Thats interesting - so really what your saying... try to match... if you cant get it below 2.0 then go with a 4:1? Isnt there a more scientific (mathematical approach) to choose the proper balun?
No, that isn't what I was saying.
First, we have an unbalanced coax feeding an unbalanced antenna, so a BALUN is
somewhat out of place already. There are actually two functions that we are
considering: a wide-range impedance matching device between the tuner and
the antenna, and a feedline choke, which is the same thing as a current balun,
to reduce the amount of RF flowing on the outside if the coax. Let's consider
these two functions separately.
First, the matter of impedance matching. The impedance of a single wire radiator
will vary over a wide range when used over a range of frequencies, such as
160m to 10m. It might be 25 ohms at quarter wave resonance, lower with some
capacitive reactance when shorter than a quarter wavelength, and up to several
thousand ohms (depending on the radiator diameter) when it is a multiple of a
half wavelength. The tuner has to match this impedance on the bands of
operation.
If you use a theoretically perfect 4 : 1 transformer, the 25 ohms will appear to the
tuner as 6.25 ohms. You can use W9CF's handy tuner simulator
http://fermi.la.asu.edu/w9cf/tuner/tuner.htmlto estimate the tuner loss in the two cases: you'll find that the losses are lower
when matching 25 ohms. In fact, many tuners tend to be more efficient matching
higher impedances than lower ones, though it does depend on the specific tuner
design, frequency, etc. So if you have the tuner right at the antenna feedpoint,
and a long as it has sufficient range, efficiency generally is higher if you don't use
a transformer to step down the impedance. In the real world it gets more complicated
because we don't have perfect transformers that operate over that range of
impedances and frequencies
When the antenna is fed via coax to a tuner in the shack, then using a 4 : 1 UN-UN to
step down the impedance may give lower coax losses in some cases. The cable length
will affect the impedance seen by the tuner, so one can't generalize whether it will make
the impedance more or less efficient to match.
You can model the antenna, transformer and feedline, and calculate the resulting
impedances and losses for each band to see which works best for you. Or you can
install such a system and measure the actual field strength to compare the two
methods if you want to know exactly which is better on each band. But, for the
end-fed radiator with a tuner right at the base, personally I would choose not to use
any sort of transformer between the tuner and the antenna unless you had problems
getting a match on one or more bands, and I'd consider adjusting the radiator length
and/or the tuner matching range before adding a transformer, because the impedances
where you have matching problems are going to be ones where the non-ideal
characteristics of the transformer tend to become most apparent.
Regardless of where the tuner is located, the coax shield from the antenna feedpoint
to the shack is connected in parallel with the radial wires, and will act like a radial
with current flowing on it in many cases. That's the reason for using the coax
choke, e.g. current balun, in the feedline near the feedpoint. On one hand it
doesn't matter which side of the tuner it is on, but if the antenna goes right into
the tuner then it goes on the coax side by default. It certainly needs to be between
the radials and the main feeder, and if the radials are bonded to the case of the
tuner, then it can't go in the lead between the tuner and the antenna.
So we come to the conclusion that, with a proper tuner right at the antenna feedpoint,
putting a feedline choke in the coax between it and the rig is likely to be the most
efficient installation. You can run models or experiments to see if that is really the
case for your specific antenna length and tuner circuit, but in general it is a good
starting point.