Four-Square
The 220-ft tower has five
catenary lines, each about 500 feet long. Four of
these lines, running NE, SE, SW, and NW support four 1/4-wavelength wire
verticals used in a 160-meter four-square antenna.
Each four-square element is made from a
single # 9 AWG
aluminum wire. The elements are fed with 50-ohm
foam dielectric
coaxial cables. Each element has about fifty 1/4-wavelength radials. These
radials are bonded to the large radial system of the 200-foot tower at points
where more than two wires cross. This makes the entire grounding system for the
200-foot and four-square elements more similar to a large screen rather than
just than individual radials.
Four-Square Design
One item overlooked throughout the history of the four-square is the
effective element spacing. Effective element spacing is not the same as the
distance along each side of the square. The effective spacing is less than that
distance, because the array fires from corner to corner. The effective array
length is 1.414 times the spacing along each side, not twice that length. With
90 degree per side array size, we really only have a 127 degree long end-fire
array when firing across diagonal corners. The correct phasing for an optimum
null at zero degrees elevation directly in line with the array is not 90 and 180
degrees, but is actually around 117 and 234 degrees! With the traditional 90 and
180 degree phasing, the array should be stretched to a corner-to-corner distance
of 180 degrees, making each side 127 degrees long. Unfortunately feed lines of
1/4-wl electrical length won’t reach that distance with velocity factor and
connection lengths involved, so the obvious choice is to use greater than
90-degree phase shift. As an additional benefit, the directivity and gain are
higher with closer spacing and larger phase shift. Performance is better for
both receiving and transmitting.
The phase and spacing used are obviously not optimum, and the popular
coupling units almost certainly do not do what we expect. They sacrifice gain
because any four-square 1/4 wl on a side really does not “want” 90-
and 180-degree phase shift, and they really are not designed for the real
impedance presented by the feed lines from the elements. Why do we use such a
design? Probably because it was originally used, and no one ever looked at the
array in any detail. It was easy to copy the original concepts, and no one
thought to check and see if the phasing systems were optimized.
Array Transmission Lines
(the following assumes lines have negligible loss)
I use 1/4-wavelength 50-ohm lines feeding each four-square element. 1/4-wavelength
lines have a unique property. When odd-quarter-wave lines are
sourced from equal voltages, the load ends of the line will
source equal currents into any load impedance.
There is a second important often overlooked property
of transmission
lines used in
phase-critical
systems. When a
transmission line is misterminated,
the line has
standing waves. When
there are standing
waves, phase shift
of the line no
longer
equals the electrical length of the line. An exception occurs when the line is
any multiple of 90-degrees.
Just as impedances invert every 1/4 wl, the fixed source voltage at one end
becomes a fixed source current at the other end. Not only that, phase shift
is constant even though the lines are terminated by different load impedances.
Many arrays use this concept to advantage.
By the way, a current sourced 1/2 wl line
would work just as well as the 1/4 wl lines if we fed the line with equal
currents instead of equal voltages. (As a matter of fact that concept is behind
a two-band transmitting array I designed.)
Current Distribution
A two-element directional system requires equal current at the current
maximum of each directional element for maximum F/B ratio and gain. A
three-element array would require a binomial 1:2:1 ratio for best pattern. The
center element, in effect, has to supply a field for each of the two outer
elements to work against, it is doing double duty. The four-square is a novel
approach to a three-element array, the center two elements are fed in phase, and
act as one common element. If all four elements have equal current, total center
element current is twice the current in each end. The 1:2:1 current distribution
is satisfied.
With elements series-fed at the point of current maximums, each element
requires equal current at the feedpoint. (If the elements were voltage-fed at
the voltage maximum, they would require equal voltages at the feedpoint to have
equal currents in the elements!) This makes transmission-line type phasing
systems easy to design. We simply design the system so each phasing-line has
unity standing wave ratio, and tie the elements directly to the phasing lines.
Because voltages are equal everywhere in the phasing system, element currents
are equal at the end of each 1/4-wavelength feed line.
Phasing Systems
My design operates the phasing line without standing waves. Since the phasing
line is not a multiple of 1/4-wl, if the delay line were misterminated phase
shift would not equal the line electrical length. Voltage at each end of the
delay line would also be different. Since the line is matched, phase shift will
be equal to the electrical length of the line and voltages will be equal at each
end of the delay line.
There really isn’t any need for “dump” resistances or hybrids in
any phasing system. If you look at the systems, the dump resistances really
don’t guarantee performance. A four-square system never requires controlled
“power splitting”. As a matter of fact, equal power in each element
would guarantee poor F/B ratio and gain.
The only way to
obtain satisfactory
F/B ratio with a
hybrid coupler is to
somehow mess up the
hybrid so it doesn’t
act like a real
hybrid!!
Keep in mind that each element, other than the two in parallel, has a
different feed impedance. With different load impedance at each element current
can’t be equal in each feed line element group if power is divided evenly. The
four-square system, at least one with 1/4 wl feed lines, actually requires equal
voltages. Equal power insures a poor pattern, while equal current at the element
(or equal voltage at the start of the 1/4 wl feed lines) guarantees optimum
patterns. Most four-squares work as well as they do only because the array is
somewhat forgiving. They are a good example of reasonable performance through
oversight, rather than careful planning.
I solved these problems in my system by placing the phasing common-point in
the direction of maximum radiation and using crossfire
phasing. This is very similar to the feed-system of a log periodic, except I
optimized phase shift and current distribution.
A crossfire delay line system feeds the center two elements in my
array. This is similar to the scheme I use in my phased
receiving antennas. Each center element has around 25 ohms of operating
impedance, and that produces 100 ohms at the end of the 1/4-wavelength 50-ohm
feed line that goes to each element. The center two elements, when paralleled,
have a combined impedance of 50 ohms.
The delay line from the common point to the center two element junction is 60-degrees
of RG-8 coax. The 180-degree “flip” comes by using a choke balun. This
is similar to the technique I use in receiving
antennas. The primary difference is in core size and materials, my
high-power inverting transformer uses eight 2-inch diameter 65-material cores
and Teflon insulated coaxial cable. This choke allows the shield and center to
be transposed at one end of that delay line. Loss is low in the delay system,
because it is a matched 50-ohm line. It is also only 60-degrees long and only
handles only about 2/3 of total system power (almost 1/3 of the system power is
applied directly to the front element).
The rear element offers a slight problem, because that element has a very low
impedance. It almost has enough current, through mutual coupling alone, to be
fully functional. As a consequence, it requires very little common point power.
With a 1/4-wavelength feed line and parallel reactance canceling, the rear
element presents several hundred ohms of resistance to the phasing network. My
solution for feeding the rear element was to build an artificial transmission
line using lumped components. For the rear delay line, I used multiple L/C
sections to simulate a transmission line with a characteristic impedance matching
the rear element. This has three advantages:
1.) Q is low, making phase-shift much less frequency critical.
2.) Voltage is equal at each end of the artificial transmission line,
allowing the delay line to all parallel each other at the
common point.
3.) I can easily “tweak” delay line characteristics with a few
adjustments and optimize the array null.
In effect, I created a high-impedance transmission line from individual L/C
components, and only needed to use 120 degrees of lag (the 240 degree lead I
needed is electrically the same as a 120 degree lag) in the network. This is all
very similar to the system in my small
receiving four-square. Because current is low, components can be modest
sized. The end result is more bandwidth, more stability, and less loss than a
simple one-stage network.
The Results
While this may sound like a complex system, it is very simple in practice.
This array has exceptional bandwidth, exhibiting useful F/B ratio and gain over
the entire 160-meter band. This also means a similar array for 80-meters would
cover almost all of 80 and 75 meters. Additionally, this array has very low loss
regardless of operating frequency. It does not divert power into a dump
resistance.
My phasing design produces higher gain than conventional 90/180 degree phased
four-squares through a tighter pattern and less loss.
Because the pattern is “tight”, I added a simple system that
provides a wide East, South, West, or North pattern. That pattern nearly equals
the gain from a traditional four-square, and provides equal or better gain than
traditional four-squares in all directions over a wider frequency range.
Here is the pattern of a traditional four-square at 15 degrees elevation,
assuming perfect distribution and phase.
This neglects losses
in the Hybrid dump
resistor, and phase
and current
distribution errors:
Note the gain is 8dBi, and the 90-degree azimuth gain is -2.5dB maximum or a
net gain of 5.5dBi in the “between” directions
Here is the pattern of the same array with 120/240 degree phasing:
The gain is 9.14dBi, and the cursor azimuth gain is -4 dB maximum for an
“in between” gain of 5.13dB. You only give up .4dB FS at the worse
point for a net gain of 1.14dB in primary directions.
Gain increase
over an optimized
Hybrid coupler
system is just over 1 dB
from the increased
directivity. In
addition to that,
there is also
decreased loss. F/B ratio change is quite noticeable, as is the
ability of the antenna to receive.
My actual working array is even more flexible, allowing the choice of eight
directions plus omni.
In concert with a large ground system (the array sits in an area that has
ground systems extending for at least a
half-wavelength in all directions) and
reduced loss in the phasing system, overall performance has been enough to
offset salt-water path and distance advantages of northeast stations using
smaller Hybrid
Coupler systems.
Since
update on Nov 11
2008
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