It's a multidimensional problem that requires more than just AC circuit
analysis when a transmission line is involved. The tuner, coupler,
matchbox, ATU are generally all performing the same function. They are RF
impedance transformers but they're doing much more than basic Z
transformation when a transmission line is involved. If we didn't have a
transmission line, we can compute complex Z and the component values needed
for any desired resulting Z and phase -- just by applying AC circuit
analysis. When a transmission line is involved, two principles are melded:
AC circuit analysis and transmission line mechanics.
When a line is involved, a tuner is performing two important functions: (1)
it transforms a complex Z (some random R+j0 value) into some other complex
Z, usually 50+j0 for most of our needs; and (2) as the tuner is adjusted to
perform a system reactance cancellation where that system is composed of an
antenna and transmission line, a precision reflection mirror is set-up at
the tuner's output terminals . A reflected wave from a load to line
mismatch that appears at the tuner output can be precisely phase-inverted
with teh tuner controls such that it recombines with the forward wave back
to the load. Any reflection on the line is created solely by a
characteristic line Z to load Z mismatch. The greater the mismatch, the
higher the line SWR.
Folks who say that a tuner is only making a transmitter happy are usually
not comprehending (2) above. They completely "get" (1) and to them, as
long as the transmitter sees 50+j0, the transmitter is "happy." But the
transmitter is even happier if we also introduce it to (2). The transmitter
is happier because not only can it deliver its full rated power into the
line, it can even deliver it all the way to the load, even under conditions
of extreme line-to-load mismatch on a nearly lossless line.
Can a tuner really tune an antenna that is not already resonant? Yes, but
it does so as a complete system when connected to a transmission line.
Tuning involves system reactance cancellation (X=0). A match involves a
reactance cancellation and a target resistance magnitude (e.g., 50+j0, or
stated another way: X=0 and R =50). No amount of tuning of the line section
can fix the load to line mismatch. It's a fixed value. But by using a
tuner, changing line length, or a combination of the two, the 50+j0 target
can bet met when the load to line mismatch is reasonable. Moreover, as long
as line loss is low, these methods can assist the transmitter in not only
delivering full power into the line, but also the load.
Finally, how many times have we heard that SWR *never* changes on a
transmission line, even a lossless line? That statement is only be true if
(1) the line's characteristic Z does not change; or (2) the line is
extremely lossy ** Line SWR does change when mixing and matching low-loss
lines of different characteristic Z. Example:
A dipole has a feedpoint Z of 50+j0 at the operating frequency.
The dipole is connected to an exact electrical half-wave of nearly lossless
transmission line with a characteristic Z of 600-ohms.
At the input end of the line we connect a random length of low-loss coax
with a characteristic Z of 50-ohms.
So, we have a dipole, then 600-ohm line then a random section of 50-ohm
line. Here's what we get:
The SWR anywhere on the 600-ohm section is 12:1
The Z at the input end of the 600-ohm line is 50+j0
The SWR anywhere on the 50-ohm line is 1:1 and we don't care how long it is
except for loss as line distance increases.
The transmitter is not only happy, it's even happier because it's delivering
full power all the way to the load.
In this example, the SWR is not the same everywhere along the complete
transmission line. We didn't use a tuner this time to get 50+j0 as seen by
the transmitter. But we could have. We could substitute the 600-ohm
section of line with a tuner and achieve the same result.
Paul, W9AC
** (e.g., with 1000 ft of RG-174 an SWR bridge will read different SWR
values at different distances from an unterminated load. It reads nearly
1:1 at the transmitter because of the high return loss (the reflection is
severely attenuated) and infinity near the unterminated end.
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