Hiya Dave
First of all, welcome to the forum!
You have the making of a good tri-band rotatable dipole by the sounds of things.
I would have thought yes to a balun for two reasons:
- Dipoles have a much more symmetrical radiation pattern when fed with a balun (choke baluns work well)
- Because the elements are shortened (by virtue of the traps adding inductive loading) I'm certain that the feed-point impedance will be lower than a true full size dipole.
Without the reflector or director present you might find that the actual resonant frequency might not alter too much, but my guess would be that the feed-point impedance would certainly have changed.
The odd thing with antennas is that very often you find that although an SWR meter may give a 1:1 reading, the impedance might be anything other than 50 Ohms.
For example a dipole may give a 1:1 SWR reading (at resonance), and yet the feed-point impedance will be 70 Ohms (not the 50 Ohms many folks expect to find). After all, SWR is the ratio of forward to reflected power, and is not a measurement of impedance. You can just as easily have a 1:1 SWR ratio on a 300 Ohm antenna as a 70 Ohm one.
However, because modern sets tend to be designed with 50 Ohm unbalanced loads in mind, and because modern unbalanced coaxial feeders are generally 50 Ohms, it would be best if we can get our antennas to also have a 50 Ohms impedance too. That way all of the losses throughout the system can be reduced to the minimum (50 Ohm transmitter, feeding 50 Ohm cable, connected to a 50 Ohm load).
My guess would be that for 20m and 15m the impedance will be below 50 Ohms,and for 10m maybe at best 50 Ohms, though again most likely below that.
The amount the impedance is reduced by would be determined by the amount of artificial loading involved, and also where it is with respect to the feed-point. Again, it is not easy to calculate and it would be quicker and easier to measure it.
If you do have access to an antenna analyser then you can find out the SWR and impedance in a matter of minutes.
Another way is to make a number of baluns with various ratios, and try each one in circuit in turn while watching the SWR readings, and also the current present on each of the dipole elements (or even measure the field strength).
Making lots of baluns can be a pain, so what I use here is an MFJ-914 Auto Tuner Extender, which is a fancy sounding name for a balun (actually an Un-Un) with switchable ratios. The '914 can step down, give one to one, or step up ratios, so it is a quick way to try a number of transformer variants and the results found may be used to help calculate a permanent fixed balun.
If you don't fancy making baluns and so on, you could use an open ended 1/4 wave stub and try different tapping points by trial and error, but the down side to that method is that the stub will generally only be helpful on one band which is of no use if you wanted to use all three bands the antenna covers.
If you're really lazy just try a one to one ratio balun and who knows, maybe you will get lucky, or at least find that the antenna is within the 3:1 SWR range that most modern auto tuners can handle (assuming you use an auto ATU that is).
Hope my ramble helps
73, Mark.