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# gain2aperture

Convert gain to effective aperture

## Syntax

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

## Description

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````A = gain2aperture(GdB,lambda)` returns the effective aperture of an antenna corresponding to an antenna gain of `GdB` for an incident electromagnetic wave with wavelength `lambda`.```

## 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 ```

## Input Arguments

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Antenna gains, specified as a scalar or as an N-element real-valued vector. If `GdB` is a vector, each element of `GdB` corresponds to the effective aperture of the same element in the output argument `A`. See Gain and Effective Aperture for a discussion of aperture and gain. Units are in dBi.

Data Types: `double`

Wavelength of the incident electromagnetic wave, specified as a positive scalar. The wavelength of an electromagnetic wave is the ratio of the wave propagation speed to the frequency. Units are in meters.

Data Types: `double`

## Output Arguments

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Antenna effective aperture, returned as a positive scalar or as an N-element vector of positive values. The elements of `A` represent the effective apertures for the corresponding elements of `GdB`. The size of `A` equals the size of `GdB`.

Data Types: `double`

## More About

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### Gain and Effective Aperture

The effective aperture describes how much energy is captured by an antenna from an incident electromagnetic plane wave. The effective area of the antenna and is not the same as the actual physical area. The array gain of an antenna G is related to its effective aperture Ae by:

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

where λ is the wavelength of the incident electromagnetic wave. For a fixed wavelength, the antenna gain is proportional to the effective aperture. For a fixed effective aperture, the antenna gain is inversely proportional to the square of the wavelength.

The gain expressed in dBi (GdB) is

`$GdB=10{\mathrm{log}}_{10}G=10{\mathrm{log}}_{10}\left(\frac{4\pi {A}_{g}}{{\lambda }^{2}}\right).$`

The effective antenna aperture can be derived from the gain in dB using

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

## References

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

[2] Richards, M. Fundamentals of Radar Signal Processing, New York: McGraw-Hill, 2005.

## Version History

Introduced in R2011a