On Jan 21, 2:25 pm, Roy Lewallen wrote:
Skin effect can, of course, be easily calculated if the conductor
diameter is at least several skin depths. If you can't make that
assumption, the calculation is much more involved, but not difficult for
a computer, involving modified Bessel functions.

There's a graph of a proximity effect factor in Johnson & Graham,
_High-Speed Signal Propagation: Advanced Black Magic_, p. 43. The
caption says it's derived from Terman's _Radio Engineer's Handbook_
(1943), p. 43. An approximate equation for calculating proximity effect
appears on p. 8-51 of Kaiser, _Electromagnetic Compatibility Handbook_
(CRC Press, 2005). It's a bit involved to try and duplicate in ASCII.

Roy Lewallen, W7EL

Owen Duffy wrote:
Can anyone point me to information on calculating the effective resistance,
including proximity effect, of conductors in a two wire open transmission
line.

Owen

I wonder if Roy's fingers got ahead of his thoughts...at least in My
copy of the '43 edition of Terman's book, it's more like page 36. He
publishes a graph there of the correction factor for resistance of
wires in a two-wire transmission line, for the wires carrying current
in opposite or in the same direction. The factor becomes large when
the center-center spacing is, say less than twice the conductor
diameter, as it would be in twisted-pair for most types of insulating
layers.

Terman gives more references. This stuff was all worked out long ago,
as I'm sure Reg would tell us if he were around. OK, quoting the
footnotes in Terman:

With respect to the calcs that went nto his published curves, which
assume skin depth small compared with other dimensions involved,

"1. The curve for currents in opposite direction is calculated by
formulas given by Sallie Pero Mead, Wave Propagation over Parallel
Tubular Conductors: The Alternating Current Resistance,
_Bell_System_Tech._Jour.,_ Vol 4, P. 327,l April, 1925. The curve
applying to currents flowing in the same direction is from S.
Butterworth, On the Alternatng Current Resistance of Solenoidal Coils,
_Proc._Roy._Soc._ (London), Vol. 107A, p 693, 1925."

With respect to calculating the effect when skin depth is not
negligible compared with the other dimensions involved,

"2. See Mead, op.cit.; also, H. B. Dwight, Proximity Effect in Wires
and Thin Tubes, _Trans._A.I.E.E.,_ Vol. 42, p. 850, 1923."

OK, Owen, if you can actually find these references, it seems like
they should do the trick for you with respect to resistance, at
least. If they also cover the effect on inductance, perhaps they'll
take care of the problem for you. I do have an explanation in a text
about how inductance varies with frequency because of the skin effect,
thereby affecting the impedance of a transmission line, but I don't
believe it covers proximity effect...

Cheers, Tom