A significant percentage of the critical nets in high-performance systems are of the pin-to-pin type. To optimally design these nets such that signal integrity is preserved, efficient analytical metrics for transmission line termination are a valuable part of a system-level designer's toolset. Using the symbolic moment-based expressions in this paper, proper termination can be determined via a single-step procedure, without any preprocessing steps and/or time-domain simulations. Driver nonlinearities and effects of nonzero rise-time are also considered in the proposed termination methodology.

The design of system level interconnects to meet signal integrity objectives is a challenging problem. This paper formulates the transmission line synthesis problem as a constrained multidimensional optimization task for performance-driven routing of the complete net, taking into account factors like loading conditions on the line, loss in the line, and rise time of the input signal. Different design variables, such as width or resistivity of the interconnect, resistive source, or far-end termination, etc., can all be considered concurrently. A novel termination metric is described that is based upon forcing the impulse response waveform to be symmetric using the first three moments of the distributed system response. This metric provides an efficient means to trade off between signal rise time and ringing without requiring a time-domain simulation. Several examples are presented to demonstrate the efficacy of the proposed methodology.

The Elmore delay is an extremely popular timing-performance metric which is used at all levels of electronic circuit design automation, particularly for resistor-capacitor (RC) tree analysis. The widespread usage of this metric is mainly attributable to it being a delay measure that is a simple analytical function of the circuit parameters. The only drawback to this delay metric is the uncertainty of its accuracy and the restriction to it being an estimate only for the step response delay. In this paper, we prove that the Elmore delay measure is an absolute upper bound on the actual 50% delay of an RC tree response. Moreover, we prove that this bound holds for input signals other than steps and that the actual delay asymptotically approaches the Elmore delay as the input signal rise time increases. A lower bound on the delay is also developed using the Elmore delay and the second moment of the impulse response. The utility of this bound is for understanding the accuracy and the limitations of the Elmore metric as we use it as a performance metric for design automation.

Electronic system design requires noise and delay analyses of lossy, low-loss, frequency dependent, and coupled transmission lines, along with lumped parasitic elements. Numerous models and techniques have been developed for simulating these interconnect circuits, however, no single method represents the optimal approach for all transmission line problems. Accuracy and efficiency considerations would suggest the use of different models and analyses for the various types of interconnects. Such an approach to simulating transmission lines requires a measure of goodness for selecting the appropriate model and analysis in terms of the circuit parameters. Toward this goal, this paper presents an efficient methodology for characterizing transmission line models into solution domains. This provides an efficient technique for automatically selecting the type of interconnect model and analysis. Specifically, for a specified acceptable modeling error, analysis domains are established for automatic model selection between the classical method of characteristics, a lumped modeling approach and the state-based convolution technique within a simulation and analysis tool. In general, however, this approach can be applied to any combination of models and analyses, if a measure of accuracy and efficiency can be established.

The Elmore delay is an extremely popular delay metric, particularly for RC tree analysis.The widespread usage of this metric is mainly attributable to it being the most accurate delay measure that is a simple analytical function of the circuit parameters.The only drawbacks to this delay metric are the uncertainty as to whether it is an optimistic or a pessimistic estimate, and the restriction to step response delay estimation.In this paper, we prove that the Elmore delay is an absolute upper bound on the 50% delay of an RC tree response.Moreover, we prove that this bound holds for input signals other than steps, and that the actual delay asymptotically approaches the Elmore delay as the input signal rise time increases.A lower bound on the delay is also developed using the Elmore delay and the second moment of the impulse response.The utility of this bound is for understanding the accuracy and the limitations of the Elmore delay metric as we use it for design automation.

RLC transmission line synthesis is a difficult problem because minimal net delay cannot be achieved or accurately predicted unless: 1) a termination scheme is chosen and properly implemented, and 2) output driver transition rates are constrained at or below the net's capability.This paper describes a method to concurrently find, for any RLC net, an optimal termination value, a maximum source transition rate, and an approximate net delay using the first few response moments.When optimal termination is accomplished and transition rates do not exceed the capabilities of the net, the resulting delay metrics are an interesting extension of the popular Elmore delay metric for RC interconnects.The task of physical RLC interconnect design is facilitated by the ease with which these first few moments are calculated for generalized RLC lines.

The design of system level interconnects to meet signal integrity objectives is a challenging problem. This paper formulates the transmission line synthesis problem as a constrained multi-dimensional optimization of the complete net, taking into account factors like loading conditions on the line loss in the line and rise-time of the input signal. Different design variables such as width or resistivity of the interconnect, resistive source or far-end termination, etc. can all be considered concurrently. The termination metric is based upon forcing the impulse response waveform to be symmetric using the first three exact moments of the distributed system. An efficient means to trade-off between signal rise-time and ringing is presented and no time-domain simulations are needed. Several examples are presented to demonstrate the efficacy of the proposed methodology.

Article Free Access Share on OTTER: optimal termination of transmission lines excluding radiation Authors: Rohini Gupta Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TXView Profile , Lawrence T. Pillage Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TX Department of Electrical and Computer Engineering, The University of Texas at Austin, Austin, TXView Profile Authors Info & Claims DAC '94: Proceedings of the 31st annual Design Automation ConferenceJune 1994 Pages 640–645https://doi.org/10.1145/196244.196600Published:06 June 1994Publication History 13citation195DownloadsMetricsTotal Citations13Total Downloads195Last 12 Months4Last 6 weeks2 Get Citation AlertsNew Citation Alert added!This alert has been successfully added and will be sent to:You will be notified whenever a record that you have chosen has been cited.To manage your alert preferences, click on the button below.Manage my AlertsNew Citation Alert!Please log in to your account Save to BinderSave to BinderCreate a New BinderNameCancelCreateExport CitationPublisher SiteeReaderPDF

Electronic system design requires simulating combinations of lossy, low-loss, frequency dependent, and coupled transmission lines. Accuracy and efficiency considerations would suggest the use of different models and analyses for the various types of interconnects. Toward this goal this paper presents an efficient methodology for characterizing transmission line models into solution domains. Specifically, given an acceptable percentage modeling error, analysis domains are established for automatic model selection between method of characteristics and a lumped modeling approach.>

Physical interconnect introduces new challenges for parameter extraction and delay calculation for application specific electronic module (ASEM) design automation. Efficiency dictates the precharacterization of extracted electrical parameters in the same manner as application specific integrated circuits (ASICs). However, ASEM interconnect is dominated by frequency dependent LC propagation which makes precharacterization difficult for all possible configurations. Moreover, simulating the transient behavior of the ASEM interconnect for noise and delay analysis requires the combined use of a variety of models and techniques for efficiently handling lossy, low-loss, frequency dependent, and coupled transmission lines together with lumped parasitic elements. We propose to use conformal mapping to generate "abstracted" models for the electrical parameters of various RLC interconnect cross-sections, including the frequency dependence caused by ground plane proximity and skin effects. Along with precharacterized lumped parasitic elements and nonlinear driver and load models, these models are simulated using a generalized time-domain macromodeling approach that can combine different types of transmission line analysis in one simulation environment. An automatic selection mechanism is derived for determination of the best time-domain macromodel for a particular distributed segment.