Computation of signal threshold crossing times directly from higher order moments

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.