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

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

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

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

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

Prediction of Stochastic Eye Diagrams via IC Equivalents and Lagrange Polynomials

This paper addresses the prediction of eye diagrams in high-speed data links with the inclusion of manufacturing tolerances. The statistical assessment of the system performance is done via the combined application of accurate and efficient IC models and of the stochastic collocation method with Lagrange interpolating polynomials. Numerical results on the computation of the eye opening profile for a realistic PCB interconnect with the inclusion of the effects of parameters uncertainties conclude the pape