I was recently told that the maximum skin depth (δ) used in waveguides is 6δ. Usually it is kept to a maximum of 5δ, as the waves cannot penetrate beyond this at high frequencies. Why is it 6δ and what is the reason for it?
Dear Suhas
Skin Depth is a measure of how closely electric current flows along the surface of a material. At d.c. (0 Hz or a constant voltage), electric current flows uniformly through a conductor. This means the current density is the same everywhere. However, at higher frequencies, the current prefers to flow along the surface, producing surface current. The skin depth equation is given below:
skin depth = (p/pi*f*mu)1/2
where p=is the resistivity of the material (in Ohms/meter; this is the inverse of conductivity),
mu= is the permeability of the material (a measure of the magnetism),
f= f is the frequency of the current.
pi= Irrational number pi (approx. 22/7)
thus resistivity, permeability depends on material n when we put its value and in certain frequency thus it gives the value of skin depth approx. 5.3
With regards
Dhanu Chettri
Can you please give me an example where the Skin Depth calculates to 5.3.
Thanks for your help, Dhanu Chettri!
Dear Suhas
Skin Depth or δ is distance in which wave's amplitude reduces to e^-1 or 0.368 of its value, So if it travels 3δ it has a 0.049 of initial amplitude and if it has travels 5δ almost it absorb totally in lossy material.
Dear Ali,
I understood from various sources that the maximum skin depth needed is 5δ. But my professor informed me that it is not 5δ, but it is 6δ in waveguides.
I want to know how (mathematically) and why?
Dear sir James W. Lamb: Thanks for your reply!
"...For 5 skin depths, the field is down by ~43 dB, for 6 skin depths it is down by 52 dB."
"...In short, the actual required thickness is dependent on you application, and 6 skin-depths probably covers most expected engineering cases."
What is the mathematics behind it? I mean at what frequency, conductivity and medium of propagation?
The formula for skin depth was given by Dhanu, above. It applies for all conducting materials and frequencies. At 10 GHz the skin depth is less than a micron in copper, silver or gold. At 50 Hz it is about 8.5 mm so cables more than 4 cm across are wasting a lot of copper. Look up skin depth in Wikipedia.
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