Polynomial Chaos-Based Tolerance Analysis of Microwave Planar Guiding Structures

This paper focuses on the derivation of an enhanced transmission-line model allowing to describe a realistic microwave interconnect with the inclusion of external uncertainties, like tolerances or process variations. The proposed method, that is based on the expansion of the well-known telegraph equations in terms of orthogonal polynomials, turns out to be accurate and more efficient than alternative solutions like Monte Carlo method in determining the transmission-line response sensitivity to parameters variability. An application example involving the analysis of the S-parameters of a realistic PCB coplanar waveguide concludes the pape

Alternative SPICE Implementation of Circuit Uncertainties Based on Orthogonal Polynomials

The impact on circuit performance of parameters uncertainties due to possible tolerances or partial information on devices can be effectively evaluated by describing the resulting stochastic problem in terms of orthogonal polynomial expansions of electrical parameters and of circuit voltages and currents. This contribution formalizes a rule for the construction of an augmented instance of the original circuit, that provides a systematic solution approach for the unknown coefficients of the expanded electrical variables. The use of SPICE as a solution engine of the augmented circuit is straightforward, thus providing a convenient and efficient alternative to the conventional approach SPICE uses for uncertainty analysis. An application example involving the stochastic simulation of a digital link with variable substrate parameters demonstrates the potential of the proposed approach

Transient Analysis of PCB Lines with the Inclusion of Parameters Uncertainties

This paper presents an effective solution for the transient analysis of long bus-like interconnects with the inclusion of geometrical and material uncertainties of the structure. The proposed approach is based on the expansion of the well-known frequency-domain telegraph equations in terms of orthogonal polynomials and on the back conversion to time domain via Fourier superposition. The method is validated by means of a systematic comparison with the results of Monte Carlo simulations, for an application example involving a PCB coupled-microstrip interconnect with uncertainties in the relative dielectric permittivity and trace separatio

Stochastic Evaluation of Parameters Variability on a Terminated Signal Bus

This paper addresses the simulation of the effects on a high-speed data link of external factors due to fabrication tolerances or uncertain loading conditions. The proposed strategy operates in the frequency domain and amounts to generating a suitable set of stochastic models for the different blocks in which the data link can be decomposed. Each model is based on the expansion of the block chain parameter matrix in terms of orthogonal polynomials. This method turns out to be accurate and more efficient than alternative solutions like the Monte Carlo method in determining the system response sensitivity to parameters variability. The advantages of the proposed approach are demonstrated via the stochastic simulation of a PCB application exampl

Polynomial Chaos Helps Assessing Parameters Variations of PCB Lines

This paper presents an effective solution for the analysis of long PCB interconnects with the inclusion of uncertainties resulting from different sources of variation, like temperature or fabrication process, on both the structure and loading conditions. The proposed approach is based on the expansion of the well-known frequency-domain telegraph equations in terms of orthogonal polynomials. The method is validated by means of a systematic comparison with the results of Monte Carlo simulations, for an application example involving a coupled-microstrip interconnect on PC

TMsim : an algorithmic tool for the parametric and worst-case simulation of systems with uncertainties

This paper presents a general purpose, algebraic tool—named TMsim—for the combined parametric and worst-case analysis of systems with bounded uncertain parameters.The tool is based on the theory of Taylor models and represents uncertain variables on a bounded domain in terms of a Taylor polynomial plus an interval remainder accounting for truncation and round-off errors.This representation is propagated from inputs to outputs by means of a suitable redefinition of the involved calculations, in both scalar and matrix form. The polynomial provides a parametric approximation of the variable, while the remainder gives a conservative bound of the associated error. The combination between the bound of the polynomial and the interval remainder provides an estimation of the overall (worst-case) bound of the variable. After a preliminary theoretical background, the tool (freely available online) is introduced step by step along with the necessary theoretical notions. As a validation, it is applied to illustrative examples as well as to real-life problems of relevance in electrical engineering applications, specifically a quarter-car model and a continuous time linear equalizer

Performance of Modal Signaling vs. medium dielectric variability

This paper addresses the feasibility of the so-called Modal Signaling (MS) transmission scheme from a stochastic viewpoint. MS has been proposed for crosstalk mitigation over interconnects and is based on the encoding of signals onto fundamental transmission-line modes. However, the design of drivers and receivers strongly depends on the physical characteristics of the channel. In this paper, the impact of random variations of these properties on MS effectiveness is efficiently analyzed by means of Polynomial Chaos (PC) techniqu