Method of optimising the performance of a MEMS rate gyroscope

1. A method of tuning a vibratory gyroscope, the gyroscope comprising: an axisymmetric disc resonator, a frame, the resonator fixed to the frame through at least three separate anchors, a plurality of electrodes, each electrode positioned on the frame or the resonator, wherein the plurality of electrodes comprises at least one drive electrode through which a drive signal is input to excite a first mode of vibration of the resonator, at least one first sense electrode configured to sense the first mode of vibration of the resonator, at least one second sense electrode configured to sense a second mode of vibration of the resonator, orthogonal to the first mode, and at least first and second tuning electrodes to which DC biasing voltages may be applied, the method comprising the steps of:

a) applying an AC drive signal to the drive electrode, the drive signal comprising a plurality of frequencies;

b) sensing a response of the resonator to the drive signal at the first and second sense electrodes;

c) determining a frequency of maximum response for the first mode of vibration, and determining a frequency of maximum response for the second mode of vibration;

d) deriving a comparison result from a comparison of the frequency of maximum response for the first mode of vibration with the frequency of maximum response for the second mode of vibration; and

e) applying a biasing voltage to one or more of the tuning electrodes dependent on the comparison result,

wherein the method comprises repeating steps a) to e) using a set of one or more first mode tuning electrodes in step (e) until the frequency of maximum response for the first mode of vibration is determined to be equal to the frequency of maximum response for the second mode of vibration, or until a difference between the frequency of maximum response for the first mode of vibration and the frequency of maximum response for the second mode of vibration is reduced to a minimum non-zero value, and if the difference between the frequency of maximum response for the first mode of vibration and the frequency of maximum response for the second mode of vibration is reduced to a minimum non-zero value, subsequently repeating steps (a) to (e) using a set of one or more second tuning electrodes in step (e) until the frequency of maximum response for the first mode of vibration is determined to be equal to the frequency of maximum response for the second mode of vibration in step (d).

2. A method according to claim 1 , comprising, in step d), determining which of the tuning electrodes to apply the biasing voltage to, based on the comparison result.

3. A method according to claim 2 , wherein, after the step of deriving the comparison result, the method comprises comparing the comparison result with a previous comparison result to determine which of the tuning electrodes to apply the biasing voltage to.

4. A method according to claim 1 , comprising, in step e), determining a magnitude of the biasing voltage dependent on the comparison result.

5. A method according to claim 4 , wherein the magnitude of the biasing voltage is increased from a previous biasing voltage by a predetermined amount.

6. A method according to claim 1 , further comprising, prior to step a), applying a preliminary drive signal to one of the plurality of the electrodes on the resonator, the preliminary drive signal comprising a plurality of frequencies, sensing the response of the resonator to the preliminary drive signal at the plurality of the electrodes, and determining which of the plurality of the electrodes to operate as drive, sense and tuning electrodes based on the sensed response of the resonator to the preliminary drive signal.

7. A method according to claim 1 , comprising recording a value of the biasing voltage or biasing voltages when the frequency of maximum response for the first mode of vibration is equal to the frequency of maximum response for the second mode of vibration.

8. A method according to claim 1 , wherein the resonator is a circular disc.

9. A method according to claim 1 , wherein the resonator and the frame comprise a single crystal of silicon.

10. A method according to claim 1 , wherein the gyroscope comprises twelve electrodes on the frame, positioned around the resonator and one electrode positioned on the resonator.

11. A method according to claim 1 , wherein the resonator is fixed to the frame through four anchors.

12. A method according to claim 1 , wherein the drive signal excites first and second trigonal modes of vibration of the resonator.