Timing oscillator having a non-linear MEMS resonator and related methods
Oscillators including mechanical resonators are described, as are methods of operating the oscillators such that the mechanical resonator exhibits non-linear behavior. The non-linear behavior may include multiple stable states, for instance being bi-stable. The non-linear behavior may exhibit hysteresis. The mechanical resonator may be driven to operate in a desired portion of the non-linear operating regime.
1. A method of operating a timing oscillator, the method comprising:
driving a temperature-compensated mechanical resonator of the timing oscillator such that the temperature-compensated mechanical resonator operates in a non-linear regime and, simultaneously, maintaining a substantially constant resonance frequency of the temperature-compensated mechanical resonator while varying a temperature of the temperature-compensated mechanical resonator.
2. The method of claim 1 , wherein driving the temperature-compensated mechanical resonator of the timing oscillator comprises providing an input signal to drive the temperature-compensated mechanical resonator such that an output signal of the temperature-compensated mechanical resonator has an amplitude that is a non-linear function of the input signal.
3. The method of claim 2 , wherein the input signal controls a strain that drives the temperature-compensated mechanical resonator.
4. The method of claim 1 , wherein driving the temperature-compensated mechanical resonator of the timing oscillator comprises driving the temperature-compensated mechanical resonator to operate in one of a plurality of stable states.
5. The method of claim 4 , further comprising producing an output signal of the timing oscillator based on vibration of the temperature-compensated mechanical resonator, wherein the output signal exhibits phase noise that is at least a factor of 2 dB less than would be exhibited by an output signal of the timing oscillator if the temperature-compensated mechanical resonator was operated in a linear regime.
6. The method of claim 4 , further comprising producing an output signal of the timing oscillator based on vibration of the temperature-compensated mechanical resonator, wherein the output signal exhibits jitter less than approximately 1 picosecond.
7. The method of claim 4 , wherein the plurality of stable states consists of two stable states.
8. The method of claim 1 , further comprising providing amplified feedback by amplifying an output signal of the temperature-compensated mechanical resonator to create an amplified signal and feeding back the amplified signal as a feedback signal to an input of the temperature-compensated mechanical resonator.
9. The method of claim 8 , wherein providing amplified feedback further comprises limiting an amplitude of the feedback signal.
10. The method of claim 9 , further comprising setting a phase of the feedback signal such that the timing oscillator exhibits self-sustained oscillations.
11. The method of claim 10 , wherein setting the phase of the feedback signal comprises setting the phase of the feedback signal to an arbitrary value.
12. The method of claim 10 , wherein setting the phase of the feedback signal comprises setting the phase of the feedback signal to be fixed in relation to a phase of an input signal to the temperature-compensated mechanical resonator.
13. The method of claim 12 , wherein a relative phase difference between the input signal of the temperature-compensated mechanical resonator and the feedback signal is arbitrary.
14. The method of claim 1 , further comprising actuating the temperature-compensated mechanical resonator by piezoelectric, electrostatic, or magnetic techniques.
15. The method of claim 1 , further comprising detecting vibrations of the temperature-compensated mechanical resonator by piezoelectric, electrostatic, or magnetic techniques.
16. A timing oscillator comprising:
a temperature-compensated mechanical resonator comprising a piezoelectric active layer and a multi-layer temperature compensation structure; and
a drive circuit configured to provide an input signal to drive the temperature-compensated mechanical resonator in a non-linear regime.
17. The timing oscillator of claim 16 , wherein the drive circuit is configured to provide the input signal such that an output signal of the temperature-compensated mechanical resonator has an amplitude that is a non-linear function of the input signal.
18. The timing oscillator of claim 17 , wherein the drive circuit is configured to provide the input signal to control a strain that drives the temperature-compensated mechanical resonator.
19. The timing oscillator of claim 16 , wherein the drive circuit is configured to provide the input signal such that the temperature-compensated mechanical resonator operates in one of a plurality of stable states.
20. The timing oscillator of claim 19 , wherein the timing oscillator is configured to provide an output signal based on vibration of the temperature-compensated mechanical resonator, wherein the output signal exhibits phase noise that is at least a factor of 2 dB less than would be exhibited by an output signal of the timing oscillator if the temperature-compensated mechanical resonator was operated in a linear regime.
21. The timing oscillator of claim 19 , wherein the timing oscillator is configured to provide an output signal based on vibration of the temperature-compensated mechanical resonator, wherein the output signal exhibits jitter less than approximately 1 picosecond.
22. The timing oscillator of claim 16 , further comprising a feedback circuit that comprises an amplifier configured to amplify an output signal of the temperature-compensated mechanical resonator to generate an amplified signal, and a feedback connection configured to feed back the amplified signal as a feedback signal to an input of the temperature-compensated mechanical resonator.
23. The timing oscillator of claim 22 , wherein the feedback circuit further comprises a limiter configured to limit an amplitude of the feedback signal.
24. The timing oscillator of claim 23 , wherein the feedback circuit is further configured to set a phase of the feedback signal to an arbitrary value.
25. The timing oscillator of claim 22 , wherein the timing oscillator is configured to provide an arbitrary relative phase difference between the input signal of the temperature-compensated mechanical resonator and the feedback signal.