What is Gain and Directivity of Antenna


RF antennas or aerials do not radiate evenly in all directions. It has been found that any practical RF antenna design will radiate more in some directions than others. The actual pattern depends on the type of antenna design, its size, environment, and other factors. This directional pattern can be used to ensure that the power being radiated is focused in the desired direction.

It is normal to refer to directional patterns and gain in terms of the transmitted signal. It is often easier to visualize an RF antenna in terms of its radiated power.

However, the antenna works in exactly the same way for reception, with the same numbers and specifications.

Antenna Directive

The directivity of an antenna is the ratio of the maximum power density P(θ,φ)max of its average value on a sphere as seen in the far field of an antenna.

Antenna Directivity Formula

It is a dimensionless ratio ≥ 1. The average power density of a sphere is given by,

Antenna Power Density Formula


Antenna Power Density

Therefore, directness,

formula 4


Directivity Formula

The smaller the beam area ΩAthe greater the directness d. In decibels,

Antenna Directivity in Decibels

The numerical value of d is always between 1 and ∞. An idealized isotropic antenna radiates equally in all directions, so its beam area is ΩA = 4π sr.

Its directness is,

Directivity of Isotropic Antenna

This is the lowest possible directivity (D = 1). All actual antennas have directives greater than 1 (D > 1).

Antenna Gain

In electromagnetics, antenna power gain or simply gain is an important performance figure that combines antenna directivity and power efficiency.

As a transmitting antenna, gain describes how well the antenna converts input power into radio waves moving in a specific direction.

As a receiving antenna, the gain describes how well the antenna transforms the radio waves coming from a specific direction of electrical power.

If no direction is specified, “profit” refers to the maximum profit value. the radiation pattern a plot of gain as a function of direction.

The gain is directly related to the antenna efficiency factor as:

Antenna Gain and Directivity Relation

ko η is the dimensionless antenna efficiency factor (0 ≤ k ≤ 1). If I the = 1, ie for a lossless antenna. In practice, the gain is always less than the directivity d.

Antenna Gain can be of two types-

  1. Power (Gp)
  2. Directive Gain (Gd)

Power (Gp): It is the ratio of the radiation intensity in a given direction to the average total input power.

Antenna Power Gain Formula

Total input power PT = Pr + Pl

Qr: Lit power

Ql: Ohmic loss of the antenna

Directive Gain (Gd): The ratio of radiation intensity in a particular direction to the average radiation power.

Antenna Directive Gain Formula

Mrd does not depend on the antenna’s power input and its ohmic loss.

The maximum value of the obtained directivity is the directivity D of the antenna.


Antenna Efficiency Formula

the: Efficiency factor that is between 0 to 1

What is the Difference Between Antenna Gain and Directivity?

  • Directivity defines the concentration of radiated power in a particular direction, while Gain determines the concentration of input power in a particular direction.
  • Gain is the combination of directivity and electrical efficiency.
  • Gain is always less than directivity because most antennas have some internal losses. Also, profit is a practical and measurable term.

You can also check this Antenna Calculator to determine the correct down-tilt antenna angle given the height of the antennas and the distance between them.

The author is a final year student of B.Tech ECE at RSET, Cochin

The article was first published on 22 July 2016 and was recently updated on 09 December 2022.


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