Antenna Limitations and Q-factor Trade-off between Parameters, Steps towards Optimal Antenna Design

Sammanfattning: Sub-wavelength antennas have become ubiquitous in essential devices, such as mobile phones, sensors, Internet of things (IoT) and machine to machine (M2M) communication devices. Such antennas are often embedded as a small part of the device chassis or their circuit-boards. The size assigned both to the antennas as well as the device tends to shrink, while demands on antenna performance are increasing. In such a context knowledge of optimal performance is of increasing importance. The subject of this thesis is on the bounds of small antennas, in particular bounds on impedance bandwidth performance.The main tool to obtain bounds is antenna current optimization. The bounds are mainly focused on determining limits on the Q-factor for small antennas, and hence implicitly on the available bandwidth at a given reflection coefficient. We investigate Q-factor bounds under a number of constraints including directivity, far-field radiation pattern, efficiency, and the embedded position of the antenna. In this process, we combine physical methods, mathematical tools, and antenna engineering. We use the Method of Moments (MoM) approach to solving the Electric Field Integral Equations (EFIE), in this context we formulate and solve antenna optimization problems where the surface current density is an unknown variable, and we solve convex and non-convex quadratically constrained quadratic programs (QCQPs). For non-convex problems, we investigate different methods to obtain the solution, but with the main focus on the semidefinite relaxation (SDR) technique. Different current optimization problems are solved for a range of shapes, where the Q-factor and the optimal surface current are determined; the results are compared with full-wave-simulation of antennas that approach the bounds.To determine the Q-factor for an available space in the device is here proposed to be an initial step of an antenna design procedure. The current optimization helps us to determine the optimal trade-off between the different performance parameters of a small antenna, and it can inspire antenna design with better performance. We furthermore show that a multi-position feeding strategy to realize an optimal current successfully realize a non-standard far-field performance. As an example, we show that the desired radiation patterns are obtained with small costs of Q-factor. The thesis ends with a discussion of initial steps to a methodology with the goal of obtaining a Q-factor optimal antenna. Here the current optimization plays an important role in the antenna synthesis and analysis stages of the process. An application to the embedded antenna is discussed in detail.