# aperture2gain

Convert effective aperture to gain

## Syntax

```G = aperture2gain(A,lambda) ```

## Description

`G = aperture2gain(A,lambda)` returns the antenna gain in decibels corresponding to an effective aperture of `A` square meters for an incident electromagnetic wave with wavelength `lambda` meters. `A` can be a scalar or vector. If `A` is a vector, `G` is a vector of the same size as `A`. The elements of `G` represent the gains for the corresponding elements of `A`. `lambda` must be a scalar.

## Input Arguments

 `A` Antenna effective aperture in square meters. The effective aperture describes how much energy is captured from an incident electromagnetic plane wave. The argument describes the functional area of the antenna and is not equivalent to the actual physical area. For a fixed wavelength, the antenna gain is proportional to the effective aperture. `A` can be a scalar or vector. If `A` is a vector, each element of `A` is the effective aperture of a single antenna. `lambda` Wavelength of the incident electromagnetic wave. The wavelength of an electromagnetic wave is the ratio of the wave propagation speed to the frequency. For a fixed effective aperture, the antenna gain is inversely proportional to the square of the wavelength. `lambda` must be a scalar.

## Output Arguments

 `G` Antenna gain in decibels. `G` is a scalar or a vector. If `G` is a vector, each element of `G` is the gain corresponding to effective aperture of the same element in `A`.

## Examples

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An antenna has an effective aperture of 3 square meters. Find the antenna gain when used to capture an electromagnetic wave with a wavelength of 10 cm.

`g = aperture2gain(3,0.1)`
```g = 35.7633 ```

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### Gain and Effective Aperture

The relationship between the gain, G, and effective aperture of an antenna, Ae is:

`$G=\frac{4\pi }{{\lambda }^{2}}{A}_{e}$`

where λ is the wavelength of the incident electromagnetic wave. The gain expressed in decibels is:

`$10{\mathrm{log}}_{10}\left(G\right)$`

## References

 Skolnik, M. Introduction to Radar Systems, 3rd Ed. New York: McGraw-Hill, 2001.