Parabolic Dish Antenna Design Calculator
Estimate dish diameter, focal length, beamwidth and gain for a parabolic reflector, and get a suggested feed beamwidth and feed gain to properly illuminate the reflector.
1. Wavelength and Dish Gain
λ = c / f
Gdish = η · (πD / λ)²
where c ≈ 3×108 m/s is the speed of light, f is the operating frequency, D is the reflector diameter, and η is the aperture efficiency (0 < η < 1).
2. Approximate 3 dB Beamwidth
θ3dB ≈ 70 · λ / D (degrees)
This is a widely used rule-of-thumb for a well-illuminated parabolic reflector. The constant (≈70) can vary slightly depending on illumination taper and edge spillover.
3. Focal Length and f/D Ratio
f / D = (focal length) / (dish diameter)
f = (f/D) · D
For typical satellite and microwave dishes, f/D is often chosen between 0.3 and 0.5, trading between feed blockage, feed spillover and mechanical depth.
4. Dish Subtended Angle and Feed Beamwidth
θrim ≈ arctan( (D / 2) / f )
Dish subtended angle ≈ 2·θrim
A feed antenna placed at the focus should illuminate the dish out to its rim with the desired edge taper (often −10 to −15 dB). As a simple first design, you can set the feed 3 dB beamwidth close to the dish subtended angle.
5. Feed Gain from Beamwidth (Approximation)
Gfeed ≈ 41,253 / θHPBW² (for circular symmetric beam, θ in degrees)
This approximation relates the half-power beamwidth of a reasonably well behaved antenna pattern to its gain. It is useful for checking whether a horn or patch-feed has an appropriate beamwidth and gain to illuminate the dish.
6. Practical Notes
- These formulas provide first-order estimates; final design should be validated with full-wave simulation or measurement.
- Aperture efficiency η accounts for illumination taper, spillover, blockage, surface errors and polarization mismatch.
- Choosing f/D too small makes the dish deep, complicating feed mounting; too large increases spillover and feed size.