An Expose on Internal Resonance, External Resonance, and Characteristic Modes

Abstract

One of the objectives of this paper is to outline the differences between the internal and external resonances of an electromagnetic structure. At an internal resonance of an object there is a component of the resonant current on the structure which is real and that current does not radiate nor does it couple to the incident field. The external resonances responsible for radiation that occurs at the singularities in the complex $s$ -plane and lead to the currents that are complex in nature. These are the same solutions as discussed in the singularity expansion method and are responsible for radiation. This paper also illustrates that the nature of the current distribution on a radiating structure cannot be correlated with the amount of radiation emanating from the structure and nor do the currents have to be real and thus correlating them to resonances. Another topic to be discussed is the characteristic modes that can not only represent the currents on the structure but also the fields on the radiation sphere provided there is no internal resonances associated with this structure. In addition, the structure has to be completely lossless. These characteristic modes can also be correlated with the properties of the impedance matrix that are generated in a numerical electromagnetic field configuration. For computational purposes for the characteristic modes to exist the impedance matrix must be symmetric in order to generate real eigenvalues and a real orthogonal basis for the currents (that does not mean the actual currents are real—the basis functions are real in most of the deployments encountered in the solution of method of moments problems). This expansion in terms of the characteristic modes is valid provided the structure has no internal resonances at the frequency of analysis, the impedance matrix that is to be decomposed is perfectly symmetric and the structure has no losses. Finally, it is illustrated that the nature of radiation cannot be predicted from the solution of the current distribution on the structure. Just because the current distribution on the structure is real that does not mean it will provide enhanced radiation. On the contrary real resonant currents could be due to internal resonances and they do not radiate. These points are discussed in this short presentation.