Ing. Jonáš Tuček

Density formulation of topology optimization is utilized within method-of-moments formalism to optimize antenna gain. The structure of the problem's solution space is outlined and compared to a solution space formed by Q-factor minimization. Dependence of antenna gain on ohmic losses includes additional complexity to the optimization problem and may negatively influence the progress of the optimization in early stages. The influence of the utilized interpolation scheme is also investigated. Optimized designs from the current state of the formulation are also presented.

Classical gradient-based density topology optimization is adapted for method-of-moments numerical modeling to design a conductor-based system attaining the minimal antenna Q-factor evaluated via an energy stored operator. Standard topology optimization features are discussed, e.g., interpolation scheme and density and projection filtering. The performance of the proposed technique is demonstrated in a few examples in terms of the realized Q-factor values and necessary computational time to obtain a design. The optimized designs are compared to the fundamental bound and well-known empirical structures. The presented framework can provide a completely novel design, as presented in the second example.

Density-based deterministic topology optimization is formulated for method-of-moments numerical technique, and the corresponding stored energy operator is exploited to evaluate and optimize antenna Q-factor. The settings are briefly discussed, including material interpolation function, density filters, and projection filters. The proposed technique is used to improve fractional bandwidth, i.e., minimize the quality factor of a current density excited on a spherical shell. The results are compared with known fundamental bounds and with realized spherical helices.

A topology optimization technique based on exact reanalysis is proposed within method-of-moments formalism. The optimization is formulated over a fixed discretization grid by performing general block structural modification. The procedure is based on an inversion-free evaluation of topological sensitivities, constituting a gradient-based local step that is iteratively restarted by the genetic algorithm. The proposed method sacrifices structural resolution at the expense of lower computational time and direct manufacturability. The method's validity and effectiveness are demonstrated in two examples.

The existent technique for shape optimization based on exact reanalysis of method-of-moments models is extended by symmetry operators. Their application is twofold: to prescribe a given symmetry and accelerate the optimization by reducing the number of unknowns, or to penalize unsymmetrical shapes, constraining thus the regularity and simplifying potential manufacturing.

The existent framework for shape optimization of electrically small antennas is extended by a new set of geometrical operators. They are capable of operating over shapes directly, controlling their regularity, amount of used material, etc. The formulation is compatible with existent physical fitness functions and known fundamental bounds. A simple example of Q-factor minimization is presented.