Abstract-Uncertainties have become a major concern in integrated circuit design. In order to avoid the huge number of repeated simulations in conventional Monte Carlo flows, this paper presents an intrusive spectral simulator for statistical circuit analysis. Our simulator employs the recently developed generalized polynomial chaos expansion to perform uncertainty quantification of nonlinear transistor circuits with both Gaussian and non-Gaussian random parameters. We modify the nonintrusive stochastic collocation (SC) method and develop an intrusive variant called stochastic testing (ST) method to accelerate the numerical simulation. Compared with the stochastic Galerkin (SG) method, the resulting coupled deterministic equations from our proposed ST method can be solved in a decoupled manner at each time point. At the same time, ST uses fewer samples and allows more flexible time step size controls than directly using a nonintrusive SC solver. These two properties make ST more efficient than SG and than existing SC methods, and more suitable for time-domain circuit simulation. Simulation results of several digital, analog and RF circuits are reported. Since our algorithm is based on generic mathematical models, the proposed ST algorithm can be applied to many other engineering problems.

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This paper is devoted to transient analysis of lossy transmission lines characterized by frequency-dependent parameters. A public dataset of parameters for three line examples (a module, a board, and a cable) is used, and a new example of on-chip interconnect is introduced. This dataset provides a well established and realistic benchmark for accuracy and timing analysis of interconnect analysis tools. Particular attention is devoted to the intrinsic consistency and causality of these parameters. Several implementations based on generalizations of the well-known method-of-characteristics are presented. The key feature of such techniques is the extraction of the line modal delays. Therefore, the method is highly optimized for long interconnects characterized by significant propagation delay. Nonetheless, the method is also successfully applied here to a short high/loss on-chip line, for which other approaches based on lumped matrix rational approximations can also be used with high efficiency. This paper shows that the efficiency of delay extraction techniques is strongly dependent on the particular circuit implementation and several practical issues including generation of rational approximations and time step control are discussed in detail.

Recent work in the area of model-order reduction for RLC interconnect networks has been focused on building reduced-order models that preserve the circuittheoretic properties of the network, such as stability, passivity, and synthesizability {1, 2, 3, 4, 5}. Passivity is the one circuit-theoretic property that is vital for the successful simulation of a large circuit netlist containing reduced-order models of its interconnect networks. Non-passive reduced-order models may lead to instabilities even if they are themselves stable. In this paper, we address the problem of guaranteeing the accuracy and passivity of reduced-order models of multipart RLC networks at any finite number of e:cpansion points. The novel passivity-preserving modelorder reduction scheme is a block version of the rational Arnoldi algorithm [6, 7}. The scheme reduces to that of {5] when applied to a single e:cpansion point at zero frequency. Although the treatment of this paper is restricted to expansion points that are on the negative real a:cis, it is shown that the resulting passive reduced-order model is superior in accuracy to the one that would result from e:cpanding the original model around a single point. Nyquist plots are used to illustrate both the passivity and the accuracy of the reducedorder models.

Gibbs random eld (GRF) models and co-occurrence statistics are typically considered as separate but useful tools for texture discrimination. In this paper we show an explicit relationship between co-occurrences and a large class of GRF's. This result comes from a new framework based on a set-theoretic concept called the \aura set" and on measures of this set, \aura measures". This framework is also shown to be useful for relating di erent texture analysis tools: We show how the aura set can be constructed with morphological dilation, how its measure yields co-occurrences, and how it can be applied to characterizing the behavior of the Gibbs model for texture. In particular, we show how the aura measure generalizes, to any number of gray levels and neighborhood order, some properties previously known for just the binary, nearest-neighbor GRF. Finally, we illustrate how these properties can guide one's intuition about the types of GRF patterns which are most likely to form.