Dr. Gerald N. Johnson
geraldj at storm.weather.net
Sun Feb 1 19:51:18 EST 2009
On Sun, 2009-02-01 at 23:11 +0000, Steve Hunt wrote:
> A picture paints a thousand words - take a look at Figure 9 here:
> it shows what I was trying to describe. Notice how unmatched loss (the
> red line) is below the matched loss (blue line) for a short distance
> back from the load.
> Steve G3TXQ
Yes, IF (and only if) you pick your point along the line for that short
line you can pick a line that has lower loss. But the loss per cable
length is based on the total loss of a line many quarter wavelengths
long, so that the peaks in Isquared R and dielectric loss average out.
And so the added loss caused by SWR computation based strictly on the
line loss over many (quarter) wavelengths and the reflection coefficient
averages. Line loss is not uniform along the line. Run a bit of RG58 a
few waves long with lots of power and you will easily detect the points
of greatest loss, about a quarter wave apart at VHF, probably more like
a half wave apart at 80 meters.
So if you pick a load and line where the V/I at that point somewhat
approximates the Z0 of the line the loss is much smaller than where the
SWR would have the impedance far different than the Z0 to emphasize
either current or voltage.
Line loss is always lower at lower frequencies because the skin depth in
the conductors is greater and the dielectric capacitive current and
hence the dielectric loss is lower. Let me pick a truly air spaced line
at a high impedance point along the standing wave and I can show you a
line with arbitrarily low loss because if the instantaneous V/I is high,
the current is small and so the line loss is small because the
dielectric loss is zero and I can reduce the conductor loss by making
the surface of the conductor large.
But the point of the formulae and the curves based on it is that the
line loss over at least a quarter wave increases with SWR because the
voltage peaks cause greater dielectric loss and the current peaks cause
greater conductor loss. There must also be the assumption besides these
that the dielectric loss increases with the applied RF voltage. That's
true of solid dielectrics but not of air. And many a coax or twinlead
has more air that dielectric in its electric field when foamed.
You know the rule of thumb that says a coax with impedance near 72 ohms
has the least loss? That came from an article in Electronics magazine
about 1948 and was based on a mostly air insulated line with copper pipe
for both conductors. And not a resonant line, a matched line. I believe
that if one was to make a series of lines of consistent outer conductor
and insulation material, but varying center conductor diameter that one
would find that the characteristic impedance for lowest transmission
loss would be different from that 72 ohms and would vary with frequency
as the dielectric loss varies with frequency for any practical
dielectric. I don't have a feeling for which way the changes would be,
though probably a lower characteristic impedance would have the lowest
loss from operating the dielectric at a lower voltage for a given
applied power. And as you have pointed out for the transmission line
case, the optimum characteristic impedance for a quarter or half wave
resonant line will depend on the dielectric and how that dielectric's
losses vary with frequency.
73, Jerry, K0CQ
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