Subgradient Techniques for Passivity Enforcement of Linear Device and Interconnect Macromodels

This paper presents a class of nonsmooth convex optimization methods for the passivity enforcement of reduced-order macromodels of electrical interconnects, packages, and linear passive devices. Model passivity can be lost during model extraction or identification from numerical field solutions or direct measurements. Nonpassive models may cause instabilities in transient system-level simulation, therefore a suitable postprocessing is necessary in order to eliminate any passivity violations. Different from leading numerical schemes on the subject, passivity enforcement is formulated here as a direct frequency-domain ${{cal H}_infty}$ norm minimization through perturbation of the model state-space parameters. Since the dependence of this norm on the parameters is nonsmooth, but continuous and convex, we resort to the use of subdifferentials and subgradients, which are used to devise two different algorithms. We provide a theoretical proof of the global optimality for the solution computed via both schemes. Numerical results confirm that these algorithms achieve the global optimum in a finite number of iterations within a prescribed accuracy leve

A Perturbation Scheme for Passivity Verification and Enforcement of Parameterized Macromodels

This paper presents an algorithm for checking and enforcing passivity of behavioral reduced-order macromodels of LTI systems, whose frequency-domain (scattering) responses depend on external parameters. Such models, which are typically extracted from sampled input-output responses obtained from numerical solution of first-principle physical models, usually expressed as Partial Differential Equations, prove extremely useful in design flows, since they allow optimization, what-if or sensitivity analyses, and design centering. Starting from an implicit parameterization of both poles and residues of the model, as resulting from well-known model identification schemes based on the Generalized Sanathanan-Koerner iteration, we construct a parameter-dependent Skew-Hamiltonian/Hamiltonian matrix pencil. The iterative extraction of purely imaginary eigenvalues ot fhe pencil, combined with an adaptive sampling scheme in the parameter space, is able to identify all regions in the frequency-parameter plane where local passivity violations occur. Then, a singular value perturbation scheme is setup to iteratively correct the model coefficients, until all local passivity violations are eliminated. The final result is a corrected model, which is uniformly passive throughout the parameter range. Several numerical examples denomstrate the effectiveness of the proposed approach.Comment: Submitted to the IEEE Transactions on Components, Packaging and Manufacturing Technology on 13-Apr-201

Behavioral Modelling of Digital Devices Via Composite Local-Linear State-Space Relations

This paper addresses the generation of accurate and efficient behavioral models of digital ICs. The proposed approach is based on the approximation of the device port characteristics by means of composite local linear state-space relations whose parameters can effectively be estimated from device port transient responses via well-established system identification techniques. The proposedmodels have been proven to overcome some inherent limitations of the state-of-the-art models used so far, and they can effectively be implemented in any commercial tool as Simulation Program with Integrated Circuit Emphasis (SPICE) subcircuits or VHDL-AMS hardware descriptions. A systematic study of the performances of the proposed state-space models is carried out on a synthetic test device. The effectiveness of the proposed approach has been demonstrated on a real application problem involving commercial devices and a data link of a mobile phon

Compressed Passive Macromodeling

This paper presents an approach for the extraction of passive macromodels of large-scale interconnects from their frequency-domain scattering responses. Here, large scale is intended both in terms of number of electrical ports and required dynamic model order. For such structures, standard approaches based on rational approximation via vector fitting and passivity enforcement via model perturbation may fail because of excessive computational requirements, both in terms of memory size and runtime. Our approach addresses this complexity by first reducing the redundancy in the raw scattering responses through a projection and approximation process based on a truncated singular value decomposition. Then we formulate a compressed rational fitting and passivity enforcement framework which is able to obtain speedup factors up to 2 and 3 orders of magnitude with respect to standard approaches, with full control over the approximation errors. Numerical results on a large set of benchmark cases demonstrate the effectiveness of the proposed techniqu

Black-box passive macromodeling in electronics: trends and open problems

Design and verification flows in the electronics industry are relying more and more on behavioral models of components, electrical interconnects, and subsystems. Such models are often derived from tabulated frequency responses obtained via direct measurements or through electromagnetic field solvers. Model extraction from this data involves a mix of system identification and approximation in the complex frequency domain. This problem becomes difficult or badly scalable due to the presence of passivity constraints, which must be enforced during model extraction. We review recent trends to deal with this complexity, and related open issues

A Multi-Stage Adaptive Sampling Scheme for Passivity Characterization of Large-Scale Macromodels

This paper proposes a hierarchical adaptive sampling scheme for passivity characterization of large-scale linear lumped macromodels. Here, large-scale is intended both in terms of dynamic order and especially number of input/output ports. Standard passivity characterization approaches based on spectral properties of associated Hamiltonian matrices are either inefficient or non-applicable for large-scale models, due to an excessive computational cost. This paper builds on existing adaptive sampling methods and proposes a hybrid multi-stage algorithm that is able to detect the passivity violations with limited computing resources. Results from extensive testing demonstrate a major reduction in computational requirements with respect to competing approaches.Comment: Submitted to the IEEE Transactions on Components, Packaging and Manufacturing Technolog

A Multi-Stage Adaptive Sampling Scheme for Passivity Characterization of Large-Scale Macromodels

This paper proposes a hierarchical adaptive sampling scheme for passivity characterization of large-scale linear lumped macromodels. Here, large-scale is intended both in terms of dynamic order and especially number of input/output ports. Standard passivity characterization approaches based on spectral properties of associated Hamiltonian matrices are either inefficient or non-applicable for large-scale models, due to an excessive computational cost. This paper builds on existing adaptive sampling methods and proposes a hybrid multi-stage algorithm that is able to detect the passivity violations with limited computing resources. Results from extensive testing demonstrate a major reduction in computational requirements with respect to competing approaches