Dish, cantenna and horn sizing calculator

Dish: gain, beam and the feed it needs

A parabolic dish collects power in proportion to its area, and an efficiency factor covers everything that keeps it from being perfect: spillover past the rim, uneven illumination, surface error, the feed's own blockage. For a home-built feed on a salvaged dish, 50 to 60 percent is a fair assumption until you've measured the Sun and know better.

The 70λ/D beamwidth is the usual figure for a feed that tapers to about −10 dB at the rim. A perfectly uniform illumination would be closer to 58λ/D, a heavier taper wider. At 1420 MHz a 1.8 m dish works out to about 26 dBi and an 8.2° beam; our own several-metre dish is narrower again. The beamwidth also tells you how long a source takes to drift through a fixed antenna: the sky moves 0.25° per minute at the celestial equator.

The f/D ratio sets the feed. The rim subtends a half-angle ψ at the focus, where tan(ψ/2) = 1 / (4 f/D), and the feed should put its −10 dB points at that angle. Deep dishes (f/D around 0.3) need a wide-beam feed; shallow offset-fed TV dishes need a narrow one. A plain open-ended cantenna is happiest around f/D 0.4. Outside that range, people add a choke ring or a short flare.

Cantenna: a circular waveguide feed

A can is a circular waveguide. It only carries the frequency you want if its inside diameter is above the TE11 cutoff, and you want it below the TM01 cutoff so a second mode doesn't start propagating:

Inside the guide the wavelength stretches to λg = λ / √(1 − (λ/λc)²). The probe, a quarter free-space wavelength long, sits a quarter guide-wavelength in from the closed back so the reflection off the back wall arrives in phase. Leave at least three quarters of a guide wavelength of can in front of it. Close to cutoff, λg grows quickly and so does the can, so aim for the middle of the range.

Worked example: a 150 mm can at the hydrogen line has its TE11 cutoff at 1171 MHz, a guide wavelength of 373 mm, the probe 93 mm from the back and 53 mm long, and wants to be at least 280 mm deep. Paint tins, ductwork end caps and large food tins all land in range.

Pyramidal horn: the no-dish option

A horn on its own is a perfectly good hydrogen-line antenna. It has a wide beam, so it doesn't resolve much, but the Galactic plane is a big target and a horn's gain is predictable from its dimensions alone, which makes it a good first antenna and a decent calibration reference later. This calculator uses the optimum-gain design procedure from Balanis's Antenna Theory: given a target gain and the feed waveguide, it solves for the aperture and flare lengths where the E-plane and H-plane flares meet the throat at the same depth, which is the condition for a horn you can physically build. An optimum horn runs at about 51 percent aperture efficiency.

Worked example: 17 dBi from a WR-650 throat at 1420.4 MHz needs a mouth about 675 mm wide by 514 mm high, flared over 480 mm. That's a weekend with aluminium flashing or foil-faced foam board. Going to 20 dBi more than doubles the flare length, which is where most people decide a dish is the better use of the garage.

If you don't have a real waveguide section, the throat can be a short rectangular box of the same inside dimensions with a quarter-wave probe, set up the same way as the cantenna: probe a quarter guide-wavelength from the back wall.