Complex modes in shielded microstrip and fin lines

An analytical approach to the study of coupled complex modes in shielded microstrip and fin lines is taken on the basis of an analysis of the normal modes of the shield at points of their double, triple, and quadruple degeneration with respect to the propagation constants. Dispersion equations for the normal modes are obtained using the quasi-static approximation of current density on the microstrip or electric field strength on the fin line. These equations are studied analytically in the framework of the weak-coupling approximation. Asymptotic expressions are obtained for the propagation constants of the complex modes, and conditions for their existence are formulated for the double degeneration of normal modes of the shield.