Strongly convergent Green´s function expansions for rectangularly shielded microstrip lines

The exact analytical treatment of the quasi-TEM mode in various cross-sectional configurations of microstrip lines may be used on Carleman-type singular integral equations (SIEs). Their kernel is a Laplacian Green´s function G with source point limited on the interface separating the dielectric media. Strongly convergent expansion for G, particularly suited for the subsequent solution of the SIE and for exact field-point evaluations in rectangularly shielded microstrip configurations, are developed. Extraction of the singular logarithmic term leads to rapidly converging series expansions for the nonsingular part. The convergence of certain of these series is further improved when the field point lies also on the interface or when the source point approaches the shielding boundaries