Design of Planar Arrays With Reduced Nonuniform Excitation Subject to Constraints on the Resulting Pattern and the Directivity

• Published in: IEEE transactions on antennas and propagation Vol. 57; no. 8; pp. 2270 - 2278
• Main Authors: Kaifas, T.N., Babas, D.G., Sahalos, J.N.
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.08.2009; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Antennas; Aperiodic arrays; Applied sciences; array synthesis; Arrays; Constraint theory; Cost function; Directivity; directivity constraint; Exact sciences and technology; Excitation; Geometry; Laboratories; Lagrange multiplier; Lagrange multipliers; Lagrangian functions; Nonuniformity; Perturbation methods; Physics; Planar arrays; Radiocommunications; Stochastic processes; Studies; Synthesis; Telecommunications; Telecommunications and information theory; Transmission line matrix methods; array synthesis; Iterative method; Perturbation; Planar antenna arrays; Independent variable; directivity constraint; Non uniform distribution; Directivity; Lagrange multiplier; Perturbation method; Aperiodic arrays; Cost function; Lagrangian function; Antenna synthesis
• ISSN: 0018-926X; 1558-2221
• DOI: 10.1109/TAP.2009.2024484

A design procedure for the synthesis of planar arrays is presented. Synthesis takes into account the desired pattern and the constraint on the directivity index. It makes use of the perturbation method in conjunction with the Lagrange multiplier theory. Starting from an initial array we perturb the element positions by employing an iterative technique. In the iteration, by setting the first variation of the Lagrangian (Cost function) equal to zero we derive the perturbed positions. Perturbation is applied simultaneously along two independent variables, (element coordinates x and y ). The final position of the elements results from the last iteration where the stopping criteria are met. The choice of the initial array takes into account the number of elements and the reduction need of nonuniformity in the excitation. Our study is used for various initial geometries and the resulting arrays are shown to comply with the desired pattern and the directivity index.