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 normal circuit research. however the strained call for for prime information speeds, coupled with miniaturizationon an extraordinary 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 might be degraded by way of lengthy interconnect lengths in comparison to the more and more shorter sig­ nal upward thrust occasions. Interconnect buildings might be different (pins, connectors, leads, microstrips, striplines, and so forth. ) 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 review (AWE) and different second matching tech­ niques have lately confirmed precious within the research of interconnect buildings and numerous networks containing huge linear constructions with nonlinear termi­ countries. formerly, all that used to be to be had to the fashion designer used to be a whole SPICE simulation or a brief yet doubtful timing estimation. second matching, utilized in linear platforms research as a style of version aid, describes a style to extract a small set of dominant poles from a wide community. the data is got from the Taylor sequence coefficients (moments) of that system.

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Extra resources for Asymptotic Waveform Evaluation: And Moment Matching for Interconnect Analysis

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RC network A small RC network is given in Fig. 2. AWE was applied to Vout in both frequency and time domain analysis. 2. 9527e-ll Moments of Fig. 2. pair was generated. 3 ns duration was simulated. The transient first order response approximation 29 Asymptotic Waveform Evaluation is given in Fig. 3. Subsequently an order 2 and order 3 approximation was performed with the results given in Fig. 4 and Fig. 5 respectively. A 2nd order approximation is seen to be enough for the waveform to converge.

Y(s) may be decomposed into DU(s), which is a direct coupling between the input and the output and needs no special calculation, cT(sl - A)-lbU(s), which is the response of the system to input U(s), and cT(sl - A)-lx(O+) which is the response of the system to an impulse source equal to the initial conditions of the network, x(O+). The AWE calculation can be simplified by calculating an impulse response once, and then using the impulse response to calculate the network response of any other input waveform.

A more general formulation containing these elements can be given using the MNA formulation. 1 LINEAR SUBNETWORK FORMULATION Consider a linear subnetwork ¢ which contains linear lumped components and Nt lossy coupled transmission line sets, with 41 nk coupled conductors in trans- 42 CHAPTER 3 mission line set k. 30), = [di,j] with elements di,j E {a, 1} and i E {I, 2, ... , N,p},j E {I, 2, ... , 2nd with a maximum of one non-zero in each row or column is a selector matrix that maps ik(t) E ~2n.

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