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.
