Characteristic Impedance in audio cables

[Richard Black]

Hello Audioholics all,

I've just joined here, nice to meet you all etc. etc. - and thanks to the organisers for an uncommonly BS-free site. Lots of very good stuff on cables - been researching this subject on and off for ages for no better reason than that I like a good engineering puzzle! Just lately managed to prove to my own satisfaction that the difference in a realistic (as far as I can see) situation between 'free' and fancy interconnects, WITH REAL MUSIC PROGRAMME, is less than -85dB once one has compensated for simple magnitude and time-delay effects (you have to do both because not far below -80dB the resistance of the interconnect will start to show up, and you'll be looking for sub-ns phase matching in order for a differencing test to make sense, plus of course lumped-element RC rolloffs). I'll explain exactly how some time when I've a lot of time spare to write it all up.....

Just like to mention the subject of characteristic impedance matching in audio cables. I was one of the first people to mention this in public, at least 15 years ago, and though my views on cables have changed in some ways since then I would like to point out the following:

EVEN AT AUDIO FREQUENCIES, a notionally impedance-matched cable gives the lowest frequency-dependent magnitude and phase discrepancies. You can do a simple lumped-parameter analysis at any frequency you like and the numbers drop out. Yes, we are talking about eliminating the last thousandth of a dB of magnitude error and fraction of a degree of phase but from an academic viewpoint anyone who claims that impedance-matching does something at audio frequencies is strictly speaking correct. Though possibly irrelevant!

Regards,

Richard

 

[jneutron]

Geeze, who do you think you are..

Richard...Give some specifics and WHY, or just keep whistling in the dark.

You and the other naysayers are the one's full of cr_p, you are the ones who hold back true science, you are the ones who have been naysaying and pooh-poohing all along, and only are reluctantly dragged to the table of the real world

YOU DON'T KNOW AUDIO WELL ENOUGH.

Only thing is, there are some poor ignorant souls who swallow your flawed line of reasoning hook,line and sinker.

never admit that your total lack of experience with high performance audio is a crippling lack.

your opinion in the world of audio means absolutely nothing, to me, and to anyone with any real experience in high performance audio.

OOOPS, waittaminute...I forgot...this is AH, not cables....sorry, nevermind...

Hi Richard...welcome..

Yah, I ran the numbers for impedance vs energy stored in the wire..it is certainly a minima when line=load..Don't know if it makes a diff for speaker runs, but it is a considerably higher fraction of the transferred energy for the lower impedance applications...something worth looking into...

Your not gonna inject this forum with good stuff, are ya??

Hey, again..welcome..

Cheers, John

 

[mtrycrafts]

Just like to mention the subject of characteristic impedance matching in audio cables. I was one of the first people to mention this in public, at least 15 years ago, and though my views on cables have changed in some ways since then I would like to point out the following:

I thought John Dunlavy had something to say on this?

But, how are you matching an 8 ohm speaker with an amp with .1 ohms or less?
Or, in the interconnect applications with impedance variation of 10 to 1?

Yes, we are talking about eliminating the last thousandth of a dB of magnitude error and fraction of a degree of phase but from an academic viewpoint anyone who claims that impedance-matching does something at audio frequencies is strictly speaking correct. Though possibly irrelevant!

Regards,

Richard

Why are you interested in that 1/1000 of a dB???

 

[Richard Black]

<<But, how are you matching an 8 ohm speaker with an amp with .1 ohms or less?>>

OK, should have specified - in any normal domestic audio application you'll only be matching one end. But that still gives benefits - albeit at the tiniest of levels. So you 'match' (with all the usual provisos about variable nominal impedance etc. etc.) the receiving end in a speaker cable, but the sending end in an interconnet.

<<Why are you interested in that 1/1000 of a dB???>>

Actually I'm not really all that interested but I just thought the intellectual point might amuse people!

Just for the record: I did some real live measurements comparing a 'free' interconnect (as given away with most components) and a medium-price one from Furukawa (long out of production as far as I know). In terms of basic lumped parameters the freebie is about 570pF with a Q of about 15, the Furukawa 120pF with a Q greater than 200. The maximum frequency response difference between them, at 20kHz, was almost exactly 0.005dB, and the phase shift between them (if you see what I mean) corresponded to less than 100ns. Just to put this in context, you probably get a bigger shift in amplitude response due to the increase in the humidity of the air in the listening as you breathe in and out for a few minutes, while 100ns is the time taken for sound to travel about 1 thou.

I have still not proved to myself that cables all sound the same but I have certainly ruled out several hypotheses as to why they might, to my own satisfaction at least. I am trying to do some measurements on a _complete_ audio system, up to and including the speakers, picking up real sound with a microphone and detecting changes (or not) due to cable swaps. This is a most entertaining head-scratcher!

Richard

 

[gene]

Richard;

Using a rough approximation of sqrt(L/C) (not entirely accurate at audio frequencies, but close enough), even the best cables we measured come out at about 50 ohms. In order to make a cable match 8 ohms or less requires a compromise, usually resulting in ultra high capacitance which can wreck havoc on amplifier stability and/or cause amplifier frequency peaking with high bandwidth amps or frequency attenuation of amps with high output impedances such as a tube amp. In addition no speaker has a constant load impedance over frequency so again it seems to be a moot point to attempt impedance matching at audio frequencies.

And for the record cables can and do sound different, but only poorly designed ones. Good cables are sonically indistinguisable.

 

[mtrycrafts]

Just for the record: I did some real live measurements comparing a 'free' interconnect (as given away with most components) and a medium-price one from Furukawa (long out of production as far as I know). In terms of basic lumped parameters the freebie is about 570pF with a Q of about 15, the Furukawa 120pF with a Q greater than 200. The maximum frequency response difference between them, at 20kHz, was almost exactly 0.005dB, and the phase shift between them (if you see what I mean) corresponded to less than 100ns. Just to put this in context, you probably get a bigger shift in amplitude response due to the increase in the humidity of the air in the listening as you breathe in and out for a few minutes, while 100ns is the time taken for sound to travel about 1 thou.

Yep, that would be about 1/10,000 of a foot or .0012"

I have still not proved to myself that cables all sound the same but I have certainly ruled out several hypotheses as to why they might, to my own satisfaction at least. I am trying to do some measurements on a _complete_ audio system, up to and including the speakers, picking up real sound with a microphone and detecting changes (or not) due to cable swaps. This is a most entertaining head-scratcher!

Richard

What did you rule out?
How did you try to demonstrate that you can tell them audibly different?

If your instrument can pick up that .005dB at 20kHz, that still doesn't tell you if that amount is audible, right? But JASA, Journal of Acoustic Society of America has an article on what is Just Audibly Noticable with very sensitive signals. And, there are others published.

So, I am at a loss what you are trying to prove or disprove? That you can measure cable differences or that you or anyone on the planet can audibly differentiate between comparable cables, even between your example of cables, one being free, the other costing much more

 

[jneutron]

Using a rough approximation of sqrt(L/C) (not entirely accurate at audio frequencies, but close enough),

Hmmm...why is Z_O= (^L/_C)^1/2..not entirely accurate at audio frequencies???

Please explain..

Cheers, John

 

[gene]

Hi John;

I recommend checking out this article which I believe was originally authored by Belden.

Characteristic Impedance of Cables

 

[jneutron]

Hi John;

I recommend checking out this article which I believe was originally authored by Belden.

Characteristic Impedance of Cables

Ah...I stand corrected..

In the course of my work on my double coax, I managed to eliminate the low freq dependence on R of the wire, so of course, I completely forgot about it..

Oooops..

I note in the link, they entirely neglect skinning and wire self inductance...I was thinking this was what you were referring to...I've looked at the belden line, and found all the inductance numbers were specified at high freq, whereas most measurement boxes typically use 60 hz or 1K..

Cheers, John...

Hey, waittaminute...

the #12 is twisted pair...I'm talkin coax, gonna hafta think and get back on this..right now..goin home..

 

[Richard Black]

So, I am at a loss what you are trying to prove or disprove? That you can measure cable differences or that you or anyone on the planet can audibly differentiate between comparable cables, even between your example of cables, one being free, the other costing much more

Oh, it's all just fiddling really, for my own satisfaction and hey, you do enough of this stuff you soon find out some interesting things, develop some useful test techniques along the way. Ultimately I suppose it's this: if anyone is going to produce a properly plausible explanation of why cables _could_ sound different from each other I'd like it to be me first!

Richard

 

[mtrycrafts]

Oh, it's all just fiddling really, for my own satisfaction and hey, you do enough of this stuff you soon find out some interesting things, develop some useful test techniques along the way. Ultimately I suppose it's this: if anyone is going to produce a properly plausible explanation of why cables _could_ sound different from each other I'd like it to be me first!

Richard

I hate to tell you but you will not be the first

"Speaker Cables: Can you Hear the Difference?", Greenhill, Larry, Stereo Review, Aug 83, pg 46-51.


Greenhill demonstrated audible differences in speaker cables, 21 years ago. No mystery to it.

An JAES paper on measurements:

"Effects of cable, Loudspeaker and Amplifier Interactions", Davis, Fred E., JAES, vol. 39, no. 6 Jun 91,

Further info from JAES

"Amplifier-Loudspeaker Interfacing", Greiner, R.A., JAES vol. 28, no. 5 May 80,

Another DBT listening:

"Wired Wisdom, The Great Chicago Cable Caper", Nousaine, Tom, Sound & Vision(Canada), Sep 95, pg. 73-76.

More technical info:

"Beating the Bafflegab & Filtering the FooFooDust", Hayward, James, Part 1- Marshall's Audio Ideas Guide(Canada) Summer/Fall 94

"Making the Connection. Part Deux: A Closer Look at the Role of Loudspeaker Cables", Hayward, James, Winter 95. Reprints available from Kimberkable.


DBT of different cables:

"1/4" Cable Roundup", Gallagher, Mitch, Keyboard, Apr 99, pg. 44-48.

Psychoacoustics for cable:

"Speaker Cables, Measurements vs Psychoacoustic Data", Villchur, Edgar, Audio, Jul 94, pg 34-37.

More psychoacoustics of detection:

"Level Discrimination as a Function of Level for Tones from .25 to 16khz", Florentine, Mary, et al, Journal of Acoustic Society of America, 81(5) May 1987, pg 1528-1541.

"On the Relations of Intensity JND's to Loudness and Neural Noise", Zwislocki, J and Jordan H., Journal of Acoustics Society of America, 79(3), Mar 86, pg 772-780.

 

[jneutron]

I recommend checking out this article which I believe was originally authored by Belden.
Characteristic Impedance of Cables

Been thinking about the analysis on that link..

My spidy sense is tingling...there is something very wrong with the assumptions, the simplifications, the analysis, the tests, and the results...

But, other than that, it's a good article...

I'm still trying to figure out how they measured the Z_cable for the lower frequencies.

For the higher frequencies, they are using tdr, or load matching..

They also specify open load reflection and shorted load reflection..

But, I think they have a serious flaw of reasoning for the lower frequency analysis....and are using the distributed resistance total in the analysis, specific to wavelength...meaning, as they go down in frequency, they are including the larger resistance of the longer wire they use for the distributed C. The low frequency model resistance they are using is incorrect. For relatively high freq's, they are tremendously right..

But, for the real calculation of the impedance, the inclusion of the dissipative elements is misleading...and for the lower freq's, incorrect.

I'm thinking about how to get around their test errors...nuttin yet...but it's a rock in my shoe..

Cheers, John

 

[FLZapped]

Hmmm...why is Z_O= (^L/_C)^1/2..not entirely accurate at audio frequencies???

Please explain..

Cheers, John

Because:

http://bwcecom.belden.com/college/techpprs/ciocahalf.htm

-Bruce

 

[Mr. Music]

Cable impedance - Transmission line theory

This issue of cable impedance is very complicated to deal with unless you are really an expert in mathematics and thus are able to understand and apply transmission line theory. On www.cardas.com you may find an example of a design method for making the cable "invisible" for the amps and speakers. You will see this method also applies to ideal speaker placement.

 

[jneutron]

Because:

http://bwcecom.belden.com/college/techpprs/ciocahalf.htm

-Bruce

Hmmmm..bruce?? it's the same link Gene posted up above...maybe you should set your alarm just a wee bit earlier...

Gotcha...

Seriously, here is the incorrect statement in that paper..

""Calculations of an equivalent capacitor and resistor to replace the infinitely long cable could be made. ""

That is an incorrect assumption..explanation to follow..

If you go to charge an infinitely long transmission line of say, 50 ohms, with 50 volts, it will forever draw 1 ampere...and the line will forever aquire energy at the rate of 50 joules per second.

If you do the same for the "equivalent capacitor and resistor", it will not...it will accept charge with an exponentially decaying current, to a final value..

To continue the modelling of the really low impedance t lines for low frequencies the way they did is inaccurate..as that premise is wrong. A model that is used as an equivalent for the purposes of analysis, MUST be impossible to discern as different from the end terminals...what they state certainly does not meet that criteria..

Luckily, this error is unimportant for their real product line...but I really hate to see the error continue ad infinitum..don't know if I care to bother telling Belden..

Cheers, John

PS..see Gene, it took a day, but I'm happier now...now, to drown some olives...

 

[mtrycrafts]

This issue of cable impedance is very complicated to deal with unless you are really an expert in mathematics and thus are able to understand and apply transmission line theory. On www.cardas.com you may find an example of a design method for making the cable "invisible" for the amps and speakers. You will see this method also applies to ideal speaker placement.

Do you have a better link where this is at?

 

[mtrycrafts]

Luckily, this error is unimportant for their real product line...but I really hate to see the error continue ad infinitum..don't know if I care to bother telling Belden..

Cheers, John

Why not? Maybe they will change their page with a footnote with your name on it.
Progress is the key just like you will publish that skin paper one day

 

[FLZapped]

Hmmmm..bruce?? it's the same link Gene posted up above...maybe you should set your alarm just a wee bit earlier...

Gotcha...

Seriously, here is the incorrect statement in that paper..

""Calculations of an equivalent capacitor and resistor to replace the infinitely long cable could be made. ""

That is an incorrect assumption..explanation to follow..

If you go to charge an infinitely long transmission line of say, 50 ohms, with 50 volts, it will forever draw 1 ampere...and the line will forever aquire energy at the rate of 50 joules per second.

If you do the same for the "equivalent capacitor and resistor", it will not...it will accept charge with an exponentially decaying current, to a final value..

If I have picked up where I think you are talking about......

Charge? Who said anything about charge? Impedance John, think impedance......he is <i>defining</i> the characterisitcs of characteristic impedance. By definition, he is quite correct, the impedance is fixed without regard to unit length and a set of lumped components, in fact, COULD be used in it's place. Radio would be impossible without this fact.

Therefore, at DC and frequencies below the transistion point, the impedance of a cable does not fit this definition as its impedance is variable with unit length, whch is what he went on to show in the paper when he talks about the effect of frequenncy.

His actual measurements in figure 7 backed up his work(through fig 6), so I don't see where the problem is.

Clear as pumpkin soup?

-Bruce

 

[FLZapped]

This issue of cable impedance is very complicated to deal with unless you are really an expert in mathematics and thus are able to understand and apply transmission line theory. On www.cardas.com you may find an example of a design method for making the cable "invisible" for the amps and speakers. You will see this method also applies to ideal speaker placement.

You need a more specific link than this.

-Bruce

 

[gene]

This issue of cable impedance is very complicated to deal with unless you are really an expert in mathematics and thus are able to understand and apply transmission line theory. On www.cardas.com you may find an example of a design method for making the cable "invisible" for the amps and speakers. You will see this method also applies to ideal speaker placement.

Cable impedance really isn't that complicated. The basic equation Zo = (L/C)^1/2 allows one to calculate the characteristic impedance. At audio frequencies this is a moot point and only starts coming into play about 1/10 the wavelength. So take 1/10 (C/f) where C = 3x10^8 m/s (speed of light) and f = frequency (20kHz) and you get about 15,000 meters! Factor in typical cable propagation of say 60% and it becomes more like 9,000 meters or 29,528 feet! Cable resistance will kill the signal long before you reach these lengths.

I have found most of the cable theory on the Cardas website to be questionable at best.

John;

I need to spend more time re-reading that article I referred you to on cable impedance. My take from that back when I read it, was they were trying to show that resistance at low frequencies is the dominant metric of concern in cables. Such is the case with speaker cables. I thought when I proofed the article it made mathematical sense, but I suppose you will have me revisit it. Why do you make things so complicated ? ?