Pattern synthesis of linear phased arrays with optimized unit circle Boundary Conditions K.Srinivasa Naik 1 , D. Madhusudan 1 , S.Aruna 2 1,2 Electronics and Communication Engineering department, 1 Vignan‘s Institute of Information and Technology, Visakhapatnam, A.P, India E-mail: 1 nivas97033205@gmail.com, 1 madhus7001@gmail.com 2 AUCE(A), Visakhapatnam, A.P, India E-mail: 2 aruna9490564519@gmail.com Abstract— The present work perturbs the synthesis of linear array patterns in periodic phases in the presence of asymmetric element pattern and mutual coupling. To mitigate the above problems in small linear phased arrays, an approach proposed using a Schelkunoff’s unit circle z-plane coupled with PSO, with zeros in z-plane constrained using intelligently defined solution space boundary conditions. The proposed optimisation scheme achieves better radiation pattern objectives in addition of mutual coupling for scanned low side lobe beam sum pattern and wide band sector-beam pattern. Convergence performance comparisons have shown that the preferred scheme, IzBC-PSO, is faster, consistent and more accurate than other optimization techniques. Significant improvement in the results is obtained by using a Bow-tie dielectric resonator antenna in 4.5 to 5.5 GHz frequency ranges. Keywords-IZBC-PSO, Schelkunoff’s Unit Circle, Bowtie dielectric resonator antenna,Mutual Coupling, intelligently defined solution space Boundary Condition I. INTRODUCTION Due to small array size, conventional pattern synthesis techniques fail to produce required results. The conventional pattern synthesis approach produced results with sub-optimal gain, side lobe level and 3dB beam width due to limited number of the elements and the effects of mutual coupling involved. Performance of the small array antennas can be limited and the estimation of the infinite array is not adequate with existence of mutual coupling. In practical small phased arrays, inaccuracy in beam pointing, beam widening and higher sidelobe level occurred with a single linear phase gradient applied to beam scanning. For low gain applications the resolution of scanned arrays reduced because of broadening the beam [1]. In the classic paper of Dolph [2], to obtain smallest beamwidth for a specified sidelobe level the current distributions are derived for equally spaced symmetric broadside linear arrays in which the elements are in phase and are symmetrically positioned from the center of the array with less than half-length element spacing. Taylor [3] proposed an excellent technique on the design of the continuous line source with narrower beam width of the main beam and decaying low sidelobes for continuous array apertures. For discrete networks, these aperture distributions are sampled and the performance of the pattern indeterminate and a recompensation is necessary. Bayliss [4] developed a method to produce monopulse difference patterns, used a technique alike to Taylor‘s method, for optimize the phase taper for the end fire array. Majority of the synthesis techniques reported is for only low- sidelobe narrow-beam array factors. A sector pattern is a shaped beam pattern that ideally has uniform radiation in the main beam with zero side lobe levels. The realized patterns are found to contain the sector beams which are close to the desired ones over specified angular regions with reduced SLLs. However, for synthesize small arrays many classical methods such as Schelkunoff‘s Polynomial method, Fourier transform method, Woodward-Lawson method, etc. They are suitable for the synthesis of beam patterns with little limitations, because of undesired ripples in trade in region. To control these pattern synthesis problems different researchers proposed a variety of solutions [5-7]. Mutual coupling is major problem in practical antenna arrays. In antenna array systems to represent mutual coupling, there are two approaches. After deriving coupling matrix various methods have been initiated to mitigate the effect