Question 8.16: Using the concept of the multiplication of patterns, find th...
Using the concept of the multiplication of patterns, find the radiation pattern of the array of four elements as shown in the figure.
This array is to be replaced with an array of two elements containing three subelements (1:2:1) each. The new array will have the individual excitations (1:3:3:1). The result according to the multiplication property (8.58) will have a radiation pattern as follows:
F(\theta ,\phi ) = F_{1}(\theta ,\phi ) F_{a}(\theta ,\phi ) (8.58)
F(\theta ) = \cos\left\lgroup\frac{\pi }{2} \cos \theta \right\rgroup \cos^{2}\left\lgroup\frac{\pi }{2} \cos \theta \right\rgroup = \cos^{3}\left\lgroup\frac{\pi }{2} \cos \theta \right\rgroupThe results are shown in the figure below: (a) the element pattern, (b) the array factor, and (c) the antenna array pattern. We note that the final pattern is narrower and has no side lobes.
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