An Analytical Model for the Scattering and Coupling of Antennas and Its Application to Wireless Energy Transfer

Abstract

This dissertation proposes analytical models for scattering by an antenna and coupling among antennas. The scattering properties of an antenna are analyzed using the theory of characteristic modes. The current of an antenna terminated in a load is expanded into the characteristic currents of a short-circuited antenna. When an antenna is very small compared to the wavelength of the incident electromagnetic field, the antenna rarely scatters unless the load reactance is close to the negative of the input reactance, i.e., the antenna can be modeled as a minimum scattering antenna. When the current of an antenna and its input impedance are determined using only one characteristic mode, the open-circuited antenna rarely scatters the electromagnetic field, i.e., the antenna can be modeled as a canonical minimum scattering antenna. The voltages and currents at the feed ports of coupled antennas can be calculated using impedance parameters. In this dissertation, three methods for calculating impedance parameters among coupled antennas are proposed. The first method is to use a generalized scattering matrix, the second is to use the current distributions of the antennas, and the third is to use the equivalent current that generates the same field as that generated by the antenna. A method is also proposed for calculating the electromagnetic fields generated by coupled antennas using a generalized scattering matrix when an electromagnetic field is incident on them or when sources are applied to their feed ports. These methods can be used both when the antennas are in free space and when they are near objects. If the antennas are minimum scattering antennas, the calculations of the impedance parameters and electromagnetic field are simplified. The models for scattering and coupling proposed in this dissertation are applied to the analysis of wireless energy transfer via the near field. Many antennas used in wireless energy transfer via the near field can be modeled as minimum scattering antennas because such wireless energy transfer generally operate at a frequency below or near the lowest resonant frequency of the antennas. In this dissertation, the maximum power transfer efficiency of a wireless energy transfer system and the load impedance that maximizes the power transfer efficiency are derived from the impedance parameters.