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Understanding Skin Effect and Frequency

Posted by: Steve Lampen on December 13, 2012

Copper tubes LRThe #1 bone of contention with my wife is number of MAGAZINES get delivered to our house. I get around 40 different magazines each month. Since I am on the road a lot of the time, I never get a chance to read them all, so the pile builds and builds next to my chair in our living room. Every so often, as I did last week, I just throw them out unread. I really want to read them. I really do. But if they're six months or more out of date, I've missed the boat already. But every so often, I pick up one and read something interesting. Here's a quote from an article on studio installation:

Studio wiring is typically time consuming, complex and represents a good portion of a new studio build expense. Analog cables are susceptible to RFI/EMI emissions and grounding issues. Even the "cleanest" installations cannot avoid cable capacitance or "skin effect" associated with long cable runs that deteriorate signal performance.

And there's a problem here. Back in the old days, when I had more time, I would have been firing off a letter to the editor on this. (Now I can just put it in my blog.) Everything in this quote is true except for one thing: that reference to "skin effect". This unusual effect on wire and cable has been cited so many times by so many people that most readers don't even know what it means. So let me have a go at it.

Skin Effect happens in all wire and cable (or in any metal object that conducts a signal, such as a trace on a circuit board or antennas, etc.). When the "signal" is DC, it uses the entire conductor, with the same amount of current flowing in the center of each wire as on the outside of the wire. As the signal changes frequency (i.e. is now a wave changing direction) a very odd effect occurs: the signal begins to move more to the outside of the conductor than the inside. For audio frequencies, which are pretty low frequencies in the spectrum, this effect is so tiny it can barely be measured. Table 1 below shows how much conductor is used at 20 kHz, pretty much the highest audible frequency, and compares that to various wire sizes. (If you want the actual formula for skin effect, drop me a line and I will send it to you.)

Table 1

Basis:
Depth at 20 kHz = 18.4 mils (.0184 in.) Radius x 2 = 36.8 mils (.0368 in.) Diameter

Amount of conductor used at 20 kHz, based on conductor size
Conductors Diameter % of conductor used
24 AWG 0.024 100% at 20 kHz
22 AWG 0.031 100% at 20 kHz
12 AWG 0.093 75% at 20 kHz
10 AWG 0.115 68% at 20 kHz


You will notice that even for largest wire size, the difference between the inside and outside of a conductor is a few percentage points. Note that this is based on frequency not on the length of the cable, as mentioned in the quote above. You can see this effect very clearly if you look at the impedance of cables at low frequencies. Figure 2 shows the impedance of a 75 ohm video cable from a frequency of 100 MHz (right margin) down to 10 Hz (left margin).You will see that this 75 ohm cable is really only 75 ohm after around 100 kHz and above.Below that it is way higher than 75 ohms.In fact, down at 10 Hz, the impedance of the cable is around 4,000 ohms.

Impedance

That high-frequency value (75 ohms) is called the "characteristic impedance" of the cable and will stay at 75 ohms (or whatever it was designed to be) out to much higher frequencies. If you compare the low frequency formula to the high-frequency formula, there is one huge difference.R (the resistance of the wire) is a major factor at low frequencies. But in the high frequency formula, there is no R, no resistance.What happened to the resistance?And the answer is "skin effect".As the frequencies got higher and higher, less and less of that conductor is being used, until, around 100 kHz, only the skin is actually carrying the signal.

This is one reason why we can't build an audio cable to a specific impedance. That number will only apply to one frequency. At a different frequency, above or below, the impedance will be a different value. That's why we don't list the impedance of most audio cables and, if we do, that impedance is measured at some high frequency, like 1 MHz, and that cable might be used for some non-audio application. But perhaps you are thinking, "If the resistance of the wire makes no difference, then why won't a small cable go as far as a big cable?"And the answer is equally simple:the big wire has more skin than the small wire.

This is why, when we make cables for high frequencies, we spend a lot of time on the surface of the wire.That's the skin. And at high frequencies, that's the only thing working. So we do a lot of things (many of which are "trade secrets") to make sure the surface of that wire is as perfect as we can possibly make it. Our digital video cables, for instance, are sweep tested and measured out to 4.5 GHz. Signals at these highest frequencies use only microinches of the outside of the conductor. If all you were carrying was high frequencies, you could use a copper tube as a conductor with no additional loss compared to a solid conductor.

This is why our broadband cables are most often copper clad steel (called "CCS" in our catalog). There's only a thin layer of copper on a steel wire.This means such a cable will only work at high frequencies/And that's OK because TV stations start at Channel 2 which is 54 MHz, well into the skin effect range.(Digital channels now start even higher than that.)But someone who uses that cable for low frequencies, such as audio, or to carry DC to power up a satellite dish, will wonder what's wrong with the cable. All the DC power will be going down the steel wire, which is seven times the resistance of copper. What you want for audio or DC power is an all-copper conductor.

Our digital video cables are all-copper, but that's so you can use them for analog or digital video, analog or digital audio, satellite dishes or pretty much any signal at any frequency from DC to 4.5 GHz. Of course copper-clad steel is a lot stronger than bare copper, something that has saved many a CATV/broadband installer who was less than gentle when installing such a cable.So the next time the salesperson is telling you about the "skin effect" in his speaker cable, well, you know the truth!

Tags:Skin Effect, Frequency, Analog Audio, Digital Audio, Digital Video, Analog Video

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Comments

 
  1. Alan
    November 06, 2014 at 12:45
     

    Excellent article! Most of the cables I deal with are hollow core. Why pay for more copper? The one that blew me away was that high tension power lines are also just tubes, all the way back to the first lines from the Hoover Dam. Skin effect at 60Hz!

     
  2. October 09, 2014 at 04:03
     

    Robin- You are correct, skin effect makes the resistance go up, but that is a linear function. (Less and less conductor working, higher and higher resistance.) At the same time there are two other factors going up too. Inductive Reactance XL (the effect of Inductance when working at frequencies) and Capacitive Reactance XC (Capacitance at frequencies). These effects are geometric, and while they track each other, they leave skin effect resistance in the dust. By the time you pass 100 kHz XL and XC are the big winners and skin effect doesn't even show up. This is why the impedance is stable after 100 kHz (the "characteristic impedance" of a cable) and stays that way (hopefully) forever. Does that help?

     
  3. Robin
    October 03, 2014 at 04:34
     

    Hello, I am finding this article confusing. The skin effect causes increased resistance at higher frequencies, your graph shows otherwise.

     
  4. August 01, 2014 at 03:16
     

    Robert- Skin effect happens at every frequency. At DC (no frequencies) the entire conductor is used. As the frequencies increase, the effective signal area gets thinner and thinner. At audio frequencies, 20 kHz and below, it is usually ignored, although it is a factor with larger wires: •24 AWG = .024 = 100% at 20 kHz •22 AWG = .031 = 100% at 20 kHz •12 AWG = .093 = 75% at 20 kHz •10 AWG = .115 = 68% at 20 kHz It's really not considered a factor until higher frequencies: Frequency Depth (mm) Depth (in.) DC Entire conductor Entire conductor 1 kHz 2.07mm 82.6 mils 10 kHz 0.663mm 26.1 mils 100 kHz 0.21mm 8.25 mils 1 MHz 65 microns 2.61 mils 10 MHz 41 microns .825 mils 54 MHz 9 microns .355 mils 100 MHz 6.63 microns .261 mils 1 GHz 2.06 microns .0825 mils 54 MHz is where the TV channels start. By then the signal is ONLY on the skin which is why many of those cables (CATV/broadband coaxes) are copper-clad steel. Most of the wire is steel, strong and cheap, and only the copper is carrying the signal.

     
  5. Robert Mathewson
    August 01, 2014 at 12:25
     

    At what frequency do we begin to see Skin Effect?

     
  6. September 12, 2013 at 03:58
     

    Tom - Agree completely with your analysis and math. What this also means is, for smaller wires (i.e. 24 AWG or so) the whole wire is working at audio frequencies. So yes, there is skin effect at audio and not the whole conductor is working if you are talking about big wires. What's the solution? Use bigger wire, I suppose. (We now go up to 6 AWG in speaker cable!)

     
  7. September 12, 2013 at 03:55
     

    Hai - Steve Lampen Stands Corrected! Thanks!

     
  8. Tom
    August 30, 2013 at 04:15
     

    I would like to see the equation used for deriving percent of wire cross-section used at 20Khz. I would assume: - calculate the area of the wire ((pi * radius) squared) - calculate the unused diameter (diameter - 2*depth) - calculate the unused area (pi R squared again) - Percent used = ((total_area - unused_area) / total_area) * 100 Using this method, I calculated the 12 AWG wire uses 63%

     
  9. Hai
    August 21, 2013 at 01:05
     

    Steve, I wouldn't agree with the following statement: But in the high frequency formula, there is no R, no resistance.What happened to the resistance?And the answer is "skin effect". For high frequency, R dissapeared not because of skin effect, which increases it. It's just the increase of R compared to f is not as significant. So as a result, the high frequency formula doesn't have R. A detailed calculation can be found at http://alignment.hep.brandeis.edu/Lab/XLine/XLine.html

     
  10. Wilson
    April 06, 2013 at 03:45
     

    Dear Steve, Thank you to give me the equation. I will appreciate to your sharing. Yours sincerely, Wilson

     
  11. Steve Lampen
    April 05, 2013 at 09:32
     

    Wilson- The formula is D (in) = 2.61/ sq rt F (Hz) To be sure you understand that (it's hard to write formulas this way): Depth (D) in inches = 2.61 divided by the square root of the frequency (F) in Hertz. However, this is ONLY for COPPER conductors. Any other metal would be slightly different. Hope this helps. - Steve

     
  12. Wilson
    April 04, 2013 at 04:08
     

    Hi. My name is Wilson and I am interested about the skin effect equation for the impedance calculation. Sir, may I request the actual skin effect equation from you since I need the actual equation for the impedance calculation for specific cable material. Thank you.

     
  13. Steve Lampen
    March 01, 2013 at 12:32
     

    Phillip replies: What about stranded wire vs solid conductors? is the internal surface area used to carry the high frequency or just the OD of the bundle? ANSWER: It's just the OD (outer diameter) of the bundle. The network cable standard (cat5, 5e and 6) specify solid conductors for longer runs, wouldn't a stranded wire have more surface area for skin effect and therefore lower attenuation at the higher throughput frequencies of modern networks. Even if the DC resistance of a solid conductor is lower. ANSWER: No, the resistance of a stranded wire is always worse than a solid wires because of all those employ spaces between the conductors (called "interstices"). The surface of the stranded wire is equally chaotic, making it a poor choice to carry high frequencies. This is one reason, when we are forced to use stranded wire at high frequencies (such as Belden 1694F or 1505F) that we run the group of strands through a die. This is known as a "compacted center" and gets the whole conductor closer to a solid in shape but stranded in flexibility.

     
  14. Phil
    February 28, 2013 at 11:49
     

    What about stranded wire vs solid conductors? is the internal surface area used to carry the high frequency or just the OD of the bundle? The network cable standard (cat5, 5e and 6) specify solid conductors for longer runs, wouldn't a stranded wire have more surface area for skin effect and therefore lower attenuation at the higher throughput frequencies of modern networks. Even if the DC resistance of a solid conductor is lower.

     
 

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