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Registered Member #190
Joined: Fri Feb 17 2006, 12:00AM
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Posts: 1567
Is there anyplace I can find the derivation of the formula for the skin depth for current at a given frequency? The best I can do so far is find the formula.
Registered Member #72
Joined: Thu Feb 09 2006, 08:29AM
Location: UK St. Albans
Posts: 1659
It depends what you mean by derivation.
Intrawinding's wiki link may satisfy you, though the first equation in it giving the current density as you go down into a flat semi-infinite conductor is itself the solution of a wave equation with a boundary between metal and vacuum media. To set up and then solve the wave equation, you will need some basic degree-level electromagnetic theory and mathematics. To solve it for a finite wire rather than a flat plate, you need Bessel functions.
Registered Member #543
Joined: Tue Feb 20 2007, 04:26PM
Location: UK
Posts: 4992
The skin depth equation is derived from the Fermi Velocity
An experiment to determine the skin depth and Fermi velocity in metals N. P. Singh, S. C. Gupta, and B. R. Sooda) Physics Departmen~Received 17 January 2002; accepted 11 April 2002!t, Punjabi University, Patiala 147 002, India
A simple experimental method for measuring the anomalous skin depth and Fermi velocity in metals is presented. The skin depth is evaluated by measuring the resistance at 77 K of a thick metal wire specimen at frequencies of 100 Hz and 0.1 MHz. The Fermi velocity is obtained by using the theoretical expression that relates the anomalous skin depth to the Fermi velocity.
Registered Member #2099
Joined: Wed Apr 29 2009, 12:22AM
Location: Los Altos, California
Posts: 1716
It's university textbook material. A classic reference (which I finally bought, used, 20 years after college) is:
Fields and Waves in Communication Electronics by Simon Ramo, John R. Whinnery, and Theodore Van Duzer. Copyright 1965, 1984, 1994.
The theory of skin effect has not changed since then. But an important research topic a few years ago was to quantify the effect of surface roughness in printed circuit traces. In the 1 to 10 GHz range (skin depth 2.1 to 0.66 um), current has to follow the bumps and pits which are deliberately formed to promote adhesion between layers.
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skin depth at high frequencies
