By Eli Chiprout
The extreme force for sign integrity has been on the leading edge ofrapid and new advancements in CAD algorithms. hundreds of thousands ofengineers, purpose on attaining the easiest layout attainable, use SPICE each day for analog simulation and common circuit research. however the strained call for for prime information speeds, coupled with miniaturizationon an unparalleled scale, has highlighted the formerly negligible results of interconnects; results which aren't continuously dealt with appro priately by way of the current degrees of SPICE. indications at those greater speeds should be degraded through lengthy interconnect lengths in comparison to the more and more shorter sig nal upward thrust occasions. Interconnect constructions should be diversified (pins, connectors, leads, microstrips, striplines, and so on. ) and current at any of the hierarchical packaging degrees: built-in circuits, published circuit forums, multi-chip modules or sys tem backplanes. research of those results in any CAD package deal has turn into a need. Asymptotic waveform assessment (AWE) and different second matching tech niques have lately confirmed worthy within the research of interconnect constructions and numerous networks containing huge linear constructions with nonlinear termi international locations. formerly, all that was once to be had to the fashion designer was once a whole SPICE simulation or a brief yet doubtful timing estimation. second matching, utilized in linear structures research as a mode of version aid, describes a style to extract a small set of dominant poles from a wide community. the data is acquired from the Taylor sequence coefficients (moments) of that system.
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Additional info for Asymptotic Waveform Evaluation: And Moment Matching for Interconnect Analysis
7704 Approximate/actual poles of Fig. 9. 3 ns duration was simulated. The convergence for different orders of approximation in the time domain can be seen in Fig. 1O-Fig. 13. The waveform converges by the 5th order. The various frequency response approximations are given in Fig. 14-Fig. 18. While the frequency response does not converge by the 5th order approximation, the transient response does due to the particular input waveform. The higher frequency harmonics are not significant enough to affect the output.
14). The authors are not aware of any published algorithm for generating the poles of such a distributed network and a finite algorithm for generating all of the poles is not possible in the general case. AWE provides a method for generating an approximate set of poles, and, as will be shown, it is possible to use CFH to extract an exact set of dominant poles. 7), we expand all terms in a Maclaurin series, (Y <1>[01 + sY <1> + s2y <1> + .. 11). 2) of the elements. 3 UNIFORM LOSSY COUPLED TRANSMISSION LINES A uniform N-conductor transmission line (Fig.
This is because an impulse is absorbed by the first energy elements it comes in contact with giving a finite step. All other nodes will change in a continuous fashion. Once the elements with no current are eliminated, the much smaller circuit may be solved for voltages. 4 EXAMPLES We use two small examples to illustrate the method. The order of the approximation refers to the number q or the number of poles generated by an 28 CHAPTER 2 approximation. 2 RC network. RC network A small RC network is given in Fig.
Asymptotic Waveform Evaluation: And Moment Matching for Interconnect Analysis by Eli Chiprout