# gain2aperture

Convert gain to effective aperture

## Syntax

```A = gain2aperture(G,lambda) ```

## Description

`A = gain2aperture(G,lambda)` returns the effective aperture in square meters corresponding to a gain of `G` decibels for an incident electromagnetic wave with wavelength `lambda` meters. `G` can be a scalar or vector. If `G` is a vector, `A` is a vector of the same size as `G`. The elements of `A` represent the effective apertures for the corresponding elements of `G`. `lambda` must be a scalar.

## Input 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 in decibels 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

 `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 the corresponding gain in `G`.

## Examples

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An antenna has a gain of 3 dB. Calculate the antenna's effective aperture when used to capture an electromagnetic wave with a wavelength of 10 cm.

`a = gain2aperture(3,0.1)`
```a = 0.0016 ```

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### Gain and Effective Aperture

The relationship between the gain, G, in decibels of an antenna and the antenna’s effective aperture is:

`${A}_{e}={10}^{G/10}\frac{{\lambda }^{2}}{4\pi }$`

where λ is the wavelength of the incident electromagnetic wave.

## References

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

## Version History

Introduced in R2011a