Frequency-domain-coupled microstrip-line normal-mode parameter extraction from S-parameters

We describe a frequency-domain normal-mode parameter (NMP) extraction method for asymmetric, uniform coupled microstrip lines. The method applies when loss is reasonably low or the lines are reasonably short, as is the case in many practical applications. The only requirement is the complete scattering parameter (S-parameter) description for a specified physical length of the coupled section. Extraction yields the frequency-dependent characteristic impedance matrix, the mode propagation constants, and the mode configurations; also the concomitant per-unit-length parameters. We develop quasi-TEM analytic expressions for the S-parameters in terms of the NMPs, and then validate the method for three lines by recovering the NMPs from this data and from simulated S-parameters