Theory of Resonant Modes and its Application

Abstract

This paper proposes a unified procedure for evaluating the resonant frequencies and the corresponding resonant modes for an arbitrary source region, based on the general expression for the difference between the stored magnetic and electric field energies in terms of the source current distribution. It is shown that the resonant frequencies and the corresponding resonant modes are governed by a homogeneous integral equation. By following a standard procedure of the method of moments (MoM), the integral equation can be discretized into a real homogenous algebraic equation, from which the resonant frequencies and the corresponding resonant modes can be determined by requiring that a non-trivial solution exists for the real homogeneous algebraic equation. Different from other modal theories that expand the fields by a linear combination of fundamental field patterns that are derived from the boundary conditions, the proposed theory of resonant modes is derived from the difference of stored field energies for an arbitrary source region. As an application of the theory of the resonant modes, a crossed-dipole antenna, a dual-band bowtie antenna, and a dual-band circular polarization antenna are designed through the appropriate excitations of the resonant modes on the three selected source regions, and they are validated by independent simulations and experiments.

Keywords

• Theory of resonant modes
• stored electromagnetic field energy
• crossed-dipole antenna
• bowtie antenna
• dual-band circular polarization antenna