Nonlinear Analyses of Unsymmetrical Locking Range of Injected Cross-Coupled Oscillator

In this article, two accurate nonlinear methods are proposed to calculate non-symmetrical locking ranges of the Injected Cross-Coupled Oscillator (ICCO) with the parallel RLC tank and series RL with a parallel C tank for both weak and strong injection levels. By writing governing differential equations of circuit elements of the ICCO, graphical presenting of current vectors, and using the averaging method for solving nonlinear equations, equations of the ICCO are simplified. Then, exact non-symmetrical locking ranges are calculated using the iterative method. Moreover, the describing function of the oscillator's nonlinear part, an inverse tangent function, is applied to the model. The inverse tangent function generates complicated governing differential equations of circuit elements that are accurate. Then, it is solved to ICCO for the first time and has novel results for calculating non-symmetrical locking ranges. There is a good agreement between theoretical and simulation results. The proposed non-symmetrical locking ranges are accurate in both weak and strong injections. The absolute percent of errors for various levels of the injection signal is less than 20%. In the bargain, proposed locking ranges are the most accurate compared to previously published results.