Frequency stabilization in nonlinear MEMS and NEMS oscillators
An illustrative system includes an amplifier operably connected to a phase shifter. The amplifier is configured to amplify a voltage from an oscillator. The phase shifter is operably connected to a driving amplitude control, wherein the phase shifter is configured to phase shift the amplified voltage and is configured to set an amplitude of the phase shifted voltage. The oscillator is operably connected to the driving amplitude control. The phase shifted voltage drives the oscillator. The oscillator is at an internal resonance condition, based at least on the amplitude of the phase shifted voltage, that stabilizes frequency oscillations in the oscillator.
1. A system comprising:
an amplifier operably connected to a phase shifter, wherein the amplifier is configured to amplify a voltage from an oscillator;
the phase shifter operably connected to a driving amplitude control, wherein the phase shifter is configured to phase shift the amplified voltage;
the driving amplitude control configured to set an amplitude of the phase shifted voltage; and
the oscillator operably connected to the driving amplitude control, wherein the phase shifted voltage drives the oscillator, wherein the oscillator is at an internal resonance condition based at least on the amplitude of the phase shifted voltage, and wherein the internal resonance condition stabilizes frequency oscillations in the oscillator,
wherein the oscillator comprises a first mode and a second mode, wherein energy is transferred from the first mode to the second mode in the resonance condition, and wherein the transferred energy stabilizes the frequency oscillations in the oscillator.
2. The system of claim 1 , wherein the transferred energy stabilizes the amplitude oscillations in the oscillator.
3. The system of claim 1 , wherein the first mode comprises a first amplitude, wherein the second mode comprises a second amplitude, wherein the energy transferred to the second mode increases the second amplitude and decreases the first amplitude.
4. The system of claim 1 , wherein the resonance condition stabilizes amplitude oscillations in the oscillator.
5. The system of claim 1 , wherein the amplified voltage is proportional to an oscillation amplitude of the oscillator.
6. The system of claim 1 , wherein the oscillator is a nano-mechanical oscillator.
7. The system of claim 1 , wherein the oscillator is a micro-mechanical oscillator.
8. The system of claim 1 , wherein the oscillator is a clamped-clamped beam oscillator.
9. A method comprising:
amplifying a voltage, using an amplifier, from an oscillator;
phase shifting the amplified voltage;
setting an amplitude of the phase shifted voltage; and
driving the oscillator using the phase shifted voltage, wherein the phase shifted voltage drives the oscillator, wherein the oscillator is at an internal resonance condition based at least on the amplitude of the phase shifted voltage, and wherein the internal resonance condition stabilizes frequency oscillations in the oscillator,
wherein the oscillator comprises a first mode and a second mode, wherein energy is transferred from the first mode to the second mode in the resonance condition, and wherein the transferred energy stabilizes the frequency oscillations in the oscillator.
10. The method of claim 9 , wherein the transferred energy stabilizes the amplitude oscillations in the oscillator.
11. The method of claim 9 , wherein the first mode comprises a first amplitude, wherein the second mode comprises a second amplitude, wherein the energy transferred to the second mode increases the second amplitude and decreases the first amplitude.
12. The method of claim 9 , wherein the resonance condition stabilizes amplitude oscillations in the oscillator.
13. The method of claim 9 , wherein the amplified voltage is proportional to an oscillation amplitude of the oscillator.
14. The method of claim 9 , wherein the oscillator is a nano-mechanical oscillator.
15. The method of claim 9 , wherein the oscillator is a micro-mechanical oscillator.
16. The method of claim 9 , wherein the oscillator is a clamped-clamped oscillator.
17. A clamped-clamped oscillator comprising:
an amplifier operably connected to a phase shifter, wherein the amplifier is configured to amplify a voltage from the clamped-clamped oscillator;
the phase shifter operably connected to a driving amplitude control, wherein the phase shifter is configured to phase shift the amplified voltage;
the driving amplitude control configured to set an amplitude of the phase shifted voltage; and
the clamped-clamped oscillator operably connected to the driving amplitude control, wherein the phase shifted voltage drives the clamped-clamped oscillator, wherein the clamped-clamped oscillator is at an internal resonance condition based at least on the amplitude of the phase shifted voltage, wherein the clamped-clamped oscillator comprises a first mode and a second mode, wherein energy is transferred from the first mode to the second mode in the internal resonance condition, wherein the transferred energy stabilizes frequency oscillations in the clamped-clamped oscillator, and wherein the transferred energy stabilizes amplitude oscillations in the clamped-clamped oscillator.
18. The clamped-clamped oscillator of claim 9 , wherein the amplified voltage is proportional to an oscillation amplitude of the clamped-clamped oscillator.