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.