Phononic comb enhanced MEMS gravity gradiometers

A method of sensing a change in an acceleration gradient δa(t) in two gravity fields a1(t) and a2(t) respectively sensed by first and second proof masses, the method comprising providing first and second resonators;

• said first and second proof masses either being coupled only to said first resonator or being individually coupled to said first and second resonators, the first resonator generating a drive signal at a frequency fD which is applied said second resonator, the second resonator being driven into a non-linear state corresponding to a modal resonant frequency fΘ thereof, the frequency fD of the drive signal being spaced from the modal resonant frequency fΘ, the second resonator producing a comb of frequencies the teeth of which are each separated from each other by a frequency Δ(t) which changes in time with changes in the acceleration gradient, wherein Δ(t) is frequency-wise proportional to said acceleration gradient δa(t), selecting an nth tooth in said comb of frequencies where the frequency of the nth tooth is equal to fD+nΔ(t), detecting a change in the frequency of the nth tooth in a PLL wherein a signal produced by the PLL is proportional to a change in nΔ(t) and hence also proportional to n times said acceleration gradient δa(t).

An apparatus for sensing a change in an acceleration gradient δa(t) between two gravity fields a1(t) and a2(t) respectively sensed by First and second proof masses, the apparatus including first and second resonators;

• said first and second proof masses either being coupled only to said First resonator or being individually coupled to said first and second resonators, the first resonator generating, in use, a signal at a frequency fD which is applied said second resonator, the second resonator being driven, in use, into a non-linear state corresponding to a modal resonant frequency fΘ wherein it generates a comb of frequencies each tooth of which is separated from each other by a frequency Δ which is frequency-wise proportional a frequency difference between fD and fΘ and also proportional to the change in said acceleration gradient δa(t), circuitry for selecting an nth tooth in said comb of frequencies where the frequency of the nth tooth is equal to fD+nΔ, circuitry for detecting a change in the frequency of the nth tooth and for generating a signal that is proportional to n times the change in an acceleration gradient δa(t).

A gravity gradiometer for detecting a gravity gradient, the gradiometer comprising at least two resonators and at least two proof masses, the at least two proof masses each being attached to one or both of said at least two resonators, a first one of said at least two resonators generating a drive signal at a frequency fD, a second one of said at least two resonators having a resonant mode at a frequency fΘ, and, in use, generating a comb of frequencies in response to the magnitude and frequency fD of the drive signal, the comb of frequencies having teeth separated by a frequency difference Δ, the frequency difference Δ being essentially equal to a frequency difference between fΘ and fD.