Preliminary Updates On the Characteristic Mode Analysis of Finite Conductor

The concept of characteristic mode analysis (CMA) inherits from the diagonalization of the far-field scattering matrix $[S_{\infty}]$ as $[S]\mathrm{E}_{n}=\lambda_{n}^{S}\mathrm{E}_{n}$. The eigenvectors of the $[S_{\infty}]$ matrix provides the characteristic field modes which maintain orthogonality over the infinite radiation sphere. Due to linear relationship of the field and current, the literature ( R. Harrington and J. Mautz, “Theory of characteristic modes for conducting bodies,” IEEE Trans. Antennas Propag., vol. AP-19, no. 5, Sep. 1971) introduced the CMA concept based on the method of moment impedance matrix which provides characteristic current modes. The characteristic field modes obtained from the characteristic current modes should satisfy the far-field orthogonality relationship such that the linear combination of the modal fields produce the total radiated field. However, in finite conductor object, this seems to be a critical issue as discussed below. The Galerkin's matching based method of moment (MoM) impedance matrix can be written as $\lceil \mathrm{Z}_{C}\rceil=\lceil \mathrm{R}_{C}\rceil+\vert \lceil \mathrm{X}_{C}\rceil=\lceil \mathrm{R}_{PEC}\rceil+\lceil \mathrm{R}_{L}\rceil+\vert \lceil \mathrm{X}_{C}$ where the MoM impedance matrix of the perfect electric conductor (PEC) is $[\mathrm{Z}_{PEC}]=[\mathrm{R}_{PEC}]+\mathrm{j}[\mathrm{X}_{PEC}]$. Let us consider two different methods of eigen decomposition (S. Ghosal, A. De, R. M. Shubair, and A. Chakrabarty, “Vertical Dipole Above the Lossy Dielectric Half-Space-A Characteristic Mode Analysis”, IEEE Trans. Electromagn. Compat., vol. 62, no. 6, Dec. 2020). as summarized below.