Hyperreal transients in transfinite RLC networks

Hyperreal waves on transfinite, terminated, distortionless and lossless, transmission lines

A prior work examined the propagation of an electromagnetic wave on a transfinite transmission line—transfinite in the sense that infinitely many one-way infinite transmission lines are connected in cascade. That there are infinitely many such lines results in the wave propagating without ever reflecting at some discontinuity This work examines the case where the line is terminated after finite...

Experiment 2: Transients and Oscillations in RLC Circuits

Transient responses of RLC circuits are examined when subjected to both long time scale (relative to the decay time) square wave voltages and sinusoidally varying voltages over a range of frequencies about the resonant frequency. In general, a good correspondence is found between theory describing the charge in the system in terms of a 2nd order differential equation with a harmonic oscillator ...

Transfinite Graphs and Electrical Networks

All prior theories of infinite electrical networks assume that such networks are finitely connected, that is, between any two nodes of the network there is a finite path. This work establishes a theory for transfinite electrical networks wherein some nodes are not connected by finite paths but are connected by transfinite paths. Moreover, the voltages at those nodes may influence each other. Th...

Zero Assignment Problem in RLC Networks

The paper deals with the problem of zero assignment in RLC networks by selection of appropriate values for the nondynamical elements, the resistors. For a certain family of network redesign problems by the additive perturbations may be described as diagonal perturbations and such modifications are considered here. This problem belongs to the family of DAP problems (Determinantal Assignment Prob...

Transfinite Equations in Transfinite Strings