  Characteristic modes 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 which can be utilized to validate the method of moments
matrix or performance of characteristic mode decomposition. Dependence on the
mesh size, electrical size and other parameters can systematically be studied,
including the performance of various mode tracking algorithms. A noticeable
advantage is the independence on feeding models. Both theoretical and numerical
aspects of characteristic mode 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.
