|Posted on February 28, 2010 at 1:01 AM|
Audio Cable Design and other selection information. here'ssome research on how electricity really works... things like the skineffect, and fun stuff like that. This battle over cable designs withinthe audio realm makes me laugh out loud sometimes...
Skindepth, Litz wire, Braided conductors, and resistance
Transmission Line Theory
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 worsethan another is remarkably inconsistent. One manufacturer's claimscountered and negated the claims made by a different manufacturer. Noneof the manufacturers offer documented, measurable evidence that it wasproducing a superior cable. Instead, we find claims of allegedlysuperior components or materials used in cable construction. Forexample, a few leading manufacturers claimed that the most importantfactor for a cable was low capacitance, using the justification thatcable capacitance shunts upper frequencies to ground. In order to lowerthe capacitance, these companies increased conductor spacing tosimultaneously achieve a goal of increased inductance. This approachhad drastic side effects, however. Merely decreasing capacitancewithout taking other realities of signal transmission intoconsideration increased the noise pickup and introduced a blockingfilter. Both of these effects would obviously degrade sonic performancerather than improving it.
Another cable manufacturer advertised that its cable "employs twopolymer shafts to dampen conductor resistance", but offered no evidenceto prove it. Still another audiophile company claimed that because itscable was flat, "with no twist, it has no inductance". In general,inductance can indeed be reduced by making conductors larger orbringing them closer together. However, physics shows that, in reality,no cable can be built without some level of inductance, so this claimis without scientific merit.
Cylindrical Cable Conductors and Skin Effect
Most of the popular loudspeaker and musical instrument cables on themarket employ cylindrical (a.k.a. round-diameter) cables as conductors.Unfortunately, cylindrical cable designs have a number of seriousdrawbacks, including current bunching, skin effect phenomenon, andfrequency effects that lower the performance of the cable.
It's a common misconception to think about electrical transmission incables in terms of direct current (DC) alone. Even experiencedelectrical engineers frequently ignore the ramifications of frequencyon cable performance. In the case of DC, current is indeed uniformlydistributed across the entire cross-section of the wire conductor, andthe resistance is a simple function of the cross-sectional area. Addingthe frequency of an electrical signal to the equation complicates thesituation, however. As frequency increases, the resistance of aconductor also increases due to skin effect.
Skin effect describes a condition in which, due to the magnetic fieldsproduced by current following through a conductor, the current tends toconcentrate near the conductor surface. As the frequency increases,more of the current is concentrated closer to the surface. Thiseffectively decreases the cross-section through which the currentflows, and therefore increases the effective resistance. The currentcan be assumed to concentrate in an annulus at the wire surface at athickness 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 bypassedby the signal as the frequency increases. In other words, most of theconductor material effectively goes to waste since little of it is usedto transmit the signal. The result is a loss of cable performance thatcan be measured as well as heard.
Current bunching (also called proximity effect) occurs in the majorityof cables on the market that follow the conventional cylindricaltwo-conductor design (i.e., two cylindrical conductors placedside-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 asclosely as possible to the supply current (flowing toward the load). Asthe frequency increases, the return current decreases its distance fromthe supply current in an attempt to minimize the loop area. Currentflow will therefore not be uniform at high frequencies, but will tendto bunch-in. The current bunching phenomenon causes the resistance ofthe wires to increase as frequency increases, since less and less ofthe wire is being used to transmit current. The resistance of the wireis related to its cross-sectional area, and as the frequency increases,the effective cross-sectional area of the wires decreases. In order toconvey the widest frequency audio signal to a loudspeaker, you want touse as much of the conductor cross-section as possible, so excessivecurrent bunching is extremely inefficient.
Disadvantages of Rectangular Conductors
As a means of bypassing the skin effect and current bunching problemsassociated with cylindrical conductor designs, some cable manufacturershave developed rectangular conductors as an alternative. These designstypically use a one-piece, solid core conductor. Computer simulationshowing the magnitude (volts/meter) of the electric field between twosolid rectangular conductors. The conductors have a cross section areaequivalent to a 10 gauge conductor. The spacing between the twoconductors is 2mm with a voltage of +1 volt applied to the topconductor and -1 volt applied to the bottom conductor.
Computer simulation showing the magnitude (volts/meter) of the electricfield between two hollow oval conductors. The conductors have a crosssection area equivalent to a 10 gage conductor. The spacing between thetwo conductors is 2mm with a voltage of +1 volt applied to the topconductor and -1 volt applied to the bottom conductor.
A solid rectangular conductor of this type is undesirable because thesharp corners produce high electric field values that over time canbreak down the dielectric, causing a failure of the cable. In general,cables with solid conductors are prone to shape distortions and kinkingdue to their poor flexibility. This becomes an especially importantissue with rectangular cable designs. The sharp corners fromrectangular conductors tend to chafe the cable dielectric if the cableis repeatedly flexed or put under stress, and this chafing can lead toa short that could conceivably damage your loudspeakers.
Characteristic Impedance Complexity
Another parameter that is critical in cable design is characteristicimpedance. But because of its complexity, this important factor isoften 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 theangular frequency (w = 2pief).
Note that this is not a simple number for a cable, but one whichchanges with frequency. It is also important to note that R, L, G, andC also change with frequency, making the impedance of a cable even morefrequency dependent.
milli-ohm/loop 100 ft . Z is a complex number, and it is commonpractice in the cable industry to simplify the situation by assuming aloss less transmission line and, in turn, assuming that R and G arezero. While this may be a valid approximation at high frequencies, itis not valid at low audio frequencies if you plan to construct anaccurate model of a cable.
For example, stating that a speaker cable has a constant,characteristic impedance of 10 ohms across the entire frequency rangeof 20 to 20,000 Hz is a drastic oversimplification that, in the end, issimply untrue. The same type of statement is also inaccurate whenapplied to loudspeakers, as the table below shows. A speaker only has aconstant impedance of 8 ohms at a single fixed frequency. To stateotherwise is to ignore the complexity of impedance changes as signalfrequency changes.
To minimize frequency blurring, it is important that the speaker cableparameters do not change with frequency. Ideally, the resistance andinductance would remain constant as the frequency of the signalchanges.
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 1Wm(-2). This is a very impressive auditory range. The ear, togetherwith the brain, constantly performs amazing feats of sound processingthat our fastest and most powerful computers cannot even approach.
As long ago as 1935 Wilska 2 succeeded in measuring the magnitude ofmovement of the eardrum at the threshold of audio sensitivity acrossvarious frequencies. At 3,000 Hz, it takes a minimal amount of eardrumdisplacement (somewhat less than 10-9 cm or about 0.01 times thediameter of an atom of hydrogen) to produce a minimal perceptiblesound. This is an amazingly small number! The extremely small amount ofacoustic pressure necessary to produce the threshold sensation of soundbrings up an interesting question. Does the limiting factor in hearingminimal level sounds lie in the anatomy and physiology of hearing or inthe physical properties of air as a transmitting medium? We know thatair molecules are in constant random motion, a motion related totemperature. This phenomenon is known as Brownian movement and producesa spectrum of thermal-acoustic noise.
In 1933, Sivian and White3 experimentally evaluated the pressuremagnitudes of these thermal sounds between 1kHz and 6 kHz. Theyobserved that throughout the measured spectrum the root-mean-squarethermal noise pressure was about 86 decibels below one dyne per squarecentimeter. The minimum root-mean-square pressure that can produceaudible sensation between 1 kHz and 6 kHz in a human being with averagehearing is about 76 decibels below one dyne per square centimeter, butin some people with exceptionally acute hearing may approach 85decibels. These figures indicate that the acuity of persons possessinga high sensitivity of hearing closely approaches the thermal noiselevel, and a particularly good auditory system actually does approachthis level. Furthermore, it is not likely that animals possess greateracuity of hearing in this spectrum, as their hearing would also belimited by thermal noise. What this means is that the human audiosystem is extremely sensitive.
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 Horschwellenamplitudendes 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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