Time-Domain Analysis and Measurement Techniques for Distributed RC Structures. I. Analysis in the Reciprocal Time Domain

Abstract

The impulse response in distributed-parameter systems results in a spectrum of delta functions in the time domain for LC structures. It is shown that for RC structures the impulse response results in a spectrum of Poisson-derived functions in the reciprocal time domain. This isomorphism is exploited for the analysis of RC devices to establish a calculus of Poisson-derived functions and a transform technique which is essentially the Laplace transform. Applications of this technique to thin-film devices and minority-carrier devices are examined and lead to the determination of the transient response for one-ports and two-ports that are subject to a wide range of terminations. Illustrative examples of excitations include the impulse, the step, and the ramp, as well as signals generated by the distributed parameter devices themselves. Significant advantages accrue from a spectral description of RC devices in the reciprocal time domain: (1) conceptual, by establishing a physical interpretation based on diffusion phenomena; (2) analytical, by developing a systematic approach to transients paralleling the network function approach in the frequency domain; (3) computational, by expressing the response by a rapidly converging spectrum of functions.