Antenna Directivity (D)

Antenna directivity (symbol: D) is a parameter that quantifies how effectively an antenna concentrates radiated power in a particular direction compared to an ideal isotropic radiator. It is expressed as a dimensionless ratio or in decibels (dBi) and represents the antenna’s focusing capability, independent of efficiency.

Definition and Formula

Directivity is mathematically defined as:

D = U(θ, φ) / U₀

Where:

• U(θ, φ) is the radiation intensity in a given direction

• U₀ is the radiation intensity of an isotropic antenna radiating the same total power

Directivity is often approximated for many antenna types using the beam solid angle:

D ≈ 4π / ΩA

Where ΩA is the solid angle of the main radiation lobe (in steradians).

Relationship to Antenna Gain

Directivity is closely related to antenna gain. Gain accounts for both the directional characteristics and the efficiency (η) of the antenna:

G = η × D

Here, both G (gain) and D (directivity) are typically expressed as linear values, not in dB. This relationship is essential when designing antennas for energy-efficient transmission.

Practical Applications

Antenna directivity is a critical design parameter in:

• Wireless communication systems

• Satellite and point-to-point radio links

• Radar systems

• Radio astronomy

High-directivity antennas focus energy into narrow beams, enabling:

• Longer communication distances at the same power level

• Reduced interference from undesired directions

• Improved signal-to-noise ratios (SNR)

However, high directivity also limits angular coverage, requiring precise alignment in directional applications.

Example

• A half-wave dipole antenna has a directivity of 1.64 (or 2.15 dBi).

• A 1-meter parabolic dish operating at 10 GHz can reach a directivity of approximately 3,000 (or 35 dBi).

These examples highlight the impact of antenna type and size on directivity performance.