossy (i.e. mid frequency audio) then an approximation is v=sqrt(LC)[1-((RG/4LC)+(G^2/8C^2)+(R^2/8L^2))/(w^2)].
Information obtained from standard textbook by Ramo, Whinnery and van Duzer.