Parabolic Antenna Characteristics

Virtual Laboratory for EEEN 566

f/D Ratio Analysis
Radiation Patterns
Gain Calculator

01 Learning Objectives

Understand Parabolic Geometry

Study the concave reflector geometry with focal point feed configuration, including f/D ratio effects on illumination.

Analyze Radiation Patterns

Visualize and interpret E-plane and H-plane radiation patterns from concave reflector configuration.

Calculate Antenna Gain

Apply the gain formula G = η(πD/λ)² for prime-focus parabolic reflectors.

Determine Beamwidth

Calculate half-power beamwidth (HPBW) and analyze focal point illumination effects.

02 Theoretical Background

Concave Parabolic Reflector Geometry

A parabolic antenna consists of a concave parabolic reflector (dish) that curves inward toward the focal point, with a feed antenna located at the focus. The parabolic shape follows the equation y² = 4fx, where f is the focal length measured from the vertex to the focal point.

The f/D ratio (focal length to diameter ratio) is critical for determining the feed horn illumination pattern. Typical values range from 0.3 to 0.5 for prime-focus reflectors, where the feed is positioned at the focal point facing the concave surface.

Gain Calculation

The gain of a parabolic antenna is given by:

G = η × (πD/λ)²

Where η is the aperture efficiency (typically 0.5-0.65), D is the diameter, and λ is the wavelength. In decibels: G(dBi) = 10log₁₀[η(πD/λ)²]

Beamwidth and Radiation Pattern

The half-power beamwidth (HPBW) is approximated by:

θ₃dB ≈ 70λ/D (degrees)

The concave reflector focuses incoming plane waves to the focal point (receiving) and transforms spherical waves from the feed into plane waves (transmitting). Edge illumination of -10 to -11 dB relative to the center provides optimal trade-off between gain and sidelobe levels.

Key Parameters

  • Reflector Type Concave
  • Feed Position Prime Focus
  • f/D Ratio 0.3 - 0.5
  • Beamwidth 0.5° - 10°
  • Gain Range 20 - 50 dBi

Feed Configurations

Prime Focus (Axial)
Cassegrain (Dual)
Gregorian
Offset Feed

03 Interactive Simulation

Antenna Parameters

1.0 m
0.1m 10m
10 GHz
1 GHz 100 GHz
0.4
0.25 1.0
60%
40% 80%
-10 dB
-15 dB -5 dB

Calculated Results

Gain 39.9 dBi
3dB Beamwidth 2.1°
Focal Length 0.40 m
Wavelength 30.0 mm

Concave Reflector Geometry & Feed Configuration

Concave Reflector
Feed Horn (Focus)
Radiation Pattern
Ray Tracing

The concave parabolic reflector focuses parallel incoming rays to the focal point where the feed horn is located.

Normalized Radiation Pattern (dB)

Main Lobe
0 dB
First Sidelobe
-24.6 dB
Front-to-Back
>60 dB

3D Radiation Pattern Visualization

Simulated 3D directive gain pattern

Max Directivity: 39.9 dBi

04 Experimental Procedure

1 Setup & Calibration

  • • Set the concave parabolic reflector diameter (D) to 1.0 meter
  • • Configure operating frequency to 10 GHz (X-band)
  • • Position feed horn at focal point using f/D ratio of 0.4
  • • Verify concave geometry visualization shows proper curvature

2 Gain Measurement

  • • Record the calculated gain from the simulation display
  • • Verify using formula: G = η(πD/λ)²
  • • Convert to dBi: G(dBi) = 10log₁₀(G)
  • • Compare with simulation results

3 Pattern Analysis

  • • Observe the radiation pattern from concave reflector
  • • Identify the -3dB beamwidth points
  • • Measure first sidelobe level relative to main beam
  • • Analyze focal point illumination effects

4 Parameter Variation

  • • Vary diameter: 0.5m, 1.0m, 2.0m, 5.0m
  • • Change frequency: 4GHz, 10GHz, 20GHz, 40GHz
  • • Adjust f/D ratio: 0.3, 0.4, 0.6, 0.8
  • • Observe feed position changes in geometry view

Concave Reflector Properties

The concave surface reflects incoming parallel rays to converge at the focal point (receiving mode) and transforms spherical waves from the feed into plane waves (transmitting mode).
The vertex of the parabola is at the bottom of the dish, with the surface curving upward and outward toward the rim, creating the concave shape facing the feed.

05 Lab Report Guidelines

Report Structure

  1. Title Page (Course, Date, Student Name)
  2. Objectives and Theory (Concave reflector principles)
  3. Experimental Setup (f/D ratio, feed position)
  4. Results and Analysis (Geometry screenshots)
  5. Discussion (Concave vs. convex comparison)
  6. Conclusion and References

Required Diagrams

  • ✓ Concave reflector geometry with ray tracing
  • ✓ Feed horn position at focal point
  • ✓ Radiation pattern plots (E-plane and H-plane)
  • ✓ Gain vs. f/D ratio characteristics

Analysis Questions

  • Q1: Why must the reflector be concave (not convex) for proper focusing? Explain using ray optics.
  • Q2: How does the f/D ratio affect the feed horn illumination angle of the concave surface?
  • Q3: What happens to the gain if the feed is moved away from the focal point of the concave reflector?
  • Q4: Compare spillover efficiency for deep (f/D=0.3) vs. shallow (f/D=0.8) concave dishes.

Submission Requirements

Submit a PDF report including screenshots of the concave geometry visualization for at least 3 different f/D ratios. Show ray tracing from the feed to the reflector surface.

Max 10 pages PDF Format Include Geometry Views