# aperture2gain

Convert effective aperture to gain

## Description

## Examples

### Compute Antenna Gain

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

## Input Arguments

`A`

— Antenna effective aperture

positive scalar |
*N*-element vector of positive values

Antenna effective aperture, specified as a positive scalar or as an
*N*-element real-valued vector of positive values. If
`A`

is a vector, each element of
`A`

corresponds is the effective aperture of a
different antenna. See Gain and Effective Aperture for a discussion of aperture and
gain. Units are in square meters.

**Data Types: **`double`

`lambda`

— Wavelength of the incident electromagnetic wave

positive scalar

Wavelength of the incident electromagnetic wave, specified as a positive
scalar. The same wavelength applies to all antennas in
`A`

. 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

`GdB`

— Antenna gain

scalar | *N*-element real-valued vector

Antenna gain, returned as a scalar or as an *N*-element
real-valued vector. The elements of `GdB`

represent the
gain corresponding to the elements in `A`

. The size of
`GdB`

equals the size of `A`

.
Units are in dBi.

**Data Types: **`double`

## More About

### 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 *A _{e}* 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

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

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.

## Extended Capabilities

### C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

Does not support variable-size inputs.

## Version History

**Introduced in R2011a**

## See Also

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