Critical excitation function of distributed-parameter devices

A technique is described to estimate the transient response of thin-film devices at time intervals which exceed the greatest time constant or which are exceeded by the smallest time constant of the device. Relevant properties of distributed-parameter network functions are evaluated by applying the extreme value limit theorem to the corresponding Laplace Transform. Each configuration is characterized by an associated excitation function which predicts the device response at extreme values in the time domain (t = 0andt = \infin). A systematic investigation of the transient response of a rectangular\bar{RC}film-type network consists of tabulating characteristics or critical excitation functions for all eight driving-point configurations and for all twelve transfer-function configurations due to excitation of the types_{-n/2}withn = 0, 1, 2, 3, 4. Once the critical excitation function is determined, the transient response for arbitrary excitations is readily available. Applications to design problems encountered in thin-film and integrated circuits are discussed. The technique becomes increasingly accurate as time intervals are approached which correspond to frequencies outside the range of break-frequencies of the device.