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This paper presents optimum lowest input energy for first-order circuits in transient state. A resistors network with a capacitor is chosen for derivation. The derivation is based on calculus of variations theory or more specifically, the Euler-Lagrange's differential equation. Essential parameters are introduced and the most energy-efficient input source function is obtained. The lowest input energy...
This paper presents the derivation of the most energy-efficient source functions by using calculus of variations. The fundamental theorem of calculus of variations for finding the functions that are local minima or local maxima of the integral is first explained. The theorem is then applied to derive analytically the source functions that minimize energy dissipation in circuits during transient. In...
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