A convex programming approach to positive real rational approximation

As system integration evolves and tighter design constraints must be met, it becomes necessary to account for the non-ideal behavior of all the elements in a system. Certain devices common in high-frequency integrated circuit applications, such as spiral inductors, SAW filters, etc., are often described and studied in the frequency domain. Models take the form of frequency domain data obtained through measurement or through physical simulation. Usually the available data is sampled, incomplete, noisy, and covers only a finite range of the spectrum. In this paper we present a methodology for generating guaranteed passive time-domain models of frequency-described subsystems. The methodology presented is based on convex programming based algorithms for fixed denominator system identification. The algorithm is guaranteed to produce a passive system model that is optimal in the sense of having minimum weighted square error in the frequency band of interest over all models with a prescribed set of system poles. An incremental-fitting reformulation of the problem is also introduced that trades optimality for efficiency while still guaranteeing passivity. Results of the application of the proposed methodologies to the modeling of a variety of subsystems are presented and discussed.