Reduced-order modeling of time-varying systems

Abstract

We present a theory for reduced-order modelling of linear time-varying systems, together with efficient numerical methods for application to large systems. The technique, called TVP (Time-Varying Padk), is applicable to deterministic as well as noise analysis of many types of communication subsystems, such as mixers and switched-capacitor filters, for which existing model reduction techniques cannot be used. TVP is therefore suitable for hierarchical verification of entire communication systems. We present practical applications in which TVP generates macromodels which are more than two orders of magnitude smaller, but still replicate the input-output behaviour of the original systems accurately. The size reduction results in a speedup of more than 500.

Behavioral Modeling of Mixed-Mode Integrated Circuits

“…For many applications where weakly nonlinear distortions are important aspects of design specifications, Volterra series provides a good choice for system description. In (Phillips, 2000;Roychowdhury, 1999), the projection-based nonlinear model order-reduction frameworks for weakly nonlinear systems were first developed by extending moment-matching projection techniques used for interconnect modeling. Here the basic idea is to view a weakly nonlinear system as a set of interconnected linear networks and then each of such linear circuits is reduced via model order reduction.…”

Variable domain transformation for linear PAC analysis of mixed-signal systems

“…Based on these Jacobian matrices, the PAC analysis performs a frequency-domain analysis to compute the PTV transfer function [22,23]. By the chain rule, the Jacobian matrices of h can be expanded into sums and products of Jacobian matrices of the subcircuits f and g: …”

“…Instead of linearizing the circuit at a DC operating point, PAC analysis linearizes the circuit over its periodic steadystate (PSS) response. The result is a periodically time-varying (PTV) transfer function described in [22,23], or equivalently a collection of LTI transfer functions between the different sidebands of the input and output signals. However, for most circuits in this category, designers are interested in only one particular LTI transfer function.…”

A hybrid approach to nonlinear macromodel generation for time-varying analog circuits

“…Various analog macromodels can be categorized according to their intended application (a good taxonomy can be found in [17]). Performance models such as those in [17] and [18] are mainly employed in synthesis for design space exploration; While other research work has focused on models with a primary application of simulation and system verification [8]- [10][12]- [16]. It should be noted, however, that the latter category is not excluded from use in design exploration when appropriate.…”

“…It is worth emphasizing that modeling system distortion is crucial for most analog applications, since circuit linearity is one of the most important design specifications. This casts the modeling task into a nonlinear model generation or nonlinear model reduction problem, both of which are substantially more challenging than their linear time-invariant model counterparts [8]- [10][12]- [16].…”