QU Hao，PENG Bei，ZENG Jian，ZHOU Wu，YU Huijun

（Department of Mechatronics Engineering，University of Electronic Science and Technology of China，Chengdu 611731，China）

Analysis of the Effect of the Equivalent Parallel Resistor of theComb Capacitive Accelerometer*

QU Hao，PENG Bei*，ZENG Jian，ZHOU Wu，YU Huijun

（Department of Mechatronics Engineering，University of Electronic Science and Technology of China，Chengdu 611731，China）

Measurement of the sensing capacitance among the structure of the comb accelerometer could be affected by the equivalent electrical parameters besides the sensing capacitance.Equivalent electrical parameters of Multilayer Ceramic Capacitance（MLCC）have been studied，since the structure of the comb accelerometer is similar to Multilayer Ceramic Capacitance（MLCC），the equivalent electrical parameters of the comb accelerometer could be analyzed in the same way.This paper will introduce the model of the sensing capacitance with equivalent electrical parameters and analyzes the effect of these parameters on the measurement result.

MEMS；comb capacitive accelerometer；pspice circuit simulation；charge amplify circuit；equivalent parallel resistor

EEACC：7320E；7230doi：10.3969/j.issn.1004-1699.2016.10.003

MEMS capacitive sensor is widely used in navigation，measurement and other fields.Comb capacitive accelerometer is one typical MEMS capacitive sensor that transforms acceleration into capacitance and generates voltage signal［1］.Measurement of sensing capacitance is an essential procedure for the capacitive accelerometer.Measurement result could be affected by the ambient temperature or the circuit parameters.The effect of temperature is discussed in［2-3］.In this paper，the effect of the equivalent parallel resistor of the comb capacitive accelerometer will be discussed.Charge amplify circuit is widely used for its simple construction，high resolution and low power consumption［4-8］.Basic schematic of the charge amplify circuit is shown in Fig.1.Cxis the unknown capacitance，Cfis the feed back capacitance.S1，S2and S3are switches and φ1，φ2are control signals［9］.If there are other electrical parameters besides sensing capacitances connected to the input of the charge amplify circuit，measurement results might be affected.The sensing structure is similar to the Multilayer Ceramic Capacitance（MLCC），with the gaps between the electrodes are filled with dielectrics.Since the equivalent electrical parameters is commonly used in the model of MLCC，sensing structure of the accelerometer can be modeled as sensing capacitance with equivalent electrical parameters.The measurement result of the detecting system is determined by all electrical parameters of the sensing structure.This paper willintroduce the model of the sensing capacitance with equivalent electrical parameters and analyzes the effect of these parameters on the measurement result.

Fig.1　Basic schematic of the charge amplify circuit

1　Model of the Multilayer Ceramic Capacitance

The structure of Multilayer Ceramic Capacitance（MLCC）is shown in Fig.2.In the structure，Sn，Ni and Cu are the connect termination that connected to the circuit.The dielectric is ceramic and the electrodes are Pb［10-11］.These parallel capacitances consist the total value of the ceramic capacitance.The equivalent circuit model of the MLCC is shown in Fig.3.

Fig.2　Circuit model of MLCC

Fig.3　Structure of MLCC

Resis the equivalent series resistor，Lesis the equivalent series conductance，and Rdis the parallel resistror.The equivalent series resistor comes from the resistor of the electrode conductor material and is very small.Rdis result from the leakage current between different electrodes through the ceramic.Thus，Rdis very large.The total impedance of the capacitance is

According to Jeffrey Cain［12］，ceramic capacitance has a Self-Resonant Frequency.When the circuit frequency equals to this frequency，Lesωs=1/（Cωs），the total impedance is Res.The ceramic capacitance degrades to a resistor.

The gaps between the electrodes of the accelerometer are filled with Nitrogen，besides sensing capacitance，Res，Lesand Rdmay also exist.However，the conductivity of the doped silicon is similar to conductor，and the Self-Resonant Frequency is larger than 1MHz，which is much higer than the circuit frequency of the charge amplify circuit，thus，Resand Lescan be ignored，only the parallel resistor should be considered.

2　The Sensing Structure Model with Parallel Resistors and Simulation Results

Sensing structure of the accelerometer is shown in Fig.4，and the equivalent circuit with parallel resistors is shown in Fig.5.

Fig.4　Sensing structure

Fig.5　Equivalent circuit

Without the parallel resistors，output voltage is derived as：

When the parallel resistors are taken into consid-eration，the input impedance will change，denote the impedances XⅠ=1/（1/Rp1+jωCx1）=Rp1/（1+jωRp1Cx1），XⅡ= 1/（1/Rp2+jωCx2）=Rp2/（1+jωRp2Cx2），and let XⅢ=Rf/（1+ jωRfCf），we can derive the output voltage as：

From equation（3），we can see that if the parallel resistor Rp1and Rp2are very large，the second parts of equation（3）is near to zero，the effect of the parallel resistors can be ignored.The simulation is carried out with Pspice.Output voltages without and with parallel resistors are shown in Fig.6 and Fig.7.

Fig.6　Output without parallel resistors

Fig.7　Output with parallel resistors

The simulation results show that stable outputs with and without parallel resistors are very close.

3　Conclusion

When the equivalent parallel resistor is introduced to the model of sensing capacitance，a new transform function of the detecting system is developed.From the new transform function of the detecting system，we can see that，if the equivalent parallel resistor is rather large，the measurement result will not be affected.

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曲昊（1988-），男，博士研究生，2011年獲得電子科技大學(xué)學(xué)士學(xué)位，2011年起攻讀電子科技大學(xué)碩士學(xué)位，2013年起攻讀電子科技大學(xué)博士學(xué)位，主要從事MEMS慣性器件檢測(cè)電路設(shè)計(jì)，微小電容檢測(cè)電路設(shè)計(jì)與測(cè)試方面的研究，708382@163.com；

彭倍（1977-）男，教授，博士生導(dǎo)師，1999年獲得北京航空航天大學(xué)學(xué)士學(xué)位，2008年獲得美國(guó)西北大學(xué)博士學(xué)位，主要從事薄膜特性，MEMS/NEMS材料特性等方面的研究，beipeng@uestc.edu.cn。

梳齒式電容加速度傳感器等效并聯(lián)電阻對(duì)器件輸出產(chǎn)生的影響*

曲昊，彭倍*，曾建，周吳，于慧君

（電子科技大學(xué)機(jī)械電子工程學(xué)院，成都611731）

梳齒式電容加速度傳感器檢測(cè)電容的測(cè)量結(jié)果會(huì)受到除感應(yīng)電容之外的其他等效電路參數(shù)的影響。梳齒式電容加速度傳感器的結(jié)構(gòu)與多層瓷片電容（MLCC）的結(jié)構(gòu)類似，因此可以借鑒多層瓷片電容中等效電路參數(shù)的研究方法對(duì)電容加速度傳感器中的等效電路參數(shù)進(jìn)行研究。本文將對(duì)梳齒式電容加速度傳感器檢測(cè)結(jié)構(gòu)中的等效電路參數(shù)進(jìn)行建模，并分析這些等效電路參數(shù)對(duì)測(cè)試結(jié)果產(chǎn)生的影響。

MEMS；梳齒式電容加速度傳感器；Pspice電路仿真；電荷放大電路；等效并聯(lián)電阻

TH824.4

A

1004-1699（2016）10-1483-03

2016-04-28修改日期：2016-06-08

項(xiàng)目來(lái)源：This work was supported in part by NSAF（U1530132）；National Natural Science Foundation of China（51505068，51575090）