Skin Effect Interview with Dr. Howard Johnson
Greetings Dr. Johnson,
Although this may seem to be a trivial matter to you, many audio cable vendors and forum cults enjoy spreading fallacies about skin effect and "strand jumping" on speaker cables and interconnects. I am attempting to disprove the relevance of Skin Effect at audio frequencies and the fallacy of "strand jumping" for this application.
Linked below is an article I wrote about Skin Effect:
Thank you for your input.
Gene DellaSala (GDS)
President of Audioholics.com
Response from Dr. Howard Johnson
Thanks for your interest in High-Speed Digital Design.
Regarding your inquiry, I'm sick of many of the claims I hear being made by audio "experts" that have no scientific backing or logic. For example, just last week a good friend of mine went into a music store to buy a new electric guitar. His old guitar is a Fender Stratocaster, and he plays it through an ancient Marshall tube-based amplifier. The new guitar looked like a regular acoustic guitar, but had a built-in microphone. The expert at the store told him he would need a new amplifier to go with this new guitar. The reason for this new expenditure was because the acoustic sound from the new guitar would be much "cleaner" than the Stratocaster sound he had been using and therefore "might damage his tubes".
WHAT!!! Wait a minute, there are a lot of things that damage tubes, like turning up the amplifier until your ears bleed, or kicking it over while on stage, or pouring beer into the chassis, but playing an acoustic guitar through the unit at reasonable volume is not going to hurt anything.
Anyways, about the skin effect, I've recently completed work on a very complete description of the skin effect (and also dielectric losses, which won't affect your application ).
This material appears in my new book, High-Speed Signal Propagation: More Black Magic. The book is available now through www.barnesandnoble.com . The first shipments should arrive from the printer in March.
The models in this book show how to derive both magnitude and phase for the skin effect resistance, and how to convert that into an overall model for signal propagation. The book provides several choices of models for the transition between the DC conduction (where the current fully penetrates the conductor) and skin-effect conduction (where the current is restricted to a shallow band just underneath the perimeter of the conductor). From my models you can prepare tables of the magnitude and phase of the skin effect at any frequency. Some simulators accept such models directly, while in others you must convert the tables to some kind of "equivalent" circuit. For work with linear systems I prefer to do all my work in the frequency domain, and convert to the time-domain only at the last step using an FFT (this method is outlined in the book, using MathCad syntax, which I see you can read and understand).
The stranding in speaker/interconnect cables effectively increases the surface roughness (also discussed in my new book), providing a further increase in series resistance at frequencies sufficiently high that the skin depth approaches the diameter of the strands (approximately 250 KHz for AWG 30 stranding). I seriously doubt that has any effect at audio frequencies, provided that the wires are not corroded and you achieve good metal-to-metal contact between the strands. Perhaps the corrosion is the genesis of the "strand-jumping" concern you mentioned. That is a new term for me (in the audio industry). If it means the same thing as in the electric-power industry, then what they are discussing is the way current moves from strand to strand as it weaves its way through a stranded cable. The dilemma here is that at high frequencies the current wants to stay near the surface of the cable, yet the darn strands keep weaving in and out around the center.
If there is good conduction between strands, the current moves from one strand to another, keeping near the surface. Such a cable suffers from increased skin-effect resistance (because current is not shared among parts of all the strands).
If there is NOT good conduction between strands, then the current, once forced into a particular distribution among the strands at one end of the cable, retains the same distribution of current as it moves along the cable.
One way to make such a cable is to actually use insulated wires (i.e., magnetic wires dipped in enamel) which are then carefully woven to ensure that each symmetrically attains the same exposure to both outer and inner regions of the cable. The symmetry helps ensure an equitable distribution of currents at the launch point. Cable woven from insulated strands is called "Litz wire". A Litz-wire cable is not subject to the skin effect (until you approach a frequency so high that the skin effect begins to affect the individual strands). There was some interest in Litz wire about sixty years ago when making large high-frequency magnets. I'm not suggesting, however, that Litz wire would actually perform any better than ordinary stranded un-insulated cables (or any ordinary wire of appropriate size), because the impact of any wire of reasonable length in a typical speaker circuit is quite negligible.
If anyone says they can hear the difference I'd like to test their abilities by placing their head in front of a 1 MW acoustic source at 100 KHz for about 1 minute :-o
If there is intermittent or corroded conduction between the strands, you might expect the resistance of the wires to change with time, or with exposure to various currents.
This is the genesis of the idea that cables are "non-linear", which is absolute baloney at acoustic levels of current and voltage.
In a high-voltage electric power generator, where you are dealing with intense, rapidly-changing magnetic fields and voltages of over 100 KV, the electric potential from strand-to-strand could approach a large enough voltage to cause internal strand-to-strand arcing. In audio applications, however, provided that you have sized the cable so that there is less than one volt dropped across the whole cable from end-to-end, non-linear arcing between strands is not going to occur.
What About Microphone Cables?
You may have noticed that no one has suggested we can't use stranded wire for microphone cables (this is the standard way to build them), yet they are subject to all the same issues with stranding and skin-effect resistance. The only difference is that the level of impedance in a microphone circuit is much higher, and the power lower, and so therefore there is much less current, but that only affects your conclusions if you are doing quantitative analysis, which the speaker-wire guys aren't doing. You should be able to make the very convincing emotional argument that if there were any distortion due to strand-jumping it would show up even more strongly in the microphone-cable example "because the volume is turned up so loud from that point forward" :-)
What About Loudspeaker Voice Coils?
Finally, let me point out to aficionados of expensive speaker cabling everywhere that the circuit they are building places their beautiful cable directly in series with the copper windings internal to the speaker coil. The speaker-coil winding itself is made from an immense quantity of very tiny copper wire, subject to skin effect losses and everything else just like the speaker cables. Electrically, you ALREADY HAVE a huge amount of tiny wire in series with your speaker, and you are ALREADY subject to skin-effect variations. Therefore, whether you use wires large or small to hook the speaker to the amplifier is insignificant. All you want to do when hooking up speakers is make sure the voltage drop across the cable remains small compared to the voltage drop across the speaker. That's something you can test with an ohm meter.
Electrostatic speakers differ from this description but still I find it the most convincing way to explain that the skin-effect issue is moot.
By the way, if you REALLY wanted to eliminate skin-effect considerations (and concern over "matching the impedance" of the speaker cable) you should be using two thin, flat, very wide conductors with a controlled spacing between them. This spacing can be adjusted to create a balanced transmission line with a characteristic impedance of approximately 4-ohms (or whatever you think best matches your speaker). If the conductors are kept thin with respect to the skin depth at 100 KHz you would have the SAME precise resistive drop at all frequencies. Since it's a ribbon, it would be fairly flexible. If you want to prototype the idea, a 50-wire ribbon made from 30 AWG conductors has a very constant DC resistance up to well over 20 KHz. Before proceeding, let me explain what I mean by "DC resistance at 20 KHz" . What constitutes "DC". I mean, how long exactly do you have to wait to measure the "DC" resistance of a structure. Is is sufficient to wait 1 sec., or 1 min., or 1 hour, or 1 year, or 1 century, or what? I bring this up because you don't know how to measure DC resistance at 20 KHz. That's because you "think" of 20 KHz as being fast, so it doesn't seem like DC to you. People who work on microwave electronics think anything below 1 GHz is DC. As commonly used, the phrase "DC" usually means the measurements are taken at a frequency low enough (i.e., a time span sufficiently long) that increasing the measurement time further doesn't change the result. Intuitively, this concept makes sense, but I should point out that on a geological time scale all your circuits will corrode into dust and therefore the concept of "DC resistance" has no mathematical meaning. We can only really talk about a plateau in impedance that seems to hold down to frequencies which are as low as we humans have the patience to generate or observe.
Ok, lets go back to the 50-wire ribbon cable construction. Just solder all 50 wires together at both ends. A system of two such ribbons with foam between them to maintain a constaint air-gap spacing would make a nice transmission line. Multiple-wire ribbons (or flat-sheet ribbons) are not subject to "strand jumping". Some triaxial cables have just the right impedance between the inner and outer shields and can be used in the same way.
Copyright 2003 Howard Johnson and Signal Consulting, Inc. , reprinted with permission.
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P.S., My business manager asks that I remind you that I teach seminars about this stuff in public and private venues all around the world to over 1000 engineers annually, and encourage you to sign up for a class. Check out the web site for times/dates. The classes are a great way to interact personally and get all your questions answered. If you've already been, please tell a friend...
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