Side lobe
Encyclopedia
In antenna
An antenna is an electrical device which converts electric currents into radio waves, and vice versa. It is usually used with a radio transmitter or radio receiver...

engineering, side lobes or sidelobes are the lobes (local maxima) of the far field
Near and far field
The near field and far field and the transition zone are regions of the electromagnetic radiation field that emanates from a transmitting antenna, or as a result of radiation scattering off an object...

In the field of antenna design the term radiation pattern most commonly refers to the directional dependence of the strength of the radio waves from the antenna or other source ....

that are not the main lobe
Main lobe
The main lobe, or main beam, of an antenna radiation pattern is the lobe containing the maximum power. This is the lobe that exhibits the greatest field strength....

.

The radiation pattern of most antennas shows a pattern of "lobes" at various angles, directions where the radiated signal strength reaches a maximum, separated by "null
In radio electronics, a null is an area or vector in an antenna's radiation pattern where the signal cancels out almost entirely.This can be an advantage, as nulls in the horizontal plane can be used to protect other transmitters from interference. If not carefully planned however, nulls can...

s
", angles at which the radiated signal strength falls to zero. In a directional antenna
Directional antenna
A directional antenna or beam antenna is an antenna which radiates greater power in one or more directions allowing for increased performance on transmit and receive and reduced interference from unwanted sources....

in which the objective is to emit the radio waves in one direction, the lobe in that direction has a larger field strength than the others; this is the "main lobe
Main lobe
The main lobe, or main beam, of an antenna radiation pattern is the lobe containing the maximum power. This is the lobe that exhibits the greatest field strength....

". The other lobes are called "side lobes", and usually represent unwanted radiation in undesired directions. The side lobe in the opposite direction (180°) from the main lobe is called the "back lobe". In transmitting
Transmitter
In electronics and telecommunications a transmitter or radio transmitter is an electronic device which, with the aid of an antenna, produces radio waves. The transmitter itself generates a radio frequency alternating current, which is applied to the antenna. When excited by this alternating...

antennas, excessive side lobe radiation wastes energy and may cause interference
Electromagnetic interference
Electromagnetic interference is disturbance that affects an electrical circuit due to either electromagnetic induction or electromagnetic radiation emitted from an external source. The disturbance may interrupt, obstruct, or otherwise degrade or limit the effective performance of the circuit...

to other equipment. Classified information may be picked up by unintended receivers. In receiving antennas, side lobes may pick up interfering signals, and increase the noise level in the receiver.

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 decibel
Decibel
The decibel is a logarithmic unit that indicates the ratio of a physical quantity relative to a specified or implied reference level. A ratio in decibels is ten times the logarithm to base 10 of the ratio of two power quantities...

s 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
Sonar
Sonar is a technique that uses sound propagation to navigate, communicate with or detect other vessels...

.

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
Canonical form
Generally, in mathematics, a canonical form of an object is a standard way of presenting that object....

of

Simple substitutions of various values of into the canonical equation yield the following results:
peak of main beam
first null
peak of first sidelobe
second null
peak of second sidelobe

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
Canonical form
Generally, in mathematics, a canonical form of an object is a standard way of presenting that object....

of

where is the Bessel function of the first kind of order 1. Simple substitutions of various values of into the canonical equation yield the following results:
peak of main beam
first null
peak of first sidelobe
second null
peak of second sidelobe

A uniform aperture distribution, as provided in the two examples above, gives the maximum possible directivity
Directivity
In electromagnetics, directivity is a figure of merit for an antenna. It measures the power density the antenna radiates in the direction of its strongest emission, versus the power density radiated by an ideal isotropic radiator radiating the same total power.An antenna's directivity is a...

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
Directivity
In electromagnetics, directivity is a figure of merit for an antenna. It measures the power density the antenna radiates in the direction of its strongest emission, versus the power density radiated by an ideal isotropic radiator radiating the same total power.An antenna's directivity is a...

.

The nulls between sidelobes occur when the radiation patterns passes through the origin in the complex plane
Complex plane
In mathematics, the complex plane or z-plane is a geometric representation of the complex numbers established by the real axis and the orthogonal imaginary axis...

. Hence, adjacent sidelobes are generally 180° out of phase to each other.

Because an antenna's far field radiation pattern
In the field of antenna design the term radiation pattern most commonly refers to the directional dependence of the strength of the radio waves from the antenna or other source ....

is a Fourier Transform
Fourier transform
In mathematics, Fourier analysis is a subject area which grew from the study of Fourier series. The subject began with the study of the way general functions may be represented by sums of simpler trigonometric functions...

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
Evanescent wave
An evanescent wave is a nearfield standing wave with an intensity that exhibits exponential decay with distance from the boundary at which the wave was formed. Evanescent waves are a general property of wave-equations, and can in principle occur in any context to which a wave-equation applies...

to the visible space).
For discrete aperture antennas (such as phased array
Phased array
In wave theory, a phased array is an array of antennas in which the relative phases of the respective signals feeding the antennas are varied in such a way that the effective radiation pattern of the array is reinforced in a desired direction and suppressed in undesired directions.An antenna array...

s) in which the element spacing is greater than a half wavelength, the spatial aliasing
Aliasing
In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...

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. The mathematics of grating lobes is the same as of X-ray diffraction.