It's easy to see who's read Chapter 8 of the ARRL Antenna Book and who
hasn't! Denny has the right idea.

What you need to do in order to get a decent front/back ratio from the
two elements is to create equal amplitude and correctly phased fields
from them. If one is shorter than the other, it needs to get more
current to produce the same field as the longer one. The current at the
feedpoint of a shunt fed tower isn't equal in either magnitude or phase
to the current in the tower itself. So adjusting the feedpoint currents
for some relative magnitude and phase won't get you the right tower
currents unless you've accounted for the transformation.

It's much easier to get 2 - 3 dB gain than to get good f/b ratio -- you
can goof up the current magnitude and phasing pretty badly and still get
noticeable gain in about the right direction. (In a way it's too bad
this is true, because a lot of people see some gain and assume it means
that they've got the phasing they planned, when in reality they're way
off. Then they extend this misinformation to other arrays and can't
figure out why they don't work.) But with the setup you've described, it
would be easy to be far enough off that you wouldn't get the gain,
either, at least not in the expected direction.

It can be done, but as Denny says, it's much more complicated than just
using a 90 degree "phasing line" as another poster suggested. That
approach generally doesn't work for even the simplest of cases (see the
Antenna Book for the reasons), and it certainly won't work here. What I
would do is model the elements without the shunt feed system and adjust
the base currents in the model (by putting current sources at the bases)
to get the desired pattern. Then I'd make an adjustable feed system like
the L network feed described in the Antenna Book or one of the other
systems described in _Low-Band DXing_. Then I'd arrange some sort of
current probes at the tower bases and adjust the currents to match the
model currents. A final adjustment could be made by putting a signal
source or detector to the rear of the array and adjusting for the best
null. If you do everything just right, you'll get right at 3 dB gain
over a single element and a very good null directly to the rear.

A parasitic array is an option, but again I'd model it. You have the
same problem of getting the right element currents, but now the only
adjustment you can make is the parasitic tower's resonant frequency. You
might have trouble getting enough current in the short tower to do you
much good. A second problem with the parasitic array approach is that
any ground loss will eat you alive. Even what you consider to be a good
ground system might not be adequate, especially for the short element.
Be sure to include a realistic amount of ground system loss in any model
you make.

Alternatively, you can just connect the towers together through some
sort of arbitrary feed system (or you can carefully cut a "phasing line"
-- you have the same probability of success with either method) and have
lots of fun seeing in which directions it seems to work well and which
it doesn't.

Roy Lewallen, W7EL

Denny wrote:
Short answer, no...
Long answer, yes...

And I cannot do a long answer justice here on a forum such as this...
Perhaps W7EL or W2DU will jump in here and rescue me...
The major issue you face is that the towers are shunt loaded which
creates phase differences between the two right from the git-go, even
when both are resonated... The fact that the feed points of the two
towers are initially out of phase needs to be tuned out in setting up
the 90 degree total phase difference...

Certainly it can be done... You will need to measure the input
impedence and reactance for each tower as built...It will take a
pick-up coil on each tower fed to an oscilloscope so that you can see
the phase difference as you adjust the phasing network / phasing lines
to reach the desired 90 degrees phase lag on the leading element...
Read W7EL's contribution to the ARRL Antenna Handbook on the subject of
properly phasing lines / antennas... This will give you enough
information to decide if you want to proceed...

I long ago decided life is too short for designing all driven arrays
when I can build, install, and tune, parasitic arrays in less time than
it takes me to work the equations for designing the needed phasing
networks for a driven array...

denny / k8do