# efficiency

Since R2021a

## Syntax

``E = efficiency(object,frequency)``
``efficiency(object,frequency)``

## Description

example

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

example

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

## Examples

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Create a top-hat monopole antenna.

```m = metal("Lead"); ant = monopoleTopHat(Conductor=m); show(ant)``` Plot the radiation efficiency of the antenna over a frequency range of 40-100 MHz.

`efficiency(ant,linspace(40e6,100e6,41))` 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

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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:

Note

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

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

collapse all 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