Cable Asylum Interconnects, speaker wire, power cords. Ask the Cable Guys.

---

[ Follow Ups ] Thread: [ Display  All  Email ] [ Cable Asylum ]

---

[ Alert Moderator ]

---

Skin effect , time smear some references and formulae

Posted by steveor (A) on November 7, 2001 at 16:30:13

Hi,

I have been reading some old articles on this board about various debates over the skin effect and its affects of smearing the higher frequencies. I though you may be interested in some reading that I did,
I work at the research labs of one of the UK telecoms companies and they have a library on site with some interesting old books on transmission lines and cable.

Here are some examples from a couple.

Taken from Lossy Transmission Lines by Fred E Gardiol ISBN 0-89006-198-X
Library of Congress Catalog Card number 87-3602 .
(there is an old fortran prog called loslin which does various calculations)

The response on a lossy line at all frequency is given by the integral

1/2*pi integral{ 1/jw exp[jwt - wx/c -kx*sqrt(jw)}dw

here k = sqrt(u/e) [ 1/Ra +1/Rb]/2Z*ln(Ra/Rb) ]

therefore large c and small k are good

Z = characteristic impedance of vacuum = sqrt[permittivity/permeability]
Ra = inner diameter for coax
Rb = outer diameter
X = distance along line eg 5m
W = angular frequency
U = permeability of material
e = conductivity
C = propagation velocity ie 83% speed of light in vacuum

There is a picture showing the smearing of a step function wave as it travels down a transmission line.

There are other amplitude attenuations

In coax

Alpha = (Rm / 2Z)[1/Ra + 1/Rb](ln(Rb/Ra)] in Neper/m

Which is frequency dependent due to Rm = metal impedance which is proportional to sqrt(frequency)

The optimum value on a saddle type curve for Rb/Ra is 3.5911

Also of interest another article which refs

Kennelly Laws Pierce "Experimental Researches on Skin effect in conductors" AIEE Trans vol 34 part 2 pp 1953-2018, 1915 Disc ., pp 2019-21

The effective conductivity of stranded wire is less than that of a solid wire having the same net x sectional area by a factor k equal to ratio of net area to gross area.

"Regarding single strand and multi strand, they found that twisting the strands increased the skin effect which was negligible at 60 c.p.s but appreciable at several kilocycles. The increase can be ascribed to the solenoidal effect, that is axial internal flux"

Now I don't claim that this explains effects that people hear, and I believe that cables do make a subtle difference, but I thought I would share this.
Theres quite a bit more but I need time to absorb it all!
I never realised wire was interesting stuff!

If you want to search for articles look for "time domain analysis" & "lossy transmission lines"

regards
Steve

This post is made possible by the generous support of people like you and our sponsors:

Schiit Audio

---

[ Top of Page ] [ Contact Us ] [ Support/Wish List ] [ Copyright © 2024, Audio Asylum, all rights reserved ]

---

[ General ] [ Speakers ] [ Tubes ] [ Vinyl ] [ Digital ] [ Hi-Rez ] [ Video Asylum ] [ Cables ] [ Tweaks/DIY ] [ Music ] [ Films ]

---