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

Transient Analysis of High-Speed Channels via Newton-GMRES Waveform Relaxation

This paper presents a technique for the numerical simulation of coupled high-speed channels terminated by arbitrary nonlinear drivers and receivers. The method builds on a number of existing techniques. A Delayed-Rational Macromodel is used to describe the channel in compact form, and a general Waveform Relaxation framework is used to cast the solution as an iterative process that refines initial estimates of transient scattering waves at the channel ports. Since a plain Waveform Relaxation approach is not able to guarantee convergence, we turn to a more general class of nonlinear algebraic solvers based on a combination of the Newton method with a Generalized Minimal Residual iteration, where the Waveform Relaxation equations act as a preconditioner. The convergence of this scheme can be proved in the general case. Numerical examples show that very few iterations are indeed required even for strongly nonlinear termination

High-Performance Passive Macromodeling Algorithms for Parallel Computing Platforms

This paper presents a comprehensive strategy for fast generation of passive macromodels of linear devices and interconnects on parallel computing hardware. Starting from a raw characterization of the structure in terms of frequency-domain tabulated scattering responses, we perform a rational curve fitting and a postprocessing passivity enforcement. Both algorithms are parallelized and cast in a form that is suitable for deployment on shared-memory multicore platforms. Particular emphasis is placed on the passivity characterization step, which is performed using two complementary strategies. The first uses an iterative restarted and deflated rational Arnoldi process to extract the imaginary Hamiltonian eigenvalues associated with the model. The second is based on an accuracy-controlled adaptive sampling. Various parallelization strategies are discussed for both schemes, with particular care on load balancing between different computing threads and memory occupation. The resulting parallel macromodeling flow is demonstrated on a number of medium- and large-scale structures, showing good scalability up to 16 computational core

Noise compliant macromodel synthesis for RF and Mixed-Signal applications

This paper proposes a compact synthesis approach for reduced-order behavioral macromodels of linear circuit blocks for RF and Mixed-Signal design. The proposed approach revitalizes the classical synthesis of lumped linear and timeinvariant multiport networks by reactance extraction, which is here exploited to obtain reduced-order equivalent SPICE netlists that can be used in any type of system-level simulations, including transient and noise analysis. The effectiveness of proposed approach is demonstrated on a real design applicatio

Scattering-based nonlinear macromodels of high-speed differential drivers

This paper introduces a scattering-based nonlinear macromodeling framework for high-speed differential drivers. Using an industrial test case, we show that the proposed scattering formulation enables more accurate and robust model identification with respect to standard voltage-current representations. The combination of proposed driver models with a Waveform Relaxation solver allows accurate and efficient transient channel simulation, including nonlinear and dynamic termination effect

Thermal Noise Compliant Synthesis of Linear Lumped Macromodels

This paper addresses the synthesis of equivalent circuits from black box state-space macromodels, as produced by model order reduction or rational curve fitting schemes. The emphasis is here on thermal noise compliance, intended as the guarantee that the produced netlists can be safely used in standard circuit solvers to perform thermal noise analysis, in addition to usual DC, AC, and transient simulations. Due to the fact that SNR is a key figure of merit in nearly all signal processing analog circuits, noise analysis is mandatory in design and verification of most analog and RF/millimeter-wave electronic applications. However, common macromodel synthesis approaches rely on components that do not (and cannot) have an associated thermal noise model, such as controlled sources or negative circuit elements. Therefore, macromodel-based noise analyses are generally not possible with currently available approaches. We propose a circuit realization derived from the classical resistance extraction synthesis, with suitable modifications for enhancing macromodel sparsity and efficiency. The resulting equivalent netlist, which is compatible with any standard circuit solver, is shown to produce exact noise characteristics, even if its elements are derived through a mathematical procedure, totally unrelated to the actual topology of the physical system under modeling. The procedure is validated by several examples