Exact solutions for shielded printed microstrip lines by the Carleman-Vekua method

Exact analytical solutions for the field of the quasi-TEM (transverse electromagnetic) mode in various cross-sectional configurations of rectangularly shielded printed microstrip lines are obtained on the basis of Carleman-type singular integral equations (SIEs). For the kernel of the SIE, strongly and uniformly convergent series expansions have recently been developed that are suitable for the exact solution of the equation by the Carleman-Vekua regularization method, which proceeds by first solving the so-called dominant equation. The procedure leads to rapidly convergent series solutions for the field of the quasi-TEM mode even when the conductors are large or very near the shield, i.e. in situations for which numerical techniques becomes inadequate. Characteristic values of the shielded microstrip lines are evaluated by summing a few terms, while field plots, requiring more terms, are shown for various configurations including the case of close proximity