📡 Parabolic Antennas

Comprehensive Study Notes for Undergraduate Electrical Engineering

1 Introduction to Parabolic Antennas

A parabolic antenna is a high-gain reflector antenna used in radio, television, data communications, and radar applications. It consists of a parabolic reflector (concave dish) and a feed antenna located at the focal point.

🔑 Key Concept

The parabolic shape is concave (curved inward), which allows it to collect and focus electromagnetic waves onto a single point (the focus), or conversely, to transmit waves from the focus into a narrow beam.

🎯 Primary Applications

  • Satellite communications (TV, radio, internet)
  • Deep space communications (NASA DSN)
  • Radio astronomy (SETI, observatories)
  • Radar systems (air traffic control, weather)
  • Microwave point-to-point links
  • 5G base stations (mmWave)

⚡ Advantages

  • High directivity and gain
  • Low side lobe levels
  • Efficient power transfer
  • Wide bandwidth capability
  • Well-defined beam shape
  • Low noise temperature
2 Geometric Principles & Wave Propagation

The parabolic reflector follows the geometric definition of a parabola: the locus of points equidistant from a fixed point (focus) and a fixed line (directrix). The concave surface faces the incoming waves for reception, or radiates outward for transmission.

Standard Parabola Equation:
y² = 4fx
where f = focal length (distance from vertex to focus)
D = diameter of the dish
f/D = focal ratio (typically 0.3 to 0.5)
Incident Parallel Rays (from distant source)
Converging to Focus
Parabolic Reflector Surface

🔧 Interactive Geometry Controls

100
350
Reception Mode: Parallel rays from distant transmitter → Reflect off concave surface → Converge at focus (feed antenna)

Transmission Mode: Feed at focus emits spherical wave → Reflects off concave surface → Forms parallel beam (plane wave)

Path Length Equality: All paths from aperture plane to focus are equal (parabolic property ensures phase coherence)
3 Radiation Characteristics

The radiation pattern of a parabolic antenna is determined by the illumination of the aperture and the f/D ratio. The main lobe is narrow and directional, while side lobes are minimized through proper feed design.

📊 Pattern Analysis Controls

10λ
65%
Parameter Formula Description
Half-Power Beamwidth (HPBW) HPBW ≈ 70λ/D (degrees) Angular width between -3dB points
First Null Beamwidth (FNBW) FNBW ≈ 140λ/D (degrees) Angular width to first null
Directivity (D) D = η(πD/λ)² Maximum directive gain
Effective Aperture (Ae) Ae = ηA = η(πD²/4) Capture area of antenna
Focal Gain G = 4πAe/λ² Power gain over isotropic
4 Feed Systems & Illumination

The feed antenna is critical for proper illumination of the parabolic reflector. Common feed types include horn antennas, dipoles with reflectors, and corrugated horns.

🔊 Primary Feed Types

  • Dipole with Reflector: Simple, low cost, narrow bandwidth
  • Pyramidal Horn: Moderate gain, good bandwidth
  • Conical Horn: Circular polarization capable
  • Corrugated Horn: Low sidelobes, wide bandwidth
  • Choke Ring Horn: Reduced back radiation

⚖️ Illumination Taper

  • Uniform: Maximum gain, high sidelobes
  • 10dB Taper: Optimal compromise (common)
  • Edge Taper: Reduces spillover loss
  • Taper Efficiency: Typically 0.8-0.9
Illumination Efficiency:
ηᵢ = [2(1 - cosⁿ⁺¹ψ₀) / ((n+1)(1 - cosψ₀))]² × cot²(ψ₀/2)
where n = illumination taper factor (typically 2-4)

Spillover Efficiency:
ηₛ = 1 - cosⁿ⁺¹ψ₀
(Power captured vs. power radiated by feed)

⚠️ Design Trade-offs

Short f/D (f/D < 0.3): Requires wide feed pattern, high spillover loss, compact design.
Long f/D (f/D > 0.6): Narrow feed pattern required, low spillover, bulky structure.
Optimal f/D: Typically 0.35-0.45 for most applications.

5 Types of Parabolic Antennas

🛰️ Prime Focus Parabolic

Feed located at the primary focal point of the paraboloid.

  • Simplest configuration
  • Feed blockage causes aperture blockage
  • Used in radio telescopes, satellite TV
  • Typical efficiency: 50-60%

🪞 Offset (Offset Gregorian)

Feed offset from the optical axis to eliminate blockage.

  • No feed blockage
  • Lower sidelobes
  • Asymmetric structure
  • Used in DBS, VSAT terminals

🔭 Cassegrain Reflector

Dual-reflector system with hyperbolic subreflector.

  • Feed behind main reflector
  • Shorter focal length
  • Convenient feed placement
  • Used in deep space networks

📡 Gregorian Reflector

Dual-reflector with elliptical subreflector.

  • Longer effective focal length
  • Better for wideband feeds
  • More compact than Cassegrain
  • Used in high-performance systems
6 Design Example & Calculator

🧮 Parabolic Antenna Design Calculator

7 Summary & Key Equations

📚 Essential Equations Summary

Gain: G = η(πD/λ)²

Beamwidth: θ₃dB ≈ 70λ/D (degrees)

Focal Length: f = D²/(16h)

f/D Ratio: Determines feed pattern requirements

Effective Area: Ae = η × πD²/4

Power Density: S = PₜG/(4πR²)

✅ Study Checklist

  • Understand the concave parabolic geometry and focal properties
  • Master the reception vs. transmission modes and wave directions
  • Calculate gain and beamwidth for given diameter and frequency
  • Compare prime focus vs. Cassegrain configurations
  • Understand illumination taper and efficiency trade-offs
  • Know applications in satellite communications and radar