Improved Synthesis Techniques for Uniformly-Spaced Planar Arrays

Abstract

English: There has until the present time been no planar array equivalent of the generalized Villeneuve (linear) distribution. The generalised Villeneuve linear distribution array synthesis method has been extended to the planar array case by means the Baklanov transformation. The Baklanov transformation ensures that the resulting planar array factor is f/1-symmetric. Aside from the sidelobe level, two additional parameters have been introduced; they are the transition index ii that determines the position at which the sidelobe must decay and the taper rate v that determines the decay rate of the far-out sidelobes. The generalised Villeneuve distribution for planar arrays enables the direct synthesis of discrete array distributions for high efficiency patterns of arbitrary sidelobe levels and envelope taper. The synthesis method is extremely rapid; consequently, design trade-off studies are feasible. For a set number of elements and sidelobe ratio, the values of the transition index and the taper rate for a specific application will depend on the relative importance of farther-out sidelobe levels and the excitation efficiency (or directivity) desired. Parametric studies of the distribution's performance have been conducted; curves of directivity versus element number as well as curves of the influence of the additional parameters {ii and v) on the array factor are provided. It has also been shown how the generalised planar Villeneuve distribution method can be used for the synthesis of planar arrays with a circular boundaries, without the directivity performance being disadvantaged. A direct method to synthesise an array factor with an arbitrarily contoured main beam has been developed. The technique utilises a transformation that divides the problem into two decoupled sub-problems. In the antenna array context, one subproblem consists of a linear array synthesis, for which there exist various powerful methods for determining appropriate element excitations. The other involves the determination of certain coefficients of the transform in order to achieve the required footprint contours. The number of coefficients which are needed depends on the complexity of the desired contour, but is very small in comparison to the number of planar array elements. The size required for this prototype linear array depends on the sidelobe level, the allowable ripple in the coverage region, number of transformation coefficients used and the planar array size. Alternatively, it could be stated that the final planar array size depends on the number of transformation coefficients and the prototype linear array size. Simple formulas then determine the final planar array excitations from the information forthcoming from the above two sub-problem solutions. Thus the method is computational efficient and the time required to perform such a synthesis is relatively short; thus trade-of studies are feasible even for very large arrays. Simple formulas for the calculation of the transform coefficients for circular and elliptical contours have been derived, but the more general contour problem has also been discussed. Application of the newly developed transformation technique has been examined through number of specific examples.

Afrikaans: Tot op hede is daar geen sintese-metode vir vlaksamestellings ekwivalent aan die veralgemeende Villeneuve-verspreiding metode nie. Die veralgemeende Villeneuve liniere samestelling sintese-metode is uitgebrei na vlaksamestellings met behulp van die Baklanov-transformasie. Die Baklanov-transfomasie verseker 'n cp-simmetriese vlaksamestelling stralingspatroon. Naas die sylobvlak is nog twee ekstra parameters bygevoeg; dit is die oorgangsindeks 1i wat bepaal waar die sylobbe moet begin afplat en die afplattempo v wat die afneemtempo van die sylobbe bepaal. Die direkte sintese van vlaksamestellings met arbitrere sylobvlakke en afplattempo's word moontlik gemaak deur die veralgemeende Villeneuve-verspreiding vir vlaksamestellings. Die sinteseproses kan vinnig uitgevoer word; dus kan ontwerpstudies geredelik gedoen word. Vir 'n vasgestelde aantal elemente en sylobvlak hang die waardes van die oorgangsindeks en die afplattempo af van die relatiewe belangrikheid van die sylobvlakke op die kante en die aandrywings-effektiwiteit (of die direktiwiteit) wat verlang word. 'n Parameteriese studie van die samestellingskenmerke is gedoen; grafieke van die direktiwiteit teenoor die aantal elemente sowel as die invloed van die addisionele parameters word vertoon. Die veralgemeende Villeneuve vlaksamestelling kan ook gebruik word om vlaksamestellings met sirkulere rande te sintetiseer sonder dat die direktiwiteit benadeel word. 'n Direkte sintese-metode vir 'n samestellingsfaktor waarvan die hooflob 'n arbitrere vorm kan he, is ontwikkel. Die metode maak gebruik van 'n transformasie om die probleem te verdeel in twee afsonderlike sub-probleme. Die een sub-probleem behels die ontwerp van 'n liniere samestelling waarvoor daar verskeie metodes bestaan. Die ander sub-probleem behels die berekening van die transformasie-koeffisiente om die verlangde vorm van die hooflob te verkry. Die aantal koeffisiente wat benodig word hang af van die kompleksiteit van die verlangde vorm, maar is klein in verhouding met aantal elemente in die vlaksamestelling. Die grootte van die liniere samestelling word bepaal deur die sylobvlakke, die hoeveelheid riffel toelaatbaar in die hooflob, die aantal transfomasie-koeffisiente en die grootte van die vlaksamestelling. Die elementaandrywings word dan met eenvoudige formules bereken. Omdat die metode vinnig uitgevoer kan word, kan baie groot samestelling geredelik gesintetiseer word. Eenvoudige formules vir die tranformasie-koeffisiente ten einde sirkulere en elliptiese kontoere te bepaal, word afgelei. Die algemene kontoerbenaderingsprobleem word ook aangespreek. Toepassing van die nuwe metode word ondersoek aan die hand van spesifieke voorbeelde.