1、課程的基本目的 掌握MEMS設計的基本過程 掌握mems機電及其耦合分析的基本理論 掌握機電結構微器件的性能分析方法 了解熱、流體的基本理論 了解MEMS的發(fā)展前沿知識 培養(yǎng)對MEMS的興趣第1頁/共49頁課程內容MEMS概述及MEMS設計的概述工藝簡要回顧系統(tǒng)設計、工藝設計及版圖設計主要的機械、電子元件及其設計基礎多域耦合設計：以機電耦合為例子器件性能的估計簡單的其他域的元件及其簡要設計要點設計實例 第2頁/共49頁本章提綱 噪聲處理的基本知識和類型 器件的分辨率 系統(tǒng)的分辨率第3頁/共49頁Noise Noise: Random fluctuation of a given paramet

2、er I(t) In addition, a noise waveform has a zero average value 2Let ( )0,0Di tI tIi twhilei22201Then ilimTDDTIIIIdtT第4頁/共49頁Noise Spectral Density We can plot the spectral density of this mean-square value:第5頁/共49頁Circuit Noise Calculations Deterministic: Random:0ijHjj 2*0iiSHjHjSHjS 0iSHjS第6頁/共49頁H

3、andling Noise Deterministically Can do this for noise in a tiny bandwidth (e.g., 1 Hz) 21111nnSfSfBf第7頁/共49頁Systematic Noise calculation procedure21ni211z1Hnniif第8頁/共49頁Systematic Noise Calculation Procedure 11onniHj 22211onniHj222123,nnnivv222221234onTOTononononvvvvv22221234onTOTononononvvvvv第9頁/共4

4、9頁噪聲源 干擾噪聲（理論可消除：隔離和共地） 機械噪聲（thermal noise : brownian noise） 電噪聲 thermal noise ( johnson noise) shot noise (散粒噪聲） 1/f noise第10頁/共49頁Mechanical (Brownian) NoiseImpinging molecules give rise to a Brownian noise force:24nBfk Tb f1/damping coefficientbMQ22221141/Bnk Tb fxfffQf第11頁/共49頁Electronic Noise S

5、ources1.Thermal noise in resistorsgenerated by random motion of electrons or holes white spectral density (up to 10 THz)24nBvk TR f2/4nBvfk TR 22/4/ 4nrmsnvfnVHzvvmV第12頁/共49頁Thermal Noise (cont.)24/Bnk TifR 244Bnk TiBWAR第13頁/共49頁Resistor Noise in MEMS第14頁/共49頁Flicker (1/f) Noise2anKIiff第15頁/共49頁MOSF

6、ET Noise sourcesWhen 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 transistors have low

7、er 1/f noise22222 143gsDmBmmCKIik Tffgfg (neglecting DC gate current and its shot noise第16頁/共49頁MOSFET Noise source (cont.)Equivalent MOSFET small-signal model with input-referred noise sourcesCrossover frequency between thermal and flicker noise can range from 1 kHz to 1 MHz第17頁/共49頁第18頁/共49頁SNR an

8、d DR, DefinedSignal-to-noise ratio = SNRNote 1: Pnoise 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,max2,10log10log20logs

9、ssnoisen rmsnPvvDRPvv第19頁/共49頁Signal and Noise waveformsSinusoid with amplitude normalized to 1Gaussian noise with rms level normalized to 1; note that peak-peak noise level is occasionally as high as 6!第20頁/共49頁第21頁/共49頁本章提綱 噪聲處理的基本知識和類型 器件的分辨率 系統(tǒng)的分辨率第22頁/共49頁對簡單模型加速度計噪聲的估計Where 4/ m/ HznBZfk TRG f

10、k 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 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

11、 in the accelerometer limit. The signal-to-noise ratio (SNR) at any frequency is then /sssnsZfa G fG fZZa mQ0/4 (11)Bk T第23頁/共49頁 Vout-n=(Vs-n+Ve1-n)A1+Ve2-n*A2 Vout-n是電路最終輸出的噪聲； Vs-n是sensor-noise; Ve1-n, Ve2-n是一級放大器和二級放大器的電噪聲； A1和A2是一級和二級放大器的放大倍數(shù)。 按照等效噪聲的功率譜計算辦法，這些信號將成平方關系，這也解釋了為什么放大器一般采用二級放大，而且第一級

12、一般采用低噪聲低倍數(shù)放大的緣故。 上式還可以看出傳感器的靈敏度是可以放大的，但分辨率和信躁比是不可以放大的。第24頁/共49頁例子：Resolution=noise (equivalent output) / sensitivity, unit is the same as input, amplify will not be useful for the resolution, but for sensitivity. (X*A1+Ynoise-equitvalent)*A2+ Yele-equitvalent=Y, X is input, Y is output, A1 is sensit

13、ivity of sensor, A2 is electrical amplifier, Ynoise-equitvalent is noise equitavalent Y, Yele-equitvalent is electronic-noise equitavalent , the whole sensitivity of system is Y/X=A1*A2, resolution of the system is （A2*Ynoise-equitvalent+ Ynoise-equitvalent）/（Y/X）由于原子的熱運動，1/2KT的隨機能量噪聲在任意地方任何靜止時刻都是存在

14、的，可以用能量的觀點來進行靜態(tài)估計；由于電子的熱運動形成了電流，電流隨機存在，均值為零，動態(tài)隨機存在，功率隨溫度可變，從頻率域看來，其功率在頻率上保持4KT，只對電阻有效；類似的，對應于機械系統(tǒng)，4KT只對應阻尼有效；對于二階機械系統(tǒng)：4KT*df*c（此處，df是帶寬，c是阻尼，不是阻尼比什么的，即F=c*v）就是系統(tǒng)的擾動功率（即1/2m*v*v/t, 也可寫作F*v， 此處，F(xiàn)是擾動力，v是速度，其大小可以用F/c算出來），相當于二階電子系統(tǒng)的V*V/R，F(xiàn)相當于R。11233: A review to last lesson.: using piezoresistor as examp

15、le Capacitor sensor: same Stonebridge as used in piezoresistor, input a Vininput positive curve and a negative curve voltage (V+-V-): a example is given to caculate sensitivitynoiseresolution anasys (with consideration with amplify circuit)noise came from the distribute capacitance which influence c

16、apacitor much more than piezoresistor112334:capacitor sensor:a calculation to how f, and resolution of a accerameter are designed due to noise. (1kHz frequency requirement and noise existing are tranfered into a resolution of 0.1mg)distributed capacitor and amplifier circuit noise, and how to get ri

17、d of those noises第25頁/共49頁Example: Gyro MDS Calculation根據(jù)下圖，畫出壓阻加速度計的噪聲模型，途中的Cp需要改成R和Cp的并聯(lián)。計算方式可參考陀螺的計算過程。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

18、 amplifier circuit第26頁/共49頁B. The simple Pressure snesor In the simple pressure snesor, the moving mass is 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 resp

19、onse Z is / (12)ZFG fkIEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 40, NO. 5. MAY 1993Mechanical-Thermal Noise 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 f

20、orce , so the signal-to-noise ratio is 4BFk TR2220/4/4 (13)snsBsBZZp Sk TRQ p Sk T m第27頁/共49頁例子：壓力-電容的例子 以差壓（電壓）電源供電來檢查電容的變化，需要后接放大電路。放大電路的輸入電容Cp對被測電容的影響較大（ Cp通常比參考電容C0要大的多），而且傳感器的輸入電容還包括：引線電容（10pf/m). 解決問題的辦法包括：第一個放大器是1：1的放大器，放大器的輸出反饋到放大器輸入電容的一端(輸入電容的另一端接放大器的輸入），這樣輸入電容處于V=0的狀態(tài)。第28頁/共49頁本章提綱 噪聲處理的基本

21、知識和類型 器件的分辨率 系統(tǒng)的分辨率第29頁/共49頁IEEE SENSORS JOURNAL, VOL. 5, NO. 3. JUNE 2005Mechanical-Thermal Noise in MEMS Gyroscopes2 12 2xxdrivexxsenseMxR xK xMyuMyR yK yMxu （ ）（ ）第30頁/共49頁Vibratory GyroscopesGenerate momentum by vibrating structuresAgain, conservation of momentum leads to mechanisms for measurin

22、g rotation rate and orentationExample: vibrating mass in a rotating frame第31頁/共49頁Basic Vibratory Gyroscope OperationPrinciple of OperationDrive/Sense Reponse spectra:Tuning Fork Gyroscope2cav2ccccrFmaaxkk 第32頁/共49頁MEMS-Based Tuning Fork GyroscopeIn-plane drive and sense modes pick up z-axis rotatio

23、nsMode-matching for maxmum output sensitivityFrom Zaman, Ayazi, et al, MEMS06第33頁/共49頁MEMS-Based Tuning Fork Gyroscope第34頁/共49頁Drive Axis Equivalent CircuitGenerates drive displacement velocity xd to which the Coriolis force is proportionalTo Sense Amplifer(for synchronization)第35頁/共49頁Drive-to-Sens

24、e Transfer FunctionRotation- Induced Coriolis Force:22 Acts in the sense mode direction2sin90cdddocddaxxax 第36頁/共49頁Gyro Redout Equivalent Circuit (for a single tine)Gyro Sense Element Output CircuitGyro Sense Element Output CircuitEasiest to analyze if all noise source are summed at common node2ccd

25、Fmamx 第37頁/共49頁Gyro Redout Equivalent Circuit (for a single tine)2ccdFmamx Gyro Sense Element Output CircuitSignal Conditioning circuit (Transresistance Amplifier)Here, and are equivalent input-referred voltage and current noise source2eqv2eqi 第38頁/共49頁Example: Gyro MDS CalculationThe gyro sense pre

26、sents a large effective source impedanceCurrents are the important variable; voltages are “opened” outMust compare i0 with the total current noise ieqTOT going into the amplifier circuit2ccdFmamx 第39頁/共49頁Example: Gyro MDS Calculation (cont)First, find the rotation to i0 transfer function:2ssssdsddd

27、ssQQxjFxmjkk2dsddsxQxj第40頁/共49頁002 Ascale factor where 2desdedsddedsixQxjiAAQxjmin0eqTOTwhen MDS, i =i input-referred noise current entering the sense amplifier in A/ Hz minmin360180 /oeqTOTeqTOTiDSiAo hrHzAhr min1Angle Random Walk = ARW = /60 Easier to determine directional error as a function of e

28、lapsed timo hrHze第41頁/共49頁Example: Gyro MDS Calculation (cont)Now, find the ieqTOT entering the amplifier input:222222iaeqTOTseqeqTOTsfiafviiiiiiiR24rxxfkTvfBrownion motion noise of the sense element determined entirely by the noise in rx 2rxf第42頁/共49頁Example: Gyro MDS Calculation (cont)Where 2222222222222, , 1144 441Thus: yxxxexxeessRxdxdxxsdxeqTOTiaiadxfflrLCcRiivjkTRjRfRikTjfRiivkTkTjfRRffR第43頁/共49頁第44頁/共49頁Example ARW CalculationExample Design:第