Improved Synthesis Techniques for Uniformly-Spaced Planar Arrays

[摘要] English: There has until the present time been no planar array equivalent of thegeneralized Villeneuve (linear) distribution. The generalised Villeneuve lineardistribution array synthesis method has been extended to the planar array case by meansthe Baklanov transformation. The Baklanov transformation ensures that the resultingplanar array factor is f/1-symmetric. Aside from the sidelobe level, two additionalparameters have been introduced; they are the transition index ii that determines theposition at which the sidelobe must decay and the taper rate v that determines the decayrate of the far-out sidelobes. The generalised Villeneuve distribution for planar arraysenables the direct synthesis of discrete array distributions for high efficiency patterns ofarbitrary sidelobe levels and envelope taper. The synthesis method is extremely rapid;consequently, design trade-off studies are feasible. For a set number of elements andsidelobe ratio, the values of the transition index and the taper rate for a specificapplication will depend on the relative importance of farther-out sidelobe levels and theexcitation efficiency (or directivity) desired. Parametric studies of the distribution'sperformance have been conducted; curves of directivity versus element number as wellas curves of the influence of the additional parameters {ii and v) on the array factor areprovided. It has also been shown how the generalised planar Villeneuve distributionmethod can be used for the synthesis of planar arrays with a circular boundaries, withoutthe directivity performance being disadvantaged.A direct method to synthesise an array factor with an arbitrarily contoured mainbeam has been developed. The technique utilises a transformation that divides theproblem into two decoupled sub-problems. In the antenna array context, one subproblemconsists of a linear array synthesis, for which there exist various powerfulmethods for determining appropriate element excitations. The other involves thedetermination of certain coefficients of the transform in order to achieve the requiredfootprint contours. The number of coefficients which are needed depends on thecomplexity of the desired contour, but is very small in comparison to the number ofplanar array elements. The size required for this prototype linear array depends on the sidelobe level, the allowable ripple in the coverage region, number of transformationcoefficients used and the planar array size. Alternatively, it could be stated that the finalplanar array size depends on the number of transformation coefficients and the prototypelinear array size. Simple formulas then determine the final planar array excitations fromthe information forthcoming from the above two sub-problem solutions. Thus themethod is computational efficient and the time required to perform such a synthesis isrelatively short; thus trade-of studies are feasible even for very large arrays. Simpleformulas for the calculation of the transform coefficients for circular and ellipticalcontours have been derived, but the more general contour problem has also beendiscussed. Application of the newly developed transformation technique has beenexamined through number of specific examples.

[发布机构] University of Pretoria