Directivity Pattern of Line Arrays

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Highly directional acoustic and electromagnetic antennae are often built from linear arrays of omnidirectional transmitting (or receiving) elements. This Demonstration plots the directivity pattern of an unshaded line array of omnidirectional elements, steered to the angle with respect to the array axis. The patterns have cylindrical symmetry about the array axis. The array elements are plotted as white dots to show their number and orientation. An even number of elements results in a null along the axial direction of the array. An odd number of elements results in an endfire sidelobe, which, for many applications, is undesirable. The directivity pattern can be regarded as a transmission or reception sensitivity pattern.

Contributed by: Christopher Purcell (March 2011)
Open content licensed under CC BY-NC-SA



The directivity pattern of an -element unshaded line array is given by , where , the wave number , is the polar angle, is the steering angle, and is the wavelength. The frequency is Hz and the array inter-element spacing is meters. The wave speed is m/s. In this Demonstration, the inter-element spacing is . You can vary the number of elements in the range 1 to 16, the steering angle in the range -90 to 90 degrees, and the number of points plotted in the azimuthal direction. The array elements are plotted as white dots.

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