Complex modes in shielded planar microstrip lines
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The authors analyze the existence of complex modes, which have important effects on the properties of planar transmission line discontinuities, in electrically shielded microstrip lines. A rigorous full-wave spectral domain approach (SDA) with a proposed and test set of basis functions can efficiently and accurately determine the complex modes of a class of general planar transmission line problems if the complex modes exist. A convergence study and the cross-sectional field patterns, which guarantee the satisfaction of the correct boundary conditions, confirm the validity of the solutions for complex modes. Theoretical results for fundamental, higher-order, evanescent, and complex modes are presented for symmetric coupled microstrip lines. It is concluded that complex modes may exist in most shielded planar and quasiplanar transmission lines.<<ETX>>