Frequency Analysis of Truncation Errors in RC Networks

This paper provides guidelines for the discretizing of the space variables in continuous systems governed by the second-order partial differential diffusion equation. Such lumping is necessary in all digital and many analog methods. To analyze the truncation error resulting from lumped analog or digital modelling, the authors demonstrate the applicability of an upper-bound criterion combining amplitude and phase errors in the frequency domain. Dimensionless variables are used to compare lumped networks corresponding to one-dimensional continuous systems. Computer results are presented which relate truncation error to frequency for lumped models containing one to ten sections.