1. SCIENCE AT WORK, PERCEPTION AT PLAY
To the continuing frustration of mainstream electrical engineers and pragmatic curmudgeons alike, high-end audio cables remain a multi-million dollar industry. Fueling the controversy is the apparent irrelevance of standard transmission-line parameters, particularly, the "first order" effects of the LRC values of cables since they are virtually meaningless at audio frequencies, and especially for the relatively short lengths of cables used in a high end audio system.
In order to argue that the affects of different cables are indeed perceptible to a keen listener, it is necessary to make a few small leaps of faith, all which have a solid basis in fact: The first is that a keen and experienced listener can hear much less than the minimum, half power point, the 3dB convention and down to as low as perhaps one tenth of a dB. This was proposed by Fletcher and Munson nearly 50 years ago. The second is that the audible, albeit subtle sonic effects of different cables are an indirect result of other phenomenon such as the contributions of ultra-sonic frequencies, including harmonics, on the envelope of audio waveform. It is likely that audiophiles are actually responding to very subtle phase shift effects that begin to show up in the upper reaches of audio well before gross frequency attention appears in actual measurements. In this light, by extending the audible limit of the audio spectrum to at least 100KHz and perhaps as high as half a Megacycle, things can begin to make some scientific sense.
Our precious music is electronically encoded in the form of a rapidly varying voltage over time, which would ideally be indistinguishable from the same pattern with which the original acoustic event modulated air molecules to produce sound. This voltage produces an electromagnetic wave that propagates through a conductive metal (wires) and causes the displacement of a shared surface cloud of electrons. People often speak of the movement of electrons (which is current) as the signal, which isn't quite right. In fact, the velocity of the signal is much faster (close to light speed) than the speed at which the electrons move. The fact that the signal does not travel at light speed is ultimately due to the reactive damping effects of the cable. The wave really travels through the conductor, displacing electrons much the way a wave, which is a non-physical entity (energy), travels through water. However, this is still an over-simplification as the exact details of signal propagation remain an enigma with no universally agreed upon complete explanation for the phenomenon. The true behavior is probably best explained by an interaction of both particle (matter) and wave (energy) properties similar to that of light conduction.
Most of the forces at work to counter the propagation of AC current (the signal) an audio cable are the result of the electric fields that form in and around conductors, and fall under the heading of proximity effects. Capacitance is a function of voltage therefore electrostatic in nature, and inductance a function of current, and therefore electromagnetic.
The distinction between the skin effect and self inductance may be a subtle to some, but not to those that truly understand the implications of the phenomenon. Contrary to the superficial propaganda parroted by the majority of the high end audio cable industry, the skin effect by itself is only relevant to very high radio frequencies (well beyond audio) and the all-too-often heard statement that "the high audio frequencies ride on the edge of the wire" is completely wrong. Only very high radio frequencies (Mhz) ride on the edge of a conductor. Therefore the "skin effect" has very different implications for the complex audio signal which consists of "bundles" of multi-frequency information spanning a very large range than it does for simple RF (radio frequency) carrier signals.
It is really the ORIGIN of the skin effect, self-inductance, not the skin effect itself, that can produce the group delay that is relevant to audio. The significance of self inductance to the audio signal is a gradient of differential resistance which has the potential to attenuate the power of the individual components of these multi-frequency "bundles" and thus introduce slight time delay's relative to each other. Otherwise, the end result of self-inductance, the "skin effect", is simply a rising DC resistance to rising frequency such that at highest frequencies (way up into the Megacycle range) DC resistance becomes so high (due to such a minute portion of conductive area available) that it becomes very significant and should be factored into impedance calculations to find the true impedance (resistance to alternating current). Normally, DC resistance of the conductor itself is dropped out of the equation for impedance for the "low to mid RF" range and is not a factor except for at AUDIO frequencies and very high Radio Frequencies.
The reason higher frequencies are continually pushed out from the center of the conductor to their ride depth (the "skin" of the wire) is due to a force, the changing magnetic field, which is produced by the rapidly fluctuating AC current. This force is a result of self-inductance which is a phenomenon resulting in the opposition to a change in direction of a signal (AC) due to locally circulating "eddy currents." Therefore, the deeper the frequency penetrates, the more it is damped, until it reaches an energetic equilibrium, which becomes its depth of penetration or "ride depth". This is analogous to the way quicker temperature changes penetrate a shorter distance into thermal-conductors than slower ones per unit of time.
This "skin depth" is often decided on from a common formula; (depth of penetration=1/sq root (frequency*pi*magnetic permeability*conductivity) to calculate the depth to which, for example, a 20K frequency will penetrate. From this formula one might mistakenly conclude that we only need to use a conductor whose radius is smaller than the depth of penetration of the highest frequency in audio (20 khz). Also, from this formula it is evident that Silver wires actually have an even shorter depth of penetration necessitating even smaller conductors than copper! This is because of the different conductive characteristics of Silver.
What is overlooked is how the depth of penetration formula was derived. In today's convenient formula based engineering world, there are many assumptions "built in" to all standard formulas, such as the 3dB, half power point in capacitance/resonance formulas. To calculate to what depth a given frequency penetrates is a function of to what degree the frequency is attenuated since it is a continuously increasing effect. The above formula actually yields the 1/e depth to which a frequency penetrates before it is damped to a 64% power loss which relates the shoulder of a sigmoid curve and thus normally a fair point to base further calculations on. We may calculate, if we want, the distance a 20Khz wave would penetrate before it is 99% damped which as you might expect, is greater. If however, we calculate the distance it can travel before it is only 1% damped, for instance, we find it is much shorter and well within the smallest conductor size used in virtually any audio cable! This formula is very conservative when applied to audio because it and others were originally derived for application in radio communication electronics where the skin effect is a vastly more serious problem due to the much higher frequencies (Mhertz and up to GHz) involved. Why should we allow any damping which is (in principle at least) a source of phase distortion when we can minimize it so easily by simply discarding with the ever present and almost universally untrue "bigger is better" "phalacy" (pun intended)?
In the light of all this, the sensible choice is simply to use conductors that are as small as possible to keep this gradient of differential resistance as short as possible which is why Silver Audio has always used multiple, very small, individually insulated conductors (the popular "Litz" concept) in place of one larger one. This is one of the two reasons we use two or more runs of the smallest feasible gauge pure Silver conductors in all our designs.
Several high end audio cable companies have created a unique marketing niche by using flat ribbon (usually just rectangular) shaped conductors as a way of combating the "skin effect" due to their thinner dimensions and supposedly reduced flux density at the center of the conductor. While this is more or less a valid concept, it is always propped up as being superior to ANY round conductor which is completely false. Of the few companies that attempt to bring science to their defense, ALL seem to have borrowed the same results from a misleading and very unfair comparison some years ago of ridiculously large diameter round conductors against very thin flat conductors when plotting DC resistance against frequency. IF these results were real, this simple but otherwise clever experiment does illustrate what mathematics proved over half a century ago, which is that higher frequencies encounter greater resistance compared to lower ones since they penetrate into a conductor less and less with increasing frequency. However, this particular "proof" of the superiority of flat conductors is misleading since the effect can only be demonstrated with a huge gauge round wire that is so thick that the difference in depth of penetration of a 20k vs. 20 cycle tone is significant enough to measure. The point is that very thin round conductors ( Silver Audio's specialty) compared to thicker flat conductors, would easily have the opposite result! Therefore, the decreased flux gradient of a flat vs. round conductor is at best, only valid when comparing equivalent gauge flat and round conductors. What make more sense and has MUCH more relevance to the skin effect as the AC phenomenon that it is, is to compare self-inductance between conductor types, and the trend is simple: Self inductance and thus the gradient of differential resistance, shrinks linearly with decreasing conductor cross sectional area down to a point where structural feasibility and the limits of measuring abilities end.
Silver Audio does not use flat conductors since they have major limitations in forming the complicated cable geometry's we use, and we feel they simply are not unconditionally superior to thin round conductors anyway. We also feel there is some question about the implications of a non-symmetrical flux gradient from the edge to center of a rectangular shape given the 3 dimensional, circular shape of the actual wave. Flat conductors can typically can only be arranged as all parallel, or with only a slight twist, or worse, in a very non-uniform bundle, but never in a rigidly symmetrical criss-crossed geometry that is especially important for a balanced cable to ensure that common mode noise rejection at the receiver is not compromised. They also cannot be arranged in the tight packed orientation necessary to drive mutual inductance down to very low levels, which is a key requirement for top performing speaker cables. Lastly, using very thin conductors of ANY shape while failing to achieve a sufficient aggregate gauge results in DC resistance high enough to slightly attenuate very low frequencies. This is the stumbling point of the all too many cables that tout "ultra thin" as their primary accomplishment.
Capacitance is an energy storage phenomenon that is put to use in an audio circuit by separating a positive and negative charge between an insulator. Audio cables are prone to this phenomenon which also has the curious property of producing energy loss in the higher (audio) frequencies (depending on the total value of capacitance). Electrical energy in the form of a charge is stored in the dielectric (insulating material) and released quickly back into the signal path as the signal changes polarity. The phenomenon is used (along with inductors) intentionally in speaker crossovers for instance to divide different frequencies to different drivers, i.e. highs to the tweeter. The problem is this stored charge is released somewhat out of phase (slightly time delayed) to the main signal which is another small source of distortion. This is why no high-end audio pre-amplifier uses tone controls and also why higher order (i.e. forth order) capacitor-based crossovers filters are generally avoided.
The closer the proximity of and the more parallel the two "plates" as they are called in text books, wires in our case, the higher the capacitance. There are several simple solutions to minimize this problem; separate the conductors in space, and again use very small gauge wire since "plate" surface area is also part of the equation for capacitance. Notice length also adds to plate surface area, which is why excessively long cable runs are to be avoided. It is not practical to separate the positive and negative conductors so far that field effects are non existent since this will severely compromise the cables "self-shielding" capabilities. More importantly, this can upset the dynamic interaction between mutual inductance and self inductance, and allow self inductance to become very large.
To our alternating current, capacitance is actually a type of resistance since it opposes voltage changes. The degree of energy storage and subsequent time-delay relates to the "propagation velocity" inherent to different types of dielectrics and is expressed as the dielectric constant. This is of some interest since it is quite possible to have two identical values of capacitance as measured in Farads, but with very different values of propagation delay. Propagation delay is only directly relevant to very high radio frequencies but again, indirect effects of different responses to ultra-sonic frequencies on audio is the issue. In the introduction, it was suggested that if anything, it is subtle phase changes, not gross frequency attenuation of capacitance that keen listeners are responding too. Recall that the line level musical signal is mostly just rapidly fluctuating voltage. Transient information refers to the initial portion of this very rapidly changing information (particularly the slope of the change over time) and is a crucial aspect of realistic playback hence the slew rate of an amplifier; the speed with which it can deliver voltage changes in response to changes in signal voltage. For these reasons, it should be no surprise that capacitance whose first order effect only attenuates frequencies beyond the audio range (20khz) could be relevant to audio.
Inductance can also be also thought of as a type of resistance since it opposes changes in current direction and/or magnitude. When a signal changes direction or magnitude as it does in our interconnect cables, self-inductance tries to resist this change which is the origin of the skin effect. Conductor size is a crucial component of self-inductance. As mentioned in the previous section, there is a dynamic interaction between mutual and self inductance. In particular, under the right orientation, mutual inductance can partially oppose self inductance. Silver Audio considers this an important and completely overlooked aspect of cable design, and has some relevance in the context of speaker cables.
Mutual inductance refers to one conductor's effect on the other and is also Electro-magnetic in nature, a function of current. The current moving in one conductor produces an electromagnetic field that tries to couple with and produce current flow in the opposite direction in the other conductor. This is the principle behind the electric motor hence the term EMF (electromotive force). Here, geometry becomes important. Steep angle crossing of opposite polarity conductors is the best way to weaken this coupling effect when that is desired.
Inductance is considered less of an issue with the line level signal than with speaker cables since the voltage to current ratio is much higher. This is also because the typical values of inductance of an interconnect are much lower in magnitude compared with typical capacitance values when compared to the values of inductance and capacitance used in a tone network that DEFINITELY make a pronounced difference.
Technicalities aside for the moment, properly designed Silver audio cables are found supremely pleasing for their lush, vivid, and above all, natural presentation. Pure Silver wiring harnesses and even transformers are the choice of many cost no object amplifiers and loudspeakers. However, just because Silver is used as a conductor does not, unfortunately, make a cable a good performer. As explained earlier, Silver is more prone to phase shift than copper due to its greater potential for group delay as a result of its different magnetic permeability and ironically, its greater conductivity. Therefore, it is crucial to use even thinner conductors than one would with copper to nullify this limitation.
An important benefit to the use of Silver is freedom from the diode-like, energy storing and distortion producing effects of its oxide (compression and other non-linear effects). This is because Silver Oxide itself is such a superior conductor. Copper Oxide on the other hand, is a semi conductor, a material a rectifier could be made of! Copper Oxide occurs at the molecular level and is the reason behind the fanatical effort expended to attempt to make "OFC" (oxygen free copper) which is not 100% possible. Copper Oxide only gets worse with age especially with repeated bending and twisting.
Because of DC and AC resistance, the "sound" of a cable is really defined by how it alters the interaction between the source and load components. AC resistance (impedance) is the result of both capacitive and inductive effects (reactance) and is far more relevant than DC resistance however. AC resistance is perhaps the main source of the "voodoo" of audio cables since a given cable design will in principle cause different audio equipment to "behave" differently due to the substantial variation in both input and output impedance's of preamplifiers, power amplifiers, and front end units.
The "voodoo" reputation of audio cables is worsened by the apparent irrelevance of typical steady state measurements. Educated "cable cynics" are fond of pointing out that calculated frequency effects (3db down!) of the capacitative and inductive values of any normal audio cable at normal lengths are much higher than any audible frequency. This simplistic argument implies that that such delicate, complex and highly variable sonic qualities affected by different audio cables (or amplifiers for that matter) such as sound stage depth, image focus and ambience could be completely explained by simple frequency attenuation. Indeed persistent attempts by solid state designers to clone the very unique manner in which vacuum tubes affect the audio signal by using simple tone networks have always been a laughable and dismal failure. While the "first order" effects of LC influenced frequency attenuation are well characterized, indirect effects of their time delay components on our perception of the more subtle aspects of playback are not. One or two degrees of phase shift can be calculated in the audio band from capacitance whose frequency attenuation is well into the ultra-sonic regions. Exactly what one degree of phase shift and perhaps one tenth of a dB of attenuation may sound like is not known and is probably very unpredictable and extremely dependant on the particular source material. Such small effects could not normally be seen since they would be hidden in the noise floor of measuring equipment. Instead actual their existence can only be suggested mathematically.
The fact that different audio cables do affect system performance differently would be especially challenging to defend if all audio cables had identical LC measurements. Luckily, this is not the case, as different interconnect and speaker cable designs result in easily measurable variations in capacitance and inductance respectively. Aside from the resulting differences in phase shift by degree, placed into the big picture of impedance, seemingly modest differences in LC measurements calculate to substantial differences in impedance (frequency variant) and characteristic impedance (frequency invariant) especially with speaker cables. Measurable differences in amplifier damping (which produces a rainbow sonic aberrations to the listener) have been easily demonstrated with different speaker cable designs, all of whose direct effects on frequency response alone should have been inconsequential! Furthermore, with the exception of digital cables, no audio interconnect or speaker cable can be terminated in their exact characteristic impedance, a condition that theoretically results in 100% power transfer (zero power loss). Therefore, all audio cables create some degree, though very slight, of so called "mismatch reflections" between source and load. It is then reasonable to assume that audio cable designs that happen to come closer to an ideal impedance should in principle reduce these distortions.
Other possible reasons are the effects of inter-modulation distortions caused by varying susceptibilities of different cable designs to low frequency interference and the nature of unique "beat frequencies" generated when higher frequencies react against lower ones (heterodyning). The former is strongly a function of geometry since conventional shielding alone cannot block very low frequency EMI. The latter is especially appealing since most exotic audio cables measure differently enough that their response to ultra-sonic frequencies (generated as harmonics of amplification stages themselves) would vary substantially as well.
When the complexity of each of these phenomenon's alone are considered against the staggering complexity of a real musical signal at the "quantum level", it is clear we are a long way from being able to truly understand the electronic behavior of any audio equipment under "real life" conditions. Thus the effects of high performance audio cables remain among the purest demonstrations of the limitations of the study natural science; which is the disparity between the naturally occurring phenomenon and the measured, simulated version of reality.
Max J Kreifeldt