Analysis of the Nonlinear Dynamics of an Injection-Locked Dual-Mode Oscillator

A detailed investigation of the nonlinear dynamics of injection-locked dual-mode oscillators, intended for a sensor application, is presented. It starts with the analytical study of a cubic-nonlinearity oscillator loaded with two distributed LC resonators. We demonstrate the stable behavior of the two periodic oscillation modes when one or two resonators are affected by the material under test (MUT). We also show the impact of the harmonic content on the oscillation frequencies and the mechanism that gives rise to the oscillatory solutions. Next, a practical transistor-based oscillator is addressed. We initially make use of a novel resonance diagram, able to predict the oscillation coexistence and then perform an accurate calculation of the periodic oscillations through an exhaustive analysis method, based on harmonic balance (HB). In the presence of the input signal, the two locking bands existing for each dielectric constant are simultaneously obtained by tracing the contours of a nonlinear current function. The phenomenon that gives rise to the switching from one oscillation to the other is identified with concepts from bifurcation theory. Finally, the MUT dielectric constant and loss tangent are detected from the central frequencies and bandwidths of the two locking bands using a linear interpolation procedure.