Hyperreal Transients in Transfinite RLC Networks

Abstract

All prior analyses of transfinite electrical networks, as in Chapters 5 and 6 and in [50], [51], [54], have been restricted to purely resistive networks. That is, the branch parameters have only been (linear or nonlinear) resistors along with voltage and current sources. However, the technique employed in Chapter 6, whereby the transfinite network N^v is viewed as the end result of a sequence of finite networks that fill out N^v, now makes it possible to analyze transfinite electrical networks whose branch parameters are also allowed to be inductors and capacitors. This is certainly so if the resistors, inductors, and capacitors are linear and positive. By an RLC network we will mean an electrical network whose parameters are so restricted.