A few comments based on my own experience with various receiving arrays:
Circle diameter of the Hi-Z array:
A circle diameter of 200 feet is specified for the Hi-Z 8-circle array on
160m. In fact, I have found that there is nothing "magic" about 200 feet.
It happens to be a "good" compromise between maximizing RDF and minimizing
sidelobe levels. You can use smaller circle diameters and still get very
good performance.
For example, with a circle diameter of 140 feet and the exact same phasing
you would use for 200 feet, you still get a very clean, highly directional
pattern with all lobes to sides and back down by more than 20 dB relative to
the peak of the forward lobe. The RDF is 12.6 dB at a 20 degree elevation
angle for the 140 foot circle vs. 13.45 dB for the 200 foot circle, so you
do give up a small amount of RDF. Considering the 140 foot circle uses half
the real estate area of the 200 foot circle, that is a fair compromise for
many people (like me).
To prove that smaller circle works in practice, I installed exactly that
system and have observed directivity that is totally consistent with the
results I modeled in EZNEC. Rejection off the sides and back are excellent.
One caveat is that the smaller array is probably less tolerant of amplitude
and phase errors, although I have not done any analysis to quantify that. I
just built everything very carefully and made the installation as "clean" as
possible. I also took care to switch in detuning of my transmit antenna
when receiving on the array.
RDF as a receiving metric:
RDF is indeed a very useful metric for comparing receiving antennas.
However, we need to be aware that it assumes the ambient background
(atmospheric) noise is uniformly distributed in 3-dimensional space, which
is not always true in specific instances. For this reason, RDF may not
exactly predict the differences between two arrays in any given situation.
It is possible for a system with a lower RDF to equal or even outperform
another system with higher RDF under certain noise conditions. If the noise
were always uniformly distributed, then RDF would perfectly predict relative
receiving performance (actually SNR).
The next point about RDF is that it is calculated for a specific signal
arrival direction in three dimensional space. In terms of azimuth, it is
the peak direction of the forward lobe. In elevation, it is common practice
to use 20 degrees, which can be considered appropriate for DX reception. If
the signal arrives from a different azimuth or elevation angle, the SNR
advantage predicted by RDF may not actually be realized. I have seen a
simple low dipole with a lousy RDF occasionally outperform my 8-circle
system by a large amount when the elevation angle of arriving signals is
very high and the RDF advantage of the array cannot be realized.
As RDF gets higher, the beamwidth of the antenna system generally gets
narrower. You can see this if you look at chart #2 in K7TJR's Dayton
presentation (http://www.kkn.net/dayton2014/HiZ_DAYTON_2014_7n2.pdf). This
brings up another point. By making the RDF very high, you are necessarily
restricting the angular sector over which the antenna delivers its best
performance. This is fine as long as the angular sector coincides with a
direction that is important to you. The flip side is you give up some of
that performance outside that sector. For switched arrays with a finite
number of selectable directions, that could be a disadvantage when a
direction of interest falls halfway between contiguous switching directions.
Looking at the pattern of the array will tell you what you give up in the
"in between" directions.
These comments with respect to RDF are not intended to be disparaging. On
the contrary I do believe RDF is an excellent tool for comparing receiving
antennas. You just have to aware of what it actually means in practice.
73, John W1FV
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