电容式微加速度计开环模式的非线性模型

Nonlinear Model of Micro-Machined Capacitive Accelerometer Operating in Open-Loop Mode

针对当前电容式微加速度计量程不高、开环模式非线性误差大的特点,根据力学理论和电路读出原理,并基于非线性特性中最大可测量加速度、初始工作点和吸合点与动定电极间距d的变化规律,提出了电容式微加速度计非线性模型.模型指出,随着输出电压的增加,可测量加速度近似成线性增加,在靠近最大可测量加速度αmax时斜率增大,其后随输出电压的增加而减小至吸合点;αmax由d和微结构梁弹性常数与质量之比λ决定,且d的作用优于λ;d在小于初始工作点时加速度计不能工作,该点由传感头参数η决定,且η的最佳取值范围为1×1019～2×1019,此时准静态条件下吸合点大于整个动电极行程的95%.该模型的提出对开环式加速度计的非线性误差纠正提供了理论支持,对加速度计的结构设计具有参考价值.

To enhance the measurement range of capacitive micro-machined accelerometer and to cope with the complex nonlinear error of open-loop accelerometers, based on the mechanics theory and the interface circuit principle, the nonlinear model of micro-machined accelerometer operating in open loop mode is proposed. With the output increase, the measurand acceleration increases roughly linear with the output voltage until it approaches the maximum acceleration αmax, then, it decrease till the point where electrodes are pulled in. The αmax is decided by d and λ, which is the ratio between the spring constant and the mass of the microstructure, and d is better than λ as far as the contribution to the α max is concerned. The accelerometer can＇t work when d is less than a critical point which is determined by transducer＇s parameterη and the optimum of η is from 1 ×10^19 to 2×10^19, where the pull in point is beyond 95% of the full travel range of the moveable electrode. The model can be applied to the nonlinear error＇s correction of open loop capacitive accelerometer and is valuable for the accelerometer＇s design.