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A study of the maximally sparse large planar arrays with electrically large elements is presented. The conditional probabilities of the element placements and their resulting auxiliary radiation integrals are derived. Through them the average and the directivity pattern formulas are also derived. Employing these formulas, we present a convex method that provides a solution to the maximally sparse problem when main lobe constraints are imposed on the directivity pattern. In particular, by taking the possible types of elements into account, we manage to obtain the lower bound of the directivity that an array should exhibit. This lower bound is analytically derived in the form of a Pareto (sub-) set that classifies the possible arrays into feasible and nonfeasible ones. This Pareto set can also enable tradeoff studies to be conducted without the need to consider the full range of every parameter. From the procedure, several acceptable combinations of elements are obtained. Simulation results, which confirm the methodology, are presented.

In this paper we present a multi-objective optimization approach to subarrayed linear antenna arrays design. We define this problem as a bi-objective one. We consider two objective functions for directivity maximization and sidelobe level minimization. Memetic algorithms (MAs) are hybrid algorithms that combine the benefits of a global search Evolutionary Algorithm (EA) with a local search method. In this paper, we introduce a new memetic multi-objective evolutionary algorithm namely the memetic generalized differential evolution (MGDE3). This algorithm is a memetic extension of the popular generalized differential evolution (GDE3) algorithm. Another popular MOEA is the nondominated sorting genetic algorithm-II (NSGA-II). MGDE3, GDE3 and NSGA-II are applied to the synthesis of uniform and nonuniform subarrayed linear arrays, providing an extensive set of solutions for each design case. Depending on the desired array characteristics, the designer can select the most suitable solution. The results of the proposed method are compared with those reported in the literature, indicating the advantages and applicability of the multi-objective approach.

An optimization procedure for the layout assessment of electrically large but finite planar arrays is presented. The synthesis takes into account the desired directivity pattern that is prescribed employing bound constraints. Moreover, the size of the radiators is taken into account, which results in a hard nonoverlapping, between the elements, constraint. The latter should not be violated if we want the attained solution not only to obey the far-field mask, but also to be physically realizable. As stated, the optimization problem is twofold. An antenna design is associated with a packing problem. In order to take the constraints on the layout into account and solve the whole problem, we propose the constraint relaxation approach, which is equipped with a packing algorithm. Our study is applied to various initial geometries, and the resulting arrays appear to comply with the desired pattern and the nonoverlapping constraint. Several examples for different cases including symmetric arrays and a study on maximally sparse arrays are presented, which show the applicability and merit of the method.

Particle swarm optimization (PSO) is an evolutionary algorithm based on the bird fly. Differential evolution (DE) is a vector population based stochastic optimization method. The fact that both algorithms can handle efficiently arbitrary optimization problems has made them popular for solving problems in electromagnetics. In this paper, we apply a design technique based on a self-adaptive DE (SADE) algorithm to real-valued antenna and microwave design problems. These include linear-array synthesis, patch-antenna design and microstrip filter design. The number of unknowns for the design problems varies from 6 to 60. We compare the self-adaptive DE strategy with popular PSO and DE variants. We evaluate the algorithms' performance regarding statistical results and convergence speed. The results obtained for different problems show that the DE algorithms outperform the PSO variants in terms of finding best optima. Thus, our results show the advantages of the SADE strategy and the DE in general. However, these results are considered to be indicative and do not generally apply to all optimization problems in electromagnetics.

In this paper, the safety evaluation of the space in the vicinity of an aperture antenna is presented. The basis of our consideration is the approximate similarity of the contours between uniformly and nonuniformly illuminated apertures. Using the equivalence of either the gain or the beam width, it was possible to derive the uniform aperture with similar contours to the corresponding nonuniform one. In order to avoid radiofrequency (RF) hazards, instead of the isoparametric contours, their envelopes have been studied. Also, in the case where the exact axial field and the radiation pattern of the aperture are known, the contours can be approximately presented. Several examples with different apertures show the procedure of drawing the contours and explain the validity of our method.

The exact solution for the electromagnetic field diffracted by a perfectly conducting slotted elliptic cone is determined. The solution is presented in the form of a dyadic Green's function, which is the most general form of a possible solution. Some numerical results are presented and compared with others given in the past for simpler geometries. >