Provided skin effect is fully operative, ie., skin depth is about
1/6th wire diameter or less, proximity effect increases wire
resistance by dividing normal skin-effect resistance of a single
straight wire by K :

K = SquareRoot( 1 - Square( D / S ) )

where D is wire diameter and S is centre-to-centre wire spacing. Note
that resistance increases towards infinity as the pair of wires
approach contact with each other. This is confirmed by precision
measurements.

To minimise line attenuation for any given wire spacing, maximise U
with respect to D :

U = D * InvCosh( S / D ) * SquareRoot( 1 - Square( D / S ) ) .

-----
Reg, G4FGQ

John - KD5YI wrote:
....

Okay, Reg, then go read the material referenced by footnote 13.
That's one
reason I included it. Maybe that way we won't need to rely on your
memory.

The confusion comes (in the quoting of the texts) because of a failure
to consider that there are two different mechanisms that can limit the
power handling capability of the line. One is power dissipation
(temperature rise), and the other is voltage breakdown. Clearly the
minimum power dissipation for a given input power and matched line
occurs where the line attenuation is minimum. But if you make the
inner conductor slightly larger, it may be able to get rid of heat
enough better (for a given line construction) that the inner conductor
temperature rise is slightly lower, even though the power dissipation
is slightly higher. I would expect, though, that the optimal
construction in most circumstances would result in an impedance only
marginally lower than the minimum attenuation case, and the improvement
would be a very small one. You'd have to convince me it was really
important to get me to worry about it beyond just minimizing
attenuation.

If it's voltage breakdown that limits the line power handling
capability, the air-insulated impedance of the line will be at a D/d
that results in about 30 ohms impedance for air-dielectric line, and
..66 times as much for solid polyethylene line.

And if it's maximum voltage-handling you want, the D/d results in
somewhere around 50 ohms with air-insulated line, about 33 ohms with
solid poly, if memory serves. I could look it up if it's really
important.

Generally in ham applications, (reasonably well matched) lines will be
power dissipation limited, not voltage limited.

Cheers,
Tom

From LF to VHF it is ALWAYS power dissipated in conductor resistance
which limits the power handling capability of the line. Voltage has
nothing to do with it. Above VHF dielectric loss becomes be the
limitation.

Consideration of ambient temperature is vital. Are you located in
Alaska at midnight in mid-winter? Or are you in the New Mexico desert
in July, at noon. It makes hell of a difference?

With coax everything depends on the temperture softening point of
polyethylene and on the the longer-term temperature deterioration
(hardening, cracking, brittleness) of the PVC sheath.

Is the cable embedded in an asbestos insulated brick wall or is it
suspended in free air with a breeze in the shade? Or in sunlight?

The power rating data provided by manufacturers for amateur grade
coaxial cables is useless nonsense. From inspection of manufacturers'
tables (watts) it can be deduced their ratings are based on the
melting point of polyethylene. Salesmen's blurbs, no doubt plagiarised
in ARRL publications, sound very good in order to sell the stuff.

To gain an elementary understanding of what it's all about, download
in a few seconds, easy to use, practical application, small program
"COAXRATE" from website below and run immediately. (Not zipped up).

Program "COAXRATE".
----
.................................................. ..........
Regards from Reg, G4FGQ
For Free Radio Design Software go to
http://www.btinternet.com/~g4fgq.regp
.................................................. ..........

Reg Edwards wrote:
From LF to VHF it is ALWAYS power dissipated in conductor resistance
which limits the power handling capability of the line. Voltage has
nothing to do with it.

What if it arcs?
--
73, Cecil http://www.qsl.net/w5dxp

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What if it arcs?
--
=================

It shows the voltage rating has been exceeded.

Reg wrote:

"From LF to VHF it is ALWAYS power dissipated in conductor resistance
which limits the power handling capability of the line. Voltage has
nothing to do with it. Above VHF dielectric loss becomes be the
limitation. "

Always? Hardly. Transmission of pulses with low duty cycle will get
you to voltage-limited operation pretty quickly. Transmission of power
to a high-resistance load where the line is a very small fraction of a
wavelength long may get you into voltage-limited operation. Those
perhaps aren't typical ham applications, but they do happen in
practice. Also, though the cable itself may not have trouble with the
applied voltage, the connectors at the ends may. They're generally
rated for much lower voltage than the line itself.

Also, for the small-diameter (nom. RG-58 size) cables I've been using
lately, conductor loss exceeds dielectric loss out past 10GHz. YYMV.

Cheers,
Tom

Reg Edwards wrote:
What if it arcs?

It shows the voltage rating has been exceeded.

But, but, but, Reg, you said "voltage has nothing
to do with it." :-)
--
73, Cecil http://www.qsl.net/w5dxp


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K7ITM wrote:
Also, though the cable itself may not have trouble with the
applied voltage, the connectors at the ends may. They're generally
rated for much lower voltage than the line itself.

Yep, during duststorms and thunderstorms, the connectors
arc. Arcing at the coax connectors of my IC-745, IC-725,
IC-706, and IC-756PRO has never seemed to injure any of
them. Is that just luck or are they that well protected?
--
73, Cecil http://www.qsl.net/w5dxp


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What if it arcs?

It shows the voltage rating has been exceeded.

But, but, but, Reg, you said "voltage has nothing
to do with it." :-)

==============================

I'm very sorry Cec, but in future I shall have to make a modest charge
for answering your questions. In advance if you wouldn't mind.

Provided skin effect is fully operative, ie., skin depth is about
1/6th wire diameter or less, proximity effect increases wire
resistance by dividing normal skin-effect resistance of a single
straight wire by K :

K = SquareRoot( 1 - Square( D / S ) )

where D is wire diameter and S is centre-to-centre wire spacing.
Note
that resistance increases towards infinity as the pair of wires
approach contact with each other. This is confirmed by precision
measurements.

To minimise line attenuation for any given wire spacing, maximise U
with respect to D :

U = D * InvCosh( S / D ) * SquareRoot( 1 - Square( D / S ) ) .

====================================

Roy, having given a little more thought to it, I think that by
differentiating U with respect to D and equating dU/dD to zero, things
will then simplify and the value of the ratio S /D, and hence Zo, will
be obtained directly.

If you still have enough enthusiasm I leave it to you to perform the
differentiation.
----
Reg.