Calculation of dispersive eigen-mode characteristic impedances of multiple coupled microstrip lines and its application to the design of planar millimeter-wave filters on a thin substrate

It is believed that for the first time the frequency-dependent eigen-mode characteristic impedances (Z_d's) for multiple coupled microstrip lines (MCMLs) have been formulated based on a reciprocity-related definition of eigen-voltage and eigen-current vectors. Explicit expressions of the dispersive Z_d's are presented for an asymmetric two-line microstrip and a symmetric three-line structure. The formulation is applied to derive the equivalent circuit of a three-line coupled section, which is used to design wideband bandpass filters at millimeter-wave frequencies. The purpose of the three-line section is to relax the line gap, which can be too narrow to be fabricated for wideband bandpass filters based on two-line coupled stages, especially on a thin substrate. Measured and simulation responses for three filters with fractional bandwidths Δ = 50% and 60% are presented.