The analogue audio link as a transmission line.

This chapter is a critical reaction on the article 'Reflections, Echos & Music' of mr. Hervé Delétraz in the november 2001 edition of Stereophile. This is the reason why this chapter is written in English.

One of the readers of  my website was so kind to send me a copy of the Stereophile article.

I reproduced the Stereophile / Delétraz article here partially, for reference to the pages where my criticism focuses.

The  reaction of mr. Delétraz is included, interleaved with my comments.

And a  in a final comment I suggest to end this discussion.

In general electronics it is widely accepted and practised that impedance matching of short cables is not necessary for a good signal transfer. "Short" must be interpreted here in relation to the wavelength of the signal passing through the cable.

For the analogue audio signal the wavelength of say a 10 Khz frequency is about 30 Km in free air or 20 Km in a cable.

So the average audio cable of 2 meters has a length of  1/1000 of the wavelength. Fairly short not?

In his explanation of how a transmission line works mr. Delétraz uses the example of a chain of humans handing over buckets of water. Certainly this is a nice way to visualize the wave propagation effects on a cable, but if seen in the proportions and dimensions of the 10 Khz wave on a 2 meter cable, the length of the human chain reduces to 0.3 mm (1/1000 of the bucket's 30 cm diameter) which makes the use of a bucket brigade somewhat inpractical.

The examples of fig. 9 and 10 in the Delétraz article correctly show signal degradation, but he performs his experiment with a 10 KHz square wave.

Now, 10 KHz is certainly audible for most people, but mr. Delétraz deliberately (*) ignores the fact that a square wave needs many (odd) harmonics to become more-or-less square. For the 10 KHz example all these harmonics lay beyond, and far beyond the range of audible frequencies. When percieved by the human ear the square wave will be reduced to a near perfect sinewave.

For the interpretation of fig. 10 mr. Delétraz deliberately (*) did not calculate or measure the consequenses of these pertuberations in the audio frequency band.

If he had done so he would have found that they are fairly neglectable.

More over, his measurements were done on a 100 meter cable and not on a more realistic 1 or 2 meter cable. Honestly he does mention this and juridically spoken he is right when he says: "Divided, yes; eliminated, no". But saying this he wipes away a factor of  ONE HUNDRED without even thinking about possible consequences.

Stepping over dimensions and proportionalities like this makes me think of the article I once read about the gravitational pull of the sun and moon on the earth. The article concluded with an advice to install your bathtub in the nort-south direction to have less chance to get seasick by tidal effects.

I did make some calculations with the transmission line of 100 meter, and 1 meter length using pSpice, the PC-version of the well known Spice program and the following model: (the red numbers are the Spice nodes)

Vsource is a voltage source (zero internal impedance) of 1 volt.

Rout  was set to 15 Ohm

The transmission line had a characteristic impedance of  75 Ohm and a delay of either 0.5 or 0.005 usec, reflecting the lenght of 100 or 1 meter.

Rload was 100 KOhms

Rdummy is a requirement of the simulation program which does not allow floating nodes. It was set to 100 GigaOhm

The simulations were done with a frequency range of 1 Hertz to 10 MHertz.

Fig 2.

Here we see the signal at the beginning (green) and the end (red) of the transmission line.

Impressive resonances are visible with peaks starting at 500 KHz.

Fig 3

Exactly the same as fig 2, but zoomed in into the 20 Khz audio range.

We see about 2 mV signal rise at the end of the cable, which corresponds to -54 dB additional effect.

Fig 4

Here the phase shift of the signal at the far end is plotted in milli degrees. As said before: about 1/1000 of 360° at 10 Khz

Fig 5

The same picture as in Fig 3, but here the delay of the transmission line was reduced to 0.005 usec to reflect a cable of 1 meter length.

Here the spice program ran into problems of numerical resolution. The red curve should have been smooth. The differences are in the order of a 0.2 microvolt, or -134 dB, far below the hearing threshold when the average volume is set to say 90 dBa, and also far below the quantisation noise of digital audio systems.

My conclusion is that the transmission line effects on a not properly terminated analogue audio cable of a length as usual in home audio systems are completely neglectable, and any attempt to match the impedance of such cables is a waste of time and mony.

Don't misunderstand me: For digital audio it is certainly necessary to use cables of the proper characteristic impedance for any length over a few meters: 75 Ohm coax for S/Pdif  or 110 Ohm shielded twisted pair for AES/EBU.

On the download site of the AES organisation you can find the official specifications.

(*) Note: I use the word 'deliberately' here, because mr. Delétraz showed in his article a reasonable mastering of the theory of signal transport on a cable. With this knowledge he certainly must be able to account or approximate the effects in the audio frequency band.

Mr. Delétraz uses an example with a 10 Khz base frequency. That strongly suggests that he is talking about an analogue audio link. If he had the intension to restrict his story to digital audio links he would have chosen say 6 MHz, which is about the data frequency for the S/Pdif digital link. Such an example would have shown reflections on a much shorter and more realistic cable length.

The fact that he left away even the slightest approximation for the effects in the audio frequency band, that he skips a factor of one hundred without any consideration, but elsewhere worries about a 2% tolerance on the termination impedance convinces me that mr. Delétraz is deliberately leading his audience into attempts to undertake experiments from which technically spoken no effects can be expected.

I wonder which goal mr. Delétraz had in mind when he so deliberately misleads his readers.

A few other comments to the article:

Some typo's: The values of the constants u0 and E0 on the 4th page (I do not have absolute page numbers)  lost the minus sign of the exponents. 

It is not clearly stated that the DIY part of the article focuses on analogue audio links. It would have been more clear when mr. Delétraz had mentioned that the digital inputs and outputs on audio equipment normally are terminated with the proper impedance. At least they should, because the specifications for these interfaces say so.

For the people at home this means that they simply have to use a cable with the proper characteristic impedance, and there is no use for additional termination resistors.

Where mr. Delétraz is worrying about a few% tolerance of the matching impedance he does not mention that this produces only a few% of reflected energy, which will be re-reflected for another few% of a few% at the other side, when there is a few%  mismatch there too.

So even if there is some mismatch the reflections will die out very rapidly.

For those who insist on experimenting with matching impedances it may be interesting to know that the effects of echo's already disappear for the most when either end of the cable is terminated with the characteristic impedance of that cable.

This can be explained as follows: For a cable terminated at the end there will be no reflections, because all energy is absorbed by the terminating resistor.

An open cable which receives its signal from a source with the characteristic impedance will reflect all energy at the far end, but this reflected signal will be absorbed by the source impedance. So it will not reflect a second time, and the signal at the end is undistorted.

This latter configuration may be an option for the situation that the source (e.g. the CD-player) does not tolerate the low impedance loading of a terminated cable.

In electronic practise however we prefer to terminate long cables on both ends of course. It makes the system less sensitive to tolerances on the matching impedances.

Another thing to keep in mind is that coaxial or shielded cable with one central wire rarely comes with a higher characteristic impedance than about 100 Ohm.

I recently measured the characteristic impedance of a piece of the standard cable wich comes with most audio equipment. I measured this impedance by varying the terminating resistor at the far end, while observing the reflections of a fast impulse with an oscilloscope at the feed side.

The optimal termination resistor appeared to be 27 Ohms. This is such a low impedance that it is quite likely that signal sources will not tolerate it.

For the english readers: The leading motto on my website is the fairy-tale  "The Emperors New Clothes"

In short:

Once upon a day the Emperor got a visit from a tailor who told that he now uses a new and very expensive material which is only visible for very smart people.

The Emperor was impressed and immediately ordered an expensive new suit. When the suit was ready to try-on the Emperor -ashamed that he could not see it- said "Oh, how a beautiful suit this is" and all of the royal household assented this.

During the following tour the Emperor sat on his horse fully nude, but no one dared to say that.

Only a little boy yelled "He, see there, a naked man on a horse"

Top

Begin january 2002 I received this reaction from mr. Hervé Delétraz. I interleaved my comments in blue.

Dear Jan,

I'm really glad that my article tilted you a bit. To tell the truth, I did not expect such number of emails I receive regularly. I've to tell you however, that you are among the smallest group,  I mean in the skepticism camp. 

Sceptisism is a philosophical stream saying roughly that 'there is nothing we can be sure of'. The adepts must be extremely busy because with every new statement from anyone they have to redo all their homework, whatever that be...

For electronics in general and for the low frequency range of audio frequencies in particular it is known and experienced for decades that the theory very well matches the reality. So far we can greatly rely on what our previous generations teached us.

So I'm not a sceptic. I am a technician who makes calculations, which you -claiming to be a technician too-, can easily verify, reproduce and draw the right conclusions from.

In fact the 'others' are sceptics, because they refuse to accept what can be easily calculated with some basic understanding of the technical science involved.

And I'm not surprised that your audience contains mainly 'believers', because with the first line of your article you positioned yourself between those who love to experiment with technical things which cannot have the slightest influence on sound quality.

I take it as a clever and sane reaction, since I was myself  not sure that matching cable really do improve the sound, if conducted properly, and as all the guys who tried told me.  

If you had these doubts while writing the article you should have mentionened them to your audience. If you remember these doubts only now you are pointed to it, why do'nt you now draw the right conclusions?

If you really are a technician you should be aware that a lot of claims being put by many other people in the High-End HiFi scene cannot be based on other mechanisms than those residing 'between the ears', and have nothing to do with electronics technology or audible sound as such.

In particular this applies to signal cables where even simple, but also thorough calculations show that the analog audio signal passes even the simplest cheap standard cables for 99.99% or better.

What in heaven or hell could you want to 'improve' then?

You're perfectly right telling that I play here with much longer lengths (100 meters) than in standard rigs (1 meter or even less). In growing multi channel setups, however, it seems no-nonsense to put the amps near the speakers and run longer lengths from the preamp to the amp. Bigger matched lengths will indeed improve even better, and the cost will remain low...  

My calculations showed  that even in the 100 meter case the effects of an impedance mismatch are in the order of  0.1% at the highest audio frequencies. The same effect of turning the 'treble' knob of your amplifier just a degree or so.

You're right in assuming that the intrinsic impedance is not perfectly matched at low frequencies, but it is sure that even if the result is not perfect, reflections cancellation can be both seen on the scope and heard by 15-30 minutes trained ears, even with short lengths. 

If you had limited the bandwidth of your oscilloscope measurements to 20 Khz / 3dB with a slope of 6 dB/oct (the human ear has a much steeper slope there) you would certainly not have been able to see the effects of reflections on a cable of even 100 meter length.

The calculated effects are so extremely small that no ear, 'trained' or not, can hear the difference.  But, I have experienced that the most offending thing which can be told to a High-End HiFi lover is that 'certain things cannot be heared by the human ear'. 

'Trained High-End HiFi Ears Just Hear Any Difference Very Clearly' seems to be one of the first articles of the HiFi catechism. 

I just realized that my article, primarily intended to be as simple as possible, was not taken as is. No problems if you want more technical and physical stuff, I'm just working on it.

I sincerly hope that your next technical article will contain technical stuff, explained with the same feeling of detail, but  not cluttered by conclusions which suggest that 'improvements' can be made where the technical reality has no room for it at all.

I can swear you that if you would just try, you will know what I tried to enlighten.

You enlightened the mechanism of reflections in mismatched cables clearly, but you obscured crucial information when applying this knowledge to the analog audio domain.

I'm a electronic designer and I don't believe in snake oil.

Probably you should revise your believe in some other 'oils' too, applying a samelike kind of sanity you said to find in my article. If you have any questions about this I'd be pleased to help you in a private discussion.

Sure that this article was maybe not some cable manufacturers' cup of tea, but what can I do for that?

I'm not a manufacturer, I have no business in any kind of HiFi stuff. I'm afraid however that several cable manufacturers will 'develop'  'special' cables and terminating devices, and sell these parts for much money to people who read your article. You and I (and I hope some readers of this dicussion) know that no improvement can be expected from such gear.

It seems that Mr. Peter B. Noerbaek - just to name but him -  was impressed enough by the method I described to write to Barry Willis the following:

" Hi Barry,
I've completed the fully impedance matched system which we will display at WCES AP 2005, I invite you and any of your reviewer buddies to come hear what this does!
It is truly astounding - a $56 pair of 75Ohm cables with BNC connectors way outperforms any interconnect cable regardless of price,  My $4000 Monster Sigma Retro sound clouded compared to this new setup.   Bring any cable you wish (6 M lenght or greater) and hear it in comparison to standard RG59 cable.
The cable guys are going to freak out about this,  just wait - it wont be long before we have $5000   75 Ohm cables  (which will sound no better than than a $50 pair since the cable does not matter in this setup!)
I by no means take credit for designing this concept - just the implementation.  I was inspired by the article in the NOV 01 issue of Stereophile describing the virtues of impedance matching.   
You might want to mention this to the big guys at Stereophile, Atkinson and Scull, I would be happy to do a private demo for any of you.
See you in Las Vegas"....

Yeeh, this is about the standard reaction I've seen often from 'believers' and from people who have a business in baked air and already see the $$ fly in.

So I think that even if you could prove that my article is too simplistic and could mislead "honest" audiophile, I personally find such above enthusiast emails a good promise. I am sorry, however, if you felt that my goal was just to put oil in the fire. My quest is the very same as most audiophiles, say the most life like reproduction.

Your article was certainly not (too) simplistic, for most of the part it was technically correct and very clear for much of the laity and certainly has contributed to the technical understanding of many of your readers. But from around fig. 10 you go so completely wild with several suggestive conclusions that it makes your integrety as a technician very doubtful.

Certainly my quest is the same as yours. The difference is that I try to withold my audience from undertaking useless experiments and investments where you encourage them to do so.

Thank you again for your email. I take this opportunity to wish you an Happy new Year 2002 !

Thank you very much.  To you the same, and may a more technical spirit be with you.

Hervé

Jan

After this I received an email from mr. Delétraz. which made me feel that he wants to end this discussion, and I feel the same, because it is quite clear that we are just turning around in circles.

I apologise that I might have been not clear about my technical background. Here it is:

For over 30 years I am a designer of electronic circuitry in the Research & Development department of a medium sized Dutch company in medical equipment, selling worldwide and being a market leader in certain areas.. 

Privately I have always wanted and been able to realize an above-average sound quality for my home equipment, but not very fanatic, and I have refrained from investments and experiments in fields where the technology has no room for 'improvements'

Mr. Delétraz raised an interesting issue regarding matching cable impedances:

I just recall to you that the very first application in matching lines was around 100 years ago, when the very first 600 ohms telephone lines were installed. If I follow your own arguments, why did they match their line, for signals frequency barely extending from 300 to 3400 Hz ? Of course the telephone lines were even much longer than 100 meters, but just think that 3400 Hz would show the same effect (or non-effect as you claim) with a 300 meters cable. Say that you put 3 kilometers and you'll still have fair good signal.

Sure reflection problems will occur here only at distances exceeding many kilometers. But there is another and more important issue involved here. 

That is the principle of the "Fork circuit"  present in any telephone set and indispensable in analogue repeaters anywhere on the lines spanning maybe thousands of kilometers. 

This type of circuit can discriminate between the signal coming from the line, and what your set tries to push into the line. It allows you  to blow your voice, without having pain in your own ear. In a classical telephone set this was implemented with a little tapped transformer and a resistor and it even supplied the DC-bias to the legendary carbon-grain microphone.

The proper operation of this circuit requires the line impedance to be within a certain narrow range.

In modern wired electronic telephone sets the fork circuit may be implemented in a different way but still relies on the chacteristic impedance of the line. 

There where analogue repeaters are still used they strongly rely on the characteristic cable impedance. Digital repeaters do the same when they deal with bidirectional signals.

I also apologise that I might have doubted mr. Delétraz to be a technician. With so many words I did doubt however his integrety as a technician, where he refused to take the consequences of  calculations based on very elementary understanding of the technology involved. I have not the slightest doubt that mr. Delétraz is able to do these calculations himself.

And I'm not seeing myself as a "master in the field". I'm just applying the very basic theory and  technology which any electronic technician or engineer can understand and should practise.