Hyperreal Operating Points in Transfinite Resistive Networks

Autor: Armen H. Zemanian
Rok vydání: 2003
Předmět:
Zdroj: Circuits, Systems and Signal Processing. 22:589-611
ISSN: 1531-5878
0278-081X
DOI: 10.1007/s00034-003-1216-z
Popis: Transfinite resistive electrical networks may (or may not) have operating points, and, even when voltages and currents do exist within them, Kirchoff’s laws may not be satisfied everywhere. Moreover, rather severe restrictions have to be placed on those networks in order to obtain such results. However, by borrowing some techniques of nonstandard analysis, we can replace the real-valued voltages and currents by hyperreal-valued voltages and currents. As a result, Kirchhoff’s laws are always satisfied so long as the transfinite network is "restorable" in the sense that the transfinite network is the end result of an expanding sequence of finite networks. No other restrictions on the transfinite network are needed. Several transfinite networks are then examined under nonstandard analysis, and explicit hyperreal currents and voltages are established for them.
Databáze: OpenAIRE
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