Towards a method for antenna impedance tailoring through shapeoptimization, with a bound on the associated cost-function
Abstract: Over the last years, there has been an interest in designing antennas that operateat higher frequencies. In most applications, these antennas work jointly withPower Amplifiers. However, most commercial Power Amplifiers have a nonstandardoptimal load-pull impedance in their optimal operating frequencies.To obtain the maximal delivered power, the antenna is required to be matchedto the optimal load-pull of the Power Amplifier. The input impedance of theantenna depends on its shape. By changing the shape of the antenna (shapeoptimization),we here search for a method to match the antenna to an arbitrarynon-standard impedance.To model the antenna-design problem, a Method of Moment solver for theSurface Integral Equations has been implemented in Matlab. The singularitiesin the kernel, due to the 1=R-behavior of the Green’s function has beentreated by using the Divergence Theorem method, increasing the accuracy ofthe solver. The shape of the antenna is changed by cutting infinitesimal cutsalong a triangular mesh over the domain. This is modeled in the Method ofMoment by loading the corresponding mesh-edge with large (infinite) resistance.The method conforms well with the Method of Moment, and it also provides avery fast way of evaluating the performance of candidate designs. Two methodshave been implemented as part of this thesis work for designing antennas.The first is the Topological Sensitivity method, which is a deterministic localoptimization tool. The second method is the Genetic Algorithm, an evolutionaryalgorithm. Additionally, a solver to compute the performance bounds tothe shape optimization problem has been implemented using Lagrange Duality.This type of lower bounds is rarely determined in for shape optimization,and to the knowledge of the author, this is the first time such bounds were computedfor shape-optimization in the impedance matching context.The design methodology has been tested on a 1 1 wavelength large rectangularantenna. The impedance performance of the suggested designs wascompared to the computed lower bound. We test scenarios such as singlefrequency matching, multiple frequency matching, embedded antenna, andmutual impedance. The results suggest that the computed lower bounds arereasonable estimates to the best possible performance obtainable. The TopologicalSensitivity yielded good design results in a short time, but it often got stuck in suboptimal local minima. The Genetic Algorithm, on the other hand,yielded better results but required a much longer time to compute. Lastly, wepresent a method to accurately realize the cuts by cutting two or more adjacentedges.
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