，

（Micro-Electromechanical System Center，Harbin Institute of Technology，Harbin 150001，China）

A Low-Noise Readout Circuit for Gyroscopes

Guanshi Wang?，Xiaowei Liu and Changchun Dong

（Micro-Electromechanical System Center，Harbin Institute of Technology，Harbin 150001，China）

In order to suppress the noise of gyroscopes，the method based on lock-in amplifier and capacitor matching of the low-noise readout circuit is proposed.Firstly，the principle to suppress the noise by lock-in amplifier is analyzed，and the noise model of front end is proposed.Secondly，the noise optimization for the charge amplifier is presented according to the noise model of front end.Finally，a readout circuit is constructed by this approach.The measurement results show that the parasitic capacitance of front end is 18 pF，and the noise at resonant frequency（4 kHz）is 133 nV／Hz1／2，and the overall bias stability is 30°／h，and the noise level is 0.003°／（s·Hz1／2）.The noise of the gyroscope with the low-noise readout by this method is suppressed effectively.

low-noise；noise optimization；charge amplifier；gyroscope；readout

1 Introduction

For most bulk gyroscopes，the main parts of noise are owing to their readouts［1-2］.Hence，a readout circuit with low noise plays a key role in boosting gyroscopes’performance［3］.In this work，a low-noise readout circuit is proposed to realize high-precision capacitive sensing.

In this paper，the means to cancel the noise produced by lock-in amplifier are verified primarily，which provide the key details relating to the amplifier design［4］.Thereafter，the noise model of sensor and front end is built.Based on the noise optimization method introduced in this work，a readout circuit with reduced noise is designed and realized.Finally，the main measurement results of the gyroscope ASIC are acquired.

2 Proposed Circuits Based on Noise Optimization

The main function of readout circuit is to detect the gyro’s angular rate input and suppress noise as much as possible［5-6］.Generally，the displacement along the sensing direction is small，equaling to a low level of capacitance change，at magnitude of aF（10-18F）or even weaker［7］.Readout noise，therefore，has great influence on sensor’s overall performance［8］.A block diagram of readout circuit is presented in Fig.1.This readout circuit includes sensor，charge amplifier，band-pass filter（BPF），and phase sensitive demodulator（PSD）.Its output is an amplitude modulation wave modulated by driving signal，the magnitude of which is the input angular rate. Demodulated by demodulator，the signal is then filtered by the LPF following to generate the final outputΩout．

According to Coriolis theory，an angular rate at the normal direction of sensing and driving planes excites the mass to oscillate along the sensing direction［9］.The magnitude of this oscillation is an AM wave modulated by driving signal，and the magnitude of this AM signal is the input angular rate.The main function of readout circuit is to detect angular rate input and suppress noise as much as possible.Generally，the displacement along sensing direction is small，there by a low level of capacitor change，at magnitude of aF（10-18F）or even lower.Noise performance，therefore，plays a key role in sensor’s overall performance.

Fig.1 Block diagram of readout with lock-in amplifier for the detection mode

Fig.2 presents the noise characteristic of precharge amplifier primarily decides the overall noise characteristics of micro mechanic gyroscope circuit，and the noise source model of the pre-charge amplifier. The model analysis is given under the condition of the amplifier working at gyroscope resonance frequency. Thermal noise of resistance R1 has been analyzed in the capacitance detection circuit of the micro accelerator ASIC，and it turns out one efficient method of reducing the equivalent input noise is to increase the value of R1.The equivalent reference voltage of input noise can be weakened to negligible degree by connecting band-gap reference source with independent LPF.The two diodes are used for electrostatic protection of the ASIC joining PAD，and have leakage currents lower than voltage noise influence，the grounded parasitic capacitance of which is equal to CP. CSand CMin Fig.2 are respectively gate capacitances for the gyro and the transistor.

Fig.2 Equivalent noise schematic of pre-charge amplifier

The noise output of pre-charge amplifier is：

In fabrication of the designed circuit with high voltage CMOS process，the input transistors are PMOS［10］，and according to the two groups of parasitic capacitance and charge sensitive capacitor parameters given by Table 1，the optimized noise curves are derived in Figs.3 and 4.The charge amplifier with smallest channel length has the lowest output noise density.For other techniques，the large coupled capacitor makes noise optimization meaningless，and the input transistors are made as large as possible［11］. Since CMOS-MEMS have low coupled capacitor，it is of significance to match capacitor，thereby decreasing input noise by optimized size.The ASIC and micro mechanic gyroscope are integrated with double chips，joining PADs of which have large parasitic capacitance（10-20 pF），and the optimistic noise parameter of their transistors is 1 000 μm×2 μm.

Table 1 Charge amplifier noise optimization parameters

Fig.3 Relationship between charge amplifier noise power density and input transistor gate width（first group）

Noise introduced by front end amplifier determines the minimum effective magnitude of input.Assuming that the noise isN0，with a gain ofA0，and the minimum effective value isN0／A0．If the input is lower than this value，it will not be distinguished from noise，thereby a false output.According to the above analysis，it is necessary to boost amplifier’s gain as much as possible with a lowN0．Significant amplification of input signal contributes to decrease the impact of noise from following stages.

In order to design a front end amplifier with low noise，it is benefit to use a simple input stage［12］.Folded cascade is commonly utilized as it has high gain，large bandwidth，and simple compensation［13］.Despite of these advantages，it consumes large power and has poor noise performance，which makes it not suitable for this design. The proposed amplifier is shown in Fig.5.The input pairs M3，M4are PMOS with size ratio gained above to decrease noise.For current mirror load M5and M6，their transconductance needs to be decreased as low as possible to make 1／fnoise drop，i.e.increasing their length as much as possible.Meanwhile，the current mirror provides a single end output.M2is current source to supply a bias for the first stage.The second stage is loaded by a current source M8.Miller capacitor CCis applied to compensate the amplifier，moving a pole to a lower frequency to boost phase margin.M9，in triode region，works as a resistor together with CCto cancel the first non-dominant pole.The front end amplifier is simulated by HSPICE. Table 2 summarizes the simulation results of the front end amplifier.

3 Experimental Results

The IC for the designed readout is fabricated in a standard 0.5 μm CMOS process.Fig.6 shows the picture of the chip.Fig.7 shows the noise of front end. Theoretical values and test results of front end amplifier are listed in Table 3.The overall performance of the sensor is listed in Table 4.

Fig.5 The front end amplifier circuit

Table 2 The simulation results of front end amplifier

Fig.6 Picture of the chip

Fig.7 Noise power spectral density of the front end amplifier

Table 3 Theoretical values and test results of front end amplifier

Table 4 Overall performance

4 Conclusion

In this work，a low-noise readout circuit is proposed based on the noise optimization for the front end，and a charge amplifier is designed.The resource of ground noise is analyzed，and the approaches to suppress this noise are introduced.The parasitic capacitor is discussed and a low-parasitic circuit is designed.The test results show that the parasitic capacitance is 18 pF，and the noise of front end at 4 kHz is 133 nV／Hz1／2，and bias stability is 30（°）／h，and noise density is 0.003（°）／（s·Hz1／2）.

［1］Mrigank S，Elie H S，Edmond C.Parametric amplification／damping in mems gyroscopes.Cancun，Mexico：MEMS 2011，2011.617-620.

［2］Sun Hongzhi，Jia Kemiao，Liu Xuesong.A CMOS-MEMS gyroscope interface circuit design with high gain and low temperature dependence.IEEE Sensors Journal，2011，11（11）：2740-2747.

［3］Sonmezoglu S，Alper S E，Akin T.An automatically modematched mems gyroscope with 50 Hz bandwidth.Paris：MEMS 2012，2012.523-526.

［4］He Chunhua，Zhao Qiancheng，Cui Jian，et al.A research of the bandwidth of a mode-matching MEMS vibratory gyroscope.Tokyo：NEMS 2012，2012.738-741.

［5］Wu Huanming，Wu Qisong，Yang Haigang，et al.A TIA-based interface for MEMS capacitive gyroscope.Beijing： 2011 IEEE 9th International Conference，2011.149-152.

［6］Cui J，He C H，Yang Z C.Virtual rate-table method for characterization of microgyroscopes.IEEE Sensor，2012，12（5）：2192-2198.

［7］Kim S H，Lee J Y，Kim C H，et al.A bulk-micromachined single crystal silicon gyroscope operating at atmospheric pressure.Proc 13th IEEE Int Conf.Tokyo：Solid-State Sens，Actuators，Microsyst，2000.476-479.

［8］Lu Wengao，F(xiàn)ang Ran，Zhang Yacong，et al.A low-noise HV interface circuit for MEMS vibratory gyroscope. Beijing：Electron Devices and Solid-State Circuits（EDSSC），2011.1-2.

［9］Igor P P，Alexander A T，Andrei M S.Compensation of drifts in high-Q MEMS gyroscopes using temperatureselfsensing.Sensors and Actuators A：Physical，2013，201：517-524.

［10］Wang X，Wu W，F(xiàn)ang Z，et al.Temperature drift compensation for hemispherical resonator gyro based on natural frequency.Sensors，2012，12（5）：6434-6446.

［11］Zotov S A，Trusov A A，Shkel A M.High-range angular rate sensor based onmechanical frequency modulation. IEEE Journal of Microelectro Mechanical Systems，2012，21（2）：398-405.

［12］Trusov A A，Prikhodko I P，Zotov S A，et al.Lowdissipation silicon MEMS tuning fork gyroscopes for rate and whole angle measurements.IEEE Sensors Journal，2011，11（11）：2763-2770.

［13］Xia D，Yu C，Wang Y.A digitalized silicon microgyroscope based on embedded FPGA.Sensors，2012，12（5）：13150-13166.

［14］Geen J A，Sherman S J，Chang J F，et al.Single-chip surface micromachined integrated gyroscope with 50／h Allan devi-ation.Solid-State Circuits，2010，37（12）：1860-1866.

［15］Lasse A，Antti K，Mika P.A 2.2 mA 4.3 mm ASIC for a 1000／s 2-axis capacitive micro-gyroscope.Solid-State Circuits，2011，46（7）：182-1692.

［16］Raman J，Cretu E，Rombouts P，et al.A closed-loop digitally controlled MEMS gyroscope with unconstrained sigma-delta force-feedback.IEEE Sensors Journal，2009，9（3）：297-305.

TN492

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：1005-9113（2015）05-0042-04

10.11916／j.issn.1005-9113.2015.05.007

2014-04-30.

?Corresponding author.E-mail：50644768＠qq.com.