Richard Clark wrote in
:

On Sun, 10 Feb 2008 00:08:33 GMT, Owen Duffy wrote:

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).

Hi Owen,

I have the following expressions found in "Reference Data for Radio
Engineers," 22-22 Transmission Lines:

Zo = 120 acosh(D/d)
Zo ~ 276 log(2D/d)
Zo ~ 120 Ln(2D/d)

where the symbol ~ means "approximately equal to."

Thanks Richard.

Yes, I saw those in that publication.

ln(x) is a good approximation of acosh(x) for large x, so that explains
one approximation, and the log expression is just a scaling of the ln
expression.

I put some importance on the difference between the approximately equal
and unqualified equal signs.

If the acosh expression fully accounts for proximity effect, it is
interesting that it is independent of frequency, conductivity, and
permeability. It would be nice to find a derivation.

I think if you derive C and L from first principles, you don't get the
same curve as acosh... which suggests that acosh is account for something
that L and C from first principles (assuming uniform current
distribution) doesn't.

Owen