[TowerTalk] 4 Square phase line length question

[Jim Lux]

----- Original Message -----
From: "Tom Rauch" <w8ji at contesting.com>
To: "Jim Lux" <jimlux at earthlink.net>; "Dan Levin" <dan at andlev.com>;
<towertalk at contesting.com>
Sent: Sunday, May 09, 2004 9:30 AM
Subject: Re: [TowerTalk] 4 Square phase line length question


> > > The hybrid does NOT provide equal voltages at the output
> > > ports, and it requires matched loads for predicted
> phase.
> >
> > However, it's presumed that one could adjust fewer
> components in the hybrid
> > to compensate for the band change than fiddling with each
> element.
>
>
> A four square has two elements on the diagonal fed in-phase
> to form a virtual single center element. It is really like a
> three-element in line array with a very wide center element.

Not exactly... those two "center" elements form a phased array with a
distinct fore and aft lobe, as opposed to a omnidirectional pattern of a
single element.  If you describe wide as being a uniformly illuminated
aperture, maybe you'd be closer, but a 4 square is somewhat different from a
1:2:1 weighted endfire array.  The forward gain will be quite close, but the
side and backlobes will be different.

If one is building the 4 square for the front/back ratio (as opposed to
forward gain) or the null/minimum off the back, then the difference is
important. And sadly, the depth of the null is quite picky with respect to
the relative currents and phases.. you can have huge errors in drive and the
forward gain won't change much, but it doesn't take much error to make a 20
dB null a 6 dB null.

Mike Tope's comment about using a scope (and Tom's use of a vector
voltmeter) at the voltage end of the 1/4 wave transformers is basically
sound, except for the fact that you are depending on the 1/4 wave behavior.
One would want to do a quick calculation of how much effect a frequency
change will have. 75 vs 80 m is roughly a 6% change, 14.1 vs 14.3 is only a
1-2% change. The 6% change in length corresponds to a 9-10% change in the
value of cosh(x) and sinh(x) around pi/2 (90 deg).  Running a quick
simulation in XLZIZL.xls... if you put 1/4 wavelength ( at 3.75 MHz) of
ideal 75 ohm coax  at 3.75 MHz) feeding 50 ohms, over the range from 3.5 to
4 MHz, the reactive component at the other end of the coax ranges from
about -5 to +5 degrees.  Not a huge variation....


>
> Let's assume we tweak components to obtain a 90-degree shift
> (which is not optimum anyway) and correct VOLTAGES at the
> output port compared to the common point. The hybrid only
> controls the current and phase relationship between two out
> of the three (virtual) elements. Tweaking the ratio and
> phase between two elements and ignoring the other isn't
> likely worth the effort. The array requires equal currents
> in each element ( the fact there are two center elements is
> what gives it what is effectively a 1:2:1 current ratio),
> and it requires a phase shift larger than 90-degrees for
> optimum pattern.

optimum defined how?
Sure, if you want to try for superdirectivity, you want a bit of excess
phase shift (say, 130 degrees), but, on the other hand, the incident wave
you're more than likely receiving or transmitting is hardly coming from the
horizon, but some degrees above, so you have to compensate for that too (the
higher the elevation angle, the smaller the phase shift would be to match it
exactly, with vertical incidence requiring zero phase shift).  And, of
course, the phase center of that 1/4 wave vertical isn't too well defined
and varies somewhat with look angle.

I suspect that other factors will more more dominant...



>
> How would we handle the remaining port in reference to the
> other elements?  Add another network? How would we measure
> and adjust that mess?
>
> I think it is better to leave it all alone than to open a
> can of worms that could likely make things worse!! Hybrids
> work OK as is. If someone wants an exceptional array, they
> wouldn't use 90/180 degree shift, a dump resistor, and they
> wouldn't use a system that forces equal power.

Most of the (amateur radio) phased array systems I've seen recently don't
try to force equal power (viz. Wilkinson divider and old ARRL antenna book
designs), but try to get the "right" currents in the elements by using some
sort of voltage sources with the right phase and 1/4wave lines to turn
voltage into current at the element.