main

Antenna Directivity: Formula, Gain and Measurement

What Is Antenna Directivity?

Quick answer: Antenna directivity describes how strongly an antenna concentrates radiated power in a particular direction compared with an ideal isotropic radiator. An isotropic radiator has a directivity of 1, or 0 dBi.

Higher directivity produces a narrower, more focused radiation pattern, while lower directivity provides broader angular coverage. Directivity depends on the shape of the radiation pattern and does not include antenna losses.

The normalized radiation pattern can be expressed in spherical coordinates as:

微信图片_20231107140527

Normalized Radiation Pattern

Antenna Directivity Formula

A normalized radiation pattern has the same shape as the original pattern, but its maximum value is scaled to 1. Antenna directivity, written as D, compares the maximum radiation intensity with the average radiation intensity over all directions.

The denominator of the equation represents the total pattern integrated over a sphere. Dividing the peak value by this spatial average shows how strongly the antenna concentrates energy in its main direction.

微信图片_20231107141719
微信图片_20231107141719

Directivity vs. Gain

Directivity describes only how the radiation pattern is concentrated. Antenna gain also accounts for radiation efficiency, including conductive and dielectric losses.

The relationship is G = ηD, where G is gain, η is radiation efficiency, and D is directivity. A lossless antenna has gain equal to its directivity; in a real antenna, gain is normally lower. Both values are commonly expressed in dBi when referenced to an isotropic radiator.

Directivity Calculation Example

As an example, consider the next two equations for the radiation pattern of two antennas.

微信图片_20231107143603

Antenna 1

2

Antenna 2

Radiation Pattern and Directivity

The following patterns vary with the polar angle θ and are assumed to remain constant with azimuth. Antenna 1 spreads its radiation more broadly, while Antenna 2 concentrates more energy around its main direction.

Because a narrower main beam represents greater concentration of radiated power, Antenna 2 is expected to have the higher directivity.

微信图片_20231107144405

Figure 1. Comparison of the two normalized radiation patterns. The more concentrated pattern has higher directivity.

Directivity Calculation Results

Applying the directivity equation to the two example patterns gives:

  • Antenna 1: D = 1.273, or 1.05 dBi
  • Antenna 2: D = 2.707, or 4.32 dBi

Antenna 2 has the higher directivity because its radiation is more concentrated around the peak direction. An isotropic radiator is used as the 0 dBi reference even though it is an ideal model rather than a realizable physical antenna.

High vs. Low Directivity Applications

Low-directivity antennas provide broad angular coverage and are useful when signals may arrive from different directions, such as mobile devices, vehicle radios, and general wireless access.

High-directivity antennas focus energy into a narrower beam. They are preferred for satellite links, radar, remote sensing, and point-to-point communication where the desired direction is known.

The table below shows approximate directivity ranges for several common antenna types.

Typical Antenna Directivity Values

Antenna type Approximate directivity ratio Approximate directivity (dBi)
Short dipole 1.5 1.76
Half-wave dipole 1.64 2.15
Patch antenna 3.2-6.3 5-8
Horn antenna 10-100 10-20
Dish antenna 10-10,000 10-40

These values are representative ranges. Actual directivity depends on frequency, electrical size, geometry, illumination, and operating conditions.

How Is Antenna Directivity Measured?

Directivity is commonly determined from a measured radiation pattern. The antenna under test is characterized over azimuth and elevation, and the resulting field or power data is normalized to create a three-dimensional pattern.

  1. Measure the relative radiation level over the required angular range.
  2. Identify the maximum radiation intensity.
  3. Integrate the radiation pattern over solid angle to obtain the spatial average.
  4. Divide the peak intensity by the average intensity and express the result as a ratio or in dBi.

Controlled antenna testing helps reduce reflections and measurement uncertainty when evaluating radiation patterns, gain, polarization, and directivity.

How Antenna Size Affects Directivity

Electrical size strongly influences the radiation pattern. A small single-element antenna normally produces a broad beam and relatively low directivity. Increasing the effective aperture in wavelengths allows an antenna or array to form a narrower beam and achieve higher directivity.

  • Lower directivity: useful for wide-area coverage and signals arriving from multiple directions.
  • Higher directivity: useful for focused links, improved angular selectivity, and rejection of signals outside the main beam.

Directivity is not determined by physical size alone. Geometry, current distribution, array spacing and phasing, aperture illumination, and operating frequency all influence the final radiation pattern.

A narrower beam generally corresponds to higher directivity, but it also requires more accurate pointing and alignment. For the relationship among directivity, efficiency, and realized performance, see antenna efficiency and gain.

Frequently Asked Questions

What is antenna directivity in simple terms?

It is a measure of how strongly an antenna concentrates radiation in one direction compared with the average radiation over all directions.

Is antenna directivity the same as gain?

No. Directivity describes pattern concentration, while gain also includes radiation efficiency. Their relationship is G = ηD.

What does 0 dBi directivity mean?

It corresponds to an ideal isotropic radiator with a directivity ratio of 1. It is the reference used to express directivity in dBi.

How can antenna directivity be increased?

Directivity can be increased by enlarging the effective electrical aperture, using reflectors or lenses, forming arrays with controlled amplitude and phase, or selecting a geometry that produces a narrower main beam.

Does higher directivity always mean a better antenna?

No. Higher directivity is beneficial when the target direction is known, but broad coverage may be more important for mobile or multidirectional applications. The correct choice depends on the link, coverage, bandwidth, efficiency, and installation requirements.

For help selecting or testing an antenna for your application, contact RF MISO or email info@rf-miso.com.


Post time: Nov-07-2023

Get Product Datasheet