Methods and devices for calibrating capacitive resonators

A resonator system comprising:

• a resonant member that can vibrate in a first mode and a second mode;
• a plurality of electrodes that are spaced from and capacitively coupled to the resonant member, the plurality of electrodes including a calibration electrode, a drive electrode, and a sense electrode;
• and
• a controller operatively coupled to the resonant member and plurality of electrodes, the controller being configured to:
• apply a polarization voltage to the resonant member and a calibration voltage to the calibration electrode, wherein the polarization voltage is a negative voltage,
• vibrate the resonant member such that the resonant member vibrates in the first mode of vibration and the second mode of vibration,
• determine if a frequency parameter of the resonant member is in compliance with a predetermined threshold, and
• if the frequency parameter is not in compliance with the predetermined threshold, adjust the frequency parameter to be in compliance with the predetermined threshold by adjusting at least one of the polarization voltage and the calibration voltage.

An integrated circuit comprising:

• a negative charge pump configured to output an output voltage, the negative charge pump including a plurality of reverse biased transistors;
• a divider configured to divide a portion of the output voltage to generate an input voltage;
• an amplifier configured to compare the input voltage with a reference voltage;
• and
• clock circuitry configured to control clock amplitude supplied to the negative charge pump.