I have found two common expressions for the Zo of a two wire line in
space.

One expression is Zo=276log(D/d).

The second is Zo=120acosh(D/d).

I have been searching for information on whether the acosh expression
takes into account proximity effect. Because it does not consider
conductivity or permeability of the conductors, one wonders if it does.

Laport has a graph that shows the log expression and a proximity
corrected line which turns out to be a very close fit to the acosh line
over the range that he plots. The curves are compared in
http://www.vk1od.net/balun/Ruthroff/R07.png .

I have another reference, Marchand (1947), which gives the log expression
then, the acosh expresssion and says "The hyperbolic cosine is obtained
because the currents are attracted to one another and become more and
more confined to the inside surface as the wires are brought closer
together."

This suggests (states) that the acosh expression (fully) accounts for
proximity effect on Zo.

Comments?

Owen