# Side lobe

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Side lobe

In antenna engineering, side lobes are the lobes of the far field radiation pattern that are not the main beam, where the terms "beam" and "lobe" are synonyms. An antenna radiation pattern is more commonly called a beam pattern. The power density in the side lobes is generally much less than that in the main beam. It is generally desirable to minimize the sidelobe level (SLL), which is measured in decibels relative to the peak of the main beam. The main lobe and side lobes occur for both conditions of transmit, and for receive. The concepts of main and side lobes, aperture shapes, and aperture weighting, apply to problems in radar and optics (two specific applications of electromagnetics) and in sonar.

For a rectangular aperture antenna having a uniform amplitude (or uniform weighting), the first sidelobe is -13.26 dB relative to the peak of the main beam because for such antennas the radiation pattern has a canonical form of
$displaystylembox\left\{Radiation Pattern \left(in units of dB\right)\right\} propto 10log_\left\{10\right\}left\left(left|frac\left\{sin\left(X\right)\right\}\left\{X\right\} ight|^2 ight\right)$
Simple substitutions of various values of $displaystyle X$ into the canonical equation yield the following results:

For a circular aperture antenna, also having a uniform amplitude, the first sidelobe level is -17.57 dB relative to the peak of the main beam because in this case, the radiation pattern has a canonical form of
$displaystylembox\left\{Radiation Pattern \left(in units of dB\right)\right\} propto 10log_\left\{10\right\}left\left(left|2frac\left\{J_1\left(X\right)\right\}\left\{X\right\} ight|^2 ight\right)$
where $displaystyle J_1\left(x\right)$ is the Bessel function of the first kind of order 1. Simple substitutions of various values of $displaystyle X$ into the canonical equation yield the following results:

A uniform aperture distribution, as provided in the two examples above, gives the maximum possible directivity for a given aperture size, but it also produces the maximum side lobe level. Side lobe levels can be reduced by tapering the edges of the aperture distribution (changing from uniformity) at the expense of reduced directivity.

The nulls between sidelobes occur when the radiation patterns passes through the origin in the complex plane. Hence, adjacent sidelobes are generally 180° out of phase to each other.

Because an antenna's far field radiation pattern is a Fourier Transform of its aperture distribution, most antennas will generally have sidelobes, unless the aperture distribution is a Gaussian, or if the antenna is so small, as to have no sidelobes in the visible space. Larger antennas have narrower main beams, as well as narrower sidelobes. Hence, larger antennas have more sidelobes in the visible space (as the antenna size is increased, sidelobes move from the evanescent space to the visible space).

For discrete aperture antennas (such as phased arrays) in which the element spacing is much greater than a half wavelength, the aliasing effect causes some sidelobes to become substantially larger in amplitude, and approaching the level of the main lobe; these are called grating lobes, and they are identical, or nearly identical in the example shown, copies of the main beams. Grating lobes are a special case of a sidelobe. In such a case, the sidelobes should be considered all the lobes lying between the main lobe and the first grating lobe, or between grating lobes. It is conceptually useful to distinguish between sidelobes and grating lobes because grating lobes have larger amplitudes than most, if not all, of the other side lobes.

For antennas used as receivers, sidelobes make the antenna more vulnerable to noise from nuisance signals coming far away from the transmit source. For transmit antennas communicating classified information, sidelobes represent security vulnerability, as an unintended receiver may pick up the classified communication.

* [http://www.antenna-theory.com/basics/radPatDefs.php Sidelobes and Beamwidths - An Antenna Tutorial]

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