CONTOUR-MODE PIEZOELECTRIC MICROMECHANICAL RESONATORS
A contour mode micromechanical piezoelectric resonator. The resonator has a bottom electrode; a top electrode; and a piezoelectric layer disposed between the bottom electrode and the top electrode. The piezoelectric resonator has a planar surface with a cantilevered periphery, dimensioned to undergo in-plane lateral displacement at the periphery. The resonator also includes means for applying an alternating electric field across the thickness of the piezoelectric resonator. The electric field is configured to cause the resonator to have a contour mode in-plane lateral displacement that is substantially in the plane of the planar surface of the resonator, wherein the fundamental frequency for the displacement of the piezoelectric resonator is set in part lithographically by the planar dimension of the bottom electrode, the top electrode or the piezoelectric layer.
1 . (canceled)
2 . A band-pass filter circuit, comprising:
an input;
an output;
a series resonator coupled between the input and the output;
a shunt resonator coupled to the series resonator;
wherein the series resonator and shunt resonator are formed of contour mode micromechanical ring resonators; and
a resistor having a resistance value selected to be the geometric mean of a reactance of the series resonator and a reactance of the shunt resonator.
3 . The band-pass filter circuit of claim 2 , wherein the series resonator and shunt resonator in combination form an L network.
4 . The band-pass filter circuit of claim 3 , wherein the L network is a first network, and wherein the band-pass filter circuit comprises cascaded networks.
5 . The band-pass filter circuit of claim 2 , wherein a ratio of a parallel capacitance of the series resonator to a parallel capacitance of the shunt resonator is one.