# signal propagation through audio cable.



## 3dbinCanada (Sep 13, 2012)

I've opened this thread to discuss signal propagation through audio cables and the electrical behaviors of the various components that comprise an audio cable. Please feel free to add links into this thread that explains the theorey of propagation. My only rule is don't post any articles published my audio cable manufacturers as they have an agenda to sell their product and thus skew the science and make statements that are not accurate in terms of engineering principles. Have fun and lets learn together.


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## lcaillo (May 2, 2006)

This should be useful. Just remember that you don't get to set the rules about what people post. If someone posts something that you think is off topic, please report it. If it contains nothing factual or generally accepted by the engineering community, it is off topic and will be removed. If there are views that are not consistent with what you believe about the topic you should refute them in a respectful manner or call them out as speculation or opinion without directing any critique at the poster.


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## 3dbinCanada (Sep 13, 2012)

lcaillo said:


> This should be useful. Just remember that you don't get to set the rules about what people post. If someone posts something that you think is off topic, please report it. If it contains nothing factual or generally accepted by the engineering community, it is off topic and will be removed. If there are views that are not consistent with what you believe about the topic you should refute them in a respectful manner or call them out as speculation or opinion without directing any critique at the poster.


I've never been disrespectful even though I may not agree with whats been said. I will go to the mods if I see things that are not factual or off topic and ask them to remove the post.


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## 3dbinCanada (Sep 13, 2012)

The first link is probabally the most important link to show why the transmission line model does not work in audio frequencies. 

http://www.allaboutcircuits.com/tex...nt/chpt-14/long-and-short-transmission-lines/

Basically, it has to do with cable lengths or what the article describes as electrically long or electrically short. If our interconnects and speaker cables approached the quarter wave length of the highest audio frequency, then that cable would be considered electrically long. Do get an idea how long this, I punched in 20 KHz into the calculator in this link; http://www.1728.org/freqwave.htm and I got an electrical wavelength (not an acoustic wavelength) to be 1.4999 e^4 meters or 14.999 kilometers. To meet the minimum requirement for "electrically long", divide this by 4 to get our quarter wavelength defintion which will be 3.75 Km. Based on these numbers, it would be safe to say that most of us have speaker cables that are electrically short. 

In an electrically short cable, the voltage/current is considered constant through out the length of the cable at a given instant in time. The voltage/current does vary with time but if one could freeze time and take out a voltage meter and measure along the cable length, one would get the same reading along any point on the cable. This means that the amplifier doesn't see the affects of the capacitance or inductance of the cable but it does see the resistance of the cable and the load attached to the end of the cable. This resistance is relatively small compared to the speaker and can be ignored if appropriately sized for the cable run length and the power its expected to carry. 

To illustrate another point... remember traveling down a road beside telephone lines and every once in a while, you would see a big lump in the line? That is a transformer along with capacitors and inductors to shape up the signal before it continues to travel along the lines and match impedances. We would require to insert this in our speaker cables if they were many times longer than the 3.75km calculated from above. 


Its stands to reason that if the speaker cable is not seen by the amplifier (capacitance and inductance values of the cable does not affect the amplifier), then swapping in and out different speaker cables will not affect the sound provided once again that the cables have sufficient cross sectional area for run length and intended power delivery.

I hope this helped in your understanding of signal propagation in the audio world.


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## chashint (Jan 12, 2011)

It is fascinating to me how the simple copper wire evokes so much errrr 'conversation' amongst the audio enthusiast community.
All a wire/cable/interconnect actually does is transfer an electrical signal from one place to another.

This article describes how electricity moves in a conductor.
http://sciencequestionswithsurprisinganswers.org/mobile/2014/02/19/what-is-the-speed-of-electricity/

Something that seems to be widely misunderstood when it comes to audio frequencies in a copper conductor is how long the wavelengths of these frequencies really are.
20KHz has a 1/4 wavelength of ~12000 ft. even if you change the velocity factor to .5 (which is an excessive reduction) to offset any insulation effects that is still ~6000 ft. for 1/4 wave.
20KHz may be high frequency for audio but it's barely more than DC as an electrical signal.

Wavelength calculator with velocity factor 
http://www.n1gnn.com/CoaxVelocityFactorLength.html 
Another wavelength calculator that accepts KHz frequency directly.
http://www.csgnetwork.com/freqwavelengthcalc.html 

Depending on medium (air vs copper) for the same frequency the wavelengths are very different, here is an audio wavelength calculator
http://www.mcsquared.com/wavelength.htm 

This link is to the standard AWG Chart and it is a handy reference.
https://en.m.wikipedia.org/wiki/American_wire_gauge 
Since the AWG chart includes a skin effect column here is a skin effect calculator that accepts KHz frequency input.
http://circuitcalculator.com/wordpress/2007/06/18/skin-effect-calculator/ 

Depending on any interest shown in this thread or questions asked I will try to post links to valid information.


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## FargateOne (Mar 3, 2015)

Very intersting links thank you


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## RBTO (Jan 27, 2010)

A cable is not only a means of transferring a signal, but it is in itself a load on the source (primarily capacitive) which can affect the signal at the far end. At audio frequencies, skin effect is for all practical purposes insignificant unless very small diameter wire is being used (which shouldn't be the case). The conductivity of the cable (wire size and material - and indirectly, overall length) is one of its most important characteristics relative to audio signal transfer but what one can get away with is determined by the end load (a low impedance load such as a speaker, demands lower resistance in the connecting cable, while a high resistance load can make use of much smaller gauge wire without serious signal loss). I appreciate the links provided by chashint which are quite relevant to this thread.


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## 3dbinCanada (Sep 13, 2012)

RBTO said:


> A cable is not only a means of transferring a signal, but it is in itself a load on the source (primarily capacitive) which can affect the signal at the far end. At audio frequencies, skin effect is for all practical purposes insignificant unless very small diameter wire is being used (which shouldn't be the case). The conductivity of the cable (wire size and material - and indirectly, overall length) is one of its most important characteristics relative to audio signal transfer but what one can get away with is determined by the end load (a low impedance load such as a speaker, demands lower resistance in the connecting cable, while a high resistance load can make use of much smaller gauge wire without serious signal loss). I appreciate the links provided by chashint which are quite relevant to this thread.


The cable capacitance only becomes a factor in "electrically long" circuits and is not noticed by the amplifier in "electrically short circuits" as mentioned in the link I provided.


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## RBTO (Jan 27, 2010)

3dbinCanada said:


> The cable capacitance only becomes a factor in "electrically long" circuits and is not noticed by the amplifier in "electrically short circuits" as mentioned in the link I provided.


I'd have to disagree.

Granted in most cables, the capacitance is quite small and has almost negligible effects, _any _cable capacitance will react with the output impedance of the source and result in a drop-off of high frequency amplitude beyond some point. That's an effect which is not dependent on the cable being electrically long or short, though cable length directly relates to the capacitance seen by the source (doubling the length of the cable will double the capacitance seen between the two conductors).

To demonstrate capacitance effects, add a 0.1 microfarad physical capacitor across the cable end (of a short length of microphone cable), and see what happens to high frequency behavior. The naturally occurring capacitance between the two conductors is basically the same though much smaller and distributed along the length of the cable, and because it is much smaller, it usually won't affect frequencies in the audio range, but if the _cable_ had 0.1 microfarads of capacitance, it _would_ be noticeable even though we're dealing with an "electrically short" case.


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## chashint (Jan 12, 2011)

http://www.learningaboutelectronics.com/Articles/Low-pass-filter-calculator.php#answer1 

It takes a lot of capacitance to mess with audio frequencies.

Plugging the 0.1uf and 0.2 ohms would put the 3dB cutoff frequency at 7,961,783 Hz.
Probably not a noticeable difference at 20,000 Hz.


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## dgmartin (Oct 29, 2011)

chashint said:


> http://www.learningaboutelectronics.com/Articles/Low-pass-filter-calculator.php#answer1
> 
> It takes a lot of capacitance to mess with audio frequencies.
> 
> ...


Yes 0.1uf/0.2Ohms gives a -3dB at this frequency. However if you use a typical amplifier input impedance of, say 50k, the numbers are quite different. Don't worry: interconnects are going to have C way below 0.1uF...


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## 3dbinCanada (Sep 13, 2012)

RBTO said:


> I'd have to disagree.


Do you have any links that can elaborate on your idea? Electrically short or electrically long is not something I made up but very real parameters that follow principles based on physics. 



RBTO said:


> Granted in most cables, the capacitance is quite small and has almost negligible effects, _any _cable capacitance will react with the output impedance of the source and result in a drop-off of high frequency amplitude beyond some point. That's an effect which is not dependent on the cable being electrically long or short, though cable length directly relates to the capacitance seen by the source (doubling the length of the cable will double the capacitance seen between the two conductors).


Please reread the definition of electrically short and electrically long. These definitions are based on cable lengths and wavelength of frequency and are real. 




RBTO said:


> To demonstrate capacitance effects, add a 0.1 microfarad physical capacitor across the cable end (of a short length of microphone cable), and see what happens to high frequency behavior. The naturally occurring capacitance between the two conductors is basically the same though much smaller and distributed along the length of the cable, and because it is much smaller, it usually won't affect frequencies in the audio range, but if the _cable_ had 0.1 microfarads of capacitance, it _would_ be noticeable even though we're dealing with an "electrically short" case.


Adding an additional component like you proposed alters the circuit, not the cable. The cable remains invisible to the amp but the amp now sees a LP filter in parallel (with a -3db point well into the Megahertz ) with the loudspeaker. You have introduced something that isn't normally there. The amplifier will see the added capacitor but it still doesn't see the cable.


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## chashint (Jan 12, 2011)

dgmartin said:


> Yes 0.1uf/0.2Ohms gives a -3dB at this frequency. However if you use a typical amplifier input impedance of, say 50k, the numbers are quite different. Don't worry: interconnects are going to have C way below 0.1uF...


Yes to all.


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## Savjac (Apr 17, 2008)

Interesting indeed, my beliefs differ from these tests, however, admittedly I have no proof beyond my ears. :dontknow:


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## RBTO (Jan 27, 2010)

chashint said:


> http://www.learningaboutelectronics.com/Articles/Low-pass-filter-calculator.php#answer1
> 
> It takes a lot of capacitance to mess with audio frequencies.
> 
> ...


That figures if you're working with a source impedance of about 0.2 Ohms and would probably hold true for the case of a speaker connection where the amplifier output impedance is that low, but in the case of a line output where the output impedance is around 10k Ohms, the cutoff drops to 159 Hz. Noticeable?

Like I said, the cable interacts with the source output impedance and that output impedance is important to consider in cable losses. Professional audio cables make use of lower output impedances (100-200 Ohms) partially for that reason (and some others), and can be run much longer distances without the capacitive losses you get with consumer cables. In any case, the longer the cable, the more capacitance one has to worry about.


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## 3dbinCanada (Sep 13, 2012)

Interconencts should be kept short as possible to prevent picking up induced noise. Still, the cables are extremely short compared to the wavelength being transmitted so it renders the capacitance as a non issue.


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## RBTO (Jan 27, 2010)

3dbinCanada said:


> Do you have any links that can elaborate on your idea? Electrically short or electrically long is not something I made up but very real parameters that follow principles based on physics.


No links off the top of my head.

I completely agree with your proposition of electrically short and long but it has more to do with the requirements of the source and load impedances being a match so no energy is reflected (radio frequency applications). In audio, as you pointed out, almost all cases are electrically short but that doesn't have anything to do with load and source impedance interactions. The cable is part of the overall load.



3dbinCanada said:


> Adding an additional component like you proposed alters the circuit, not the cable. The cable remains invisible to the amp but the amp now sees a LP filter in parallel (with a -3db point well into the Megahertz ) with the loudspeaker. You have introduced something that isn't normally there. The amplifier will see the added capacitor but it still doesn't see the cable.


I suggested adding the capacitance simply as an example that long/short doesn't come into play. Whether that capacitance is in the cable or external doesn't matter at all. That exercise was just to point out that _any _capacitance paralleling the conductors of the cable will have an effect on high frequencies (and yes, if the cable and source impedances are low, that effect will not be in the audio range), but in some cases (where source output impedance is high) capacitance is definitely a consideration. You always have some capacitance in an audio cable just due to the two conductors running parallel to each other. The amount of that capacitance has to do with spacing and the material between the two conductors (the insulation), as well as the length of the run.

In electrically long cases, the impedances of the source, cable, and load, all have to be considered and usually matched to prevent reflections. Not to worry about in most audio cases.

Likewise, as mentioned, most cable capacitance is pretty low (except for long runs) and won't harm audio transfer, BUT, capacitance IS a consideration and is the key contributor to high frequency loss in cables.


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## 3dbinCanada (Sep 13, 2012)

RBTO said:


> No links off the top of my head.
> 
> I completely agree with your proposition of electrically short and long but it has more to do with the requirements of the source and load impedances being a match so no energy is reflected (radio frequency applications). In audio, as you pointed out, almost all cases are electrically short but that doesn't have anything to do with load and source impedance interactions. The cable is part of the overall load.


I agree but its only the resistive part that's seen. 



RBTO said:


> I suggested adding the capacitance simply as an example that long/short doesn't come into play. Whether that capacitance is in the cable or external doesn't matter at all. That exercise was just to point out that _any _capacitance paralleling the conductors of the cable will have an effect on high frequencies (and yes, if the cable and source impedances are low, that effect will not be in the audio range), but in some cases (where source output impedance is high) capacitance is definitely a consideration.


I think noise pickup in interconnects would play a bigger role in signal degradation than the distributed capacitance exhibited by interconnects. What I'm saying if you swap out interconnects of equivalents length, the changes in capacitance by even several hundreds of pf will be inaudible. Please remember that the voltage along the entire length of the cable for a given signal in any point time is constant across the cables entire length.



RBTO said:


> In electrically long cases, the impedances of the source, cable, and load, all have to be considered and usually matched to prevent reflections. Not to worry about in most audio cases.


 Agree.


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## 3dbinCanada (Sep 13, 2012)

A link describing the velocity of propagation of audio signals;

http://www.computeraudiophile.com/blogs/ringenesherre/velocity-propagation-audio-frequencies-169/


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## chashint (Jan 12, 2011)

Good link.


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## 3dbinCanada (Sep 13, 2012)

Here's another link that states that audio cables only behave like transmission lines when run lengths are extremely long (talking about kilometer length cables) and for 99.999% of audio installations, run lengths are far too short for transmission line affects to take place. Moral of the story is this... if anyone uses transmission line theory to describe the detrimental effects of capacitance and inductance in cables, then they are wrong and the analysis can be tossed out the window. That's why I cringe when I read the pseudo science of cable manufacturers. I equate their analysis to nothing more than fraud. 


http://audiosystemsgroup.com/CableCapacitance.pdf


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## Savjac (Apr 17, 2008)

Is this propagation something you can hear ? If so what can be heard....nothing I am guessing by the attached literature and if it can be heard...what do you hear.

These attachments do not mean that all cables sound alike, they have merely disposed of one area imagined to be problematic.


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## 3dbinCanada (Sep 13, 2012)

Savjac said:


> Is this propagation something you can hear ? If so what can be heard....nothing I am guessing by the attached literature and if it can be heard...what do you hear.
> 
> These attachments do not mean that all cables sound alike, they have merely disposed of one area imagined to be problematic.


What these documents are proving is that the amplifiers don't see the affects of the cables (assuming typical installation lengths and adequate cable diameter for intended run lengths) . Since the amplifiers don't see the affects of the cable, they don't affect the signal going through it or alter it in anyway. If the signal is not affected, then the principles of cause and affect would say that cables don't impart a sound.


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## Savjac (Apr 17, 2008)

I understand and am thankful for your post showing how various external issues may not ever affect the cables proper. However, it is my strongest belief that for some reason that might not have been made clear, cables do sound different....sometimes a great deal of difference can be determined. This is something I am prepared to prove once someone I am familiar with and trust will take it on.
:T


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## 3dbinCanada (Sep 13, 2012)

Savjac said:


> I understand and am thankful for your post showing how various external issues may not ever affect the cables proper. However, it is my strongest belief that for some reason that might not have been made clear, cables do sound different....sometimes a great deal of difference can be determined. This is something I am prepared to prove once someone I am familiar with and trust will take it on.
> :T


I'm interested in your methodology for proving that cables impart a sound.  I state this because I'm a firm believer that hearing involves other senses other than our ears; especially sight and one's frame of mind. If these latter two senses are engaged during the audition process and not removed from the audition, how does one know what one is hearing is not being influenced by the other senses?


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## Savjac (Apr 17, 2008)

Great question really. 
I am not able to buy expensive cables that might make me prone to defending a costing model, nor am I am engineer so I have no bias against the cable itself in way of type or methods of winding....except for one bias in that produce a product made of up a large number of very tiny individual wires as to me the mids and highs tend to be exaggerated. Now if I was in congress I would obviously buy the most expensive wire on the planet.

Also, once I listen long enough and form an opinion, I bring the tested product to my long term listening buddy and let him hear the cables with no input from me. More often than not, we tend to agree on what is being changed in the sound of the system. On occasion we disagree on what sounds better but we always agree if a difference is heard. 

I hope this makes sense. :smile:

I do think I should start my own thread and not mess up yours.


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## 3dbinCanada (Sep 13, 2012)

Savjac said:


> Great question really.
> I am not able to buy expensive cables that might make me prone to defending a costing model, nor am I am engineer so I have no bias against the cable itself in way of type or methods of winding....except for one bias in that produce a product made of up a large number of very tiny individual wires as to me the mids and highs tend to be exaggerated. Now if I was in congress I would obviously buy the most expensive wire on the planet.
> 
> Also, once I listen long enough and form an opinion, I bring the tested product to my long term listening buddy and let him hear the cables with no input from me. More often than not, we tend to agree on what is being changed in the sound of the system. On occasion we disagree on what sounds better but we always agree if a difference is heard.
> ...


I'm not booting you out of my thread. :grin2: 

I'm thinking we're coming down to a difference of opinions that cannot be reconciled. I'm going to leave it that. Have a good weekend.


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## Savjac (Apr 17, 2008)

Please dont take me wrong, I never thought you wished rid of me, nope as you said we are speaking different languages.


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## 3dbinCanada (Sep 13, 2012)

Savjac said:


> Please dont take me wrong, I never thought you wished rid of me, nope as you said we are speaking different languages.


No worries.. i thought the big grin would have conveyed that there was nothing to worry about.


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