Locking Range Maximization in Injection-Locked Class-E Oscillator-A Case Study for Optimizing Synchronizability

We propose a method for designing optimal external forcings of injection-locked oscillators. This method enables to maximize the locking range of general injection-locked oscillators under certain practical constraints that encompass the power, magnitude, or area of forcing waveforms. Here, as a case study, we focus on a class-E oscillator in the injection-locked mode, for which we obtain the following systematic results. First, by using the proposed method, the optimal waveform of external forcings is obtained analytically under three different constraints, i.e., the power- (i.e., root mean square-) reduced, magnitude-reduced, and area-reduced constraints. Second, through systematic circuit simulations, those predicted optimal forcings are verified to outperform any other forcings. Third, circuits experiments confirm that the theoretical predictions and the circuit simulation results are correct and consistent, regarding lock range maximization. These findings result in a first demonstration of locking range maximization for practical electrical oscillators.