Global passivity enforcement algorithm for macromodels of interconnect subnetworks characterized by tabulated data

Abstract

With the continually increasing operating frequencies, complex high-speed interconnect and package modules require characterization based on measured/simulated data. Several algorithms were recently suggested for macromodeling such types of data to enable unified transient analysis in the presence of external network elements. One of the critical issues involved here is the passivity violations associated with the computed macromodel. To address this issue, a new passivity enforcement algorithm is presented in this paper. The proposed method adopts a global approach for passivity enforcement by ensuring that the passivity correction at a certain region does not introduce new passivity violations at other parts of the frequency spectrum. It also provides an error estimate for the response of the passivity corrected macromodel.Index Terms-High-speed interconnects, measured subnetworks, passive macromodels, positive real system, signal integrity, system identification, tabulated data.

Guaranteed Passive Parameterized Macromodeling by Using Sylvester State-Space Realizations

“…The transfer function of the macromodel related to a generic point in the design space is converted from the rational pole residue form (7) obtained by means of VF into the barycentric realization [15], [21] ( 8) with basis function (9) where the barycentric basis poles are fixed and do not depend on . The barycentric realization (8) can be split into a numerator and a denominator, i.e., (10) where (11) (12) This factorization can be seen as a special case of the so-called right coprime factorization [22]. A state-space realization for each root macromodel is obtained by means of (11) and (12).…”

Parameterized models for crosstalk analysis in high-speed interconnects

“…Once these per-unit-length parametric macromodels are built, given a fixed set of values for the design parameters, they can be reduced to univariate frequency-dependent functions as in [23]. The stability of the univariate models can be imposed in the reduction step using pole flipping, and, subsequently, passivity can be enforced in a post-processing step by means of standard techniques (see [27] and [28]). …”

Rational Modeling Algorithm for Passive Microwave Structures and Systems

“…Nevertheless, passivity of the macromodel is of crucial importance since a non-passive macromodel may lead to unstable transient simulations in an unpredictable manner [12,13]. This paper applies a new passivity enforcement technique that is able to enforce passivity to a non-passive rational macromodel by means of an overdetermined least-squares fitting algorithm [14].…”