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From: Earl W Cunningham <k6se@juno.com>
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About a week ago, Mike Knowlton posted a query on this reflector
regarding an array of two Flag antennas. Both I and Tom, W8JI replied to
Mike via the reflector, and our opinions disagreed. Tom was pro-endfire
for Mike's proposed array and I was pro-broadside. Tom and I
subsequently exchanged e-mails privately several times about the matter,
and we both spent a good amount of time modeling to come to a conclusion.
Tom's reasons for recommending an endfire configuration were mainly that
it required less space and that nulls could be steered completely around
a 360-degree circle. My main reason for recommending a broadside
configuration is that beam steering of the main lobe was available to a
limited extent.
First, here is the summation of how an array of two Flags or Pennants in
an endfire configuration with 135-foot spacing will behave when varying
the phasing. The phase angle convention used here is the phase of the
signal in the front element of the array is varied while the phase angle
in the rear element is held at 0 degrees. The frequency used for all
modeling was 1.830 mHz.
With the front element at -90 degrees (which is the usual amount of phase
difference for two endfire elements spaced 1/4 wave), there is a
single-lobe cardioid-shaped pattern with maximum received signal from the
front of the array. The maximum signal elevation angle for this array is
30.2 degrees above the horizon over "good" (as defined by the ARRL)
ground. All subsequent modeling results for this array were taken at
this same elevation angle. The horizontal half-power beamwidth at this
elevation angle was 123.6 degrees, with a deep null at the rear of the
array, 61.94 dB down from the front.
Changing the phasing of the front element in steps of 10 degrees, i.e.,
-80, -70, -60, etc., showed a gradual broadening of the cardiod lobe,
resulting in a progressively wider horizontal beamwidth. The deep null
at the rear
of the array continued to exist. This broadening of the horizontal
beamwidth continued until the phasing reached -10 degrees when the
flattening of the cardioid pattern caused the signal at the direct front
of the array to be down 0.02 dB from the maximum (which was now at plus
and minus 22 degrees from the front). At 0 degrees phasing, the front
was down 0.11 dB from the max which was now at plus and minus 34 degrees
from the front. So far, the deep null at the rear of the array remained.
For this first 90 degrees of phase rotation, there appears to be no
advantage whatsoever for receiving weak signals. On the contrary, poorer
reception will most likely result due to the poorer S/N of the array as
the phase angle advances and the pattern broadens.
>From 0 degrees until +80 degrees, the horizontal pattern resembles the
shape of a lima bean, i.e., is kidney-shaped, with the pattern off of the
front of the array becoming progressively flatter as the phase angle
increases. At the same time, maximum signal progressively moves away
from the front. The deep null at the rear is still there.
At +90 degree phasing the front of the horizontal pattern becomes
indented, which is the beginning of a second null directly off of the
front of the array. This shallow null is 12.06 dB down from the two
lobes which are forming (due to the splitting of the main lobe), now at
plus and minus 88 degrees from the front of the array.
At +100 degree phasing the front null deepens to 26.91 dB down from the
two lobes which are at plus and minus 93 degrees from the front.
At +102 degree phasing, the front null reaches its maximum, 50.12 dB down
from the maximum of the two lobes at +/- 94 degrees. The deep null at
the rear still exists and the horizontal pattern look like a slightly
lop-sided figure "8". The is the first point which could have some real
usefulness - that of nulling an unwanted signal (or noise) directly to
the front of the array while receiving a signal off to the side.
After +102 degree phasing, the front null begins to fill in with a new
lobe. At +110 degree phasing, the front lobe is down only 13.82 dB from
the two "main" lobes which are now at +/- 97 degrees from the front.
There are deep nulls now at each side of the front lobe, at +/- 26
degrees from the front of the array.
We are now in the phasing region where useful nulls exist. At +120 degree
phasing the front lobe has grown to -5.89 dB down from the "main" lobes
at +/- 102 degrees from the front. The deep front nulls are now at +/-
40 degrees from the front.
At +130 degree phasing, the front lobe is now down only 1.10 dB down from
the other two lobes at +/- 106 degrees. The deep nulls each side of the
front lobe are at +/- 50 degrees from the front.
At +133 degree phasing, the front lobe and the other two lobes (now at
+/- 107 degrees) are all equal in amplitude. The two nulls each side of
the front lobe are at +/- 53 degrees from the front.
At +140 degree phasing, the front lobe is now the largest, with the two
other lobes at +/- 110 degrees down 2.57 dB from the front lobe. The
deep nulls each side of the front lobe are at +/- 59 degrees from the
front
At +150 degree phasing, the two minor lobes at +/- 114 degrees are now
5.70 dB down from the front lobe. The deep nulls each side of the front
lobe are at +/- 67 degrees from the front.
At +160 degree phasing, the two minor lobes at +/- 118 degrees are down
8.54 dB from the front lobe. The deep nulls each side of the front lobe
are at +/- 75 degrees from the front.
At +170 degree phasing, the two minor lobes at +/- 123 degrees are down
11.24 dB from the front lobe. The deep nulls each side of the front lobe
are at +/- 83 degrees from the front.
At 180 degree phasing, the two minor lobes at +/-127 degrees are down
13.9 dB from the front lobe. The deep nulls each side of the front lobe
are directly off the sides of the array at +/-90 degrees.
At this point the horizontal pattern takes on the appearance of a fish,
with the front lobe as the body of the fish and the minor lobes as the
tail fins.
>From +190 (-170) degree phasing to +230 (-130) degree phasing, the "tail
fins" continue to decrease in size and the deep nulls continue to
progress towards the rear of the array.
At +240 (-120) degree phasing, the "tail fins" (now at +/- 157 degrees)
are 36.63 dB down from the front lobe. The deep nulls at +/- 140 degrees
each side of the front are no longer very meaningful because the rear
lobes are already quite small.
Progressing from +250 (-110) degree phasing, the rear lobes continue to
disappear until they are completely gone when the phasing is back where
we started at +270 (-90) degrees with the original cardioid pattern.
Throughout this 360-degree rotation of phasing, a deep null remained at
the rear of the array.
=====
Here are the results using a 2-element array of Flags or Pennants with
200-foot broadside spacing. All lobe angles and null angles given here
are at an elevation angle of 31.5 degrees, which is the angle above the
horizon over "good" ground where maximum signal occurs off of the front
of the array when both elements are in phase.
With 0-degree phasing there is one lobe, shaped like a narrow cardioid,
with a horizontal half-power beamwidth of 83.6 degrees. There is a deep
null to the rear, 43.5 dB down from the front.
With the left-hand element (as viewed from the rear of the array) fed
with +10 degree phasing (the other element always remains at 0 degrees),
maximum signal is skewed 4 degrees to the left, with a beamwidth of 83.7
degrees. The deep rear lobe remains directly to the rear of the array.
To shift the maximum lobe 4 degrees to the right, feed the right element
with +10 degree phasing instead of the left one.
>From here on, we'll change the phasing of only the left element, knowing
that if we phase shift the right element instead that the pattern will
shift the opposite way.
At +20 degree phasing, the maximum signal is 7 degrees to the left of
front with a beamwidth of 83.8 degrees. The deep null to the rear is
still directly to the rear of the array.
At +30 degree phasing, the max is 11 degrees to the left of front with a
beamwidth of 84.3 degrees. The rear null is still at 180 degrees.
At +40 degree phasing, the max is 14 degrees to the left with a beamwidth
of 84.7 degrees. The rear null stays at 180 degrees. An assymetrical
horizontal pattern is evolving, being squeezed in on the right side of
the array.
At +50 degree phasing, max is 18 degrees to the left with a beamwidth of
85.3 degrees. The rear null is still at 180 degrees. The "squeeze" on
the right side of the array is forming into a null at 96 degrees to the
right of front, and 21.91 dB down from max.
At +60 degree phasing, max is 21 degrees to the left with a beamwidth of
85.8 degrees. The rear null remains at 180 degrees. The new null is 92
to the right of front, 30.27 dB down from max.
At +66 degree phasing max is 24 degrees to the left with a beamwidth of
86.0 degrees. The null at the right side is at its deepest, 61.7 dB down
from max and 93 degrees to the right of front. Almost directly to the
rear of the main lobe, a minor lobe is formed by the right null and the
still-present null at 180 degrees. The minor lobe is 21.26 down from the
main lobe and the pattern is fairly symetrical, beaming at 24 degrees to
the left of front.
At +70 degree phasing, a new lobe begins to grow out out the area where
the deep null was at +66 degree phasing. This new lobe is centered at 88
degrees to the right of front and is 32.67 db down from max. Deep nulls
now exist each side of the minor lobe, at 74 and 106 degrees to the right
of front. The lobe between the 106 and 180-degree nulls is 21.88 db down
front max. Max is 25 degrees to the left of front with a beamwidth of
86.1 degrees.
At +80 degree phasing, the new lobe centered at 85 degrees to the right
of front is 21.80 dB down from max, which is 28 degrees to the left of
front with a beamwidth of 86.2 degrees. The other lobe is centered at
151 degrees to the right of front and is 23.49 dB down from max. Deep
nulls exist at 61 and 119 degrees to the right of front, with the rear
null still at 180 degrees.
At +90 degree phasing, the max is at 32 degrees to the left with a
beamwidth of 86.1 degrees. The two minor lobes are centered at 82 (16.87
dB down) and 155 (25.22 dB down) degrees to the right of front. The deep
nulls are at 52 and 128 degrees to the right of front and the
ever-present null at 180 degrees.
At +100 degree phasing, the max is at 35 degrees to the left with a
beamwidth of 85.7 degrees. The two minor lobes are centered at 80 (13.16
dB down) and 158 (27.12 dB down) degrees to the right of front. The deep
nulls are at 44 and 136 degrees to the right of front and at 180 degrees.
At +110 degree phasing, the max is at 39 degrees to the left with a
beamwidth of 84.9 degrees. The two other lobes are centered at 77
(-11.03 dB) and 161 (-29.25 dB) degrees to the right of front. Deep
nulls are at 38 and 142 degrees to the right of front and at 180 degrees.
At +120 degree phasing, the max is at 42 degrees to the left with a
beamwidth of 83.8 degrees. The other two lobes are centered at 75 (-8.94
dB) and 164 (-31.69 dB) degrees to the right of front. Deep nulls are at
32 and 148 degrees to the right of front and at 180 degrees.
At +130 degree phasing, the max is at 45 degrees to the left with a
beamwidth of 82.4 degrees. The other two lobes are centered at 72 (-7.13
dB) and 167 (-34.55 dB) degrees to the right of front. Deep nulls are at
26 and 154 degrees to the right of front and at 180 degrees.
At +140 degree phasing, the max is at 48 degrees to the left with a
beamwidth of 80.8 degrees. The other two lobes are centered at 70 (-5.52
dB) and 170 (-38.06 dB) degrees to the right of front. Deep nulls are at
20 and 160 degrees to the right of front and at 180 degrees.
At +150 degree phasing, the max is at 51 degrees to the left with a
beamwidth of 78.9 degrees. The other two lobes are centered at 67 (-4.04
dB) and 172 (-42.64 dB) degrees to the right of front. Deep nulls are at
15 and 165 degrees to the right of front and at 180 degrees. The lobe at
172 degrees has grown so small that it's like a broad null from 165 ro
180 degrees. The other lobe at 67 degrees has grown considerably.
At +160 degree phasing, the max is at 54 degrees to the left with a
beamwidth of 76.8 degrees. The other big lobe is centered at 65 degrees
to the right of front and is down 2.65 dB from the main lobe. there is a
deep null at 10 degrees to the right of front and a broad deep null from
170 degrees to the right of front to 180 degrees. The pattern looks like
a lop-sided figure "8".
At +170 degree phasing, the max is at 57 degrees to the left with a
beamwidth of 74.4 degrees. The othe lobe, centered at 62 degrees to the
right of front, is now only 1.31 dB down from the main lobe. Deep nulls
are at 5 degrees to the right of front and at 175 to 180 degrees.
At +180 degree phasing, both lobes are equal in amplitude with max at 60
degrees either side of the front of the array. Each lobe has a beamwidth
of 72 degrees. The deep nulls are directly to the front and to the rear
of the array.
It's not necessary to run the phasing at +190 (-170), +200 (-160), etc.,
degrees because the patterns are a mirror image of the ones already run,
but with max to the right of front and the nulls to the left of front.
In summary, with the endfire configuration, nulls can be steered
completely around the array by phasing the front element + 102 to +240
degrees while holding the rear element at 0 degrees phasing. Some lobe
control is also available, but with multple lobes, such as the
triple-lobe pattern with +133 degree phasing.
With the broadside configuration, the forward lobe can be steered left or
right of directly forward by up to as much as 60 degrees, but +/- 30
degrees is probably more practical due to the growth of the minor lobe
off to the side when greater skewing of the pattern is used. With this
in mind, a phase difference from 0 degrees up to +/- 90 degrees in either
broadside element will do the job. Limited null steering is also
available, but is not as thorough as with the endfire array.
It was noted that, when changing the phasing from the normally-used
pattern, the elevation angle of max signal increased several degrees for
the endfire array, but decreased for the broadside array.
During the modeling tests, only phasing was changed, but not the
amplitudes. Whenever the currents were not kept equal in each element of
the array, any nulls would severely deteriorate, i.e., the pattern would
be smoothed out. This is analogous to altering the amplitudes into the
receiver from each element of the array. Tom pointed out that modeling
assumes a perfect world, but that in practice, varying the gain controls
on the MFJ-1026 can be of use in steering the nulls (in addition to the
phasing controls).
If one wants to steer nulls completely around the array to attenuate
noise or QRM, the endfire configuration is best. If you want to steer
the forward lobe a limited amount, then use the broadside configuration.
Sorry about the length of this post, but it may be of value to those
planning a 2-element array of Flags or Pennants.
73, de Earl, K6SE
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