Theory, design principles, and applications of high-gain directional antennas. From satellite communications to radio astronomy.
Achieve gains of 30-50 dBi with narrow beamwidths, ideal for long-distance communication links.
Based on the paraboloid property: all rays from focus reflect parallel to the axis (and vice versa).
Satellite communications, radio astronomy, radar systems, and deep space networks.
Understanding the physics and mathematics behind parabolic reflectors
A parabolic reflector is formed by rotating a parabola about its axis. The standard equation in Cartesian coordinates:
Where f is the focal length. In cylindrical coordinates (ρ, φ, z):
The f/D ratio (focal length to diameter ratio) is crucial for design, typically ranging from 0.25 to 0.5.
The defining characteristic of a parabola is that any ray emanating from the focus reflects off the surface and travels parallel to the axis. Conversely, incoming parallel rays converge at the focus.
The feed antenna illuminates the reflector with a specific pattern. The aperture field distribution determines:
Ideal Gain (no losses):
G = (πD/λ)²
With Aperture Efficiency (η):
G = η(πD/λ)²
In dBi:
G(dBi) = 10log₁₀[η(πD/λ)²]
Typical aperture efficiency η ranges from 0.5 to 0.7 (50-70%) due to spillover, blockage, and non-uniform illumination.
Half-Power Beamwidth (HPBW):
θ₃dB ≈ 70λ/D (degrees)
Null-to-Null Beamwidth:
θ_null ≈ 140λ/D (degrees)
First Sidelobe Level (uniform illumination):
-17.6 dB
Beamwidth is inversely proportional to diameter. Larger dishes produce narrower beams, requiring precise pointing.
Simple half-wave dipole backed by a small plane reflector. Used for small parabolic dishes.
Most common feed for parabolic reflectors. Provides controlled illumination pattern.
Hyperbolic subreflector allows feed to be placed at the vertex. Shorter mechanical structure.
The feed pattern must illuminate the reflector edge at a lower level than the center (typically -10 to -12 dB). This taper:
Edge Taper Trade-off: -10 dB edge taper typically gives ~80% illumination efficiency with -20 dB first sidelobes.
Wavelength
30 mm
Gain
38.1 dBi
3dB Beamwidth
1.4°
Focal Length
0.60 m
Depth at Center
0.35 m
Half-Angle
64°
VSAT terminals, DBS reception, and earth station antennas. Diameters: 0.6m to 30m.
Jansky Very Large Array, Arecibo (305m), Green Bank Telescope (100m).
Air traffic control, weather radar, and military tracking systems.
NASA's 70m dishes for interplanetary communication with spacecraft.
The Deep Space Network (DSN) uses 70-meter parabolic antennas to communicate with distant spacecraft. These massive dishes feature:
Diameter
Gain at X-band
Beamwidth
Parabola equation: ρ² = 4fz
Depth: h = D²/(16f)
Half-angle: ψ₀ = 2arctan(D/4f)
Surface area: A = (πD⁴)/(64f²) [approx]
Gain: G = η(πD/λ)²
Beamwidth: θ₃dB ≈ 70λ/D
Directivity: D₀ = (πD/λ)²
Effective area: Ae = ηAphysical
Edge taper: ET = 20log₁₀(Cosⁿ(ψ₀))
Spillover efficiency: ηs = ∫∫|E|²dΩ / Ptotal
Taper efficiency: ηt = [∫∫E dA]² / [A∫∫|E|²dA]
Free space path loss: FSPL = (4πR/λ)²
Received power: Pr = PtGtGrλ²/(4πR)²
Antenna noise: Ta = Tground + Tsky + Tspill