It is known that high frequency in the teraHertz range (THz) have unique advantage in the reflective properties for biological objects and penetration through dielectric material. These radiations are non-ionizing for use in civilian applications. High frequency aperture size can be fairly small allowing the equipment to be portable. THz components mainly consist of sources detectors up-converters down-converters mixers and circulators and associated femto second laser generators. These components are under active development. However each component of these high frequency modules for transmission and reception can be fairly large. In this paper a deterministic thinning procedure is derived for designing an array, with sidelobe control, of these transmission and receiver modules. Circular as well as elliptical arrays are discussed. Algorithm is developed based on Taylor synthesis procedure with zero sampling. Grid locations of these large arrays are given with some examples. Using the results of thinned circular array we design elliptical array using invariant principal of the synthesis. The array design is based on analytic solutions of aperture integral equations. Side lobe control is achieved by controlling the illumination of the aperture. This illumination corresponds to the density of the elements in the sparse array, with each element of the array having uniform amplitude.