PROJECT TITLE :

Derivation of the Most Energy-Efficient Source Functions by Using Calculus of Variations

ABSTRACT:

This paper presents the derivation of the most energy-economical supply functions by using calculus of variations. The fundamental theorem of calculus of variations for finding the functions that are native minima or local maxima of the integral is first explained. The theorem is then applied to derive analytically the supply functions that minimize energy dissipation in circuits throughout transient. In explicit, the foremost energy-efficient input current function and voltage supply operate for charging series R-C circuit are derived and proved to be a relentless operate and a raised ramp operate respectively. The theorem of calculus of variations is extended for other common initial order linear circuits moreover. Their most energy-economical supply functions and lowest energy dissipation expressions are summarized in compact parameters involving speed and energy trade off limits. Numerical results are illustrated to depict the upper limit of speed-energy trade off and to justify the consistency with the analytical results. Application of the most energy-economical supply perform for charging and discharging the capacitor of supercapacitor and adiabatic circuits is mentioned along with comparison with different functions.