Nonstandard versions of conventionally infinite networks

Many conventionally infinite networks do not have operating points. The difficulty is two-fold. Infinitely, many elements may lead to infinite voltages and currents. Also, standard calculus does not allow certain limit processes to be interchanged. However, nonstandard analysis overcomes both problems and thereby produces operating points for all such networks, albeit with hyper-real voltages and currents. This leads to a new kind of electrical network, the nonstandard one wherein the infinite network is viewed as an expanding sequence of finite subnetworks. This idea can be extended in a variety of ways-to transfinite networks of both the linear and nonlinear types, and to linear RLC networks under ac steady-state regimes as well as transient regimes on hyper-real extensions of the time line.