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

Owen

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

Edmund Laport's RADIO ANTENNA ENGINERING has a good treatment of open wire
lines, including a chart on page 398 showing the Zo of balanced,
two-conductor line as functions of wire OD and c-c spacing. The text says
the plot includes proximity effect and non-uniform peripheral charge
distribution. The chart shows a proximity effect only for low ratios of
conductor spacing/OD (below about 4). I could scan it and send it to you if
you wish.

Laport also shows the general equation as:

Zo = 276 log [2*h*a / p*SQRT(4*h^2 +a^2)]

where

h = height above ground
a =spatial dimension in the line cross-section
p = wire radius

RF

On Jan 21, 1:04 am, 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

Reg Edwards' "LINE_ZIN" program includes a term for proximity effect.
It happens to be one of the programs for which he provided Pascal
source code. There are a couple lines of interest:

Rc:=2*Sqrt(Freq)*Len/12/Dia; { conductor
resistance }
Rc:=Rc/Sqrt(1-Sqr(Dia/Space)*(1-Sqrt(SD/Dia))); { corrected for
proximity }

I'd suggest you look up the source code yourself, though, and make
sure that taking these two lines out of context doesn't destroy their
meaning. The above two lines are taken from the archive at
http://www.zerobeat.net/G4FGQ/

There's what seems to me to be a pretty nice qualitative explanation
of proximity effect at http://www.sigcon.com/Pubs/news/4_1.htm. I
realize that's not what you asked about, but lurkers may be interested
in it.

Cheers,
Tom

On Jan 21, 1:04 am, 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

Also, though it covers proximity effect with relation to coils and not
transmission lines, the article at http://www.g3ynh.info/zdocs/comps/part_1.html
may be of interest. He provides a reference or two, though I'm pretty
sure the references will talk exclusively about proximity effect in
coils, too.

Cheers,
Tom

Richard Fry wrote:
"Edmund Laport`s RADIO ANTENNA ENGINEERING has a good treatment of open
wire lines, including a chart on page 398 showing Zo of balanced
two-conductor lines as functions of wire OD and c-c spacing."

Yes and on pages 380 and 381 he gives transmission line height as 120
inches.

Best regards, Richard Harrison, KB5WZI

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

Roy, Tom, Richard and Richard,

Thanks.

I only asked half the question, I was also interested in a proximity
corrected calc for Zo.

The chart in Laport looks useful Richard. I have digitised it and tried a
number of curve fits. I think I will just use a cubic spline
interpolation to my digitised points where D/d2.5 and 1.1, and above
that range I will use 120acosh(D/d). Laport doesn't give an expression
from the graph, so I suspect that it is derived from experimental data.

Tom, thanks for the pointer to Reg's expression. I wish I knew where he
got it from, or something against which to validate it... but it is a
start. Interestingly, Reg doesn't seem to consider proximity effect in
calculating Zo (other than indirectly from the implied R element).

Roy, I note from Googling that a lot of work has been done in recent
years on skin effect in PCB tracks, ie small rectangular tracks over a
large ground plane, but haven't seen work on traditional two wire open
line.

I am playing with a model of a Ruthroff 1:4 balun. My model treats the
windings as a coiled lossy transmission line, so good estimation of Zo
and R are important to the results.

The ugly part of ferrite baluns is the ferrite. I have used published u'
and u'' vs frequency curves to calculate the choke impedance for a more
realistic estimate.

Comments appreciated.

Again, thanks to all for the hints.

Owen

Roy wrote:
"The caption says it`s derived from Terman`s _Radio Engineer`s
Handbook_(1943), p43."

Yes it`s there. Fig. 6 - "Proximity factor in parallel cylinters or
tubes for very high frequencies."

Best regards, Richard Harrison, KB5WZI

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

Thanks Tom,

I did mean to note in my last post that Laport's graph of D/r vs Zo with
proximity correction is frequency independent.

I thought the effect would be frequency dependent. Perhaps not sufficient
to be concerned about, perhaps he overlooked it?

I did ask Reg about the R calc a long time ago, and he dismissed the
discussion with an explanation that it was from notes in his engineering
notebook from a long time ago, and then went on the tell me the value of
his book of personal 'recipes', but he didn't share it.

When he did publish the source of a few of his progs, it didn't occur to
me to look at them for possibly useful hints.

I think the model I have now is probably adequately accurate to question
some of the golden rules of baluns. At the end of the day, the
uncertainty in characterising ferrites at a frequency, at a temperature,
at a flux level, and on a given day is the main worry. I don't think I
need to get into Bessel functions for the actual current distribution,
and trying to derive corrected values for R and Zo from first principles.

Owen