Integral Identities for Passive Systems and Spherical Waves in Scattering and Antenna Problems

Abstract: Sum rules and physical limitations within electromagnetic theory and antenna theory have received significant attention in the last few years. However, the derivations are often relying on application specific and sometimes unsupported assumptions, and therefore a mathematically rigorous and generally applicable approach seems timely. Such an approach is presented in this thesis, along with examples and all the necessary proofs. The approach is also applied in the thesis to derive sum rules and physical limitations on electromagnetic spherical wave scattering. This has not been done before, despite the widespread use of spherical wave decompositions. For example, spherical waves and the antenna scattering matrix provide a complete and compact description of all the important properties of an antenna, are crucial parts in spherical near-field antenna measurements, and have been used recently to model antenna-channel interaction and multiple-input multiple-output (MIMO) communication systems. This thesis is also the first to present a method to estimate spherical wave coefficients from propagation channel measurements. The results of this thesis can roughly be divided into three categories: Firstly, a general approach to derive sum rules and physical limitations on input-output systems based on the assumptions of causality and passivity is presented (Paper I). Secondly, sum rules and physical limitations on the scattering and matching of electromagnetic spherical waves are derived, and the implications for antennas are explored (Papers II-IV). Thirdly, a method to estimate spherical wave coefficients from channel measurements, and the results of a measurement campaign, are presented and analysed (Paper V). The thesis consists of a General Introduction and five appended papers.