Leading line stolen from Walt Maxwell .....
What AA4LR just presented is truth, what Wal Maxwell has written
is the same truth. This subject is the most misunderstood in
all of hamateur radio. Let me be foolish enough to try to
explain it perhaps more clearly.
A load (antenna) at the end of a feedline of characteristic
impedance Zo has an impedance of Za = Ra + jX. We will
assume that X is not zero, that is, the antenna is not
resonant. Resonance is that condition in which net
reactance X = 0.
Here is the theorem in network theory underwhich all this
falls. I state it in as simple terms as I can.
Given a source (TX) and a load (ANT) connected
by a lossless transmission line of impedance Zo (no matter
what value), place a four port network consisting of only
lossless L and C components anywhere along the transmission
line (feedline) and adjust L and C such that a conjugate
match is acheived. THEN, cut that feedline anywhere and
measure the impedance looking into both sections at the
point of the cut. If the impedance looking into one
section is R + jX then the impedance looking into the
other section is R  jX, which are conjugate impedances,
which when combined produce net X = 0, or RESONACE at
the point .... therefore the system is resonant everywhere.
Therefore, cut the line at the point where it connects
to the antenna and you have R + jX of the antenna matched
to R  jX of the line and hence, the feedpoint has no
net reactance, the ANTENNA IS TUNED! The four port
network is the antenna "tuner" we all have in the shack!
Introducing losses in the feedline affect the above condition
only in the matter of efficiency, which is reduced only thru
power loss to heat. The antenna is still tuned to resonance!
After the conjugate impedance match is acheived at the antenna
feedpoint we are left with a resulting impedance that is a pure
resistance, consisting of the antenna resistance and the system
loss resistances. We now have the feedline terminated in a
net resistance of Ra which seldom, if ever, comes out to be Zo.
If Ra=Zo, then the line SWR is 1:1, otherwise NOT! The only
two parameters that set line SWR are the terminating impedance
(here Ra) and Zo. Nothing else plays except line loss in
practical lines which only tends to improve (lower) the SWR
at the input point.
The feedline transforms the termination Ra into an impedance
Zi = Ri + jXi at the feedline input (in the shack) and
now the tuner transforms (matches) Zi into the source (TX)
impedance and all the power is transferred from the rig to
the line. How much ends up radiating depends on how much
line loss you have and the reflection coefficent determined
by Ra and Zo. If you have a lossless feedline, all the
power goes into the antenna and is radiated only if the
antenna is 100% efficient! Antenna efficiency is the bear
to determine ... it equates to knowing the true GAIN of the
antenna .... which FEW (including most mfrs!) have little
real knowledge of .... efficiency is NOT 100%, count on it!
If you don't have a lossless feedline, efficiency is not 100%,
and practically the most power robbing element in the antenna
system is always the feedline loss itself. Tuners seldom
exhibit significant loss! Thus, if you have lossline line
(open wire comes close!!!) then SWR is of no concern whatsoever!
SWR problems didn't exist way back when, blame the dude who invented
coax (introduced lossy feedlines) ... (chuckle chuckle).
Walt Maxwell has clearly stated time and time again that a
transmatch/tuner/ATU, whatever, TUNES and MATCHES. TUNES
means tunes the antenna and MATCHES means taking the resulting
Ra and matching its transformation impedance Zi at the source,
i.e., in the shack for us. Walt has explained the reflection
physics very very well in the ARRL Ant Handbook ... it's real
world stuff ... the way things ARE!
Even in practice you can consider that all coils and capacitors
are lossless, their actual losses are due to associated resistances
which you can lump into a loss resistance. Hence, the above
theorem holds. The smaller those losses, the higher the system
efficiency ... which you CAN easily compute by the way. Walt has
given you all you need to know in SIMPLE calculations in the ARRL
antenna handbooks.
Perchance an example is worth it: Assume a feedline of 50 ohms,
and ideal with NO LOSS. Let the 100 Watt TX be 50 ohms also and let the
antenna impedance be 300 + j200, clearly nonresonant. Without
the antenna tuner the line SWR is 8.7 and 36.9 watts is transferred
to the antenna (if the antenna is lossy less than 36.9 watts is
radiated!) 63.1 watts is reflected. Total efficiency (antenna eff
withstanding) is therefore 36.9, I call this transfer efficiency.
Oops, forgot to mention the reflection coefficent at the antenna
feedpoint in this case is 0.8.
Now, put a tuner in the shack and adjust it properly. The line SWR
is now 6 (300/50 because X=0!), the reflection coefficient is 0.7, a
slight improvement. Forward power at the transmatch is 204.2 watts,
100 watts is transferred to the antenna, 104.2 watts is reflected,
a 49% transfer and 104.2 watts is returned to the shack. Mismatch
loss is 0 (line loss is zero who cares about SWR!), shack SWR = 1:1
and 100 watts is delivered to the antenna! Thus an improvement of
63.1 watts if no tuner was used! The important point to note here and
in all other cases, with a tuner, is that the reflected power arriving
back at the tuner is reflected IN PHASE with the transmitter output
thus increasing the forward power by that amount. This power DOES NOT
go back into the rig and "BURN UP DEM FINALS!" .... wisdumb on the
airwaves!
Now, same two cases except we put 3 db loss in the feedline. First
case no tuner. Line SWR is still 8.7, reflection coeff is 0.8. 50.1
watts leaks out at the antenna end of the feedline, 49.1 watts heat
up the coax (totally lost to heat) Efficienty of transfer is still
36.9 percent and 18.5 watts goes into the antenna, 31.6 is reflected
back to the shack. Only 15.8 arrives at the shack (feedline loss).
SWR of 8.7 at the antenna now reads only 2.3 in the shack and the
total efficiency is a mere 18.5 watts out into the antenna.
Now put the tuner in the shack and adjust it correctly. Line SWR is
still
6.0, reflection coefficient is still 0.7. Forward power 114.7 watts,
57.5
watts arrives at the end of the feedline and 28.2 watts goes into the
antenna, the transfer efficiency is still 49%. 29.3 watts is reflected
back to the shack and only 14.7 watts arrive. Shack SWR 1:1, 100 watts
is delivered into the system by the transmitter (this is what those of
grate wisdumb call "fooling the transmitter"!) for a total efficiency of
28.2 percent. Loss due to mismatch at the feedpoint amounts to only
7.3 watts. Thus, if you were to replace the antenna with one whose net
resistance after tuning to resonance was 50 ohms (matching the feedline)
you would only gain 7.3 watts output. So the 300 ohm antenna match (SWR
= 6)
is only 80 percent as "efficient" as the perfect Ra=50 match. That
amounts to
a difference of a mere 1 db! An Sunit is 6 db!
Like Walt said : Too low an SWR and KILL YOU!.... meaning we chase SWR
and
"resonance" with such zeal that if you climb the tree enuff times
trimming the
antenna for that last ounce of ummmp, you'll eventually fall out of the
tree
and kill yourself ... for NOTHING! :) You wanna make a difference in
your
signal, use the lowest loss feedline you can afford ... open wire
reigns!!!!
Perchance this long speel is of some value .... de Dave W0MHS (utahfolk)
P.S. Why not bring up the debate on whether the antenna tuner needs to
be put at
the antenna feedpoint and that all feedlines have to be half wavelength
multiples .... that'll keep things going for another hunnert years ...
BTW
I'll be found on the low end contesting while the debate rages ....

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