Nonlinearity and dynamics in RF Oscillators: Analysis and design implications

In this paper a novel nonlinear analysis and design approach for VCOs based on modeling the circuit in the higher-dimensional state space is presented. Using the center manifold theorem, we reduce the higher-dimensional system to a two dimensional parameter dependent nonlinear system that maintains the dynamics of the higher-dimensional system. By applying the Andronov-Hopf bifurcation analysis to the reduced system, it is possible to perform a stability analysis and to approximate the amplitude and frequency of the individual state variables. The applicability of the method is verified by designing and analyzing a 2.4 GHz VCO using a 0.25 μm RF CMOS technology.