📡 Reflector Antennas

Comprehensive Study Notes for Undergraduate Electrical Engineering

Parabolic Reflectors Cassegrain Gregorian Aperture Efficiency Beamwidth Gain

🎯 Introduction

Reflector antennas are high-gain directional antennas that use a reflecting surface to concentrate electromagnetic energy into a narrow beam. They are essential components in modern communication systems, radar, radio astronomy, and satellite communications due to their ability to achieve very high gains and narrow beamwidths.

Key Principle: Reflector antennas operate on the principle of geometrical optics, where a feed antenna placed at the focal point illuminates the reflector surface, which then collimates the energy into a parallel beam (transmit mode) or focuses incoming parallel rays to the feed (receive mode).

Why Use Reflector Antennas?

Historical Note: The parabolic reflector concept dates back to optical telescopes. The first radio parabolic reflector was built by Grote Reber in 1937 for radio astronomy. The Cassegrain configuration is named after Laurent Cassegrain (1672), who adapted the optical telescope design for antennas.

🔍 Types of Reflector Antennas

1. Plane Reflector Antenna

The simplest form consisting of a primary antenna and a flat reflecting surface. While useful for redirecting energy, it does not provide good collimation.

Characteristics:
  • Simple construction
  • Used for redirecting radiation pattern
  • Limited directivity improvement
  • Image theory applies for analysis

2. Corner Reflector Antenna

Consists of two or three mutually intersecting conducting flat surfaces (dihedral or trihedral). The feed element (typically a dipole) is placed at the apex.

Dihedral Corner Reflector

Two flat plates intersecting at angle θ (typically 90°)

  • Common angle: 90°
  • Gain: 10-12 dBi
  • Used in UHF/VHF bands

Trihedral Corner Reflector

Three mutually perpendicular surfaces

  • Used as radar targets
  • Retroreflective properties
  • Returns signal directly to source

3. Parabolic Reflector Antenna

The most common high-gain reflector antenna. The reflector surface follows a paraboloid of revolution defined by the equation:

r' = 2f / (1 + cos θ') = f / cos²(θ'/2)

where f is the focal length and r' is the distance from focus to reflector surface at angle θ'

Key Geometric Relationships:

Parameter Formula Description
Focal Length f = D² / (16 × d) D = diameter, d = depth at center
f/D Ratio f/D = 1 / (4 tan(θ₀/2)) θ₀ = half-angle subtended by reflector
Half-Angle θ₀ = 2 arctan(D / 4f) Angle from focus to reflector edge
Depth d = D² / (16f) Depth of paraboloid at center

Feed Configurations:

Prime Focus (Front Feed)

Feed located at focal point, pointed back at reflector

Pros: Simple, direct illumination
Cons: Aperture blockage, long transmission lines

Cassegrain Feed

Hyperbolic subreflector redirects energy to feed at vertex

Pros: Short transmission lines, convenient access
Cons: Subreflector blockage, complex alignment

Gregorian Feed

Elliptical subreflector between focus and vertex

Pros: Better spillover control, reduced noise
Cons: Longer physical structure, larger subreflector

Offset Feed

Feed positioned off-axis to avoid blockage

Pros: No aperture blockage, better efficiency
Cons: Asymmetric pattern, complex design

Parabolic Reflector Geometry

F (Focus) Feed Horn D (Diameter) Parabolic Reflector Parallel Beam θ₀

Figure: Parabolic reflector showing focal point, feed horn, and ray tracing demonstrating the collimation property

⚡ Fundamental Principles

Aperture Theory

The gain of a reflector antenna is directly related to its physical aperture area and the efficiency of illumination. The fundamental relationship is derived from the effective aperture concept.

Gain Formula:
G = η × (4πAₑ) / λ² = η × (πD / λ)²
G(dBi) = 10 log₁₀[η × (πD / λ)²]
  • G = Power gain over isotropic antenna
  • η = Aperture efficiency (typically 0.5 to 0.8)
  • Aₑ = Effective aperture area = η × (πD²/4)
  • D = Diameter of reflector
  • λ = Wavelength of operation
Rule of Thumb: For a typical parabolic antenna with 50% efficiency (η = 0.5), the gain in dBi can be approximated as: G(dBi) ≈ 20 log₁₀(D/λ) + 7.5

Beamwidth Calculations

The half-power beamwidth (HPBW) is inversely proportional to the antenna diameter in wavelengths.

Beamwidth Approximation:
HPBW ≈ 70° × (λ / D) (for circular aperture with uniform illumination)
HPBW ≈ 58° × (λ / D) (for typical tapered illumination)

The exact beamwidth depends on the illumination taper across the aperture. Higher edge taper results in wider beamwidth and lower sidelobes.

Illumination Taper

The radiation pattern of the feed antenna determines the illumination across the reflector aperture. Optimum illumination requires:

Edge Illumination Level:
EI(dB) = Feed Pattern(θ₀) + Space Attenuation
Space Attenuation = 20 log₁₀[(1 + cos θ₀) / 2]

where θ₀ is the half-angle subtended by the reflector

Aperture Efficiency Components

Total aperture efficiency is the product of several factors:

η = η₁ × η₂ × η₃ × η₄ × η₅
  • η₁ (Illumination) = Efficiency due to amplitude taper (typically 0.8-0.9)
  • η₂ (Spillover) = Energy captured by reflector vs. total radiated (typically 0.9-0.95)
  • η₃ (Phase) = Phase uniformity across aperture (typically 0.95-0.99)
  • η₄ (Blockage) = Loss due to feed/subreflector blocking aperture (typically 0.9-0.95)
  • η₅ (Surface) = Surface accuracy tolerance (typically 0.95-0.99)

Typical Overall Efficiency: 50% to 70% for well-designed systems

Surface Accuracy Requirements

Ruze Criterion: The surface error tolerance must satisfy:
εᵣₘₛ < λ / (4√π) ≈ λ / 16

where εᵣₘₛ is the root-mean-square surface deviation. For 1% gain loss, surface errors should be less than λ/20.

🔧 Design Considerations

Feed Design

The feed antenna is critical for overall system performance. Common feed types include:

Feed Type Characteristics Applications
Dipole with Reflector Simple, broad beam, moderate bandwidth Small dishes, low frequencies
Pyramidal Horn Good directivity, moderate bandwidth Standard parabolic feeds
Conical Horn Symmetric pattern, good for circular polarization Satellite communications
Corrugated Horn Low sidelobes, wide bandwidth, low cross-polarization High-performance systems
Choke Ring Horn Excellent pattern control, very low sidelobes Radio astronomy, deep space

Dual-Reflector Design (Cassegrain & Gregorian)

Cassegrain Configuration

Uses hyperbolic subreflector

  • Virtual focus behind subreflector
  • Subreflector is convex
  • Magnification M = (e + 1)/(e - 1)
  • e = eccentricity > 1

Gregorian Configuration

Uses elliptical subreflector

  • Real focus between reflectors
  • Subreflector is concave
  • Magnification M = (1 + e)/(1 - e)
  • e = eccentricity < 1
Subreflector Magnification Factor:
M = tan(θₑ/2) / tan(θᵢ/2)
  • θₑ = Half-angle of main reflector edge from subreflector
  • θᵢ = Half-angle of feed pattern illuminating subreflector
  • M typically ranges from 2 to 5

Offset Configurations

Offset reflectors eliminate aperture blockage by using a section of the paraboloid away from the axis of symmetry.

Advantages of Offset Feeds:
  • No feed/subreflector blockage → Higher efficiency (up to 75-80%)
  • Reduced sidelobes and backlobes
  • Lower noise temperature (no spillover to ground)
  • Improved cross-polarization performance

Design Trade-offs

Parameter Small f/D (Deep Dish) Large f/D (Shallow Dish)
Feed Position Close to vertex Far from vertex
Feed Beamwidth Wide (harder to design) Narrow (easier to design)
Spillover Higher Lower
Aperture Illumination More tapered More uniform
Cross-polarization Higher Lower
Typical Range f/D = 0.25 - 0.4 f/D = 0.4 - 0.6

🧮 Interactive Design Calculator

Parabolic Antenna Parameter Calculator

Enter basic parameters to calculate gain, beamwidth, and other characteristics

Wavelength: 0.03 m
Gain: 39.4 dBi
Beamwidth: 1.74°
Focal Length: 1.2 m
Half-Angle θ₀: 64°
Directivity: 40.0 dBi

Practical Design Example

Example: Design a 12 GHz satellite TV receive antenna with 1 meter diameter.
  • λ = 3e8 / 12e9 = 0.025 m (2.5 cm)
  • D/λ = 1 / 0.025 = 40
  • With η = 0.6: G = 0.6 × (π × 40)² = 9475 (39.8 dBi)
  • Beamwidth ≈ 70/40 = 1.75°
  • Choose f/D = 0.4: Focal length = 0.4 m
  • Half-angle θ₀ = 2 arctan(1/1.6) = 64°

🌍 Applications

🛰️

Satellite Communications

Earth station antennas (VSAT, DBS), tracking antennas, deep space networks

Typical sizes: 0.6m to 70m

📡

Radar Systems

Air traffic control, weather radar, military surveillance, automotive radar

High gain for long-range detection

🔭

Radio Astronomy

Single dish observations, interferometer arrays (VLA, ALMA), cosmic microwave background

Extreme surface precision required

📶

Terrestrial Microwave

Long-distance telephone links, backhaul for cellular networks, point-to-point data

High reliability, high data rates

🚀

Spacecraft

Communication satellites, planetary probes, GPS satellites

Deployable and inflatable reflectors

🏠

Consumer Electronics

Satellite TV dishes (DTH), 5G base stations, WiFi backhaul

Low-cost mass production

Modern Developments

📝 Knowledge Check

Test your understanding of reflector antenna concepts:

1. What is the primary geometric property of a parabolic reflector?

Select the correct answer:

📚 Summary & Key Takeaways

Essential Points to Remember:

  1. Geometrical Optics: Parabolic reflectors convert spherical waves from the feed into plane waves (transmit) or focus plane waves to the feed (receive)
  2. Gain Formula: G = η(πD/λ)² where η is typically 0.5-0.7 for practical systems
  3. Beamwidth: Inversely proportional to D/λ ratio; HPBW ≈ 70°λ/D for uniform illumination
  4. Optimum Illumination: Edge illumination should be 10-11 dB below center for best gain/sidelobe tradeoff
  5. Dual Reflectors: Cassegrain (hyperbolic) and Gregorian (elliptical) move feed to convenient location behind main reflector
  6. Surface Accuracy: RMS surface error should be less than λ/16 for <1 dB loss
  7. Applications: Satellite comm, radar, radio astronomy - anywhere high gain and narrow beamwidth are needed

Further Study Resources:

  • Antenna Theory: Analysis and Design (Balanis) - Chapters on reflector antennas
  • Antenna Engineering Handbook (Volakis) - Comprehensive design procedures
  • Radio Astronomy (Kraus) - Large reflector antenna considerations
  • IEEE Transactions on Antennas and Propagation - Latest research papers