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For discrete aperture antennas (such as phased arrays) in which the element spacing is greater than a half wavelength, the spatial 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 either identical, or nearly identical as shown in the figure, copies of the main beams.
A typical radiation pattern of phased arrays whose inter-element spacing is greater than half a wavelength, hence the radiation pattern has 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 ...
Now, suppose that the excitation coefficients are positive real variables. In this case, always in the domain of , the array factor magnitude has a main lobe with maximum value at =, called mainlobe, several secondary lobes lower than the mainlobe, called sidelobes and mainlobe replicas called grating-lobes. Grating lobes are a source of ...
These equations can be solved to predict the nulls, main lobe, and grating lobes of the array. Referring to the exponents in the array factor equation, we can say that major and grating lobes will occur at integer , =,,, … solutions to the following equations: [4] [41] [page needed]
Typically the grating period is the same size as the Bragg wavelength, as shown above. For a grating that reflects at 1,500 nm, the grating period is 500 nm, using a refractive index of 1.5. Longer periods can be used to achieve much broader responses than are possible with a standard FBG. These gratings are called long-period fiber grating ...
Side lobes are normally the largest of the minor lobes. The level of minor lobes is usually expressed as a ratio of the power density in the lobe in question to that of the major lobe. This ratio is often termed the side lobe ratio or side lobe level. Side lobe levels of −20 dB or greater are usually not desirable in many applications.
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The sidelobes are all at least 20 dB below (1/100 the power density of) the main lobe, and most are 30 dB below (if this pattern was drawn with linear power levels instead of logarithmic dB levels, all lobes other than the main lobe would be much too small to see).