Main Content


Radiation efficiency of antenna

Since R2021a



E = efficiency(object,frequency) returns the radiation efficiency of the antenna or array over the specified frequency.


efficiency(object,frequency) plots the radiation efficiency of the antenna or array over the specified frequency.


collapse all

Create a top-hat monopole antenna.

m = metal("Lead");
ant = monopoleTopHat(Conductor=m);

Figure contains an axes object. The axes object with title monopoleTopHat antenna element, xlabel x (m), ylabel y (m) contains 5 objects of type patch, surface. These objects represent Lead, feed.

Plot the radiation efficiency of the antenna over a frequency range of 40-100 MHz.


Figure contains an axes object. The axes object with title Efficiency, xlabel Frequency (MHz), ylabel Efficiency contains an object of type line.

Create and visualize patch microstrip antennas with PEC, copper, silver, and aluminium metal patches.

ant_patchPEC = patchMicrostrip(Substrate=dielectric("Air"),Conductor=metal("PEC"));
ant_patchCopper = patchMicrostrip(Substrate=dielectric("FR4"),Conductor=metal("Copper"));
ant_patchSilver = patchMicrostrip(Substrate=dielectric("FR4"),Conductor=metal("Silver"));
ant_patchAluminium = patchMicrostrip(Substrate=dielectric("FR4"),Conductor=metal("Aluminium"));

Compare the radiation efficiency of these antennas at the frequency of 1 GHz.

Eff_patchPEC = efficiency(ant_patchPEC,1e09)
Eff_patchPEC = 1
Eff_patchCopper = efficiency(ant_patchCopper,1e09)
Eff_patchCopper = 0.4889
Eff_patchSilver = efficiency(ant_patchSilver,1e09)
Eff_patchSilver = 0.4319
Eff_patchAluminium = efficiency(ant_patchAluminium,1e09)
Eff_patchAluminium = 0.4870

Input Arguments

collapse all

Antenna or array to calculate the efficiency, specified as an antenna or array from the catalog, a pcbStack object or custom antenna or array created using either of these:


Only homogeneous arrays are supported for efficiency calculation, with an exception of conformalArray.

Frequency or frequency range over which to calculate the radiation efficiency, specified as a scalar or a vector in Hz.

Example: 50e6:1e6:100e6

Data Types: double

Output Arguments

collapse all

Radiation efficiency of the antenna, returned as a scalar or a vector with values in the range [0,1].

More About

collapse all

Radiation Efficiency

The time-average power density radiated by an antenna is:

where, r = radius of the sphere,

θ, φ = spherical coordinate angles,

E, H = electric and magnetic field intensity respectively.

The total power radiated by antenna is:

where, U = radiation intensity (W/ unit solid angle),

dΩ = element of solid angle.

The radiation efficiency is given as:

where, Pin = total input power.

Version History

Introduced in R2021a