Modeling Methods and Predicting Spur Levels for Mutually Coupled Phase-locked Loops

In this study, we derived the relationship between the stability conditions of mutually coupled PLLs and the phase error and spur level of the output clock using linear model theoretical analysis, nonlinear differential equations, and circuit simulations using electromagnetic field analysis tools. In particular, the electromagnetic coupling between the coils of the oscillators was assumed to be a factor causing mutual interference, and its dependence on the distance between the coils was demonstrated. We also demonstrated the validity of the analysis by measuring of an evaluation circuit, and presented the conditions for the distance between the oscillators and the PLL bandwidth that ensure the stability conditions of the PLL. Furthermore, we predicted the spur level based on the relationship between the coupling strength and the distance between the oscillators of mutually coupled PLLs. Our analysis clarifies the relationship between the performance of mutually coupled PLLs and the parameters that determine it. We believe that this research will contribute to improving the accuracy of predictions regarding the effects of interference in systems employing multiple PLLs.