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Cable Esoterica Note - 1st cut

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Audio Cable Esoterica
12-3-99 by Jon M. Risch

Characteristic Impedance vs. Frequency
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Most conventional wisdom has it that characteristic impedance is of absolutely no concern for audio frequencies, because the length of the cable is not such that it is a significant portion of the signal wavelength. This may indeed be the case, but again, this conventional wisdom is based on RF experience, and may not be wholly relevant to audio and it's very wide dynamic range. Then there is also some evidence that short lengths of cable might have more problems with termination issues than conventional wisdom allows for. See: ELANTEC Aplication Note #9, "Driving Reactive Loads with High Frequency Op-Amps". , Fig 1.1 , 1.2, and 1.3.
This shows a five foot unterminated cable showing a Z minimum at approx. 250 kHz, with a maximum somewhere below 150 kHz. An abrupt phase discontinuity at approx. 250 kHz as well, indicating a reflection mode. This is an amazingly low frequency, and is not intuitively obvious. Does provide some food for thought.

With RF, all you are worried about is signals that range down to -46 dB or so at most, while with audio, signals at - 90 dB may influence what we hear.

This premise is based on the results of several different audio artifacts and discernable distortions, one of which is digital audio dither, and the fact that without dither, artifacts at -90 db and below are clearly audible, and even with dither, different types of dither spectrums are audible at -90 dB down. While with the lack of any dither, we are talking about a gross discontinuity at these levels, with the different dither spectrums, we are talking about much more subtle things, essentially the shape of a noise floor at such low levels.

Obviously, if different dither spectrums are audible, with their differences in effect at such low low levels, this indicates that other mechanisms of such low level could also influence perceived sound.

Now with the idea that audio artifacts that are way down may be a problem, cable reflections at audio frequencies may actually be an issue, as the kind of impedance mismatch that occurs at audio frequencies will be of a nature that would only be able to cause reflections of a very low level nature. That is, they would be down much lower in level than those used to working in RF would be concerned about, yet still be of concern for audio dynamics.

How would you go about minimizing such reflections? Well, the classic method used for RF work is to provide a source impedance that is the same as the cable's, and then terminate the signal line in that same characteristic impedance. Most audio components use the voltage source conection method, where the source Z is as low as posible, the input Z is as high as possible, and the cable fends for itself. What this means in practical terms is that the source attempts to muscle the cable and load impedances around just like a power amp does with a load. If it has enough current delivery to overcome the capacitive charge/discharge demands, in addition to the resistive load component, then this approach can be successful.

However, many modern preamps do not have the capability to drive long runs of interconnect. So many of the integrated circuit based preamps will not drive anything but a 1-2M cable with good fidelity. This is because many of the IC's are unstable driving capacitvie loads that exceed several hundred pF. It is not just the output Z and the potential for HF roll off, but a matter of avoiding oscillitory and unstable behavior. Even using low capacitance cables, some preamps would not be capable of driving over 10 feet of interconnect cleanly.

There are several op-amps (when used with the proper topology and designs) that can adeqautely drive more than a few hundred pF. The old standby 5532/34 can do OK, at least it does not completely lose it with a capacitive load. The OPA -2604 can handle a decent amount of capacitance, as can several others. Many of the cheaper op-amps, or super high bandwidth ones may have problems driving UNTERMINATED capacitive loads. The super bandwidth op-amps originally designed for video use need a 75 ohm build-out AND 75 ohm termination in order to operate properly in the face of capacitive loading.

In some cases, it may be possible to insert an additional series output resistor of another hundred ohms or so, and alleviate this instability, without incurring too much in the way of HF roll off problems.

Some of the beefier preamps that have discrete output stages, and resemble a small power amp output (Bryston comes to mind readily), can not only drive a capacitive load that would bring even acceptable IC based preamps to their knees, but can also drive into a fairly low value resistive load.

What is the characteristic impedance of an audio cable? Well, for a twisted pair type of interconect cable it is usually much higher than the rated RF Z at low audio frequencies, around several thousand ohms, which drops to around 400-700 ohms in the midrange, and still around 100-200 ohms at 20 kHz, dropping toward 75 ohms above 500 KHz.

For those interested in a graph depicting this, see:
http://www.belden.com/products/ciocahalf.htm, almost at the end of the article.

It should be obvious, that if we are going to try and match impedance for the cable, that the classic voltage source connection must be modified and rethought.

The source impedance should be some minimum amount, more likely to aid in energy absorption if any reflctions do make there way back from the load, and yet should not be so high as to cause any RC lumped parameter HF roll-offs. A good compromise value might be around 100 to 150 ohms or so. If a given preamp already had a series resistor of approximately this value, it would not be worth taking it out and replacing it for a slight change.

The biggest change would be at the load end. Rather than just place a single low resistive value across the cable, and hence the source, we would want to stagger the loading with frequency, to approximate what the cable itself is doing. In theory, this would minimize any tendency for reflected energy to disturb the audio signal transmission.

This would involve taking the loading of the load itself into account, as many SS amps have an input impedance of around 10Kohms.

If all you want to try is a single simple load resistance for something as hearty as the Bryston, a 600 ohm load resistor should do the trick, for 5532/34 or OPA-2604 based units, a 1K resistor should do the trick. Those units based on video op-amps should respond well to a 75 ohm build-out (series output R), and a 75 ohm termination R at the far end of the cable. Using such low values (75 ohms) would preclude any necessity for a staggered loading scheme.

Some preamps are rated to drive professional loads, and as such are rated to drive 600 ohm loads without any deleterious effects. Often, but not always, this is true of devices designed to output a true balanced output. Each signal polarity (pin 2 and pin 3) would get a load resistor to ground, and they should be well matched resistors, 1% tolerance units from the same batch of resistors (typically matched to each other better than 1%).

This simple single resistor loading of the the input (load end of cable) should greatly reduce the effects of the dielectric. This also brings up the sensitivity somewhat to the cable's conductor purity and materials, but as long as it is bare pure copper or pure silver, this should not be as much of an issue, and the overall situation should be improved. Those with the right gear capable of driving such a demanding load without OTHER sonic penalties, try it out and see what you think.

For those that want to try the staggered load approach, lets analyze this further.

A series output R of about 50 (47 is nominal common parts value) ohms might be the best option, at least at RFI frequencies, the output would be proper for best absorption, and the output Z would not be too high. it helps to realize that many op-amps have a rising output impedance with frequency, and so may add a few ohms to the total at 20 kHz and a few dozen ohms higher up.

This lower value also allows less attenuation due to the staggered loading effects. More about this later.

If we attempt to follow the characteristic Z curve of a typical audio cable, then we might try a set of three staggered RC shunts at the load end. Say 150 ohms with 0.04 uF for the highs, and about 500 ohms with 0.27 uF for the mids, and about 1 kohm with 5 uF for the lows. According to theory, this would greatly reduce any tendency for the audio signal to be reflected back down the cable, perhaps several times, and muddy the sound. The caps would need to be of the highest quality (as would the resistors), and would have an effect on the overall sound.

Unfortunately, there is a side effect that will throw things off a bit. The relatively low R for the highs, coupled with the source R will create a low pass filter voltage divider, one that will have the potential for about a 3 dB roll-off at 20 kHz, and a 1 dB shelf from about 1 kHz. This would obviously create a tonal balance situation that would exceed known limits for audibility due to just the FR variations, and the cable would sound quite warm, perhaps even dark or dull, just due to the FR variations.

We could compensate for this in the output of the source, by creating an equal but opposite FR compensation, a bit of boost to make things come out flat again. This could be acomplished in the output stage or some other portion of the circuitry inside. Then we could listen to just the effects of the staggered impedance compensation. Or a method that would allow use of two staggered compensation cables, would be to include compensation in a source cable loading box for the next stage's cable (say the preamp to power amp connection) by "boosting" the signal to compensate for two loading networks. However, this would still require knowledge of the source impedances involved, and the need to assure the boost and attenuation were totally complementary. The use of such pre-compensation would end up spending about 6 dB of signal strength for a two cable scenario. As you can see, the whole situation has become quite complex, and the need to allow use with industry standard components makes it difficult to address these other issues without special considerations being made and accounted for.

Maybe a single relatively low value loading R is not such a bad idea after all!

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Dielectric constant vs. frequency

More properly called a dielectric coefficient, the multiplier used to show the amplifying effect of the dielectric over the properties of a vacuum (or air). As an aside, it is important to note that this is truly an amplification of the capacitors charge capacity, and as such, the dielectric material is acting as a charge amplifier. Many of the distortions that you can conceive of regarding power amps have their analog in the distorted amplification of the capacitors dielectric coefficient. Why make the distinction between dielectric coefficient and dielectric constant? Because many of the common dielectrics are not constant across the audio band.

For instance, PVC can vary from around 6.3 (or higher) at 100 Hz, down to around 3.5 or 4 at 20 kHz. Polyethylene and teflon are constant across the audio band, at around 2.4 and 2.1 respectively.

Ready for a stunning revealation? The COLOR of the PVC will affect the dielectric coefficient! Black colored PVC is worse than white colored!
When you stop to think about it, the addition of coloring agents to any pure plastic will tend to cause the dielectric proerties to degrade, as the plastics purity has been compromised and altered.

So when certain people try to make light of audio cable construction details and materials concerns, and they start talking about the color of the wire having an effect, well, little do they know how true it is!

The proof for this is at:
http://www.belden.com/products/ciocahalf.htm, about half way down the page.

For more information on how the dielectric in a cable can be a problematic capacitor, see:
http://www.capacitors.com/pickcap/pickcap.htm

and for information on how dielectric absorption can affect signal pulses, see:

http://www.nsc.com/rap/Application/0,1570,28,00.html

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ETP copper vs. OFHC copper

The most common conductor for audio cables is copper. While copper is a fine and cost effective material, it has it's problems. When cast, and drawn through a die, it tends to form more numerous and fragmented crystals, with lesser purity materials incuring more crystal formation. See:
http://microstructure.copper.org/coppers.htm

Note the differences between the OFHC copper, and the ETP coppers (you must take into account the scale factor of the various microphotographs, use a graphics program to resize and place the pictures on an equal footing before judging relative crystal sizes).

Note that the OFHC has crystals that are literally tens of times larger than the ETP copper. This means that there are less boundaries for the signal current to pass through on it's way from one end of the wire to the other.

Some of the audio cable companies make claims for the purity or crystalline structure of their copper, with AudioQuest, TARA and Harmonic Tech being the prime examples.

Harmonic Technologies has microphtographs of OFHC vs. their OCC copper at:
http://www.harmonictech.com/techgraph.htm

Once again, the difference in the size and number of crystal domains is easily seen.

The effect of the signal having to jump many more crystal boundaries would not necessarily show up as a change in the DCR, or even the AC impedance, but might manifest as a grainy sonic signature, one that would be the difference between a completely silent and clear backdrop for the music, and one that was not as clearly defined and obvious.

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Resonances

It might seem that physical resonance of an audio cable would not have any bearing on the signal passing through it. This just goes to show how single-minded some of us have become in our thinking processes. A cable is not an isolated electrical device, with only text-book perfect L, C and R to be concerend with. Nor is it only of concern what the proper model of these far from perfect LCR parameters will do to the signal as it passes through the cable. There are many aspects to be concerned with.

One of those aspects is the physical resonance behavior of the cable. How in the world can that affect the signal? Let's look at some basic physics. There is a basic property of electromagnetic fields, one that allows our generators and motors to function. The basic property is: whenever a conductor is moved through a magnetic field, a current will be generated in that conductor. The converse of that is whenever a current carrying conductor is inside a magnetic field, a physical force is generated on that conductor. These are the basic principles behind motors and generators.

How will these basic properties of electromagnetism affect an audio cable? Well, for one, all audio cables carry some amount of current. In the case of speaker cables, it can be many amps, in the case of interconnects, it will be on the order of milliamps. If the audio signal consisted of a pure DC signal, then there would be no issues to address. However, audio is a constantly changing signal, and the current flow is constantly changing.

What happens when you pass a transient through a speaker cable?
A current pulse is generated, and as the current flows through the speaker cable, a magnetic field is present also. Since the current is changing, the magnetic field is changing also. If we look at a single wire, carrying one half of the audio signal, it will be exposed to varying magnetic fields from it's own current flow, and therefore will have a current generated inside of itself that is related to those magnetic fields. This current is opposite in polarity and a mirror image of the original current. This phenomenon is due to Lenz's law, and can be considered to be the mechanism behind self-inductance.

Since the single wire has the magnetic field it generates centered on itself, the net result is that of no appreciable physical torque or force on the wire. In isolation, the only ill that occurs is an increasing resistance to higher frequencies, due to the self inductance. This a linear effect, and does not assume the proportions of gross signal distortion. While there is loss of high frequencies, in theory, they could be restored via EQ or a complementary response tone control.

The problem occurs because we have two wires that are in close proximity, and they are carrying current in opposite directions. This causes a force to be developed that is pulling the two wires together.

You might think that since the wires are covered in some sort of insulator, and may even be bonded together, or at the least, they are contained within a common jacket, that they would not be able to move at all. This would be true if either of two things were true: if the cables were infinitely heavy, the sheer inertia would prevent them from moving, or if the cable materials were all infinitely rigid, then the two conductors could not move. If you have ever picked up a speaker cable, then the first item is not true, and if you have ever felt a speaker cable, then you know that often, very flexible materials are used in the construction of the cable. For zip cords, soft pliable vinyl is used, and for other constructions, the two wires may not even be twisted around one another, or bonded, such as with Romex.

Hence, even the most esoteric cables have the potential to move in reaction to a musical transient, and to generate a false signal is response to that transient. The false signal will be delayed in time, due to the mass and stiffness of the cable conductors, and the stiffness of the cable insulators, but there will be some minute amount of movement, that will generate a small signal. This is where the cables physical resonance will come into play. If a cable has a tendency to resonate physically, when the cable assembly is excited by a musical transient, it will be as if the cable wires were plucked and the physical resonace will now determine to some extent how the false signal will develop and how long it will continue past the transient. The false signal caused by the relative movement of the cable conductors will definitely have the resonant signature of the cable superimposed upon upon it, and this will further color and make noticable the false signal.

This motor/generator action within the cable is commonly refered to as magnetostriction. This is not exactly correct, as magnetostriction is the change in size of a material itself in response to a magnetic field, but it does describe what is happening within the cable as a system. Several cable companies go to great pains over cable resonance. Kimber uses different sized wire strands in its braided cables, and Cardas has a patent on using different sized wires, in a ratio known as Phi, to spread any tendency for the wires to want to resonate at the same frequency. Some motion or vibration inside the cable is inevitable, so why not make it as harmless as possible? Other cable companies also refer to resonance control or vibration control, with regard to the RCA plugs, the cable itself, or the cable assembly as a whole.

There is also the factor of the sound vibrations from the speakers themselves, moving the cable wires as they carry current. These vibrations are further delayed compared to the delayed vibrations from the signal the cable is carrying, as they had to travel through then air, and at a speed of approx. 1 mS for every 13 inches of travel, the delay is quite a bit greater than that of the physical inertia and resonance of the cable assembly. It is also likely that these false signals will be on the bass heavy side, as it is the bass which will be moving the cables the most, even more so than for the magnetostriction action.

The signals produced by these vibrations and current pulses are not up around the nominal signal level, they are down as much as 60 dB or so. This may sound like these false signals will be too far down to hear, or that they would be masked by the original signal. IF they were all occuring at the exact same time as the original signal, and IF they were ocuring one at a time, then this might be true. However, from my research into multitone test signals, which are more like music with it's complex harmonies and harmonic structures, I have found that when there are many distortion products occuring at the same time, the total amount of distortion is raised considerably. If there are 10 distortion products all at about the same levels, then the total level is 10 dB above the individual distortion products. For 100 products, the overall level is up 20 dB. This raises the effectivity of the motor/generator distortion to levels that are not as low as they might seem initially. The other factor is the amount of time delay, actually two distinct and separate amounts of time delay, that will cause transient signals to have delayed false signals. Once the false signals are not right underneath the original signals in the time domain, they are capable of a much easier exposure in terms of audibility.

So cable resonances are indeed a possible factor, and I think that anyone who has experimented with vibration control can relate to the kinds of improvements that can accrue. It would be relatively easy to place sand bags under and on top of the interconnects and speaker cables in most home systems to give it a listen, and see what you might hear from such an experiment.

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Skin Effect

http://www.csolve.net/~add/system/trcskin.htm

Skin effect is often brought up as a factor in audio cables, and the typical analysis goes something like this: for audio frequencies, skin effect does not affect the conductivity that much, as the resultant increase in total direct cable loop impedance is not that significant. If all we were concerned with was high level amplitude response, then that might be the way to look at skin effect.

It helps to keep in mind that the skin depth of a conductor is NOT absolute, that is, the very definition of the skin depth is the point where the current flow is down to 37% of the total, hence, there is a continuous change between the current density at the surface, and the current density toward the center.

In copper, the skin depth is commonly refered to at 20 kHz as 0.463 mm, and many take this to mean that if you have a 20 gauge wire, with a typical diameter of 0.813 mm, and less than twice this skin depth, that there will be no difference for the current flow for the highs and lows. Obviously, if the skin depth is not absolute, and the depth only refers to a relevant point on the curve of current reduction, then this is a false and misleading concept.

Hence, for a 26 gauge wire, the current flow in the center at 20 Khz will be down to roughly 2/3 that of the surface. While the net effect in terms of ONLY total resistance of the wire at 20 Hz, vs, 20 kHz is not that great, I think the fact that the current is still being pushed out toward the surface, even in such a small wire, is significant. It obviouisly means that surface conditions for the wire are important in terms of cyrstaline integrity, freedom from contaminants, including silver or other platings.

It also means that the phenomenon of strand jumping in stranded wires is a real possibility, and not for just at 20 kHz frequencies either.

AudioQuest makes a point of the theory of strand jumping, where the push of current flow to the outside of a wire bundle and the fact that wires do not stay in a perfectly similar relationship to all the other wires in a bundle, lead to the signal current being forced to jump from one strand to the next as that strand "dives" back into the center of the wire bundle. See: http://www.audioquest.com/theory/theory3.html
It is probable that this occurs, but to what extent and how far down in level are the distortions that are invoked.

Even if the distortions that occur are so far down, say -150 dB from full signal level, then you might not beleive that they can possibly make any difference in the audible quality of the signal. Similar to the cable resonance issues, there would be literally thousands or tens of thousands of occurances of this strand jumping going on, and the total sum power level of this multitude of super low level distortions would be added up to 30-40 dB or even more from that single event -150 dB level. Now we are not so low in absolute level.


Cable References, a non-ABX oriented listing.

Ben Duncan, Loudspeaker cables, Case Proven, Proc. The Institute of Acoustics, UK, Nov '95.
Also published in Studio Sound & Broadcast Engineering (UK); and Stereophile (USA) - both Dec 95.
Ben Duncan, Modelling cable, Electronics World (UK), Feb 96.
Ben Duncan, Measuring speaker cable differences, Electronics World (UK), June/July '96.
Ben Duncan, Black Box (column), Hi-Fi News & Record Review (UK), June & July '96.
Malcolm Omar, Mawksford, The Essex Echo, Hi-Fi News, Aug '85; Aug & Oct '86 & Feb '87. Reprinted in Stereophile.

Jon Risch

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Copyright Jon M. Risch 1999 all rights reserved, except
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Topic - Cable Esoterica Note - 1st cut - Jon Risch 15:45:03 12/03/99 (3)


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