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1、 2Let ( )0,0Di tI tIi twhilei22201Then ilimTDDTIIIIdtT0ijHjj 2*0iiSHjHjSHjS 0iSHjS 21111nnSfSfBf21ni211z1Hnniif 11onniHj 22211onniHj222123,nnnivv222221234onTOTononononvvvvv22221234onTOTononononvvvvv24nBfk Tb f1/damping coefficientbMQ22221141/Bnk Tb fxfffQf24nBvk TR f2/4nBvfk TR 22/4/ 4nrmsnvfnVHzvvm
2、V24/Bnk TifR 244Bnk TiBWAR2anKIiffWhen biased in saturation, (VDSVDS,sat), the noise can be represented by an input noise voltage and an input noise current Origin of 1/f noise in MOSFETs: surface states22 143fmBmoxKfvk TfgWLCf channel resistance in saturationinverse dependence on gate area large tr
3、ansistors have lower 1/f noise22222 143gsDmBmmCKIik Tffgfg (neglecting DC gate current and its shot noiseEquivalent MOSFET small-signal model with input-referred noise sourcesCrossover frequency between thermal and flicker noise can range from 1 kHz to 1 MHzSignal-to-noise ratio = SNRNote 1: Pnoise
4、is calculated over a limited bandwidthNote 2: Vn,rms is taken as the minimum detectable signal, in the absence of special coding or signal processingDynamic range = DR222,10log10log20log20logssssnn rmsnnPvvvSNRPvvv2,max,max,max2,10log10log20logsssnoisen rmsnPvvDRPvvSinusoid with amplitude normalized
5、 to 1Gaussian noise with rms level normalized to 1; note that peak-peak noise level is occasionally as high as 6!Where 4/ m/ HznBZfk TRG fk 222200222000 1/1/ 6and 4/, In the accelerometer limit (), the noise displacement becomes 4/ (7) 4nBBnG fffffQfk mffZfk TR kkZf 300202s/4/ (8)The signal response
6、 is /G (9)but is the magnitude of the input acceleration, a(in meters per square second per roBsssTkQk TmQZffffYY 202ot hertz), so / (10)1 in the accelerometer limit. The signal-to-noise ratio (SNR) at any frequency is then /sssnsZfa G fG fZZa mQ0/4 (11)Bk T根据下图,画出压阻加速度计的噪声模型,途中的Cp需要改成R和Cp的并联。计算方式可参
7、考陀螺的计算过程。2ccdFmamx The gyro sense presents a large effective source impedanceCurrents are the imprtant variable; voltages are “opend” outMust compare i0 with the total current noise ieqTOT going into the amplifier circuitB. The simple Pressure snesor In the simple pressure snesor, the moving mass is
8、 directly exposed to the incident acoustic pressure and the displacement of this mass is measured. Such a sensor is shown schematically in Fig. 3. For an arbitrary force F, the displacement response Z is / (12)ZFG fkIEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 40, NO. 5. MAY 1993Mechanical-Thermal No
9、ise in Micromachined Acoustic and Vibration SensorsFor signal, the force F=psS, where S is the area of the transducer face and ps is the spectral density of the signal pressure; for noise, the force , so the signal-to-noise ratio is 4BFk TR2220/4/4 (13)snsBsBZZp Sk TRQ p Sk T mIEEE SENSORS JOURNAL,
10、VOL. 5, NO. 3. JUNE 2005Mechanical-Thermal Noise in MEMS Gyroscopes2 12 2xxdrivexxsenseMxR xK xMyuMyR yK yMxu ( )( )Generate momentum by vibrating structuresAgain, conservation of momentum leads to mechanisms for measuring rotation rate and orentationExample: vibrating mass in a rotating framePrinci
11、ple of OperationDrive/Sense Reponse spectra:Tuning Fork Gyroscope2cav2ccccrFmaaxkk In-plane drive and sense modes pick up z-axis rotationsMode-matching for maxmum output sensitivityFrom Zaman, Ayazi, et al, MEMS06Generates drive displacement velocity xd to which the Coriolis force is proportionalTo
12、Sense Amplifer(for synchronization)Rotation- Induced Coriolis Force:22 Acts in the sense mode direction2sin90cdddocddaxxax Gyro Sense Element Output CircuitGyro Sense Element Output CircuitEasiest to analyze if all noise source are summed at common node2ccdFmamx 2ccdFmamx Gyro Sense Element Output C
13、ircuitSignal Conditioning circuit (Transresistance Amplifier)Here, and are equivalent input-referred voltage and current noise source2eqv2eqi The gyro sense presents a large effective source impedanceCurrents are the important variable; voltages are “opened” outMust compare i0 with the total current
14、 noise ieqTOT going into the amplifier circuit2ccdFmamx First, find the rotation to i0 transfer function:2ssssdsdddssQQxjFxmjkk2dsddsxQxj002 Ascale factor where 2desdedsddedsixQxjiAAQxjmin0eqTOTwhen MDS, i =i input-referred noise current entering the sense amplifier in A/ Hz minmin360180 /oeqTOTeqTO
15、TiDSiAo hrHzAhr min1Angle Random Walk = ARW = /60 Easier to determine directional error as a function of elapsed timo hrHzeNow, find the ieqTOT entering the amplifier input:222222iaeqTOTseqeqTOTsfiafviiiiiiiR24rxxfkTvfBrownion motion noise of the sense element determined entirely by the noise in rx
16、2rxfWhere 2222222222222, , 1144 441Thus: yxxxexxeessRxdxdxxsdxeqTOTiaiadxfflrLCcRiivjkTRjRfRikTjfRiivkTkTjfRRffRExample Design: 120Get rotation rate to output current scale factor:10225020520000.0000242.83 1015dsdedskAQ xjkCk 82222228/1015/ 50310151.25 1031510503 0.0000241.25 103dssddsdssdjQjkkkjkjj
17、jkkjkkkQkkjk 0000022010020005 20001pphwCCCVxddx2222eqTOT2Then, get noise:i441 fffiaiadxffivkTkTjRRR102282154.6 10110.6508.85 10sxsekmRkQk22020222eqTOT21.66 101.66 10i120.0000240.01f110.611npkMM22eqTOT26213i1.68 10/1.30 10/ffeqTOTeqTOTiAHziAHz13min1236001801.30 1018036009448/2.83 10oeqTOToishrHzAhrmin11And finaly: ARW=9448157 / Almost turned 6060 around in 1 hour!ohrARW?ds 70If 15, th
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