Substrate-decoupled high-coriolis-coupling pitch/roll gyroscope

1. A pitch or roll gyroscope, comprising:

a resonator member; and

at least one anchor structure connected to a substrate and suspending the resonator member over a surface thereof such that the resonator member is decoupled from the substrate for an in-plane resonance mode thereof comprising movement parallel to the surface of the substrate and an out-of-plane resonance mode thereof comprising movement non-parallel to the surface of the substrate, wherein a Coriolis force on the resonator member in the in-plane resonance mode thereof coincides with deformation of the resonator member in the out-of-plane resonance mode thereof;

wherein the resonator member includes concentric frame members that are mechanically coupled together by rigid support structures extending therebetween; and

wherein opposing ends of each of the rigid support structures correspond to respective nodes of the resonator member that experience a minimum of modal displacement during the in-plane resonance mode.

2. The pitch or roll gyroscope of claim 1 , wherein the in-plane resonance mode and the out-of-plane resonance mode are two Coriolis-coupled resonance modes supported by the gyroscope at: (i) a high Coriolis-coupling coefficient in a range from greater than about two-thirds to 1, and (ii) with a sufficiently low support loss resulting from energy leakage to the substrate that Q support exceeds 6×10 6 , where Q support corresponds to a quality factor limit caused by the support loss.

3. The pitch or roll gyroscope of claim 1 , wherein an effective mass of the resonator member is distributed such that anti-nodal points of the resonator member for the out-of-plane resonance mode thereof coincide with anti-nodal points of the resonator member for the in-plane resonance mode thereof; and wherein the in-plane resonance mode and the out-of-plane resonance mode are two Coriolis-coupled resonance modes supported by the gyroscope at a high Coriolis-coupling coefficient in a range from greater than about two-thirds to 1.

4. The pitch or roll gyroscope of claim 3 , wherein the concentric frame members have annular or rectangular shapes that are mechanically coupled together by four of the rigid support structures, wherein the concentric frame members are balanced in momentum and angular momentum for the in-plane resonance mode and the out-of-plane resonance mode; and wherein the four rigid support structures comprise semiconductor beam structures.

5. The pitch or roll gyroscope of claim 1 , wherein the at least one anchor structure comprises:

outer anchors that are outside of a perimeter of the resonator member and are positioned at nodal points of the resonator member for the in-plane resonance mode thereof that coincide with nodal points of the resonator member for the out-of-plane resonance mode thereof; and

inner anchors connected by respective flexible tethers to an innermost one of the concentric frame members and to a corresponding portion of a comb-drive element associated with a sense electrode, which is located within a perimeter of the innermost one of the concentric frame members; and

wherein the outer anchors do not provide a balancing force on the resonator member for the in-plane resonance mode and the out-of-plane resonance mode.

6. A pitch or roll gyroscope, comprising:

a resonator member including concentric frame members that are mechanically coupled together by rigid support structures extending therebetween; and

at least one anchor structure connected to a substrate and suspending the resonator member over a surface thereof such that the resonator member is decoupled from the substrate for an in-plane resonance mode thereof comprising movement parallel to the surface of the substrate and an out-of-plane resonance mode thereof comprising movement non-parallel to the surface of the substrate, wherein a Coriolis force on the resonator member in the in-plane resonance mode thereof coincides with deformation of the resonator member in the out-of-plane resonance mode thereof;

wherein the at least one anchor structure includes a plurality of outer anchors that are connected to an outer one of the concentric frame members at nodes of the resonator member for the in-plane resonance mode where movement of the resonator member in the in-plane resonance mode is parallel to the surface of the substrate; and

wherein a plurality of regions within an inner one of the concentric frame members undergo deformation in opposite directions relative to a corresponding plurality of regions within the outer one of the concentric frame members, for both the in-plane resonance mode and the out-of-plane resonance mode.

7. The gyroscope of claim 6 , wherein the nodes of the resonator member for the in-plane resonance mode coincide with nodes of the resonator member for the out-of-plane resonance mode where movement of the resonator member in the out-of-plane resonance mode is non-parallel to the surface of the substrate.

8. The gyroscope of claim 6 , wherein the outer one of the concentric frame members is a rectangular frame; and wherein an inner one of the concentric frame members is an annular frame.

9. The gyroscope of claim 6 , wherein the at least one anchor structure includes a plurality of inner anchors that are connected to an innermost one of the concentric frame members at additional nodes of the resonator member for the out-of-plane resonance mode, where the additional nodes do not coincide with the nodes of the resonator member for the in-plane resonance mode.

10. The gyroscope of claim 9 , wherein the outer one of the concentric frame members is a rectangular frame; and wherein the innermost one of the concentric frame members is an annular frame.

11. The gyroscope of claim 6 , wherein the in-plane resonance mode and the out-of-plane resonance mode are two Coriolis-coupled resonance modes supported by the gyroscope at a high Coriolis-coupling coefficient in a range from greater than about two-thirds to 1.

12. The gyroscope of claim 6 , wherein the in-plane resonance mode and the out-of-plane resonance mode are two Coriolis-coupled resonance modes supported by the gyroscope at: (i) a high Coriolis-coupling coefficient in a range from greater than about two-thirds to 1, and (ii) with a sufficiently low support loss resulting from energy leakage to the substrate that Q support exceeds 6×10 6 , where Q support corresponds to a quality factor limit caused by the support loss.

13. The gyroscope of claim 6 , wherein the concentric frame members are mechanically coupled together by four rigid support structures; and wherein opposing ends of each of the four rigid support structures correspond to respective nodes of the resonator member that experience a minimum of modal displacement during the in-plane resonance mode.

14. The gyroscope of claim 6 , wherein opposing ends of each of the rigid support structures correspond to respective nodes of the resonator member that experience a minimum of modal displacement during the in-plane resonance mode.

15. A pitch or roll gyroscope, comprising:

a resonator member including concentric frame members that are mechanically coupled together by rigid support structures extending therebetween; and

at least one anchor structure connected to a substrate and suspending the resonator member over a surface thereof such that the resonator member is decoupled from the substrate for an in-plane resonance mode thereof comprising movement parallel to the surface of the substrate and an out-of-plane resonance mode thereof comprising movement non-parallel to the surface of the substrate, wherein a Coriolis force on the resonator member in the in-plane resonance mode thereof coincides with deformation of the resonator member in the out-of-plane resonance mode thereof;

wherein the at least one anchor structure includes a plurality of outer anchors that are connected to an outer one of the concentric frame members at nodes of the resonator member for the in-plane resonance mode where movement of the resonator member in the in-plane resonance mode is parallel to the surface of the substrate;

wherein the concentric frame members are mechanically coupled together by four rigid support structures; and

wherein opposing ends of each of the four rigid support structures correspond to respective nodes of the resonator member that experience a minimum of modal displacement during the in-plane resonance mode.