Learning from these first experiments...
I decided to re-read some of the material I used so far. I realized then that there are quite a few areas where I could improve things.
Feed
ARRL's The Antenna Book, 19th edition, 1992, has a great section on helical antenna's on page 19-29. I suspect later editions will have this section as well (but this is the edition I own).
It explains how the intrinsic impedance of a helix is around 140 ohm. To match them to 50 ohm impedance feeds (i.e. the chassis-mount N connector!) it show two commonly used matching techniques. And indeed, all of the helix feed articles I've read so far use of those two techniques! Now I understood the techniques described in all the above helix feeds to match feed point impedance!
My helix uses the "first half turn close to backplane" method to match the impedance. I realized that my half turn is not nearly flat enough. Using the formula supplied, I estimated the impedance to be around 100 ohm! A better match will certainly help!
Things kept getting worse.. From the above, and design examples in W0LMV's article on Offset Dish Helix Feeds and K5OE's article on MMDS dishes and feeds, I realized that the diameter of the copper I'd been using was probably too small for a flat reflector. It seems like I took the 'best of both worlds' and combined then into the worst of both! :-)
Dish
I used the measurement of the RCA dish as described in W1GHZ's addendum, and ran the numbers through his performance analysis program, hdl-ant.exe (see table of content of the book to download it). This showed that at 50% efficiency, I would get about 18dB gain out of this dish! That might just be enough when the squint angle is good...
I also found that the dish has an equivalent f/D ratio of 0.7, and that I need a 3dB bandwidth in the feed of about 45 degrees. I now think that due to the lack of cupped reflector my feed was probably too wide, ie. it over-illuminated the disk, causing substantial loss.
This is the output of HDL_ANT.EXE (v3.4beta):
OFFSET PARABOLIC DISH ANTENNA CALCULATIONS
Frequency in MHz: 2401
PLEASE ENTER:
Diameter of large axis of dish in mm. : 495
Diameter of small axis of dish in mm. : 457
Depth of dish at deepest point in mm. : 43
Distance of deepest point from bottom edge along large axis in mm. : 228
Focal length = 283.8 mm.
This offset reflector is a section of a full parabola with a diameter
of 917.82 mm. whose vertex is at the bottom edge of the offset reflector.
The full parabola has an f/D = 0.31, which determines criticality of focal
length.
The focal point of the dish is 283.77 mm. from the bottom edge of the
reflector and 469.31 mm. from the top edge of the reflector.
For operation with the main beam on the horizon with the feed at the bottom,
the dish must be tilted forward so that the large axis is 68 degrees
above horizontal.
Illumination angle for feed = 77.9 degrees on the large axis and 79.2 degrees
on the small axis. A feedhorn with a 3 dB beamwidth of 45.9 degrees is
needed,equivalent to the feed for a conventional dish with f/D = 0.7
Gain at 50% efficiency = 18.2 dBi
If you do really well, you might get 60% efficiency for a gain = 19 dBi
To design a feedhorn, use f/D = 0.7 in Menu option F
Location
My one attempt to hear the AO-40 middle beacon was with a relatively low elevation, from the north side of my house (ie. my back yard). The neighbor's house was straight inline with the bird. This in and by itself was probably enough to not having any chance what soever to hear the beacon. Next time, I will setup in my driveway, on the south side, with a clear view of most of the southern sky!
Results
I decided for my second attempt, to build the 'cupped groundplane helix' described by K5OE, and be a bit more careful with the matching section of the helix. This should give better impedance, and better illumination of the dish by narrowing the beam.