Lumped approximation to distributed RC notch networks for linear integrated circuits

Handling of the transcedental equations arising in distributed networks is rather cumbersome. Therefore, in this paper, a lumped approximation to the RC network has been examined. Generalized expressions have been derived for the open circuit voltage transfer function valid for n-lumped sections. This is a rational polynomial and as such easier to handle for analytical purposes. Application has been made to the cases of n = 2 to seven sections and the results obtained have been compared with the ones from exact analysis of the RC notch network. Root-locus graphs have also been derived and plotted for three and seven sections.