Combined Field Integral Equation-Based Theory of Characteristic Mode

Abstract

Conventional electric field integral equation based theory is susceptible to the spurious internal resonance problem when the characteristic modes of closed perfectly conducting objects are computed iteratively. In this paper, we present a combined field integral equation based theory to remove the difficulty of internal resonances in characteristic mode analysis. The electric and magnetic field integral operators are shown to share a common set of non-trivial characteristic pairs (values and modes), leading to a generalized eigenvalue problem which is immune to the internal resonance corruption. Numerical results are presented to validate the proposed formulation. This work may offer efficient solutions to characteristic mode analysis which involves electrically large closed surfaces.

Theory of characteristic modes for lossy structures: Formulation and interpretation of eigenvalues

“…Hence, in the lossless case, eigenvalues are real, and Formulas (11) and (14) agree, while for lossy structures, complex eigenvalues are obtained.…”

“…Due to relative coarse mesh used in the VIE approach, some differences between numerical and analytical results can be observed. To verify Equation (11), (33) and (14) power expressions (21) to (23) are evaluated using the eigencurrents and eigenfields of VIE-H. Clearly, the eigenvalues of VIE-H satisfy Equation (11).…”

“…Eventually as losses are high enough, all eigenvalues accumulate to zero. The reason for this phenomenon becomes evident by studying Equation (11). As losses are increased, the dissipated power in the denominator of Equation (11) start to dominate.…”

“…Figure 3 shows the real parts of 10 low-order modes in linear and logarithmic scales found with EFIE-OH for a rectangular 145 mm × 70 mm resistive plate at 500 MHz when the real part of Z s is varied from 10 −8 to 10 0 and the imaginary part of Z s is zero. The results computed using Equation (11) are shown too when the required power expressions are evaluated using the eigencurrents of EFIE-OH. Clearly, the eigenvalues of EFIE-OH satisfy Equation (11), ie, they have the same interpretation as the eigenvalues of VIE-H. We also observe a similar clustering of the eigenvalues as with VIE-H when the losses, ie, the real part of Z s , are increased.…”

“…Left) Eigenvalues in linear scale and (right) absolute values of the eigenvalues in logarithmic scale for a dielectric sphere of radius 15.76 mm at 3 GHz with r2 = 9.1 + i ′′ r2as ′′ r2 is varied from 10 −4 to 10 1 . Solutions of VIE-H formulation are compared with Equations (32) and(11) …”