Antenna Parameters

Antenna parameters such as directivity, gain, radiation efficiency, and effective aperture are quantitative measures that characterize antenna performance. Every antenna system design and every GATE problem involving antennas ultimately reduces to computing or comparing one or more of these parameters.

Directivity

The directivity D of an antenna is defined as the ratio of the radiation intensity in a given direction to the radiation intensity averaged over all directions. When the direction is not specified, directivity refers to the maximum value. Mathematically, D = 4π U_max / P_rad, where U_max is the maximum radiation intensity in watts per steradian and P_rad is the total radiated power in watts. Directivity is a dimensionless quantity and is purely a function of the antenna's shape — it does not depend on material losses.

For an isotropic radiator (hypothetical antenna radiating equally in all directions), D = 1 (or 0 dBi). A half-wave dipole has D = 1.64 (2.15 dBi). A short dipole has D = 1.5 (1.76 dBi). These are standard values that appear repeatedly in GATE and other competitive examinations and must be memorized.

Gain and Radiation Efficiency

The gainradiation efficiency, defined as the ratio of total radiated power P_rad to total input power P_in. Since every real antenna has some ohmic loss in its conductors and dielectric, η is always less than or equal to 1, and therefore G is always less than or equal to D.

Gain is directly measurable — it is the parameter that appears in link budget calculations. In the Friis transmission equation, it is gain (not directivity) that determines the received power, because gain accounts for real-world losses. Gain is expressed in dBi (decibels relative to isotropic) or dBd (decibels relative to a half-wave dipole). The conversion is 0 dBd = 2.15 dBi.

Effective Aperture

The effective aperture (also called effective area) A_e represents the equivalent area that an antenna presents to an incoming wave for the purpose of power collection. If a plane wave with power density S (W/m²) is incident on a receive antenna, the received power is P_r = S × A_e. The effective aperture is related to gain by A_e = G λ² / (4π). This relation is universal — it applies to any antenna regardless of its physical size or shape.

For an aperture antenna such as a parabolic reflector with physical aperture area A_phys, the aperture efficiency η_ap = A_e / A_phys. Well-designed reflector antennas achieve η_ap between 0.55 and 0.75. This efficiency accounts for illumination taper, spillover, and surface error losses.

Mathematical Expression

The Friis transmission equationfree space path loss factor (inverse). In dB form: P_r (dBW) = P_t (dBW) + G_t (dBi) + G_r (dBi) − FSPL (dB), where FSPL = 20 log₁₀(4πr/λ).

Practical Understanding

In satellite communication, the receive antenna gain and system noise temperature together determine the figure of merit G/T, which is the key measure of receiver performance. In radar, the two-way path means the received power depends on G² of the radar antenna. Optimizing gain while maintaining bandwidth and managing side lobes are the central tradeoffs in practical antenna engineering.

Given:
Transmit power P_t = 10 W, Transmit antenna gain G_t = 20 dBi = 100 (linear), Receive antenna gain G_r = 10 dBi = 10 (linear), Frequency f = 1 GHz → λ = 0.3 m, Distance r = 10 km = 10000 m

Why this formula applies:
Friis transmission equation gives received power in a line-of-sight free space link.

Formula:
P_r = P_t × G_t × G_r × (λ / 4πr)²

Substitution:
P_r = 10 × 100 × 10 × (0.3 / (4π × 10000))²

Calculation:
4π × 10000 = 125664
λ / 4πr = 0.3 / 125664 = 2.387 × 10⁻⁶
(λ / 4πr)² = 5.698 × 10⁻¹²
P_r = 10000 × 5.698 × 10⁻¹² = 5.698 × 10⁻⁸

Final Answer with units:
P_r ≈ 56.98 nW ≈ 57 nW
Received power at 10 km is approximately 57 nanoWatts.

Exam Tip: In GATE, directivity and gain are often confused. Directivity D depends only on the radiation pattern shape — it is lossless by definition. Gain G = ηD includes ohmic losses. For a lossless antenna η = 1 and G = D. Also, effective aperture A_e = Gλ²/(4π) — this formula works for any antenna including dipoles, not just aperture types.

• Directivity D = 4π U_max / P_rad — function of pattern shape only, independent of losses.
• Gain G = η × D — always less than or equal to directivity; η = radiation efficiency.
• Effective aperture A_e = Gλ²/(4π) — applicable to any antenna type.
• Friis equation: P_r = P_t G_t G_r (λ/4πr)² — fundamental formula for link budget.
• Isotropic: D = 1. Short dipole: D = 1.5. Half-wave dipole: D = 1.64 (2.15 dBi).

Quick Revision

• Directivity: ratio of maximum radiation intensity to average — shape dependent, lossless.
• Gain = η × D. For a lossless antenna, G = D. G is always ≤ D.
• Effective aperture: A_e = Gλ²/4π. Received power P_r = S × A_e.
• Friis equation in dB: P_r = P_t + G_t + G_r − FSPL. FSPL = 20 log(4πr/λ) dB.
• Half-wave dipole: G = 1.64 (lossless), D = 1.64 — memorize this standard value.
• 0 dBd = 2.15 dBi — conversion between dipole-referenced and isotropic-referenced gain.
• Trap: effective aperture is not physical area — a dipole has A_e even though it has no physical aperture.