In this paper, we present a methodology for generating guaranteed passive time-domain models of subsystems described by tabulated frequency-domain data obtained through measurement or through physical simulation. Such descriptions are commonly used to represent on- and off-chip interconnect effects, package parasitics, and passive devices common in high-frequency integrated circuit applications. The approach, which incorporates passivity constraints via convex optimization algorithms, is guaranteed to produce a passive-system model that is optimal in the sense of having minimum error in the frequency band of interest over all models with a prescribed set of system poles. We demonstrate that this algorithm is computationally practical for generating accurate high-order models of data sets representing realistic, complicated multiinput, multioutput systems.

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. For high-speed digital, and microwave systems, it is increasingly important to model previously neglected frequency domain effects. In this paper, results from Nevanlinna-Pick interpolation theory are used to develop a bounded real matrix rational approximation algorithm. A method is presented that allows for the generation of guaranteed passive rational function models of passive systems by approximating their scattering parameter matrices. Since the order of the models may in some cases be high, an incremental fitting strategy is also proposed that allows for the generation of smaller models while still meeting the required passivity and accuracy requirements. Results of the application of the proposed method to several real-world examples are also shown.

Verification of contemporary integrated circuits requires accurate modeling of high-frequency effects in all passive component sub-systems. Often, descriptions of those subsystems are only available in the frequency-domain. In this paper, we propose a simple, scalar, constrained-passive rational approximation scheme that incorporates a grid-based test for strict positive realness. In contrast to similar recent work based on convex optimization and the positive real lemma, the methodology is potentially more efficient, since it does not introduce a quadratic number of auxiliary variables, is potentially more accurate, since pole locations can be re-adjusted during the optimization, but possibly less reliable, since it relies on the solution of optimization problems that are not convex. There-fore, because of the use of local constrained non-convex optimization, the generation of feasible initial guesses is also considered.

The problem of computing rational function approximations to tabulated frequency data is of paramount importance in the modeling arena.In this paper we present a method for generating a state space model from tabular data in the frequency domain that solves some of the numerical difficulties associated with the traditional fitting techniques used in linear least squares approximations.An extension to the MIMO case is also derived.