Application of the Waveform Relaxation Technique to the Co-Simulation of Power Converter Controller and Electrical Circuit Models

In this paper we present the co-simulation of a PID class power converter controller and an electrical circuit by means of the waveform relaxation technique. The simulation of the controller model is characterized by a fixed-time stepping scheme reflecting its digital implementation, whereas a circuit simulation usually employs an adaptive time stepping scheme in order to account for a wide range of time constants within the circuit model. In order to maintain the characteristic of both models as well as to facilitate model replacement, we treat them separately by means of input/output relations and propose an application of a waveform relaxation algorithm. Furthermore, the maximum and minimum number of iterations of the proposed algorithm are mathematically analyzed. The concept of controller/circuit coupling is illustrated by an example of the co-simulation of a PI power converter controller and a model of the main dipole circuit of the Large Hadron Collider

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

Numerical Solution of Dynamic Equilibrium Models under Poisson Uncertainty

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households.continuous-time DSGE, Poisson uncertainty, waveform relaxation

Optimized Schwarz Waveform Relaxation for Advection Reaction Diffusion Equations in Two Dimensions

Optimized Schwarz Waveform Relaxation methods have been developed over the last decade for the parallel solution of evolution problems. They are based on a decomposition in space and an iteration, where only subproblems in space-time need to be solved. Each subproblem can be simulated using an adapted numerical method, for example with local time stepping, or one can even use a different model in different subdomains, which makes these methods very suitable also from a modeling point of view. For rapid convergence however, it is important to use effective transmission conditions between the space-time subdomains, and for best performance, these transmission conditions need to take the physics of the underlying evolution problem into account. The optimization of these transmission conditions leads to a mathematically hard best approximation problem of homographic type. We study in this paper in detail this problem for the case of linear advection reaction diffusion equations in two spatial dimensions. We prove comprehensively best approximation results for transmission conditions of Robin and Ventcel type. We give for each case closed form asymptotic values for the parameters, which guarantee asymptotically best performance of the iterative methods. We finally show extensive numerical experiments, and we measure performance corresponding to our analysisComment: 42 page

Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering

We study causal waveform estimation (tracking) of time-varying signals in a paradigmatic atomic sensor, an alkali vapor monitored by Faraday rotation probing. We use Kalman filtering, which optimally tracks known linear Gaussian stochastic processes, to estimate stochastic input signals that we generate by optical pumping. Comparing the known input to the estimates, we confirm the accuracy of the atomic statistical model and the reliability of the Kalman filter, allowing recovery of waveform details far briefer than the sensor's intrinsic time resolution. With proper filter choice, we obtain similar benefits when tracking partially-known and non-Gaussian signal processes, as are found in most practical sensing applications. The method evades the trade-off between sensitivity and time resolution in coherent sensing.Comment: 15 pages, 4 figure

Signal tracking beyond the time resolution of an atomic sensor by Kalman filtering

We study causal waveform estimation (tracking) of time-varying signals in a paradigmatic atomic sensor, an alkali vapor monitored by Faraday rotation probing. We use Kalman filtering, which optimally tracks known linear Gaussian stochastic processes, to estimate stochastic input signals that we generate by optical pumping. Comparing the known input to the estimates, we confirm the accuracy of the atomic statistical model and the reliability of the Kalman filter, allowing recovery of waveform details far briefer than the sensor's intrinsic time resolution. With proper filter choice, we obtain similar benefits when tracking partially-known and non-Gaussian signal processes, as are found in most practical sensing applications. The method evades the trade-off between sensitivity and time resolution in coherent sensing.Comment: 15 pages, 4 figure

A Preconditioned Waveform Relaxation Solver for Signal Integrity Analysis of High-Speed Channels

This work presents a fast transient solver for Signal Integrity analysis of high-speed channels. We consider general chip-to-chip coupled interconnect structures, including arbitrary discontinuities at chip, package and board level. An external characterization of the interconnect in terms of tabulated scattering frequency samples is first converted to a closed-form macromodel, whose transient effects on input signals can be computed very efficiently through recursive convolutions. When combined with suitable models for drivers and receivers, a large-scale but very sparse system of equations is obtained. The latter is solved by an iterative scheme based on the Generalized Minimal RESidual (GMRES) method, further enhanced by a preconditioner based on Waveform-Relaxation. Contrary to previous formulations, the proposed scheme is guaranteed to converge in few iterations. Numerical examples show that the proposed solver outperforms standard SPICE in terms of runtime, with no loss of accuracy

Custom Integrated Circuits

Contains reports on nine research projects.Analog Devices, Inc.International Business Machines, Inc.Joint Services Electronics Program (Contract DAALO03-86-K-0002)U.S. Air Force - Office of Scientific Research (Grant AFOSR 86-0164)Rockwell International CorporationOKI SemiconductorU.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)Charles Stark Draper LaboratoryDARPA/U.S. Navy - Office of Naval Research (Contract N00014-80-C-0622)DARPA/U.S. Navy - Office of Naval Research (Contract N00014-87-K-0825)National Science Foundation (Grant ECS-83-10941)AT&T Bell Laboratorie