On the Switches Absorbed Energies in Capacitor–Switch Circuits: The Asymptotic Approach via Distributions

ABSTRACT A new algebraic method is presented for calculating the energy absorbed by ideal switches in capacitor–switch circuits without topological degeneracy (i.e., circuits with capacitor‐only loops are not allowed). It is based on the embedding already used by the author to asymptotically address the well‐known two‐capacitor circuit, that is, each ideal switch is embedded into a family of non‐ideal switches with finite transition time that converge to the ideal one as this parameter approaches zero. Concepts and tools from distribution theory are extensively used to demonstrate that the power absorbed by the ideal switches can be expressed in terms of a set of distributions and that these distributions are proportional to the Dirac delta, due to the constraints on them. Therefore, the looked for energy is easily obtained in closed form by integrating the power between and . To illustrate the use of 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.