Impact on signal integrity of interconnect variabilities

In this paper, literature results on the statistical simulation of lossy and dispersive interconnect networks with uncertain physical properties are extended to general nonlinear circuits. The approach is based on the expansion of circuit voltages and currents into polynomial chaos approximations. The derivation of deterministic circuit equivalents for nonlinear components allows to retrieve the unknown expansion coefficients with a single circuit simulation, that can be carried out via standard SPICE-type solvers. These coefficients provide direct statistical information. The methodology allows the inclusion of arbitrary nonlinear elements and is validated via transmission-line networks terminated by diodes and driven by inverter

Comprehensive and modular stochastic modeling framework for the variability-aware assessment of Signal Integrity in high-speed links

This paper presents a comprehensive and modular modeling framework for stochastic signal integrity analysis of complex high-speed links. Such systems are typically composed of passive linear networks and nonlinear, usually active, devices. The key idea of the proposed contribution is to express the signals at the ports of each of such system elements or subnetworks as a polynomial chaos expansion. This allows one to compute, for each block, equivalent deterministic models describing the stochastic variations of the network voltages and currents. Such models are synthesized into SPICE-compatible circuit equivalents, which are readily connected together and simulated in standard circuit simulators. Only a single circuit simulation of such an equivalent network is required to compute the pertinent statistical information of the entire system, without the need of running a large number of time-consuming electromagnetic circuit co-simulations. The accuracy and efficiency of the proposed approach, which is applicable to a large class of complex circuits, are verified by performing signal integrity investigations of two interconnect examples

Stochastic modeling of high-speed data links with nonlinear dynamic terminations

This paper addresses the statistical modeling and simulation of high-speed interconnects with uncertain physical properties and nonlinear dynamical terminations. The proposed approach is based on the expansion of voltage and current variables in terms of orthogonal polynomials of random variables. It extends the available literature results on the generation of an augmented deterministic SPICE equivalent of the stochastic link to the case in which the terminations are nonlinear and dynamical, like those modeling IC buffers. A single and standard SPICE simulation of the aforementioned equivalent circuit allows to efficiently compute the expansion coefficients that provide statistical information pertinent to the interconnect response. The feasibility and strength of the approach are demonstrated by means of a coupled microstrip interconnect with drivers and receiver

Performance assessment of multi-walled carbon nanotube interconnects using advanced polynomial chaos schemes

2019 Spring.Includes bibliographical references.With the continuous miniaturization in the latest VLSI technologies, manufacturing uncertainties at nanoscale processes and operations are unpredictable at the chip level, packaging level and at board levels of integrated systems. To overcome such issues, simulation solvers to model forward propagation of uncertainties or variations in random processes at the device level to the network response are required. Polynomial Chaos Expansion (PCE) of the random variables is the most common technique to model the unpredictability in the systems. Existing methods for uncertainty quantification have a major drawback that as the number of random variables in a system increases, its computational cost and time increases in a polynomial fashion. In order to alleviate the poor scalability of standard PC approaches, predictor-corrector polynomial chaos scheme and hyperbolic polynomial chaos expansion (HPCE) scheme are being proposed in this dissertation. In the predictor-corrector polynomial scheme, low-fidelity meta-model is generated using Equivalent Single Conductor (ESC) approximation model and then its accuracy is enhanced using low order multi-conductor circuit (MCC) model called a corrector model. In HPCE, sparser polynomial expansion is generated based on the hyperbolic criterion. These schemes result in an immense reduction in CPU cost and speed. This dissertation presents the novel approach to quantify the uncertainties in multi-walled carbon nano-tubes using these schemes. The accuracy and validation of these schemes are shown using various numerical examples

Mobile array designs with ANSERLIN antennas and efficient, wide-band PEEC models for interconnect and power distribution network analysis

A mobile, wide-band antenna system has been developed around the ANSERLIN antenna element and a 3-dB splitter design. The size of the antenna elements was reduced over previous versions by introducing dielectric substrates. Additionally, new variations of the antenna were designed to influence radiation characteristics. To further reduce the number of components in the array, a very low profile splitter was designed and mounted below one of the antenna elements, doubling as the return plane for the antenna. The partial-element equivalent circuit (PEEC) method has been used for 3D interconnect analysis and numerous other applications. Being based on the same ideas as the method of moments, the PEEC method generates dense matrices for its cell interactions. This thesis contains research focused on efficiently using a limited number of cells for accurate results. This has been approached with a hybrid method and also with grid refinements. Additionally, the accuracy of PEEC coupling over electrically long distances has been addressed using wide-band accurate partial parameter calculations --Abstract, page iii

Novel methods to quantify aleatory and epistemic uncertainty in high speed networks

2017 Summer.Includes bibliographical references.With the sustained miniaturization of integrated circuits to sub-45 nm regime and the increasing packaging density, random process variations have been found to result in unpredictability in circuit performance. In existing literature, this unpredictability has been modeled by creating polynomial expansions of random variables. But the existing methods prove inefficient because as the number of random variables within a system increase, the time and computational cost increases in a near-polynomial fashion. In order to mitigate this poor scalability of conventional approaches, several techniques are presented, in this dissertation, to sparsify the polynomial expansion. The sparser polynomial expansion is created, by identifying the contribution of each random variable on the total response of the system. This sparsification is performed primarily using two different methods. It translates to immense savings, in the time required, and the memory cost of computing the expansion. One of the two methods presented is applied to aleatory variability problems while the second method is applied to problems involving epistemic uncertainty. The accuracy of the proposed approaches is validated through multiple numerical examples

Stochastic Analysis of Switching Power Converters via Deterministic SPICE Equivalents

This letter addresses the stochastic analysis of nonlinear switching power converters via an augmented circuit equivalent and a single deterministic SPICE simulation. The proposed approach is based on the expansion of the constitutive relations of the circuit elements in terms of orthonormal polynomials within the well-established framework of polynomial chaos. The feasibility and strength of the method are demonstrated on a dc–dc boost converter described by either detailed nonlinear components or via its averaged linear circuit. Excellent modeling accuracy as well as remarkable speed-ups compared to traditional sampling-based approaches are achieved

The SLH framework for modeling quantum input-output networks

Many emerging quantum technologies demand precise engineering and control over networks consisting of quantum mechanical degrees of freedom connected by propagating electromagnetic fields, or quantum input-output networks. Here we review recent progress in theory and experiment related to such quantum input-output networks, with a focus on the SLH framework, a powerful modeling framework for networked quantum systems that is naturally endowed with properties such as modularity and hierarchy. We begin by explaining the physical approximations required to represent any individual node of a network, eg. atoms in cavity or a mechanical oscillator, and its coupling to quantum fields by an operator triple $(S,L,H)$. Then we explain how these nodes can be composed into a network with arbitrary connectivity, including coherent feedback channels, using algebraic rules, and how to derive the dynamics of network components and output fields. The second part of the review discusses several extensions to the basic SLH framework that expand its modeling capabilities, and the prospects for modeling integrated implementations of quantum input-output networks. In addition to summarizing major results and recent literature, we discuss the potential applications and limitations of the SLH framework and quantum input-output networks, with the intention of providing context to a reader unfamiliar with the field.Comment: 60 pages, 14 figures. We are still interested in receiving correction