Flavio Canavero

Stability, Causality, and Passivity in Electrical Interconnect Models

Modern packaging design requires extensive signal integrity simulations in order to assess the electrical performance of the system. The feasibility of such simulations is granted only when accurate and efficient models are available for all system parts and components having a significant influence on the signals. Unfortunately, model derivation is still a challenging task, despite the extensive research that has been devoted to this topic. In fact, it is a common experience that modeling or simulation tasks sometimes fail, often without a clear understanding of the main reason. This paper presents the fundamental properties of causality, stability, and passivity that electrical interconnect models must satisfy in order to be physically consistent. All basic definitions are reviewed in time domain, Laplace domain, and frequency domain, and all significant interrelations between these properties are outlined. This background material is used to interpret several common situations where either model derivation or model use in a computer-aided design environment fails dramatically. We show that the root cause for these difficulties can always be traced back to the lack of stability, causality, or passivity in the data providing the structure characterization and/or in the model itself.

Transient analysis of lossy transmission lines: an efficient approach based on the method of Characteristics

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.

M/spl pi/log, macromodeling via parametric identification of logic gates

This paper addresses the development of computational models of digital integrated circuit input and output buffers via the identification of nonlinear parametric models. The obtained models run in standard circuit simulation environments, offer improved accuracy and good numerical efficiency, and do not disclose information on the structure of the modeled devices. The paper reviews the basics of the parametric identification approach and illustrates its most recent extensions to handle temperature and supply voltage variations as well as power supply ports and tristate devices.

Parametric macromodels of digital I/O ports

Addresses the development of macromodels for input and output ports of a digital device. The proposed macromodels consist of parametric representations that can be obtained from port transient waveforms at the device ports via a well established procedure. The models are implementable as SPICE subcircuits and their accuracy and efficiency are verified by applying the approach to the characterization of transistor-level models of commercial devices.

Parameters Variability Effects on Multiconductor Interconnects via Hermite Polynomial Chaos

This paper focuses on the derivation of an enhanced transmission-line model allowing the stochastic analysis of a realistic multiconductor interconnect. The proposed model, which is based on the expansion of the well-known telegraph equations in terms of orthogonal polynomials, includes the variability of geometrical or material properties of the interconnect due to uncertainties like fabrication process or temperature. A real application example involving the frequency-domain analysis of a coupled microstrip and the computation of the parameters variability effects on the transmission-line response concludes this paper.

Stochastic Analysis of Multiconductor Cables and Interconnects

This paper provides an effective solution for the simulation of cables and interconnects with the inclusion of the effects of parameter uncertainties. The problem formulation is based on the telegraphers equations with stochastic coefficients, whose solution requires an expansion of the unknown parameters in terms of orthogonal polynomials of random variables. The proposed method offers accuracy and improved efficiency in computing the parameter variability effects on system responses with respect to the conventional Monte Carlo approach. The approach is validated against results available in the literature, and applied to the stochastic analysis of a commercial multiconductor flat cable.

Stochastic Modeling-Based Variability Analysis of On-Chip Interconnects

In this paper, a novel stochastic modeling strategy is constructed that allows assessment of the parameter variability effects induced by the manufacturing process of on-chip interconnects. The strategy adopts a three-step approach. First, a very accurate electromagnetic modeling technique yields the per unit length (p.u.l.) transmission line parameters of the on-chip interconnect structures. Second, parameterized macromodels of these p.u.l. parameters are constructed. Third, a stochastic Galerkin method is implemented to solve the pertinent stochastic telegraphers equations. The new methodology is illustrated with meaningful design examples, demonstrating its accuracy and efficiency. Improvements and advantages with respect to the state-of-the-art are clearly highlighted.

Overview of Signal Integrity and EMC Design Technologies on PCB: Fundamentals and Latest Progress

This paper reviews the fundamentals and latest progress of modeling, analysis, and design technologies for signal integrity and electromagnetic compatibility on PCB and package in the past decades. Most results in this field are based on the very rich and highly educational literature produced by Prof. C. Paul in his long scientific career. The inclusion of parameters variability effects is also considered, and it is demonstrated how statistical simulations can become affordable by means of recently-introduced stochastic methods. Finally, the necessity of practical training of designers is mentioned, and an experience relying on realistic PCB demonstrators is illustrated.

Accurate Extraction of Noise Source Impedance of an SMPS Under Operating Conditions

An accurate measurement method to extract the common mode (CM) and the differential mode (DM) noise source impedances of a switched-mode power supply (SMPS) under its operating condition is developed and validated. With a proper premeasurement calibration process, the proposed method allows extraction of both the CM and the DM noise source impedances with very good accuracy. These noise source impedances come in handy to design an electromagnetic interference filter for an SMPS systematically with minimum hassle.

Systematic Electromagnetic Interference Filter Design Based on Information From In-Circuit Impedance Measurements

Based on a two-probe measurement approach, the noise source and noise termination impedances of a switched-mode power supply (SMPS) under its normal operating condition are measured. With the accurate noise source and noise termination impedances, an electromagnetic interference (EMI) filter can be optimally designed. A practical example of the design of an EMI filter to comply with a regulatory conducted EMI limit using the proposed procedure is demonstrated and compared with the cases, where the noise source and noise termination impedances are not taken into account, or coarse estimates of them are considered. Although all approaches allow filtered SMPS to pass the regulation limits, designing EMI filters with the accurate noise source and termination impedances leads to optimal component values and avoids overdesign.