Transmission Lines as Applied to Audio

[Cogito]

It took having a DC-coupled device and re-reading an old article in Stereophile that got me thinking about transmission lines. The article was based on audio and I thought that transmission-line theory only applied to RF (or digital). So in the past I took what was published with a "grain of salt." Before re-reading the particular Stereophile article I had months ago changed the 6-ohm output impedance of my DAC to 250-ohms and the load at the preamp end from 100k-ohms to 18k-ohms utilizing an adapter fabricated with XLR connectors with much improved performance. I chose not to modify the input impedance of my pre-amp for the obvious reasons.

Saturday was the day that I decided to waste a set of high-quality XLRs and give it a try with 250-ohms for the load to match the 250-ohm source impedance previously installed. It appears that matching load impedance to the source impedance is not only valid in terms of RF theory but seems valid in audio terms as well by eliminating interconnect issues. Of course you can’t take advantage of this source/load matching mod with capacitive-coupled tube equipment because of severe bass roll-off.

Why 250-ohms? I would not recommend a value lower than 100-ohms, but I happen to have had a cache of 250-ohm precision bobbin resistors that are superior to anything Vishay has on offer especially in terms of series inductance.

I found decades ago that solid-state amplifiers, either pre-amps or the gain blocks in a DAC or phono stage (whether discrete or based on I.C. op-amps or unity gain buffers) do not like cable reactance. Even if the circuit is supposedly designed for it -- such as my Mark Levinson no. 36S DAC with its differential FET-based 6-ohm output impedance. The late Walter Jung demonstrated to me that buffer resistance is needed between the output of a device and the “outside” world. Anytime I installed a buffer there was always improved performance in all parameters that matter for sound reproduction.

Auditioning the results of this mod on Saturday with the matched impedance (DAC to pre-Amp -- 250-ohms source/250-ohms load) offered new benefits besides improved transparency, fine detail and sweetness (breath of life) over what I was getting before -- the sound got BIGGER and more enveloping. I expected a change – even hopefully an improvement – but the extent of the improvement was much greater than what I expected. WOW!

This mod relies on an output stage that can drive a 100 to 250-ohm load (it does require a certain amount of current) and it relies on an enough gain of the piece of kit next in line. This mod in essence is an aggressive voltage divider. With those required capabilities one is rewarded with much improved sound reproduction.

Walt,

By increasing the output independence of DAC and reducing the input impedance of Pre-Amp, are you not loosing significant amount of gain?

[SoundMods]

Walt,

By increasing the output independence of DAC and reducing the input impedance of Pre-Amp, are you not loosing significant amount of gain?[/quote]


Granted the change created an aggressive voltage divider, but the no. 36S has a strong output stage and seems to take it stride -- plus my BAT pre-amp has plenty of gain.

So far (knock on wood) the reproduction is much more relaxed, open, and "BIG." It has been a cool experience having the music leave the speakers and envelope me.

I am not talking about so-called "audiophile" productions either. Live event recordings such as in a night club are really cool. It was well worth the effort.

One recording I have there were voices that I hadn't noticed before behind me on the right -- I thought my wife was trying to ask me a question -- IT WAS IN THE RECORDING! WTF?!

[J-ROB]

As David mentioned, the characteristic impedance has nothing to do with distance. The cable looks like an infinite number of series inductances paralleled by an infinite number of capacitances. No many how many you cut off the combination of each inductor and capacitor still yields the same impedance. What does change with length is attenuation of the signal.

I was referring to transmission lines. We can discuss transmission lines when the cable is a length that is significant in terms of wavelength, such that the wave nature of the AC signal becomes apparent. Voltage and current, hence impedance will vary at different distances along the line. The length of the line becomes significant for impedance matching considerations.

There is more going on than varying attenuation with changes in length, in other words,

A half wave transmission line is a step up transformer, so a 50 ohm nominal load is transformed to 3000 or so ohms at the end of the half wave section.

Now an electrical wavelength at 20hz, assuming that the propagation through the wire is at the speed of light is 186,000 mi/20 or 9300 miles.

Multiply by maybe 0.8 to account for the velocity factor of the wire and make it 7440 miles of speaker wire.

That's for one channel, of course.

If you cut that wire the impedance will no longer be 8 ohms @20hz at the amplifier end. In fact, it will only be 8 ohms with the entire wavelength of cable.

And for any other frequency, the wire wil no longer be a full wavelength, so you will have to calculate the complex impedance of the speaker at each frequency and then look at the impedance transformation characteristics of the line....unless we only want to listen to 20hz tones.

To counter resistive losses, better make sure that the wire is #0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 gauge OFC, although 5N silver would be preferable in terms of detail and silvery highs.

Also, don't forget, it is usually a good idea to bi-wire!


The question of characteristic impedance is a somewhat separate issue,. I suppose you could look for reflection with a pulse reflectometer and find a configuration that will minimize reflections at 8 ohms. Too bad most speakers will only be 8 ohms at one point, if that, otherwise there will be reflections. And you will need a few thousand miles of it to make a transmission line for AF.

Speakers won't have a resistive impedance, except for David's weird Polks, so you will have to take the ratio of capacitive to inductive reactances into account. But since that will vary with frequency, things become very tricky indeed.

The transmission line concept doesn't seem to have any relevance for audio frequency, thank god! I'm not sure that controlled impedance cable do either, but it may seem a good marketing ploy to some. If one could sell a 15000 thousand miles of high end cable at a time, we're talking some serious bank!

[Cogito]

I was referring to transmission lines. We can discuss transmission lines when the cable is a length that is significant in terms of wavelength, such that the wave nature of the AC signal becomes apparent. Voltage and current, hence impedance will vary at different distances along the line. The length of the line becomes significant for impedance matching considerations.

There is more going on than varying attenuation with changes in length, in other words,

A half wave transmission line is a step up transformer, so a 50 ohm nominal load is transformed to 3000 or so ohms at the end of the half wave section.

Now an electrical wavelength at 20hz, assuming that the propagation through the wire is at the speed of light is 186,000 mi/20 or 9300 miles.

Multiply by maybe 0.8 to account for the velocity factor of the wire and make it 7440 miles of speaker wire.

That's for one channel, of course.

If you cut that wire the impedance will no longer be 8 ohms @20hz at the amplifier end. In fact, it will only be 8 ohms with the entire wavelength of cable.

And for any other frequency, the wire wil no longer be a full wavelength, so you will have to calculate the complex impedance of the speaker at each frequency and then look at the impedance transformation characteristics of the line....unless we only want to listen to 20hz tones.

To counter resistive losses, better make sure that the wire is #0000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 gauge OFC, although 5N silver would be preferable in terms of detail and silvery highs.

Also, don't forget, it is usually a good idea to bi-wire!


The question of characteristic impedance is a somewhat separate issue,. I suppose you could look for reflection with a pulse reflectometer and find a configuration that will minimize reflections at 8 ohms. Too bad most speakers will only be 8 ohms at one point, if that, otherwise there will be reflections. And you will need a few thousand miles of it to make a transmission line for AF.

Speakers won't have a resistive impedance, except for David's weird Polks, so you will have to take the ratio of capacitive to inductive reactances into account. But since that will vary with frequency, things become very tricky indeed.

The transmission line concept doesn't seem to have any relevance for audio frequency, thank god! I'm not sure that controlled impedance cable do either, but it may seem a good marketing ploy to some. If one could sell a 15000 thousand miles of high end cable at a time, we're talking some serious bank!

Joe,

You are talking about propagation of pure sine waves. Audio signals are not pure sine waves.

What are the transmission line effects and how do they apply to audio frequencies? I can gather this which seems very relevant to audio.

As a mental shortcut, so as not having to analyze the harmonic components of a signal, compare the rise time of the signal to the propagation delay. If the rise time is less than twice the propagation delay, transmission line effects must be considered. So if the propagation delay of a wire or trace is 5ns, then any signal with a rise time of less than 10ns will be affected due to transmission line effects.

https://www.allaboutcircuits.com/techni ... sion-line/

Lets look at a simple application of addition of three sine wave frequencies. Its not hard to imagine where harmonics will create a waveform whose propagation delay is less than the twice the rise time.

IOW, transmission lines might help preserve the harmonics and dynamics. How they do it, is beyond me. Maybe, David will chime in.

[J-ROB]

,

You are talking about propagation of pure sine waves. Audio signals are not pure sine waves

Well, I am talking about single frequency RF waves, although they can be modulated in ways that will no longer resemble a simple sine wave.

Well, there is frequency modulation in which the frequency is varied over a relatively constrained bandwidth, 15kc-1mc deviation typical. However, it would take a very high Q antenna system for this deviation to matter very much in a real world transmission line situation

Once you add the wide range of audio frequencies in a complex wave format, the situation becomes far more complicated if there are frequency sensitive aspects to the line, obviously.

Still, I am not sure that I would call the phenomenon you discuss "transmission line effects." I'd count that as non linear frequency transmission behavior.

What little I know about this stuff I learned in ham radio, but I think I understand enough to see profound obstacles to considering AF wiring as transmission lines, per se.

By the way, 5nS delay in a wire where propagation equals the speed of light would be like 5 feet of conductor

Presuming there is some velocity factor effect at AF, this would in practice be even shorter.

We might have bigger problems than most of us realize.

[Cogito]

By the way, 5nS delay in a wire where propagation equals the speed of light would be like 5 feet of conductor

that assumes the entire wavelength must be contained within the length of the conductor. The horns on the side of my head (ears) are at most 2", yet they work perfectly well with 56 feet wavelength wave (20Hz). Length of the conductor by itself (assuming no transmission losses) is not important.

As I read it, the 1:2 ratio of propagation time vs raise time is important. Since the rise happens in only one direction at a time, wave velocity should be at least twice as fast as the rise, otherwise, the peaks will be distorted resulting in the harmonic distortion. This is more of a factor for radio frequencies where the propagation delays are extremely tiny, but it might apply to audio frequencies also where the high order of harmonics are present like Piano, or very busy and dynamic music.

[SoundMods]

The author of the article that inspired me do what I did used a dual-trace scope and square waves. Different connection schemes illustrated what was going on by virtue of the scope images that clearly showed echoes, ringing, and/or roll-off.

The article was authored by a Swiss national -- Herve' Dele'traz -- and published in the Stereophile Magazine on November 2001 (Vol.24, No.11). He also crunched the numbers for those math-wiz types.

[J-ROB]

By the way, 5nS delay in a wire where propagation equals the speed of light would be like 5 feet of conductor

that assumes the entire wavelength must be contained within the length of the conductor. The horns on the side of my head (ears) are at most 2", yet they work perfectly well with 56 feet wavelength wave (20Hz). Length of the conductor by itself (assuming no transmission losses) is not important.

I calculated the distance light travels in 5nS. That would be the length of a wire with 5nS propagation delay, minus velocity factor effects, if any.

Can't confuse acoustic wavelength with electrical wavelength here! Electricity moves much faster than sound in air.

You comments about fitting the whole wave in a conductor is exactly what transmission lines are about! The wire has to be long enough that the effects of the wave nature of the signal become apparent.

Hence, if you don't have the Goertz 7500 mile pair, or worse yet half that length, you don't have to worry about transmission lines!

As I see it, your discussion is about lumped reactances in cables, not transmission line behavior.

[dberning]

You guys are missing my point. I am concerned about whether ultrasonic reflected stuff can affect the way the circuits are working.

David

[SoundMods]

You guys are missing my point. I am concerned about whether ultrasonic reflected stuff can affect the way the circuits are working.

David

And this surprises you?