The limitations of RC ladder networks as process simulators

A definition of controllability in terms of the attenuation/phase relationship at zero frequency is used to derive a formula for the controllability of an n-stage RC ladder network. Formulae are obtained for networks satisfying the condition of least controllability under various sets of constraints. The results emphasize the difficulty of approximating a non-interacting set of lags by an interacting set, and suggest that, for practical purposes, the best approximation is a network with R´s and C´s in geometric progression.