The Iterated Network and Its Application to DIifferentiators

By induction on the Cayley-Hamilton theorem, a convenient and compact expression for the transmission matrix of an n-tuply iterated, 4-terminal passive network is obtained. The resulting expression is used for the analysis of the behavior of an iterated RC differentiating network. It is shown that such networks are of advantage in applications requring a very short effective time constant. The effective time constant of an n-tuply iterated structure is shown to be 2r/n(n+ 1), where r = RC is the time constant of the unit structure.