Passivity verification and enforcement—A review paper

Abstract

Today's advanced high‐speed technology requires building behavioral models of systems, from measured/simulated data, with increasingly higher operating frequencies. Different research efforts have come to light in literature for macromodeling, based on such types of data. Ensuring passivity is one of the most fundamental issues affecting system macromodeling, because system‐level performance can be unstable if even a single component of the system becomes nonpassive. Thus, from the computer‐aided design perspective, generation and provision of macromodels, while preserving passivity, is a significant challenge. In this paper, we carefully review novel techniques of passive macromodeling as well as their passivity verification and enforcement, from the early days to the present. We critically review the prominent methods in literature developed for macromodeling, and for verification and enforcement of passivity, and emphasize on their strengths and shortcomings.

Stability, Causality, and Passivity Analysis of Canonical Equivalent Circuits of Improper Rational Transfer Functions With Real Poles and Residues

“…that take the frequency-dependent network parameters matrix as input and identify the pole/residue components of a rational function that may then be converted [5] to a SPICE equivalent circuit [1] of the response. Also, there are various stabilization algorithms [6]- [10] via passivity enforcement.…”

“…This paper makes several main contributions, as follows. (1) We determine the relationships between minimum-phaseness, relative degree of the system, positive realness, and passivity of the canonical system in frequency-domain, (2) we provide equivalent expressions for closed-form transformation of pole/residue to/from pole/zero form, and also introduce bi-directional expressions for transformation of pole/zeros to/from equivalent circuit form, (3) we present the time-domain and frequency-domain expressions for the admittance and impedance transfer functions in a form which is useful to direct analysis of stability and causality of the system, (4) we derive the expressions of instantaneous, average, and cumulative-average power in dissipative, transient, and reactive power terms of equivalent circuit excited by an ideal voltage source or an ideal current source, and use it to inspect the passivity of system, (5) we derive SCP conditions for ATF and ITF in the time-domain and in the frequency-domain, (6) we elucidate system's SCP characteristics by providing tables that conveniently summarize the relationships between the parameters in the equivalent circuit form, the pole/zero terms in the TF form, and the system characteristics of SCP, (7) we analyze the effect of negative gain coefficient on passivity of certain (non-minimum phase) systems and pertinent conditions in Table V, (8) we rearrange the parametric states into a new table and specify the states which may have similar SCP properties that may be used to expedite the optimization space in passivity algorithms, and (9) we validate the formulations through several representative numerical examples. An analogous presentation is being prepared for the R a -L-R b -C circuit branch (based on a pair of complex-conjugate pole/residue) in parallel with R shunt and C shunt .…”

On the passivity of the quasi‐static partial element equivalent circuit method

“…Passivity is a fundamental property for the time‐domain simulations of circuit models connected to terminations at their electrical ports . Stable, but nonpassive, models can produce unstable systems when connected to other stable, even passive, loads.…”

“…Should a circuit turn out to be non passive (for example because of numerical errors related to the mesh discretization for PEEC circuits), then passivity enforcement techniques can be used to enforce passivity. The topic of passivity enforcement has a broad literature and is out of the scope of this paper. While some techniques are applicable to a state‐space model or a pole‐residue model (macromodeling area), the approach described in the study of Dou and Wu is directly applicable to a general physically meaningful RLC circuit model.…”

“…Passivity is a fundamental property for the time-domain simulations of circuit models connected to terminations at their electrical ports. [15][16][17][18] Stable, but nonpassive, models can produce unstable systems when connected to other stable, even passive, loads. A system is denoted as passive when it is unable to generate energy and hence can only absorb energy from the sources used to excite it.…”