# Documentation

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## Grating Lobes

Grating lobes are the maxima of the main beam, as predicted by the pattern multiplication theorem. When the array spacing is less than or equal to $\lambda /2$, only the main lobe exists in the visible space, with no other grating lobes. Grating lobes appear when the array spacing is greater than $\lambda /2$. For large spacing, grating lobes can appear in the visible space even at a zero scan angle.

Consider a linear array of seven elements spaced one-half wavelength apart. This array contains no grating lobes.

When you increase the element spacing to one wavelength, the number of side lobes increases.

When you increase the element spacing to 1.5 wavelengths apart, the grating lobes appear in the visible region.

The grating lobes move in or out of the visible region depending on the spacing between the elements and the relative phase between them.

## References

[1] Stutzman, W.L. Thiele, G.A. Antenna Theory and Design, 3rd Edition. New York: Wiley, 2013, p. 307.