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Helix feed for dish

How many turns should a helix be to give a -10 dB beam width of 90?  So far
all I've been able to find is formulas for -3 dB beam widths.

I've been given a Sony SAN-18S2 DSS dish which I'm going to try to use for
AO40 on S-band.  I'm building a helix feed for it and am stumped trying to
figure out how many turns I need to properly illuminate the dish.  Since it
is an offset fed dish, I measured the angle from the top to the bottom as 90
degrees when viewed from the old feed horn location.  Measuring from side to
side was also 90 degrees.  Based on what I've read so far I would want a
feed with a -10 dB beam width of 90 degrees.

The dish dimensions are 473mm (18 5/8 inch) wide and 538mm (21 3/16 inch)


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