Hyperreal transients in transfinite RLC networks

✍ Scribed by A. H. Zemanian

• Publisher: John Wiley and Sons
• Year: 2001
• Tongue: English
• Weight: 137 KB
• Volume: 29
• Category: Article
• ISSN: 0098-9886
• DOI: 10.1002/cta.174

✦ Synopsis

Abstract

Up to the present time, there have been no transient analyses of RLC transfinite networks. Standard analyses of transfinite networks have been restricted to purely resistive ones. In this paper, it is shown how non‐standard analysis can be used to examine the transient behaviour of transfinite networks having lumped resistors, inductors, and capacitors. To do so, the time line is expanded into the hyperreal time line, and the transients obtained take on hyperreal values. It is also shown how the diffusion of signals on artificial RC cables and the propagation of waves on artificial RLC transmission lines can ‘pass through infinity’ and penetrate transfinite extensions of those cables and lines. Less precisely but more suggestively, we can say that diffusions and waves can reach—with appreciable values—nodes that are transfinitely far away from their starting points, but that it will take infinitely long times in order to get there. Copyright © 2001 John Wiley & Sons, Ltd.