Multi-tunable microelectromechanical system (MEMS) resonators

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 RL satisfying the following equation:
• μ
• =
• ω
• 0
• ⁢
• c
• 0
• ⁢
• R
• L
• (
• 1
• -
• λ
• )
• where
• μ is no more than 0.1;
• ω0 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.

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 RL satisfying the following equation:
• μ
• =
• ω
• 0
• ⁢
• c
• 0
• ⁢
• R
• L
• (
• 1
• -
• λ
• )
• where
• μ is no more than 0.1;
• ω0 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.