Multi-tunable microelectromechanical system (MEMS) resonators

• US 7,095,295 B1
• Filed: 05/21/2003
• Issued: 08/22/2006
• Est. Priority Date: 05/21/2003
• Status: Expired due to Fees

• Current Assignee: National Technology & Engineering Solutions Of Sandia LLC (Honeywell International Inc.)
• Original Assignee: Sandia Corporation (Martin Marietta Corporation)
• Inventors: Schubert, W. Kent, Butler, Michael A., Stalford, Harold L.
• Primary Examiner(s): Tokar, Michael
• Assistant Examiner(s): Mai, Lam T.
• Application Number:
  US10/443,951
• Time in Patent Office: 1,189 Days
• Field of Search: 333/186, 333/193, 333/194, 333/187, 333/189
• US Class Current: 333/186
• CPC Class Codes: H03H 9/02409 by application of a DC-bias voltage H03H9/02417 takes precedence

Abstract

A method for tuning a vibratory device including a cantilevered resonator comprising the steps of increasing a voltage V₀ supplied to the vibratory device to thereby increase the bandwidth of the vibratory device; and keeping the resonant frequency of the vibratory device at substantially that natural frequency of the cantilevered resonator, wherein the vibratory device comprises: a capacitor including a movable plate and a fixed plate spaced from each other, the movable plate being part of the cantilevered resonator; a voltage source connected to the capacitor for providing voltage V₀ across the capacitor to produce an attractive force between movable plate and fixed plate; a circuit connecting the voltage source to the capacitor; and a load resistor in said circuit having a resistance R_L satisfying the following equation: $\mu =\frac{{\omega }_0{c}_0{R}_L}{\left(1-\lambda \right)}$
where: μ is at least 10; ω₀ is the beam constant for the cantilevered resonator; c₀ is the capacitance for the capacitor; and λ is the voltage dependent coupling parameter for voltage V₀.

Claims

1. A method for tuning a vibratory device including a cantilevered resonator comprising the steps of:

increasing a voltage V₀ supplied to said vibratory device to thereby increase the bandwidth of said vibratory device; and

keeping the resonant frequency of said vibratory device at substantially the natural frequency of said cantilevered resonator, wherein said vibratory device comprises;

a capacitor including a movable plate and a fixed plate spaced from each other, said movable plate being part of said cantilevered resonator;

a voltage source connected to said capacitor for providing said voltage V₀ across said capacitor to produce an attractive force between said movable plate and said fixed plate;

a circuit connecting said voltage source to said capacitor; and

a load resistor in said circuit having a resistance R_L satisfying the following equation;

$\mathrm{\mu <br><br>}=\frac{{\mathrm{\omega <br><br>}}_0<br><br>c_0<br><br>R_L}{\left(1-\mathrm{\lambda <br><br>}\right)}$

where

μ

is at least 10;

ω

₀ is the beam constant for said cantilevered resonator;

c₀ is the capacitance for said capacitor; and

λ

is the voltage dependent coupling parameter for said voltage V₀.

2. The method of claim 1, wherein the tuning of said vibratory device is actively tuned.

3. The method of claim 1, wherein said vibratory device is part of an array.

4. The method of claim 1, wherein said vibratory device is a MEMS resonator.

5. The method of claim 1, wherein said bandwidth and said resonant frequency are independently tuned.

6. The method of claim 5, wherein said resonant frequency is independently tuned up to match a chosen frequency.

7. The method of claim 5, wherein said resonant frequency is independently tuned down to match a chosen frequency.

8. The method of claim 1, further comprising the step of decreasing said voltage V₀ to thereby increase the bandwidth of said vibratory device.

9. A method for tuning a vibratory device including a cantilevered resonator comprising the steps of:

increasing a voltage V₀ supplied to said vibratory device to thereby increase the bandwidth of said vibratory device; and

simultaneously decreasing the resonant frequency of said vibratory device below the natural frequency of said cantilevered resonator, wherein said vibratory device comprises;

a capacitor including a movable plate and a fixed plate spaced from each other, said movable plate being part of said cantilevered resonator;

a voltage source connected to said capacitor for providing said voltage V₀ across said capacitor to produce an attractive force between said movable plate and said fixed plate;

a circuit connecting said voltage source to said capacitor; and

a load resistor in said circuit having a resistance R_L satisfying the following equation;

$\mathrm{\mu <br><br>}=\frac{{\mathrm{\omega <br><br>}}_0<br><br>c_0<br><br>R_L}{\left(1-\mathrm{\lambda <br><br>}\right)}$

where

μ

is no more than 0.1;

ω

₀ is the beam constant for said cantilevered resonator;

c₀ is the capacitance for said capacitor; and

λ

is the voltage dependent coupling parameter for said voltage V₀.

10. The method of claim 9, wherein the tuning of said vibratory device is actively tuned.

11. The method of claim 9, wherein said vibratory device is part of an array.

12. The method of claim 9, wherein said vibratory device is a MEMS resonator.

13. The method of claim 9, wherein said bandwidth and said resonant frequency are independently tuned.

14. The method of claim 13, wherein said resonant frequency is independently tuned up to match a chosen frequency.

15. The method of claim 13, wherein said resonant frequency is independently tuned down to match a chosen frequency.

16. The method of claim 9, further comprising the step of decreasing said voltage V₀ to thereby increase the bandwidth of said vibratory device.

17. A method for tuning a vibratory device including a cantilevered resonator comprising the steps of:

increasing a voltage V₀ supplied to said vibratory device to thereby increase the bandwidth of the vibratory device; and

varying the resonant frequency of said vibratory device by adjusting the self-inductance L of an inducer of said vibratory device, wherein said vibratory device comprises;

a capacitor including a movable plate and a fixed plate spaced from each other, said movable plate being part of said cantilevered resonator;

a voltage source connected to said capacitor for providing said voltage V₀ across said capacitor to produce an attractive force between said movable plate and said fixed plate;

a circuit connecting said voltage source to said capacitor, said circuit including said inducer; and

a load resistor in said circuit having a resistance R_L satisfying the following equation;

$\mathrm{\mu <br><br>}=\frac{{\mathrm{\omega <br><br>}}_0<br><br>c_0<br><br>R_L}{\left(1-\mathrm{\lambda <br><br>}\right)}$

where

μ

is no more than 0.1;

ω

₀ is the beam constant for said cantilevered resonator;

c₀ is the capacitance for said capacitor; and

λ

is the voltage dependent coupling parameter for said voltage V₀.

18. The method of claim 17, wherein said self-inductance L of said inducer satisfies the equation:

$\mathrm{\delta <br><br>}=\frac{{\mathrm{\omega <br><br>}}_0<br><br>c_0<br><br>\left(L<br><br>\text{\hspace{1em}<br><br>}<br><br>{\mathrm{\omega <br><br>}}_0\right)}{\left(1-\mathrm{\lambda <br><br>}\right)}-1$

wherein |δ

| is less than μ

.

19. The method of claim 17, wherein the tuning of said vibratory device is actively tuned.

20. The method of claim 17, wherein said vibratory device is part of an array.

21. The method of claim 17, wherein said vibratory device is a MEMS resonator.

22. The method of claim 17, wherein said bandwidth and said resonant frequency are independently tuned.

23. The method of claim 22, wherein said resonant frequency is independently tuned up to match a chosen frequency.

24. The method of claim 22, wherein said resonant frequency is independently tuned down to match a chosen frequency.

25. The method of claim 17, further comprising the step of decreasing said voltage V₀ to thereby increase the bandwidth of said vibratory device.