here's some research on how electricity really works... things like the skin effect, and fun stuff like that. This battle over cable designs within the audio realm makes me laugh out loud sometimes...
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kindepth, Litz wire, Braided conductors, and resistance Transmission Line Theory Skin effect
Here's some more trivia for your sunday reading....
What Makes a Good Audio Cable?
Criteria for what supposedly made one cable perform better or worse than another is remarkably inconsistent. One manufacturer's claims countered and negated the claims made by a different manufacturer. None of the manufacturers offer documented, measurable evidence that it was producing a superior cable. Instead, we find claims of allegedly superior components or materials used in cable construction. For example, a few leading manufacturers claimed that the most important factor for a cable was low capacitance, using the justification that cable capacitance shunts upper frequencies to ground. In order to lower the capacitance, these companies increased conductor spacing to simultaneously achieve a goal of increased inductance. This approach had drastic side effects, however. Merely decreasing capacitance without taking other realities of signal transmission into consideration increased the noise pickup and introduced a blocking filter. Both of these effects would obviously degrade sonic performance rather than improving it.
Another cable manufacturer advertised that its cable "employs two polymer shafts to dampen conductor resistance", but offered no evidence to prove it. Still another audiophile company claimed that because its cable was flat, "with no twist, it has no inductance". In general, inductance can indeed be reduced by making conductors larger or bringing them closer together. However, physics shows that, in reality, no cable can be built without some level of inductance, so this claim is without scientific merit.
Cylindrical Cable Conductors and Skin Effect
Most of the popular loudspeaker and musical instrument cables on the market employ cylindrical (a.k.a. round-diameter) cables as conductors. Unfortunately, cylindrical cable designs have a number of serious drawbacks, including current bunching, skin effect phenomenon, and frequency effects that lower the performance of the cable.
It's a common misconception to think about electrical transmission in cables in terms of direct current (DC) alone. Even experienced electrical engineers frequently ignore the ramifications of frequency on cable performance. In the case of DC, current is indeed uniformly distributed across the entire cross-section of the wire conductor, and the resistance is a simple function of the cross-sectional area. Adding the frequency of an electrical signal to the equation complicates the situation, however. As frequency increases, the resistance of a conductor also increases due to skin effect.
Skin effect describes a condition in which, due to the magnetic fields produced by current following through a conductor, the current tends to concentrate near the conductor surface. As the frequency increases, more of the current is concentrated closer to the surface. This effectively decreases the cross-section through which the current flows, and therefore increases the effective resistance. The current can be assumed to concentrate in an annulus at the wire surface at a thickness equal to the skin depth. For copper wire the skin depth vs. frequency is as follows:
60 Hz = 8.5 mm, 1kHz =2.09 mm, 10 kHz =0.66 mm, 100 kHz =0.21 mm.
Note that the skin depth becomes very small as the frequency increases. Consequently, the center area of the wire is to a large extent bypassed by the signal as the frequency increases. In other words, most of the conductor material effectively goes to waste since little of it is used to transmit the signal. The result is a loss of cable performance that can be measured as well as heard.
Current Bunching
Current bunching (also called proximity effect) occurs in the majority of cables on the market that follow the conventional cylindrical two-conductor design (i.e., two cylindrical conductors placed side-by-side and separated by a dielectric).
When a pair of these cylindrical conductors supplies current to a load, the return current (flowing away from the load) tends to flow as closely as possible to the supply current (flowing toward the load). As the frequency increases, the return current decreases its distance from the supply current in an attempt to minimize the loop area. Current flow will therefore not be uniform at high frequencies, but will tend to bunch-in. The current bunching phenomenon causes the resistance of the wires to increase as frequency increases, since less and less of the wire is being used to transmit current. The resistance of the wire is related to its cross-sectional area, and as the frequency increases, the effective cross-sectional area of the wires decreases. In order to convey the widest frequency audio signal to a loudspeaker, you want to use as much of the conductor cross-section as possible, so excessive current bunching is extremely inefficient.
Disadvantages of Rectangular Conductors
As a means of bypassing the skin effect and current bunching problems associated with cylindrical conductor designs, some cable manufacturers have developed rectangular conductors as an alternative. These designs typically use a one-piece, solid core conductor. Computer simulation showing the magnitude (volts/meter) of the electric field between two solid rectangular conductors. The conductors have a cross section area equivalent to a 10 gauge conductor. The spacing between the two conductors is 2mm with a voltage of +1 volt applied to the top conductor and -1 volt applied to the bottom conductor.
Computer simulation showing the magnitude (volts/meter) of the electric field between two hollow oval conductors. The conductors have a cross section area equivalent to a 10 gage conductor. The spacing between the two conductors is 2mm with a voltage of +1 volt applied to the top conductor and -1 volt applied to the bottom conductor.
A solid rectangular conductor of this type is undesirable because the sharp corners produce high electric field values that over time can break down the dielectric, causing a failure of the cable. In general, cables with solid conductors are prone to shape distortions and kinking due to their poor flexibility. This becomes an especially important issue with rectangular cable designs. The sharp corners from rectangular conductors tend to chafe the cable dielectric if the cable is repeatedly flexed or put under stress, and this chafing can lead to a short that could conceivably damage your loudspeakers.
Characteristic Impedance Complexity
Another parameter that is critical in cable design is characteristic impedance. But because of its complexity, this important factor is often misunderstood.
The characteristic impedance of a cable is given by Z = [(R + jwL)/(G + jwC)]1/2 where R is the series resistance, L is the series inductance, G is the shunt conductance, C is the shunt capacitance, and w is the angular frequency (w = 2pief).
Note that this is not a simple number for a cable, but one which changes with frequency. It is also important to note that R, L, G, and C also change with frequency, making the impedance of a cable even more frequency dependent.
milli-ohm/loop 100 ft . Z is a complex number, and it is common practice in the cable industry to simplify the situation by assuming a loss less transmission line and, in turn, assuming that R and G are zero. While this may be a valid approximation at high frequencies, it is not valid at low audio frequencies if you plan to construct an accurate model of a cable.
For example, stating that a speaker cable has a constant, characteristic impedance of 10 ohms across the entire frequency range of 20 to 20,000 Hz is a drastic oversimplification that, in the end, is simply untrue. The same type of statement is also inaccurate when applied to loudspeakers, as the table below shows. A speaker only has a constant impedance of 8 ohms at a single fixed frequency. To state otherwise is to ignore the complexity of impedance changes as signal frequency changes.
Frequency Blurring
To minimize frequency blurring, it is important that the speaker cable parameters do not change with frequency. Ideally, the resistance and inductance would remain constant as the frequency of the signal changes.
The faintest sound wave a normal human ear can hear is 10(-12) Wm(-2). At the other extreme of the spectrum, the threshold of pain is 1 Wm(-2). This is a very impressive auditory range. The ear, together with the brain, constantly performs amazing feats of sound processing that our fastest and most powerful computers cannot even approach.
As long ago as 1935 Wilska 2 succeeded in measuring the magnitude of movement of the eardrum at the threshold of audio sensitivity across various frequencies. At 3,000 Hz, it takes a minimal amount of eardrum displacement (somewhat less than 10-9 cm or about 0.01 times the diameter of an atom of hydrogen) to produce a minimal perceptible sound. This is an amazingly small number! The extremely small amount of acoustic pressure necessary to produce the threshold sensation of sound brings up an interesting question. Does the limiting factor in hearing minimal level sounds lie in the anatomy and physiology of hearing or in the physical properties of air as a transmitting medium? We know that air molecules are in constant random motion, a motion related to temperature. This phenomenon is known as Brownian movement and produces a spectrum of thermal-acoustic noise.
In 1933, Sivian and White3 experimentally evaluated the pressure magnitudes of these thermal sounds between 1kHz and 6 kHz. They observed that throughout the measured spectrum the root-mean-square thermal noise pressure was about 86 decibels below one dyne per square centimeter. The minimum root-mean-square pressure that can produce audible sensation between 1 kHz and 6 kHz in a human being with average hearing is about 76 decibels below one dyne per square centimeter, but in some people with exceptionally acute hearing may approach 85 decibels. These figures indicate that the acuity of persons possessing a high sensitivity of hearing closely approaches the thermal noise level, and a particularly good auditory system actually does approach this level. Furthermore, it is not likely that animals possess greater acuity of hearing in this spectrum, as their hearing would also be limited by thermal noise.
References
1 Henry W. Ott, Noise Reduction Techniques in Electronics System (New York, NY John Wiley and Sons, 1988, p. 150)
2 Wilska, A.: Eine methode zur Bestimmung der Horschwellenamplituden des Trommelfells bei verschiedenen Frequenzen, Skandinav. Arch. Physiol., 72:161, 1935.
3 Sivian, L.J., and White, S.D.: On minimum audible sound fields, J. Acous. Soc. Am., 4:288, 1933
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