In antenna engineering, sidelobes are the lobes (local maxima) of the far field

radiation pattern In the field of antenna design the term radiation pattern (or antenna pattern or far-field pattern) refers to the ''directional'' (angular) dependence of the strength of the radio waves from the antenna or other source.Constantine A. Balanis: “A ...

of an antenna or other radiation source, that are not the '' main lobe''. 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 Null may refer to: Science, technology, and mathematics Computing * Null (SQL) (or NULL), a special marker and keyword in SQL indicating that something has no value * Null character, the zero-valued ASCII character, also designated by , often use ...

s''", angles at which the radiated signal strength falls to zero. This can be viewed as the

diffraction pattern Diffraction is defined as the interference or bending of waves around the corners of an obstacle or through an aperture into the region of geometrical shadow of the obstacle/aperture. The diffracting object or aperture effectively becomes a ...

of the antenna. In a directional antenna in which the objective is to emit the radio waves in one direction, the lobe in that direction is designed to have a larger field strength than the others; this is the "'' main lobe''". The other lobes are called "''sidelobes''", and usually represent unwanted radiation in undesired directions. The sidelobe directly behind the main lobe is called the back lobe. The longer the antenna relative to the radio

wavelength In physics, the wavelength is the spatial period of a periodic wave—the distance over which the wave's shape repeats. It is the distance between consecutive corresponding points of the same phase on the wave, such as two adjacent crests, t ...

, the more lobes its radiation pattern has. In

transmitting In electronics and telecommunications, a radio transmitter or just transmitter is an electronic device which produces radio waves with an antenna. The transmitter itself generates a radio frequency alternating current, which is applied to th ...

antennas, excessive sidelobe radiation wastes energy and may cause interference to other equipment. Another disadvantage is that confidential information may be picked up by unintended receivers. In receiving antennas, sidelobes may pick up interfering signals, and increase the noise level in the receiver. The power density in the sidelobes 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 sidelobes occur for both transmitting and receiving. The concepts of main and sidelobes, radiation pattern, aperture shapes, and aperture weighting, apply to

optics Optics is the branch of physics that studies the behaviour and properties of light, including its interactions with matter and the construction of instruments that use or detect it. Optics usually describes the behaviour of visible, ultrav ...

(another branch of electromagnetics) and in acoustics fields such as

loudspeaker A loudspeaker (commonly referred to as a speaker or speaker driver) is an electroacoustic transducer that converts an electrical audio signal into a corresponding sound. A ''speaker system'', also often simply referred to as a "speaker" or ...

and

sonar Sonar (sound navigation and ranging or sonic navigation and ranging) is a technique that uses sound propagation (usually underwater, as in submarine navigation) to navigate, measure distances (ranging), communicate with or detect objects on o ...

design, as well as antenna design. Because an antenna's far field

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).

Sidelobes for case of uniformly-illuminated aperture

For a rectangular aperture antenna having a uniform amplitude distribution (or uniform weighting), the first sidelobe is relative to the peak of the main beam. For such antennas the radiation pattern has a

canonical form In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical expression. Often, it is one which provides the simplest representation of an ...

of Simple substitutions of various values of into the canonical equation yield the following results: style="margin-left: auto; margin-right: auto; border: none;" ! ! Radiation Pattern ! Explanation , - , 0 , style="text-align:right;" , , peak of main beam , - ,

\displaystyle 3.14=\pi

, style="text-align:right;" , −∞ dB , first null , - ,

\displaystyle 4.49\approx\frac

, style="text-align:right;" , , peak of first sidelobe , - ,

\displaystyle 6.28=2\pi

, style="text-align:right;" , −∞ dB , second null , - ,

\displaystyle 7.72\approx\frac

, style="text-align:right;" , , peak of second sidelobe , - For a circular aperture antenna, also having a uniform amplitude distribution, the first sidelobe level is relative to the peak of the main beam. In this case, the radiation pattern has a

of where

\displaystyle J_1(x)

is the

Bessel function of the first kind Bessel functions, first defined by the mathematician Daniel Bernoulli and then generalized by Friedrich Bessel, are canonical solutions of Bessel's differential equation x^2 \frac + x \frac + \left(x^2 - \alpha^2 \right)y = 0 for an arbitrary ...

of order 1. This is known as the Airy pattern. Simple substitutions of various values of into the canonical equation yield the following results: style="margin-left: auto; margin-right: auto; border: none;" ! ! Radiation Pattern ! Explanation , - , 0 , style="text-align:right;" , , peak of main beam , - , 3.83 , style="text-align:right;" , −∞ dB , first null , - , 5.14 , style="text-align:right;" , , peak of first sidelobe , - , 7.02 , style="text-align:right;" , −∞ dB , second null , - , 8.42 , style="text-align:right;" , , peak of second sidelobe , - 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 sidelobe level. Sidelobe 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.

Grating lobes

{{Main, Grating lobes For discrete aperture antennas (such as phased arrays) in which the element spacing is greater than a half wavelength, the spatial

aliasing In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or ''aliases'' of one another) when sampled. It also often refers to the distortion or artifact that results when ...

effect causes some sidelobes to become substantially larger in amplitude, and approaching the level of the main lobe; these are called

grating lobes For discrete aperture antennas (such as phased arrays) in which the element spacing is greater than a half wavelength, a spatial aliasing effect allows plane waves incident to the array from visible angles other than the desired direction to be coh ...

, and they are either identical, or nearly identical as shown in the figure, 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 sidelobes. The mathematics of grating lobes is the same as of X-ray diffraction.

External links

Sidelobes and Beamwidths - An Antenna Tutorial
Antennas Radio frequency propagation de:Antennendiagramm#Elemente eines Antennendiagramms