Analysis of resonant sensors based on mutually injection-locked oscillators beyond the critical Duffing amplitude

Abstract

Sensor architectures based on coupled resonators are receiving increased interest from the resonant sensing community. Certain output metrics of such sensors have an increased sensitivity to the measurand, compared to conventional resonant sensors with frequency-modulated outputs. In the present paper, we extend our study of the properties of mutually injection-locked oscillators (MILOs) into the nonlinear domain, assuming the resonators are subject to cubic restoring forces. Our analysis shows that, depending on the softening or hardening character of the nonlinearity, some MILOs may be operated well above the critical Duffing amplitude. Moreover, it turns out that all the output metrics of such MILOs are not similarly affected by noise. A typical example is given, in which we show that, above the critical Duffing amplitude, phase difference measurements are limited by the A-f effect, whereas amplitude ratio measurements are not. These theoretical results are supported by transient simulations.