Bias voltage tuning of MEMS resonator operation point
View Patent ↗A method of configuring a device comprising a MEMS resonator includes initiating operation of the device, estimating a first parameter of the MEMS resonator based on the initiated operation, the first parameter not varying with the bias voltage, monitoring the operation of the device at a plurality of levels of the bias voltage, calculating a second parameter of the MEMS resonator based on the monitored operation, the second parameter varying with the bias voltage, determining an operational level of the bias voltage based on the estimated first parameter and the calculated second parameter, and configuring the device in accordance with the determined operational level of the bias voltage.
1. A method of configuring a device comprising a micro-electromechanical systems (MEMS) resonator, the MEMS resonator comprising a resonant structure to which a bias voltage is applied, the method comprising:
initiating operation of the device;
estimating a first parameter of the MEMS resonator based on the initiated operation, the first parameter not varying with the bias voltage;
monitoring the operation of the device at a plurality of levels of the bias voltage;
calculating a second parameter of the MEMS resonator based on the monitored operation, the second parameter varying with the bias voltage;
determining an operational level of the bias voltage based on the estimated first parameter and the calculated second parameter; and
configuring the device in accordance with the determined operational level of the bias voltage.
2. The method of claim 1 , wherein configuring the device comprises storing data indicative of the operational level of the bias voltage in a memory of the device.
3. The method of claim 1 , wherein determining the operational level of the bias voltage is further based on a frequency model of the MEMS resonator.
4. The method of claim 3 , wherein the frequency model of the MEMS resonator is based on empirical data representative of the operation of the device.
5. The method of claim 1 , wherein determining the operational level of the bias voltage comprises estimating the bias voltage that gives rise to an offset in resonant frequency.
6. The method of claim 5 , wherein the offset is about 10 parts per million (ppm).
7. The method of claim 1 , wherein the first parameter is indicative of a thickness of the resonant structure.
8. The method of claim 1 , wherein the second parameter is indicative of a gap between the resonant structure and an electrode to which an excitation voltage is applied.
9. The method of claim 5 , wherein the offset is between 5 ppm and 15 ppm.
10. The method of claim 1 , wherein initiating the operation comprises determining a minimum level of the bias voltage for oscillation of the MEMS resonator.
11. The method of claim 10 , wherein estimating the first parameter comprises measuring a first resonant frequency of the MEMS resonator at a first low level of the plurality of levels of the bias voltage, the first low level being above the minimum level of the bias voltage to ensure a stable start.
12. The method of claim 11 , wherein:
the first parameter is a thickness of the resonant structure; and
estimating the first parameter further comprises estimating the thickness of the MEMS resonator based on the measured resonant frequency and a predetermined, nominal size of a gap between the resonant structure and an electrode of the MEMS resonator.
13. The method of claim 11 , wherein monitoring the operation comprises measuring a second resonant frequency of the MEMS resonator at a second low level of the plurality of levels of the bias voltage differing from the first low level.
14. The method of claim of claim 13 , wherein calculating the second parameter comprises estimating a gap between the resonant structure and an electrode of the MEMS resonator based on the first and second resonant frequencies and the first and second low levels of the bias voltage.
15. The method of claim 14 , wherein calculating the second parameter further comprises:
estimating the operational level of the bias voltage based on the estimated gap, a predetermined offset in the resonant frequency, and a frequency model of the MEMS resonator;
measuring a third frequency of the MEMS resonator at the estimated operational level of the bias voltage; and
calculating a final value for the gap based on the second low level of the bias voltage, the operational level of the bias voltage, and the second and third resonant frequencies.
16. The method of claim 15 , wherein estimating the operational level of the bias voltage comprises lowering the operational level of the bias voltage in accordance with a safety margin.
17. The method of claim 15 , wherein calculating the final value comprises subtracting first and second instances of a resonant frequency deviation model from one another to cancel out a zero-frequency term of the resonant frequency deviation model, wherein the first and second instances are based on the second and third resonant frequencies and the second low level of the bias voltage, and the operational level of the bias voltage.
18. The method of claim 13 , wherein estimating the gap comprises subtracting first and second instances of a resonant frequency deviation model from one another to cancel out a zero-frequency term of the resonant frequency deviation model, wherein the first and second instances are based on the first and second resonant frequencies and the first and second levels of the bias voltage.
19. The method of claim 1 , wherein:
the first parameter is indicative of a thickness of the resonant structure; and
the second parameter is indicative of a gap between the resonant structure and an electrode of the MEMS resonator.
20. The method of claim 19 , wherein the MEMS resonator is configured such that the resonant frequency is proportional to the thickness of the resonant structure.