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

Analysis of crosstalk and field coupling to lossy MTL's in a SPICE environment

This paper proposes a circuit model for lossy multiconductor transmission lines (MTLs) suitable for implementation in modern SPICE simulators, as well as in any simulator supporting differential operators. The model includes the effects of a uniform or nonuniform disturbing field illuminating the line and is especially devised for the transient simulation of electrically long wideband interconnects with frequency dependent per-unit-length parameters. The MTL is characterized by its transient matched scattering responses, which are computed including both dc and skin losses by means of a specific algorithm for the inversion of the Laplace transform. The line characteristics are then represented in terms of differential operators and ideal delays to improve the numerical efficiency and to simplify the coding of the model in existing simulators. The model can be successfully applied to many kinds of interconnects ranging from micrometric high-resistivity metallizations to low-loss PCBs and cables, and can be considered a practical extension of the widely appreciated lossless MTL SPICE model, which maintains the simplicity and efficienc

A Waveform Relaxation Solver for Transient Simulation of Large-Scale Nonlinearly Loaded Shielding Structures

This article introduces an algorithm for transient simulation of electromagnetic structures loaded by lumped nonlinear devices. The reference application is energy-selective shielding, which adopts clipping devices uniformly spread along shield apertures to achieve a shielding effectiveness that increases with the power of the incident field, thereby blocking high-power interference while allowing low-power communication. Transient simulation of such structures poses a number of challenges, related to their large-scale and low-loss nature. In this work, we propose a waveform relaxation (WR) scheme based on decoupling the linear electromagnetic structure from its nonlinear terminations. In a preprocessing stage, the electromagnetic subsystem is characterized in the frequency domain and converted into a behavioral rational macromodel. Transient simulation is performed by refining estimates of the port signals through iterations. The proposed scheme combines a time partitioning approach with an inexact Newton–Krylov solver. This combination provides fast convergence also in those cases where standard WR schemes fail due to a strong mismatch at the decoupling sections. Numerical results on several test cases of increasing complexity with up to 1024 ports show that the proposed approach proves as reliable as HSPICE in terms of accuracy, with a speedup ranging from one to three orders of magnitude

Iteration Dependent Waveform Relaxation for Hybrid Field Nonlinear Circuit Problems

This article presents a novel waveform relaxation scheme to solve electromagnetically large structures loaded with lumped linear and nonlinear elements. The scheme partitions the problem into a linear electromagnetic structure and a possibly nonlinear lumped circuit, which are coupled using Thévenin interfaces across the steps of an iterative waveform relaxation scheme. The main novel contribution is an adaptive selection of the decoupling resistances used as port references to define incident and reflected scattering signals, whose time-domain samples are refined through iterations. The decoupling resistances are updated through iterations, with the main objective of improving convergence speed and ultimately runtime. The resulting scheme is self-adapting to terminations exploiting high dynamic range in their impedance profiles and is able to provide a suboptimal convergence rate. Three-dimensional shielding structures loaded with nonlinear elements are employed as numerical examples to demonstrate the proposed method

Modeling and Simulation of Nonlinearly Loaded Electromagnetic Systems via Reduced Order Models - A Case Study: Energy Selective Surfaces

L'abstract è presente nell'allegato / the abstract is in the attachmen

A Macromodeling-Based Hybrid Method for the Computation of Transient Electromagnetic Fields Scattered by Nonlinearly Loaded Metal Structures

In this article, we present a hybrid numerical scheme to compute the transient electromagnetic fields scattered by a metallic structure loaded with lumped nonlinear loads. The proposed scheme is based on three successive steps. First, the field coupling problem to the structure with the nonlinear loads removed is solved in the frequency domain using a method-of-moments (MoM) formulation. The unloaded structure is thus characterized as a generalized multiport Thevenin equivalent, whose components are represented as time-domain operators by performing a set of rational approximations followed by closed-form Laplace transform inversion. Transient port voltages and currents in the presence of nonlinear loads are then computed using a standard circuit solver. As a last step, the substitution theorem is used to solve the radiation problem again in the frequency domain using a MoM solver, the results of which are then translated into the time domain by means of rational approximations and recursive convolution operations. The proposed method enables an accurate and efficient evaluation of the transient nonlinearly scattered fields by the loaded structure, with a good potential for scalability to large-scale high-complexity nonlinear shields. Extensive validations are provided to demonstrate the accuracy of the proposed method, which is here applied to the characterization of energy-selective shielding for protection of sensitive devices from high-intensity radiated fields

Parametric macromodeling of lossy and dispersive multiconductor transmission lines

We propose an innovative parametric macromodeling technique for lossy and dispersive multiconductor transmission lines (MTLs) that can be used for interconnect modeling. It is based on a recently developed method for the analysis of lossy and dispersive MTLs extended by using the multivariate orthonormal vector fitting (MOVF) technique to build parametric macromodels in a rational form. They take into account design parameters, such as geometrical layout or substrate features, in addition to frequency. The presented technique is suited to generate state-space models and synthesize equivalent circuits, which can be easily embedded into conventional SPICE-like solvers. Parametric macromodels allow to perform design space exploration, design optimization, and sensitivity analysis efficiently. Numerical examples validate the proposed approach in both frequency and time domain

Influence of the line characterization on the transient analysis of nonlinearly loaded lossy transmission lines

The analysis of nonlinearly terminated lossy transmission lines is addressed in this paper with a modified version of a method belonging to the class of mixed techniques, which characterize the line in the frequency domain and solve the nonlinear problem in the time domain via a convolution operation. This formulation is based on voltage wave variables defined in the load sections. The physical meaning of such quantities helps to explain the transient scattering process in the line and allows us to discover the importance (so far often overlooked) of the reference impedance used to define the scattering parameters. The complexity of the transient impulse responses, the efficiency of the algorithms, and the precision of the results are shown to be substantially conditioned by the choice of the reference impedance. The optimum value of the reference impedance depends on the amount of line losses. We show that a low-loss line can be effectively described if its characteristic impedance or the characteristic impedance of the associated LC line is chosen as the reference impedance. Based on the physical interpretation of our formulation, we are able to validate the numerical results, and to demonstrate that, despite claimed differences or improvements, the formulations of several mixed methods are fundamentally equivalen

Compact Parameterized Black-Box Modeling via Fourier-Rational Approximations

We present a novel black-box modeling approach for frequency responses that depend on additional parameters with periodic behavior. The methodology is appropriate for representing with compact low-order equivalent models the behavior of electromagnetic systems observed at well-defined ports and/or locations, including dependence on geometrical parameters with rotational symmetry. Examples can be polarization or incidence angles of a plane wave, or stirrer rotation in reverberation chambers. The proposed approach is based on fitting a Fourier-rational model to sampled frequency responses, where frequency dependence is represented through rational functions and parameter dependence through a Fourier series. Several examples from different applications are used to validate and demonstrate the approach