EE C245 ME C218 Introduction to MEMS Design

Transcription

1 EE C45 ME C18 Introduction to MEMS Design Fall 008 Prof. Clark T.-C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 9470 Lecture 6: Output t Sensing & MDS EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 1

2 Lecture Outline Reading: Senturia, Chpt. 6, Chpt. 14, Chpt. 16 Lecture Topics: Detection Circuits Position Sensing Velocity Sensing Gyro Circuit Modeling Minimum Detectable Signal (MDS) Noise Angle Random Walk (ARW) EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08

3 MEMS-Based Tuning Fork Gyroscope Sense Electrodes Sense Ω r z Tuning Electrodes Drive Voltage Signal (-) Sense Output Current (+) Sense Output Current Tuning Electrodes Sense Electrodes Drive Electrode Drive [Zaman, Ayazi, et al, MEMS 06] Drive Oscillation Sustaining Amplifier Differential TransR Sense Amplifier EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 3

4 Drive Axis Equivalent Circuit 180 o 1:η e l x c x r x η e :1 i o C o1 x d C o Drive Voltage 180 o Signal i i Drive Oscillation Sustaining Amplifier Generates drive displacement velocity x d to which the Coriolis force is proportional To Sense Amplifier (for synchronization) EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 4

5 Drive-to-Sense Transfer Function x& d x & d = ω x d d Am mplitude Drive/Sense Response Spectra: Drive Response Sense Response f o (@ T Drive Mode Driven 1 ) Velocity Ω ω x& s x& s = ω x s Sense Velocity s Sense Mode EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 5

6 r F c Gyro Readout Equivalent Circuit (for a single tine) Noise Sources r r r = mac = m ( x & d Ω ) i f F c l x c x f r x r x η e :1 i o v x i 0 ia C p ia - + R f v Gyro Sense Element Signal Conditioning Circuit Output Circuit (Transresistance Amplifier) Easiest to analyze if all noise sources are summed at a common node EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 6

7 r F c = Example: Gyro MDS Calculation (cont) r ma c = l x c x r r m ( x & Ω) f r x r x d η e :1 i o v F x& i v 0 c s eq C p eq - + R f Noiseless First, find the rotation to i o transfer function: EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 7

8 Example: Gyro MDS Calculation (cont) EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 8

9 Scale Factor Stability EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 9

10 Gyro Project Design Procedure 1. Determine what approximate values of mass, stiffness, frequencies, etc., you will need to make the specs.. Choose a structure and technology, being mindful of scale factor stability and cost considerations. 3. Determine the dimensions, number of fingers, etc., needed for your structure to make the specs. Do this by hand analysis. 4. Draw up process cross-sections and write up the traveler. 5. Layout the structure. 6. Model the structure with equivalent circuits. 7. Simulate the equivalent circuits to verify performance. 8. Write your report. EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 10

11 Lecture Outline Reading: Senturia, Chpt. 6, Chpt. 14, Chpt. 16 Lecture Topics: Detection Circuits Position Sensing Velocity Sensing Gyro Circuit Modeling Minimum Detectable Signal (MDS) Noise Angle Random Walk (ARW) EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 11

12 Velocity-to-Voltage Conversion To convert velocity to a voltage, use a resistive load EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 1

13 Velocity-to-Voltage Conversion To convert velocity to a voltage, use a resistive load EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 13

14 Velocity-to-Voltage Conversion To convert velocity to a voltage, use a resistive load EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 14

15 Position-to-Voltage Conversion To sense position (i.e., displacement), use a capacitive load C D EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 15

16 Position-to-Voltage Conversion To sense position (i.e., displacement), use a capacitive load C D EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 16

17 Velocity Sensing Circuits EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 17

18 Velocity-to-Voltage Conversion To convert velocity to a voltage, use a resistive load EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 18

19 Problems With Purely Resistive Sensing x b F d1 k 1 Ele ectrode d 1 d m e lectrod E i o C p R D v o i C C 1 1 v 1 V P Includes C o, line C, bond pad C, and next stage C EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 19

20 Problems With Purely Resistive Sensing x b In general, the sensor output must be connected to the F d1 k inputs of further signal 1 Ele ectrode d 1 d m e lectrod E conditioning circuits input R i of these circuits can load R D i o C p i C C 1 1 These change w/ hook-up not good. R D v o R i v 1 V P Problem: need a sensing circuit that is immune to parasitics or loading. Soln: use op amps. EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 0

21 F d1 The TransR Amplifier Advantage x b k The virtual ground provided by the ideal op amp eliminates the parasitic capacitance C p and R i R 1 Ele ectrode d 1 d e i i - m C p + = 0ΩΩ lectrod R ERo o The zero output resistance of the (ideal) op amp can i C C 1 1 v 1 di drive virtually it anything v 0 V P EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 1

22 Position Sensing Circuits EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08

23 Problems With Pure-C Position Sensing To sense position (i.e., displacement), use a capacitive load C D EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 3

24 F d1 Ele ectrode The Op Amp Integrator Advantage x d 1 d b k e C 1io - m lectrod E The virtual ground provided by the ideal op amp eliminates the parasitic capacitance C p R 1 R >> sc (for biasing) C p 0 + v i C C 1 1 v 1 V P EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 4

25 Differential Position Sensing EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 5

26 Differential Position Sensing Example: ADXL-50 Tethers with fixed ends Proof Mass Sense Finger C 1 C Fixed Electrodes V P Suspension Beam in Tension C 1 V o C -V P EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 6

27 Buffer-Bootstrapped Position Sensing +V P Includes capacitance from interconnects, bond pads, and C gs of the op amp v 0 C p C gd + - Unity Gain Buffer v 0 v0 -V P C gd = gate-to-drain capacitance of the input MOS transistor Bootstrap the ground lines around the interconnect and bond pads No voltage across C p It s effectively not there! Interconnect Ground Plane 1 EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 7

28 Effect of Finite Op Amp Gain +V P Total ADXL-50 Sense C ~ 100fF C p + C gd - Unity Gain Buffer v 0 -V P EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 8

29 Integrator-Based Diff. Position Sensing +V P R i o - C F 1 R >> sc (for biasing) C v0 p + -V P EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 9

30 Determining Sensor Resolution EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 30

31 MEMS-Based Tuning Fork Gyroscope Sense Electrodes Sense Ω r z Tuning Electrodes Drive Voltage Signal (-) Sense Output Current (+) Sense Output Current Tuning Electrodes Sense Electrodes Drive Electrode Drive [Zaman, Ayazi, et al, MEMS 06] Drive Oscillation Sustaining Amplifier Differential TransR Sense Amplifier EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 31

32 Drive Axis Equivalent Circuit 180 o 1:η e l x c x r x η e :1 i o C o1 x d C o Drive Voltage 180 o Signal i i Drive Oscillation Sustaining Amplifier Generates drive displacement velocity x d to which the Coriolis force is proportional To Sense Amplifier (for synchronization) EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 3

33 Drive-to-Sense Transfer Function x& d x & d = ω x d d Am mplitude Drive/Sense Response Spectra: Drive Response Sense Response f o (@ T Drive Mode Driven 1 ) Velocity Ω ω x& s x& s = ω x s Sense Velocity s Sense Mode EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 33

34 r F c Gyro Readout Equivalent Circuit (for a single tine) Noise Sources r r r = mac = m ( x & d Ω ) i f F c l x c x f r x r x η e :1 i o v x i 0 ia C p ia - + R f v Gyro Sense Element Signal Conditioning Circuit Output Circuit (Transresistance Amplifier) Easiest to analyze if all noise sources are summed at a common node EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 34

35 Minimum Detectable Signal (MDS) Minimum Detectable Signal (MDS): Input signal level when the signal-to-noise ratio (SNR) is equal to unity Sensed Signal Sensor Scale Factor Circuit Gain Output t Sensor Noise Sensor Circuit Output Noise Signal Conditioning Circuit Includes desired output plus noise The sensor scale factor is governed by the sensor type The effect of noise is best determined via analysis of the equivalent circuit for the system EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 35

36 Move Noise Sources to a Common Point Move noise sources so that all sum at the input to the amplifier circuit (i.e., at the output of the sense element) Then, can compare the output of the sensed signal directly to the noise at this node to get the MDS Sensed Signal Sensor Scale Factor Circuit Gain Output Sensor Noise Sensor Circuit Input- Referred Noise Signal Conditioning Circuit Includes desired output plus noise EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 36

37 r F c Gyro Readout Equivalent Circuit (for a single tine) Noise Sources r r r = mac = m ( x & d Ω ) i f F c l x c x f r x r x η e :1 i o v x i 0 ia C p ia - + R f v Gyro Sense Element Signal Conditioning Circuit Output Circuit (Transresistance Amplifier) Easiest to analyze if all noise sources are summed at a common node EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 37

38 r F c Gyro Readout Equivalent Circuit (for a single tine) r r r = mac = m ( x & d Ω ) Noise Sources Noiseless l x c x f r r x r x η e :1 i o v F x i 0 c eq C p eq - + R f v Gyro Sense Element Output Circuit Signal Conditioning Circuit (Transresistance Amplifier) v eq i eq Here, and are equivalent input-referred voltage and current noise sources EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 38

39 Noise EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 39

40 Noise Noise: Random fluctuation of a given parameter I(t) In addition, a noise waveform has a zero average value Avg. value (e.g. could be DC current) I D I(t) t We can t handle noise at instantaneous times But we can handle some of the averaged effects of random fluctuations by giving noise a power spectral density representation Thus, represent noise by its mean-square value: Let i ( t ) = I ( t ) I D Then i 1 = ( I I ) = D lim I T T T 0 I D dt EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 40

41 Noise Spectral Density We can plot the spectral density of this mean-square value: i Δf [units /Hz] One-sided spectral density used in circuits measured by spectrum analyzers Two-sided spectral density (1/ the one-sided) d) Often used in systems courses i = integrated mean-square noise spectral density over all frequencies (area under the curve) EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 41

42 Inputs Circuit Noise Calculations Deterministic Outputs v i ( jω) ) ( jω) ) H ( jω) S i (ω ) S o o( (ω ) Deterministic: Random: Linear Time-Invariant System Random v π v o (t) ( jω) ω o v o t ω ( jω) H ( jω) v ( jω) o = i v o ω ο S o (t) S ( jω) ) t S o ω ο Mean square spectral density * Random: S ( ω ) = [ H ( j ω ) H ( j ω )] S ( ω ) = H ( j ω ) S ( ω ) o i S ( ω) = H ( jω) S ( ω) How is it we o Root mean square amplitudes i can do this? EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 4 i ω

43 Handling Noise Deterministically Can do this for noise in a tiny bandwidth (e.g., 1 Hz) S n v n n 1 = S1 ( f Δf ω ο B ( jω) ) ω Can approximate this v = S ( f ) B v n 1 S S o i 1 ( ω ο ω ω o ω [This is actually the principle by which oscillators work oscillators are just noise going through a tiny bandwidth filter] B by a sinusoidal voltage generator (especially for small B, say 1 Hz) v o τ ~ (t) 1 B A cosω t Why? Neither the amplitude nor the phase of a signal can change appreciably within a time period 1/B. EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 43 o t

44 Systematic Noise Calculation Procedure H ( jω) H5( jω) General Circuit With Wth Several Noise Sources v n i n1 v n3 i n5 i n4 v n6 v on H1( jω) Assume noise sources are uncorrelated 1. For i n1, replace w/ a deterministic source of value in1 n 1 = i Δff (1Hz) EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 44

45 Systematic Noise Calculation Procedure v 1( ω) i 1( ω) H ( jω). Calculate n (treating it like a deterministic signal) 3. Determine on = v on1 = in1 H ( jω) 4. Repeat for each noise source:,, i n1 1 v n n3. p f,,v n3 5. Add noise power (mean square values) v ontot = v on1 + v on + v on3 + v on4 +L v ontot = v on1 + von + von3 + von4 +L Total rms value EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 45

46 Determining Sensor Resolution EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 46

47 r F c = r ma c Example: Gyro MDS Calculation = l x c x r r m ( x & Ω) f r x r x d η e :1 i o v F x& i v 0 c s eq C p eq - + R f Noiseless The gyro sense presents a large effective source impedance Currents are the important variable; voltages are opened out Must compare i o with the total current noise i eqtot going into the amplifier circuit EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 47

48 r F c = Example: Gyro MDS Calculation (cont) r ma c = l x c x r r m ( x & Ω) f r x r x d η e :1 i o v F x& i v 0 c s eq C p eq - + R f Noiseless First, find the rotation to i o transfer function: EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 48

49 Example: Gyro MDS Calculation (cont) EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 49

50 r F c = Example: Gyro MDS Calculation (cont) r ma c = l x c x r r m ( x & Ω) f r x r x d η e :1 i o v F x& i v 0 c s eq C p eq - + R f Noiseless Now, find the i eqtot entering the amplifier input: EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 50

51 Example: Gyro MDS Calculation (cont) EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 51

52 LF356 Op Amp Data Sheet EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 5

53 Example ARW Calculation Example Design: Sensor Element: m = (100μm)(100μm)(0μm)(300kg/m )(0 )(300k 3 ) = 4.6x10-10 kg ω s = π(15khz) ω d = π(10khz) k s = ω s m = 4.09 N/m Sense Sense x d = 0 μm Electrodes 000 r Q s = 50,000 Ω z V P = 5V h = 0 μm d = 1 μm Sensing Circuitry: R f = 100kΩ i ia = 0.01 pa/ Hz v ia = 1 nv/ Hz Tuning Electrodes Sense Electrodes Tuning Electrodes Drive Electrode EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 53 Drive

54 Example ARW Calculation (cont) EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 54

55 Example ARW Calculation (cont) EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 55

56 What if ω d = ω s? EE C45: Introduction to MEMS Design Lecture 6 C. Nguyen 1//08 56