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In Reply to: Re: Skin effect , time smear some references and formulae posted by steve b on November 07, 2001 at 17:47:03:
While this site seems to offer a fairly complete analysis of skin effect in wires at audio frequencies, it does overlook at least two things which may be significant in terms of audio cables.In addition, the losses due to skin effect are erroneously calculated and displayed in terms of power, which is not relevant for interconnects, and not a good way to look at it for speaker cables due to the ratio between the source and load impedances. Use of power to calculate and display losses would reduce the apparent amount of signal loss.
I have to question the intentions of such a site, when it seems that an overly analysis is being used that is superficially rigourous, yet incomplete, and ignores the fact that other things are going on.
If the web site presentation did not intend to create such an erroneous impression, then at the least it is misleading and incorrect in it's final conclusions due to these oversights and errors.
It is promising that the section on wires:
http://www.st-and.ac.uk/~www_pa/Scots_Guide/audio/part6/page1.html
does point out that the signal exists in the EM fields OUTSIDE the wire, this is a fairly decent portrayal of this important fact, one often overlooked by those derisive of insulation quality.
Jon Risch
Follow Ups:
Interesting bit about dielectrics taken from "Handbook of Wiring, Cabling,And Interconnecting for Electronics" 1972, ISBN 0-07-026674-3 by Charles HarperA fine book, 1200 pages of everything you never wanted to know about solder joints,Crimping , cable types and standards, dielectrics , sleeving , geometry, shielding , etc.
A very good read and highly recommended.Just goes to show dielectrics shouldn't be viewed as perfect.
DIELECTRIC STRENGTH
The simple definition of dielectric strength is the voltage at which electrical breakdown of a specimen of electrical insulating material between two electrodes occurs, divided by the thickness of the insulating material at the point of puncture.
Unfortunately, materials suppliers persist in publishing the short-term dielectric-strength values of their materials as a sales point. These values have little use and very frequently mislead users; they have essentially no relationship to design use.
Dielectric-strength values obtained for a single material depend on the thickness of the specimen, the area of the electrode, the radius of curvature of the edge of the electrode, the prior history of conditioning of the sample and its moisture content, the temperature, the rate of rise of voltage, the test frequency, and the medium in which the test-electrode system is immersed. Repeatability of duplicate sets of specimens of a given sample is rarely better than ±10 percent.
Dielectric strength is useful primarily as a quality-control procedure on material or processing to assure some degree of continued uniformity.
The voltage-time curve is useful information. A typical one, shown in Fig. 13)
represents a large number of individual tests. For each point, a selected value of voltage is applied and the time to failure is determined.
Obviously if a very high voltage is applied, the life will be short. An average of a number of specimens is determined and the result plotted. Next this is repeated with a lower voltage, and a longer life results. This is repeated until life values of thousands of hours, and preferably of years, are obtained. There is an asymptotic value of voltage parallel to the time axis below which no failure would occur. This is the rated voltage of this insulation with this particular test electrode and test medium and temperature. A typical curve for an air medium is the solid line in Fig. 13.If the same series of tests are run in an oil medium, it will be found that the voltage value asymptotic with the time axis is much higher. The difference is usually due to the suppression of ionization by the oil. In air, the asymptotic voltage coincides with the corona-extinction voltage.
The implications are obvious. If air or gas is included in the dielectric circuit,life will be long only at stresses below those for the formation of ionization, i.e.,
at levels generally below 200 V/mil and more generally below 50 V/mil on ac. If,however, gaseous regions can be removed from the stressed areas, somewhat higher stresses can be used, up to 400 V/mil rms in many instances.
The above discussion implies materials that are low or medium-loss (power factor) and have high resistivities.DIELECTRIC STRENGTH—AS INFLUENCED BY DIELECTRIC LOSSES
Test pieces under dielectric testing are subject to dielectric heating, and if the material is lossy, failure may be by melting or decomposition rather than a simple puncture.
The dielectric-heating rate is given by
Watts/cm3 = 5.55 X 10-13 fS*SK tan(delta)
perm at 1000Hz PE= 2.25-2.35 Teflon 2.05 FEP 2.1
perm at 1000000 PE =2.25 Teflon 2.05
delta at 1000Hz PE < 0.0005 Teflon < 0.0002 PVC 0.07-0.16
delta at 1000000Hz PE < 0.0005 Teflon < 0.0002 PVC 0.04-0.14where f = power-source frequency, Hz; S = electric stress, V/cm (to convert from V/mil, multiply the latter by 400); K = relative dielectric constant; and tan S = dissipation factor [also equivalent to PFsqrt((l — (PF)*(PF)) where PF is the fractional
power factor]. The term K*tan(delta) is called loss factor and is proportional to the watts loss/( cm3) (Hz) (V/cm)2.
If dielectric-strength testing is being done, S (the stress) is obviously high and heat can be generated more rapidly than it can be dissipated if the loss factor is high. The resulting high temperature usually raises the loss factor and a runaway
condition is set up. This is referred to as a thermal breakdown.
Dielectric-strength tests at high frequencies are complicated by the proportionately higher heating rates, and many materials which have a conventional behavior at 60 Hz have thermal failures at I to 100 MHz,DIELECTRIC STRENGTH—INFLUENCE OF FREQUENCY
Even excellent dielectrics of low-loss characteristics tend to lose dielectric strength at elevated temperatures and frequencies. See Table 2 for polyethylene and Table
3 for Teflon, The effect of frequency is rather more pronounced than that of temperature; this was to be expected for the low-loss materials.
Polyethylene— Electric Strength. S V/mil, for 30-milFunctions of Temperature and Frequency*
25 degrees 60Hz 1kHz 38KHz 180kHz 2MHz 18MHz 100Mhz
1300 970 500 460 340 180 130
Teflon
Functions of Temperature and Frequency*
25 degrees 60Hz 1kHz 38KHz 180kHz 2MHz 18MHz 100MHz
850 810 540 500 380 210 140
*Taken from J. J. Chapman and L. J. Frisco, A Practical Interpretation of Dielectric
measurements up to 100 Mc, Johns Hopkins University, Contract DA-36-039-SC 73156,
File No.0199-PH-57-91 (3400).
Fascinating
regards
Steve
The things I do like about this article is the trends that the analysis predicts, which are generally correct. Trends such as:1) forward and return conductor proximity reduces group delay and increases bandwidth
2) small conductors exhibit less skin-effect and therefore can achieve higher bandwidth and less group delay change
3) low conductivity materials exhibit very large skin-depth and therefore do not suffer from skin-effect much, but they suffer from fixed attenuation at all frequencies
Some of the things that are not modeled are:
1) multistrand effects that increase inductance due to conductor surface oxides
2) an effective tradeoff between wire diameter and spacing, given skin-effects
3) contrasting requirements of interconnects versus spaeker cables
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