Array pattern multiplication – phased array antenna

Articles in this series

• Phased Array Antenna – an introduction
• Electronic Scanning Arrays
• Grating lobes in electronic scanning
• Array pattern multiplication (this article)

Array pattern multiplication

If the element pattern of an array is very broad (as in an Omni directional antenna element) the pattern of the array is mostly the Array Factor since it is more directional. However, if the element pattern has some distinctive features by employing specific illumination function, then the composite radiation pattern is obtained by the principal of pattern multiplication. If F_arrayis the Fourier transform of the array field and F_element is the Fourier transform of the element field, the combined pattern is given by the pattern multiplication

Composite antenna pattern = F_array × F_element

Example:

1. Uniformly illuminated array produces a first sidelobe level of -13.5 dB [=20×log₁₀ (field amplitude)]. Due to the vast difference in levels between major and minor lobes, logarithmic (dB) scale is preferred in such measurements to provide the required dynamic range. This illumination function produces a better aperture efficiency (gain), sharper beamwidth but at the cost of near sidelobes getting elevated.

2. The cosine aperture distribution on a pedestal attempts to deal with a maximized gain along with control on the sidelobe levels. The accompanying figure below is the array pattern with illumination function of the type f(x) =0.9×cos(x) +0.1, where x refers to the linear position of the element.

Instead of tapering the edge illumination to zero, the cosine function sits on a pedestal to provide a constant illumination, but at a lower percentage level, at the peripheral geometry of the radiating element. The main beam is broadened but the first sidelobes are at -23.5dB level, an order of improvement on the -13.5 dB level of the previous case.

Several sophisticated illumination functions are available to the designer now to optimize array design.

Concluding remarks

It should be stressed that a Phased Array produces huge opportunity for designers to exploit its dynamic properties; but at the same time, it challenges us with system engineering and integration complexity, maintainability and finally in the cost factor. In an evolving era of technology, limitations in engineering and operation, would always witness a better tomorrow, provided the basic scientific validation and sustainability are present in all of the newer innovations. 

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