Entrainment ability maximization in nonlinear oscillators by using calculus of variations, and its applications to practical design problems

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Since injection-locking improves frequency stability in the oscillator, its researches have been steadily progressed for various applications. However, as far as we know, any design methodology for optimizing such injection-locking ability has not yet been established. In this study, using a newly developed optimization theory by calculus of variations it becomes possible to maximize locking ranges of several practically important oscillators; CMOS ring oscillators and Class-E oscillators for power electronics, under realistic constraints.