antenna-theory.com

[Mrcelloman99]

So I was looking at the expression for R_loss for a short dipole antenna, and I need some clarification. I know that the skin effect plays a role, but I do not understand where the 6 in the denominator comes from. Also, shouldn't the 2 in the radical denominator be cancelled by the 2 in the radical numerator when converting the angular frequency to f?

Thanks much

[bigSteve]

we should be able to derive it

The d.c. resistance represents a measure of the ohmic loss due to current flow in a non-perfect conductor.

R = (pho)*L/A = L/Area/conductivity

for the short dipole antenna, the area would be approximated as 2*pi*radius*skin_depth

the length would just be L/2

But for a short dipole antenna, the current drops off linearly. Hence this is where an additional 1/3rd factor would come in.

One thing that appears missing is the resistivity that should start at the front. I think I'll check on that.

Does this make sense?

[Mrcelloman99]

Yeah, it did not occur to me at first to integrate current distribution form -L/2 to L/2 and normalize that by Io, which brings the L/3 factor. That times the sheet resistance divided by the "skin effect" area gives the expression on the website, except, again, I'm not getting 2*sigma in the radical denominator, but just sigma.

Your explanation does make sense though and it intuitive, thanks!

[bigSteve]

I wrote up my derivation of it. I also didn't get the 2 in the denominator. I'll leave that as a question now. The textbooks have it there, so I'll see if someone corrects it at some point:

http://www.antenna-theory.com/antennas/shortdipole-lossresistance.php

[Mrcelloman99]

hm, strange.

Well thanks for doing the drivation, much appreciated!