By Eli Chiprout
The extreme force for sign integrity has been on the vanguard ofrapid and new advancements in CAD algorithms. hundreds of thousands ofengineers, cause on attaining the easiest layout attainable, use SPICE every day for analog simulation and basic circuit research. however the strained call for for top information speeds, coupled with miniaturizationon an remarkable scale, has highlighted the formerly negligible results of interconnects; results which aren't consistently dealt with appro priately through the current degrees of SPICE. indications at those better speeds should be degraded by way of lengthy interconnect lengths in comparison to the more and more shorter sig nal upward thrust instances. Interconnect constructions might be assorted (pins, connectors, leads, microstrips, striplines, and so on. ) and current at any of the hierarchical packaging degrees: built-in circuits, revealed 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 evaluate (AWE) and different second matching tech niques have lately confirmed important within the research of interconnect constructions and numerous networks containing huge linear buildings with nonlinear termi international locations. formerly, all that used to be 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 platforms research as a mode of version relief, describes a mode to extract a small set of dominant poles from a wide community. the knowledge is got 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
8 respectively. RLC network Consider the small RLC network in Fig. 9. Formulating the equations in terms of Gq, and Cq, we get for each respectively, 30 CHAPTER 035 .. 8 2 x 10'" RC network transient response: 1st order approximation. 050'---0... 2~--1.... 4 x 10" RC network transient response: 2nd order approximation. _ .. 2'---... _... 1 - - 1.... 2-~1..... 5 xl~ RC network transient response: 3rd order approximation. _ .. 25 i AWE 1.. 0.... 6 I 10 1• RC network frequency response: 1st order approximation.
14) Pj of the network and the number of residues, k j , of the selected output. While the poles of the network are the same at every output node, the residues will vary from node to node. The constant c also varies with the output and indicates direct coupling between the input and the output. 14) is more convenient for an inversion of Laplace transform into the time domain. 16) j=1 In large networks, N p , and therefore the order of Q(s), can be of the order of hundreds or thousands. Generating the N p poles of even a small network is very CPU intensive.
3 MNA FORMULATION While the formulation of the above equations was in the form of the system matrix A, it is not always necessary to reduce the network to this formulation. Extracting the A requires the elimination of all linearly dependent variables such as dependent capacitor voltages in capacitor loops or dependent inductor currents in inductor cut-sets. If we assume that a linear subnetwork ¢ contains only lumped elements, then the modified nodal admittance (MNA)[HRB75] formulation of the subnetwork may be used.
Asymptotic Waveform Evaluation: And Moment Matching for Interconnect Analysis by Eli Chiprout