On the Switches Absorbed Energies in Capacitor‐Switch Circuits: The Asymptotic Approach

ABSTRACT The energies absorbed by ideal switches in general capacitor‐switch circuits, both without and with topological degeneracy, are investigated through the so‐called asymptotic approach. The core of this approach (already used by the author to address the well‐known two‐capacitor paradox) is the embedding of each ideal switch into a family of non‐ideal switches with finite transition time, which converge to the ideal one when this parameter tends to zero. The conclusion of the investigation, performed through extensive use of graph theory and matrix calculus, is that the energy calculation is feasible, provided that each ideal switch is accompanied by information on its half‐rise resistance. This result is the main contribution and novelty of the paper. To illustrate the method, two examples are treated in detail: a series circuit with three capacitors and one switch, and a ladder circuit with three capacitors and two switches (without and with an additional bridge capacitor).