Parabolic Reflector Antenna

When extremely high gain and a very narrow beam are required — as in satellite uplinks, deep-space communication, radio telescopes, and radar systems — a parabolic reflector antenna is the standard solution. The parabolic dish shape has a unique geometric property: all rays emanating from its focal point are reflected as a perfectly parallel beam, and conversely, all parallel incoming rays converge at the focal point. This property makes the parabolic reflector the most efficient way to convert a spherical wave from a small feed antenna into a highly collimated, high-gain plane wave radiation.

Core Concept Explanation

The key to understanding the parabolic reflector is its geometric property: any point on a parabola is equidistant from the focal point and from the directrix (a line perpendicular to the axis). This means that rays traveling from the focal point to different parts of the dish surface all travel the same total path length to the aperture plane. Consequently, all reflected rays arrive at the aperture with the same phase — they form a planar phase front. A planar phase front corresponds to a perfectly collimated beam, which is the definition of maximum directivity.

The feed antenna is placed at the focal point of the paraboloid. It is typically a horn antenna, a dipole with a small reflector, or a patch antenna. The feed illuminates the dish surface with its own radiation pattern. The reflector then converts this spherical wave into a plane wave for transmission (or the reverse for reception). An important design consideration is that the feed pattern should uniformly illuminate the dish surface — under-illumination wastes aperture area, while over-illumination (spillover) causes radiation outside the dish, reducing efficiency.

The gain of a parabolic reflector depends on two factors: the physical size of the aperture relative to wavelength, and the aperture efficiency η. Aperture efficiency accounts for spillover loss, illumination non-uniformity, phase errors (due to surface imperfections), and blockage by the feed support structure. Practical dish antennas have η between 0.55 and 0.75, with 0.6 (60 percent) being a commonly used design assumption.

The beamwidth of a parabolic dish is inversely proportional to the electrical size D/λ. Very large dishes (D/λ is large) produce extremely narrow beams — radio telescopes like the 25-meter dishes used in deep space tracking have beamwidths of a fraction of a degree at microwave frequencies.

Mathematical Expression

The gain formula for a parabolic reflector is G = η (πD/λ)², where D is the dish diameter, λ is the operating wavelength, and η is the aperture efficiency. In decibels, this becomes G(dB) = 10 log(η) + 20 log(πD/λ). The half-power beamwidth is approximately HPBW = 70λ/D degrees (for a uniformly illuminated circular aperture, this is about 58.5λ/D degrees, but 70λ/D is the practical approximation for a tapered illumination pattern). These two formulas — gain and beamwidth — are the most commonly tested aspects of parabolic reflector antennas in GATE.

The focal length f and diameter D are related by the parabola geometry. The f/D ratio determines the depth of the dish and the optimum feed design. A shallow dish has f/D close to 0.5 to 0.6 and is easier to support structurally. A deep dish has f/D closer to 0.3, and the feed sits closer to the dish surface. Most practical dish antennas use f/D between 0.35 and 0.55.

Practical Understanding

Surface accuracy is critical for parabolic reflectors at high frequencies. If the dish surface deviates from the ideal paraboloid by more than λ/16 RMS (root mean square), the gain begins to drop and sidelobe levels rise significantly. This is why large dishes for millimeter-wave applications require very precisely machined or formed aluminum or composite panels, while dishes for lower frequency satellite TV reception (Ku-band, 10 to 12 GHz) can be mass-produced with standard accuracy.

The feed blockage problem occurs because the feed support structure and feed itself block some of the reflected radiation from leaving the aperture. This causes a small reduction in gain and an increase in sidelobe levels. Offset-feed designs (where the feed is not on the main axis but at a geometric offset) eliminate feed blockage entirely and are widely used in modern satellite TV dishes and radar systems.

Parabolic reflectors are used in satellite ground stations, radio telescopes, radar systems (especially search and tracking radars), point-to-point microwave backhaul links, and direct-to-home satellite TV reception. In all these applications, the core advantage is achieving very high gain (40 to 70 dBi for large antennas) from a passive reflector structure with a simple feed.

Given:
Dish diameter D = 2 m
Operating frequency f = 10 GHz (Ku-band)
Aperture efficiency η = 0.60
c = 3 × 10^8 m/s

Why this formula applies:
Parabolic reflector gain is proportional to aperture area (D²)
divided by λ², scaled by aperture efficiency.

Formula:
λ = c / f
G = η × (πD / λ)²
G(dB) = 10·log10(G)
HPBW = 70 × λ / D  (degrees)

Substitution:
λ = (3 × 10^8) / (10 × 10^9) = 0.03 m
G = 0.60 × (π × 2 / 0.03)²
  = 0.60 × (209.44)²
  = 0.60 × 43,865
  = 26,319

Calculation:
G(dB) = 10 × log10(26319) = 10 × 4.420 = 44.2 dBi
HPBW = 70 × 0.03 / 2 = 1.05°

Final Answer:
Gain = 44.2 dBi
Half-power beamwidth = 1.05° (very narrow, high directivity)

Exam Tip: For GATE, use G = η(πD/λ)² with η = 0.6 unless otherwise stated. HPBW ≈ 70λ/D degrees. Remember: doubling D quadruples gain (adds 6 dB) and halves beamwidth. These two scaling rules together are a common quick-check question.

• The parabola's focal property ensures all path lengths from feed to aperture plane are equal, producing a planar phase front and thus a highly directive beam.
• Gain formula: G = η(πD/λ)². Aperture efficiency η ≈ 0.6 for practical designs.
• HPBW ≈ 70λ/D degrees. Larger dish → narrower beam → higher gain.
• Doubling D increases gain by 6 dB (factor of 4) and halves beamwidth.
• Surface accuracy must be better than λ/16 RMS to keep gain penalty below 1 dB.
• Offset-feed design eliminates feed blockage; used in modern satellite TV dishes.

Quick Revision

• Parabolic reflector converts spherical wave from focal point feed into plane wave — all rays reflect parallel.
• Gain: G = η(πD/λ)² where η ≈ 0.55 to 0.75. Use η = 0.6 in GATE problems unless stated.
• HPBW ≈ 70λ/D degrees. Beamwidth and gain are inversely related.
• f/D ratio: 0.3 to 0.6 for practical dishes. Controls dish depth and feed design.
• Surface accuracy requirement: RMS deviation less than λ/16 for minimal gain degradation.
• Exam trap: Gain scales as D² and as 1/λ² — doubling frequency (halving λ) at fixed D increases gain 4× (6 dB) only if surface accuracy still meets λ_new/16 requirement.
• Applications: satellite ground stations, radio telescopes, radar, microwave backhaul, DTH reception.