Complex modes in shielded planar microstrip lines

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.<>