RICE: Rapid interconnect circuit evaluator
DAC '91 Proceedings of the 28th ACM/IEEE Design Automation Conference
On the stability of moment-matching approximations in asymptotic waveform evaluation
DAC '92 Proceedings of the 29th ACM/IEEE Design Automation Conference
An explicit RC-circuit delay approximation based on the first three moments of the impulse response
DAC '96 Proceedings of the 33rd annual Design Automation Conference
h-gamma: an RC delay metric based on a gamma distribution approximation of the homogeneous response
Proceedings of the 1998 IEEE/ACM international conference on Computer-aided design
PERI: a technique for extending delay and slew metrics to ramp inputs
Proceedings of the 8th ACM/IEEE international workshop on Timing issues in the specification and synthesis of digital systems
A delay metric for RC circuits based on the Weibull distribution
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Delay and slew metrics using the lognormal distribution
Proceedings of the 40th annual Design Automation Conference
Simple metrics for slew rate of RC circuits based on two circuit moments
Proceedings of the 40th annual Design Automation Conference
PRIMA: passive reduced-order interconnect macromodeling algorithm
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Efficient linear circuit analysis by Pade approximation via the Lanczos process
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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This work introduces a simple method for calculating the times at which any signal crosses a pre-specified threshold voltage (e.g. 10%, 20%, 50%, etc.) directly from the moments. The method can use higher order moments to asymptotically improve the accuracy of the estimated crossing times. This technique bypasses the steps involved in calculating poles and residues to obtain time-domain information. Once q moments are calculated, only 2q multiplications and (q-I) additions are required to determine any threshold crossing time at a certain node. Moreover, this technique avoids other problems such as pole instability. Several orders of approximations are presented for different threshold crossing times depending on the number of moments involved. For example, the worst case error of a first to a seventh order (single to seven moments) approximation of 50% RC delay is 1650%, 192.26%, 11.31%, 3.37%, 2.57%, 2.56%, and 1.43%, respectively. If the whole waveform is required it can be easily determined by interpolation between different threshold crossing points. The presented technique works for RC circuits for both step and nonstep inputs, including piecewise linear waveforms.