Time-switched frequency modulated accelerometer long-term stabilization

A system for improving long-term stability in a time-switched frequency modulated accelerometer, comprising:

• the time-switched frequency modulated accelerometer;
• and
• an electronic device, wherein the electronic device demodulates a frequency of the time-switched frequency modulated accelerometer, calculates a slope, and uses a linear model with an out-of-phase response to compensate for bias drift of an in-phase response of the time-switched frequency modulated accelerometer;
• wherein the time-switched frequency modulated accelerometer is a single-body multi-mode mechanical resonator including:
• two or more spring mass devices, wherein the two or more spring mass devices include two or more lumped masses and one or more anchor springs where the one or more anchor springs
• attach the two or more lumped masses to a fixed substrate and the two or more spring mass devices have an anti-phase mode and an in-phase mode;
• one or more coupling springs, wherein the one or more coupling springs are attached to each lumped mass and couple the motion of the two or more lumped masses;
• one or more phase 1 tuning electrodes and one or more phase 2 tuning electrodes, wherein the one or more phase 1 tuning electrodes and the one or more phase 2 tuning electrodes are attached to each lumped mass and apply forces to the in-phase mode that yield equal in magnitude, but opposite in sign frequency shifts of the anti-phase mode;
• a plurality of interdigitated shaped combs, wherein the plurality of interdigitated shaped combs is attached to each lumped mass and compensates for a frequency drift of the anti-phase mode and cancels first-order displacement effects of the plurality of interdigitated shaped combs;
• a plurality of interdigitated drive combs, wherein the plurality of interdigitated drive combs are attached to each lumped mass and are aligned to the anti-phase mode, with a frequency selective excitation, can excite the anti-phase mode with a low voltage when the multi-mode mechanical resonator is operated within a low-pressure environment;
• a plurality of interdigitated sense combs, wherein the plurality of interdigitated sense combs are attached to each lumped mass and are aligned to the anti-phase mode, are grounded when the multi-mode mechanical resonator is polarized, and are capable of cancelling common-mode noise effects.