For estimating and education only. Results come from the simplified models described below, are provided as is with no warranty, and are not a substitute for engineering analysis, simulation or measurement. Check them before relying on them in a design, purchase or safety decision. See the terms of use.
Equations
G = \eta\left(\frac{\pi D}{\lambda}\right)^2, \qquad G_\mathrm{dBi} = 10\log_{10} GA_e = \eta\,\frac{\pi D^2}{4}m²\mathrm{HPBW} \approx 70\,\frac{\lambda}{D}degrees, typical feed taperR_\mathrm{ff} = \frac{2D^2}{\lambda}mE(\theta) = \frac{2J_1(u)}{u}, \qquad u = \frac{\pi D}{\lambda}\sin\thetauniform apertureUniform
\mathrm{HPBW} \approx 58.9\,\frac{\lambda}{D}degrees; 2J1(u)/u = 0.707 at u = 1.616Variables
| Symbol | Meaning | Unit |
|---|---|---|
D | Reflector diameter | m |
\lambda | Wavelength | m |
\eta | Aperture efficiency (spillover, taper, blockage, surface error) | — |
A_e | Effective aperture | m² |
J_1 | Bessel function of the first kind, order 1 | — |
Worked example
| Input | Value |
|---|---|
| Diameter | 0.6 m |
| Frequency | 10 GHz |
| Efficiency | 55 % |
| Result | Value |
|---|---|
| Gain | 33.37 dBi |
| Half-power beamwidth (≈ 70 λ/D) | 3.5 ° |
| Effective aperture | 0.156 m² |
| Wavelength | 2.998 cm |
| Far-field distance 2D²/λ | 24 m |
Doubling the diameter, or the frequency, adds 6 dB of gain and halves the beamwidth.
Load this example in the calculatorValidity
- Valid for D larger than about 10 wavelengths.
- Efficiency of 50–65 % is typical for prime-focus dishes; offset-fed and Cassegrain designs can do better.
- Measure gain in the far field, beyond 2D²/λ.
Sources
- C. A. Balanis, Antenna Theory: Analysis and Design, 4th ed., Wiley, 2016. Chapter on reflector antennas.
- W. L. Stutzman and G. A. Thiele, Antenna Theory and Design, 3rd ed., Wiley, 2012 (reflector antennas).