Validating the Characteristic Modes Solvers

Characteristic modes (CMs) of a spherical shell are found analytically as spherical harmonics normalized to radiate unitary power and to fulfill specific boundary conditions. The presented closed-form formulas lead to a proposal of precise synthetic benchmarks that can be utilized to validate the method-of-moments matrix or performance of CM decomposition. Dependence on the mesh size, electrical size, and other parameters can systematically be studied, including the performance of various mode tracking algorithms. A notable advantage is the independence on feeding models. Both theoretical and numerical aspects of CM decomposition are discussed and illustrated by examples. The performance of state-of-the-art commercial simulators and academic packages having been investigated, we can conclude that all contemporary implementations are capable of identifying the first dominant modes while having severe difficulties with higher order modes. Surprisingly poor performance of the tracking routines is observed notwithstanding the recent ambitious development.