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Aim of this work is the analysis of the propagation of bound and leaky modes in perfectly conducting open single and coupled microstrip lines with polygonal cross-section. The problem is formulated as a new numerically stable one-dimensional electric field integral equation (EFIE) in the spectral domain. Quick convergence is achieved by expanding the unknown surface current density with functions reconstructing the edge behaviour and continuity conditions in a Galerkin scheme. Due to the reciprocity, the impedance matrix has symmetries allowing to cut down the number of coefficients to be numerically evaluated. The choice of analytically Fourier transformable expansion functions leads to reduce the coefficients of the impedance matrix to single integrals efficiently evaluated by means of an analytical acceleration technique.