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Abstract: This study considers a method for minimising the energy dissipation when charging a variable-gap capacitor. The authors assume a capacitor coupled with repulsive mechanical potential energy. The potential energy is proportional to 1/d^sup n^, where d is the plate distance. With this capacitor model, the authors use the method of Lagrange multipliers to investigate a way to minimise the energy dissipation. When n = 3 (Q = pV^sup 2^ is satisfied in this case), the authors confirm that the conventional equal-step charging does not minimise the energy dissipation. From the viewpoint of the charge transfer per step, conventional constant-charge-transfer charging does not minimise the energy dissipation, but increasing-charge-transfer charging (small charge transfer at the initial step and large charge transfer at the final step) does minimise the energy dissipation. From analyses of the charging and discharging processes, it becomes clear that the ratio of energy dissipations between the conventional and proposed methods approaches 0.89 when the step number increases. This means the proposed method reduces the energy dissipation by 11% compared with the conventional one. A circuit that enables the minimum energy dissipation as discussed above is also described.
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1 Introduction
Adiabatic charging has been widely researched because it can decrease energy dissipation to almost zero and might provide high reliability in nanoscale electronic circuits [1-5]. Ideally, adiabatic charging does not cause Joule energy dissipation [6, 7]. This dissipationless transport resembles superconductivity. Such adiabatic operation can be realised by gradual charging using a stepwise power supply [8-12].
Until now, adiabatic charging has been considered for only a capacitor with a determined gap [6 - 14]. However, some systems, such as recent micromechanical systems [15, 16], contain a largely variable-gap capacitor. A comb-structure micro-electro-mechanical system (MEMS) is a well-known example [17]. Moreover, variable-gap capacitors have various potential applications because they can function as switching devices: They can serve as micrometre-scale electrical switches that change electrical paths or cut electrical paths to eliminate leakage current in the standby mode, and as micrometre-scale switches (or valves) that change the direction of the flow of a fluid or gas for research-level or for practical use.
Regarding scale, besides micrometer-scale switches, decimetre-scale switches will be possible as well. By applying decimetre-scale switches...