Real-Part Sufficiency and Its Application to the Rational Function Fitting of Passive Electromagnetic Responses

For passive networks real-part sufficiency describes the fact that their driving-point impedance or admittance is uniquely defined in terms of its real part alone. We have exploited this fact in the development of a methodology for the generation of passive rational function approximations of electromagnetic transfer functions. More specifically, by utilizing in the fitting process only data for the real part of the driving-point impedance or admittance, our methodology attempts to ensure the passivity of the rational fit by construction. This paper reports several improvements in our methodology, which provide for enhanced accuracy in the fitting of broadband data and improved robustness and computational efficiency of the fitting algorithm. The improved algorithm is demonstrated through its application to the rational fitting of the driving point impedance of interconnect circuits using both numerically-obtained and measured data over multi-GHz bandwidths.