MEMS微波功率传感器拉格朗日模型的研究

Research on the Lagrange-model of MEMS microwave power sensor

为了改善热电式微机电系统（MEMS）微波功率传感器的综合性能,首先对负载电阻至热电堆的距离、热偶长度、热偶数目建立灵敏度、噪声系数和时间常数的理论解析模型。根据理论解析模型,分析得到了时间常数、噪声系数对于灵敏度的制约作用。然后基于拉格朗日乘数法建立了在特定噪声系数、时间常数限制下的灵敏度优化解析模型。最终,依据所建立的灵敏度优化模型,得到热电式MEMS微波功率传感器灵敏度最大时的负载电阻至热电堆的距离、热偶长度、热偶数目。实验表明：与传统结构的传感器相比,依据该结构参数设计的传感器的灵敏度特性有了较大改善。因此,所建立的基于拉格朗日乘数法的灵敏度优化解析模型对于研究热电式MEMS微波功率传感器具有一定的参考价值和指导意义。

In order to improve the comprehensive performance of the thermoelectric micro-electro-mechonical system（ MEMS） microwave power sensor,the theoretical analysis model of sensitivity,noise figure and time constant is established based on the distance between thermopile and load resistance,the length and number of thermopile. Firstly,according to the theoretical analysis model,the limits of time constant and noise figure on the sensitivity are obtained. Then,the sensitivity optimization analysis model is built under the restriction of specific noise figure and time constant based on the lagrange-multiplier method. Finally,using the established sensitivity optimization model,the length and number of thermocouple and the distance between the load resistance and thermopile are obtained corresponding to the maximum sensitivity of the thermocouple MEMS microwave power sensor. Experiments show that the sensitivity characteristics of the designed sensor based on the structural parameters is improved significantly,compared with the sensors with traditional structure. Therefore,the proposed analytical model of sensitivity optimization based on lagrange-multiplier method can provide certain reference and guide for the research of thermoelectric MEMS microwave power sensor.