Influence of the temperature dependent A-f effect on the design and performance of oscillators

In this work, we develop a theoretical explanation for the temperature dependence of the nonlinear amplitude-frequency (A-f) effect in micromechanical resonators. Using this theory, we explain the discrepancy in frequency-temperature (f-T) characteristics between open-loop observation and closed-loop measurements. We show how the temperature dependence of the A-f effect introduces bias voltage dependence in the f-T characteristics of an oscillator system. Based upon this understanding, we present a new method to remove the temperature dependence of the A-f effect from an oscillator system, thereby eliminating the bias voltage (V_bias) dependency, and enabling predictable f-T characteristics.