General radiation-pattern synthesis technique for array antennas of arbitrary configuration and element type, страница 4

6.3 Constrained solutions It is necessary often to have a phase/amplitude distribution which is 'smoothly varying'. To obtain this we can fit a set of orthogonal functions 0 to A, and or a,, and solve for factors cd), , for h = 1-ff' 'vherp H ^ N. In this way the solution can be directly constrained to be symmetric, antisymmetric or possibly a combination of low-order terms.

Other contraints can be imposed by the antenna configuration, for example if the antenna is an array-fed reflector or lens, or composed of a group of dissimilar subarrays. Each element-reflector or subarray pattern can then be treated as a separate element and the appropriate synthesis procedure used. The effects of mutual coupling can be included in a similar way, by calculating or measuring the immerged element patterns of each element or group of elements within the array.

7   Some applications of the method

A computer program named SYNFF [52] was written which utilises the above methods, and over the past few years many practical antennas have been designed using it. These antennas were for two main applications:

(a) Radar antennas where cosecant-squared type elevation patterns were required

(ft)   Satellite   communication   antennas   where contoured-beam shapes are necessary for the spacecraft segment.

The following Sections use this work to provide examples, and to compare SYNFF with some alternative synthesis methods.

. 7.7 Synthesis of cosecant squared patterns One common use of radiation-pattern synthesis is to obtain cosecant-squared elevation patterns to give constant-height radar coverage. These patterns are used

here to compare this technique with the Woodward, Elliot! and Chu methods.

When synthesising a consecant squared pattern there arc three main parameters to consider:

(a) Sidelobe level

(b) Cut-off rate

(c) Cover.

7.2 Comparison of S YNFF and Woodward [24 ] Many patterns were synthesised, using both methods, so that comparisons of the conflicting parameters could be made. It was found that patterns with a high illumination efficiency also had a high cut-off efficiency, but that the higher these two factors were, the higher the degree of main-beam ripple became. These effects are shown for both Woodward and SYNFF in Fig. 3. Here the required cosecant-squared pattern has been synthesised using a linear array composed of 25 elements at 0.5 wavelength spacing. On comparing the two patterns it is evident that the cut-off rate and directivity of the two patterns are virtually the same, but that all the other parameters of the SYNFF pattern represent improvements on Woodward's. For example, the sidelobe level is about 4 dB lower and the main beam ripple has been reduced by a similar amount. Figs. 4 and 5 are graphs that summarise the relations between illumination/cut-off efficiency and main-beam ripple for the two methods. The illumination efficiency is with respect to a uniformly illuminated aperture; the cut-off efficiency is denned here as the ratio of the angle between the —3dB and —20 dB power points of the pattern in question and that of an equivalent-sized uniformly illuminated aperture. Also included are some points from Elliott's method [38, 53].

Typical amplitude and phase distributions of the methods are given in Fig. 6. The distributions obtained using this method are no more sensitive to errors than those obtained using Woodward's method. A comparison between the measured and predicted performance of a secondary surveillance radar antenna is given in Fig. 7.

The array consisted of 33 vertical triplate distribution networks. Each network fed ten vertical dipoles with the appropriate amplitude and phase distribution. The dipoles were spaced 0.165 m apart. The results are for the performance of the network at 1060 MHz.