Stochastic modeling of nonlinear circuits via SPICE-compatible spectral equivalents

This paper presents a systematic approach for the statistical simulation of nonlinear networks with uncertain circuit elements. The proposed technique is based on spectral expansions of the elements' constitutive equations (I-V characteristics) into polynomial chaos series and applies to arbitrary circuit components, both linear and nonlinear. By application of a stochastic Galerkin method, the stochastic problem is cast in terms of an augmented set of deterministic constitutive equations relating the voltage and current spectral coefficients. These new equations are given a circuit interpretation in terms of equivalent models that can be readily implemented in SPICE-type simulators, as such allowing to take full advantage of existing algorithms and available built-in models for complex devices, like diodes and MOSFETs. The pertinent statistical information of the entire nonlinear network is retrieved via a single simulation. This approach is both accurate and efficient with respect to traditional techniques, such as Monte Carlo sampling. Application examples, including the analysis of a diode rectifier, a CMOS logic gate and a low-noise amplifier, validate the methodology and conclude the paper

Passivity check of S-Parameter descriptor systems via S-Parameter generalized hamiltonian methods

This paper extends the generalized Hamiltonian method (GHM) (Zhang , 2009; Zhang and Wong, 2010) and its half-size variant (HGHM) (Zhang and Wong, 2010) to their S-parameter counterparts (called S-GHM and S-HGHM, respectively), for testing the passivity of S-parameter descriptor-form models widely used in high-speed circuit and electromagnetic simulations. The proposed methods are capable of accurately detecting the possible nonpassive regions of descriptor-form models with either scattering or hybrid (impedance or admittance) transfer matrices. Their effectiveness and accuracy are verified with several practical examples. The S-GHM and S-HGHM methods presented here provide a foundation for the passivity enforcement of $S$- parameter descriptor systems. © 2006 IEEE.published_or_final_versio

Model order reduction of fully parameterized systems by recursive least square optimization

This paper presents an approach for the model order reduction of fully parameterized linear dynamic systems. In a fully parameterized system, not only the state matrices, but also can the input/output matrices be parameterized. The algorithm presented in this paper is based on neither conventional moment-matching nor balanced-truncation ideas. Instead, it uses “optimal (block) vectors” to construct the projection matrix, such that the system errors in the whole parameter space are minimized. This minimization problem is formulated as a recursive least square (RLS) optimization and then solved at a low cost. Our algorithm is tested by a set of multi-port multi-parameter cases with both intermediate and large parameter variations. The numerical results show that high accuracy is guaranteed, and that very compact models can be obtained for multi-parameter models due to the fact that the ROM size is independent of the number of parameters in our approach

On the passivity of polynomial chaos-based augmented models for stochastic circuits

This paper addresses for the first time the issue of passivity of the circuit models produced by means of the generalized polynomial chaos technique in combination with the stochastic Galerkin method. This approach has been used in literature to obtain statistical information through the simulation of an augmented but deterministic instance of a stochastic circuit, possibly including distributed transmission-line elements. However, transient simulations raise the critical question as to whether such an augmented network is passive or not. This paper discusses the general requirements for the augmented circuits to be passive and provides a sufficient condition for their passivity. Some numerical examples illustrate the theoretical results and conclude the paper

Efficient variability analysis of electromagnetic systems via polynomial chaos and model order reduction

We present a novel technique to perform the model-order reduction (MOR) of multiport systems under the effect of statistical variability of geometrical or electrical parameters. The proposed approach combines a deterministic MOR phase with the use of the Polynomial Chaos (PC) expansion to perform the variability analysis of the system under study very efficiently. The combination of MOR and PC techniques generates a final reduced-order model able to accurately perform stochastic computations and variability analysis. The novel proposed method guarantees a high-degree of flexibility, since different MOR schemes can be used and different types of modern electrical systems (e. g., filters and connectors) can be modeled. The accuracy and efficiency of the proposed approach is verified by means of two numerical examples and compared with other existing variability analysis techniques

Fast Stochastic Surrogate Modeling via Rational Polynomial Chaos Expansions and Principal Component Analysis

This paper introduces a fast stochastic surrogate modeling technique for the frequency-domain responses of linear and passive electrical and electromagnetic systems based on polynomial chaos expansion (PCE) and principal component analysis (PCA). A rational PCE model provides high accuracy, whereas the PCA allows compressing the model, leading to a reduced number of coefficients to estimate and thereby improving the overall training efficiency. Furthermore, the PCA compression is shown to provide additional accuracy improvements thanks to its intrinsic regularization properties. The effectiveness of the proposed method is illustrated by means of several application examples