A method of an open loop characterization of an electrostatic MEMS based resonator with a varying gap, the method including: converting, via a trans-impedance amplifier circuit, an output current signal of the resonator into a voltage; multiplying the output current signal converted into the voltage, by means of a multiplier circuit, with an AC signal or with a different signal at a frequency of the resonator and carrying a second harmonic signal to a main tone; and measuring a frequency response of a signal cleared of frequencies apart from the main tone using a network analyzer.

Micromachined microelectromechanical systems (MEMS) based resonators offer integration with other MEMS devices and electronics. Whilst piezoelectric film bulk acoustic resonators (FBAR) generally exhibit high electromechanical transduction efficiencies and low signal transmission losses they also suffer from low quality factors and limited resonance frequencies. In contrast electrostatic FBARs can yield high quality factors and resonance frequencies but suffer from increased fabrication complexity. lower electromechanical transduction efficiency and significant signal transmission loss. Accordingly, it would be beneficial to overcome these limitations by reducing fabrication complexity via a single metal electrode layer topping the resonator structure and supporting relatively low complexity/low resolution commercial MEMS fabrication processes by removing the fabrication requirement for narrow transduction gaps. Beneficially, embodiments of the invention provide MEMS circuits with electrostatic tuning and provide resonator designs combining the advantages of piezoelectric actuation and bulk-mode resonators.

In some embodiments, a micro electro mechanical system (MEMS) includes a proof mass, sense electrodes, sense circuitry, and a frequency matching circuitry. The proof mass is configured to move responsive to stimuli. The sense electrodes are configured to generate a signal responsive to the proof mass moving. The sense circuitry is coupled to the sense electrodes. The sense circuitry is configured to receive the generated signal and further configured to process the generated signal. The frequency matching circuitry is configured to apply a DC voltage to the sense electrodes. The DC voltage is configured to change a stiffness of a spring of the proof mass. According to some embodiments, the change in the stiffness of the spring matches a resonance frequency between a sense mode and a drive mode. According to some embodiments, the sense electrodes are a comb structure.

A method of an open loop characterization of an electrostatic MEMS based resonator with a varying gap, the method including: converting, via a trans-impedance amplifier circuit, an output current signal of the resonator into a voltage; multiplying the output current signal converted into the voltage, by means of a multiplier circuit, with an AC signal or with a different signal at a frequency of the resonator and carrying a second harmonic signal to a main tone; and measuring a frequency response of a signal cleared of frequencies apart from the main tone using a network analyzer.

In some embodiments, a micro electro mechanical system (MEMS) includes a proof mass, sense electrodes, sense circuitry, and a frequency matching circuitry. The proof mass is configured to move responsive to stimuli. The sense electrodes are configured to generate a signal responsive to the proof mass moving. The sense circuitry is coupled to the sense electrodes. The sense circuitry is configured to receive the generated signal and further configured to process the generated signal. The frequency matching circuitry is configured to apply a DC voltage to the sense electrodes. The DC voltage is configured to change a stiffness of a spring of the proof mass. According to some embodiments, the change in the stiffness of the spring matches a resonance frequency between a sense mode and a drive mode. According to some embodiments, the sense electrodes are a comb structure.

Micromachined microelectromechanical systems (MEMS) based resonators offer integration with other MEMS devices and electronics. Whilst piezoelectric film bulk acoustic resonators (FBAR) generally exhibit high electromechanical transduction efficiencies and low signal transmission losses they also suffer from low quality factors and limited resonance frequencies. In contrast electrostatic FBARs can yield high quality factors and resonance frequencies but suffer from increased fabrication complexity. lower electromechanical transduction efficiency and significant signal transmission loss. Accordingly, it would be beneficial to overcome these limitations by reducing fabrication complexity via a single metal electrode layer topping the resonator structure and supporting relatively low complexity/low resolution commercial MEMS fabrication processes by removing the fabrication requirement for narrow transduction gaps. Beneficially, embodiments of the invention provide MEMS circuits with electrostatic tuning and provide resonator designs combining the advantages of piezoelectric actuation and bulk-mode resonators.