Every component characteristic in the closed loop of resonant sensors is analyzed. Based on the component characteristics, the relation between the excitation force and the displacement of the resonator is confirmed. And the closed loop differential equation of resonant sensors is build. The phase drift of the closed loop control system is brought into the differential equation. By solving the differential equation with phase error of the closed loop control system, the relation between phase drift and the difference between the resonant frequency of the closed loop and the natural frequency of the resonator is gained. It is found that the measure error between the resonator natural frequency and the resonant frequency of the closed loop is proportional to tangent of the phase drift of the closed loop control system. The proportion coefficient is negative -3dB bandwidth of the resonator.
[1]
David Clarke,et al.
A self-validating digital Coriolis mass-flow meter: an overview
,
2000
.
[2]
J. Gardner,et al.
A Laterally Driven Micromachined Resonant Pressure Sensor
,
1995,
Proceedings of the International Solid-State Sensors and Actuators Conference - TRANSDUCERS '95.
[3]
M. Esashi.
Resonant sensors by silicon micromachining
,
1996,
Proceedings of 1996 IEEE International Frequency Control Symposium.
[4]
J. Greenwood,et al.
A high accuracy resonant pressure sensor by fusion bonding and trench etching
,
1999
.
[5]
Helmut Seidel,et al.
Resonant accelerometer with self-test
,
2001
.