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Removing the reflector so that only the reception element remains will Increase the beam width to a Very Wide Beam Width.
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Adding directors or placing multiple elements in a horizontal array will narrow the horizontal beamwidth. Reflectors increase forward gain by suppressing the rear lobe.
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With the reflector screens removed , the CS4 ,,,,, is Bi Directional.
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Absolutely correct.
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With the reflector screens removed , the CS4 has Very Wide Beam Widths a.....
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This is incorrect. The reflector on a panel-style antenna,whether loops or bowties, has little effect on the horizontal beamwidth of the antenna's main forward lobe.
In any event, trying to pick up signals from 45° off boresight with an antenna that exhibits a horizontal beamwidth of less than 45° won't work unless you happen have a side-lobe that lines up with the signal path on the frequencies of interest.
I don't have polar plots of the C4 sans reflectors, but I do have ones of a single tapered loop with and without reflectors that exhibit the behavior I described. I've also located some plots of a commercial 8-bay with and without reflectors that also exhibit the expected behavior.