On the Relation of Characteristic Modes of Different Conducting Structures

A formalism is derived to analyze the scattering of a conducting structure based on the characteristic modes of another structure whose surface is a superset of the first structure. This enables the analysis and comparison of different structures using a common basis of characteristic modes. Additionally, it is shown that the scattering matrices and perturbation matrices are no longer diagonal in these cases. Based on this, a modal transformation matrix is defined to describe the mapping between the characteristic fields and the weighting coefficients of the two structures. This matrix enables the conversion of the perturbation matrices in different bases. Finally, two examples are provided along with a discussion of some aspects of the theory. The first example aims to validate and illustrate the formalism. The second example shows how the formalism can be applied in the design process of an antenna element that is gradually modified, starting from a base structure.