EE C245 ME C218 Introduction to MEMS Design
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1 EE C45 ME C8 Introduction to MEMS Design Fall 007 Prof. Clark T.-C. Nguyen Dept. of Electrical Engineering & Computer Sciences University of California at Berkeley Berkeley, CA 9470 Lecture 5: Output t Sensing EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08
2 Lecture Outline Reading: Senturia, Chpt. 6, Chpt. 4 Lecture Topics: Input/Output Modeling I/O Equivalent Circuit Models Electromechanical Coupling Mechanical Coupling Detection Circuits Position Sensing Velocity Sensing EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08
3 F d Complete Electrical-Port Equiv. Circuit d d e Ele ectrode x b l x = m Static electrode- c = to-mass overlap k x k capacitance r x = b I I m E lectrod I C C I V I :η e l x c x r x η e : V x C o C - o - C o I η = = e VP V P x d V C C o ηe = VP = VP V P x d EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 3 C I V
4 Input Impedance Into Port I :η e l x c x r x η e : V x C o C - o - What is the impedance seen looking into port with port shorted to ground? I V EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 4
5 Input Impedance Into Port I :η e l x c x r x η e : V x C o C - o - What is the impedance seen looking into port with port shorted to ground? I V EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 5
6 Port to TransG Across the Circuit I :η e l x c x r x η e : V x C o C - o - What is the transconductance from port to port with port shorted to ground? I V EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 6
7 Port to v i -to-i o Transfer Function EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 7
8 Condensed Equiv. Circuit (Symmetrical) I I :η e l x c x r x η e : V x V Holds for the C o C o symmetrical case, - - I If η e = η e, then L x C x R x I where port and port are identical L x m = η where C x = k V V C o C b o - - R x = η EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 8 e ηe e
9 Phasings of Signals F d x b k Below: plots of resonance electrical and mechanical signals vs. time, showing the phasings between them d d Ele ectrode m e lectrod E I C C I I V V V P EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 9
10 Sensing Circuits EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 0
![MEMS 06] Drive Oscillation](/docs-images/87/96973523/images/11-6.jpg "Sustaining Amplifier")
11 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 5 C. Nguyen /5/08
12 Detecting Velocity Versus Position Velocity Transfer Function: υ F ( s) ωo s = d ( s ) k s ( ω o Q ) s ωo υ(s) (s) F d Bandpass Biquad Position (i.e., displacement) Transfer Function: X F X ( s ) F ( s) d ( s ) ω o = d ( s) k s ( o ω Q) s ω o Lowpass Biquad ω o ω Detect velocity when the output is at resonance or when a bandpass response is required ω o Detect position when the output is varying slowly, i.e., at low frequencies ω EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08
13 Detecting Velocity Versus Position Position (i.e., displacement) Velocity Transfer Function: Transfer Function: ) ( o s X ω Transfer Function ) ( ) ( ) ( o Q s k F s ω υ = ) ( ) ( ) ( o o o d s Q s k s F ω ω = ) ( ) ( o o d s Q s k s F ω ω EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 3
14 Output Current Measures Velocity I :η e l x c x r x η e : V x C o C - o - Relationship between output current and velocity: I V i =η o e x& Output current is proportional p to velocity, and thus, directly measures velocity To turn current into voltage (for a voltage output), send the current into a resistor R L To get position, must integrate send the current into a capacitor C L EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 4
15 Velocity-to-Voltage Conversion To convert velocity to a voltage, use a resistive load EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 5
16 Position-to-Voltage Conversion To sense position (i.e., displacement), use a capacitive load EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 6
17 Velocity Sensing Circuits EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 7
18 Problems With Purely Resistive Sensing x b F d k Ele ectrode d d m e lectrod E i o C p R D v o i C C v V P Includes C o, line C, bond pad C, and next stage C EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 8
19 Problems With Purely Resistive Sensing x b In general, the sensor output must be connected to the F d k inputs of further signal Ele ectrode d d m e lectrod E conditioning circuits input R i of these circuits can load R D i o C p i C C These change w/ hook-up not good. Now: v v R o D R i = Θ V ω D ( ( s) = ( s) R ) D Ri C, p P vi Rx s EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 9 R D v o R i ω D
20 F d 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 Ele ectrode d 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 v di drive virtually it anything v 0 V P EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 0
21 Position Sensing Circuits EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08
22 Problems With Pure-C Position Sensing x b k F d Ele ectrode d d m e lectrod E i o C p C D v o i C C v V P EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08
23 F d Ele ectrode The Op Amp Integrator Advantage x d d b k e C io - m lectrod E The virtual ground provided by the ideal op amp eliminates the parasitic capacitance C p R R >> sc (for biasing) C p 0 v i C C v V P EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 3
24 Differential Position Sensing EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 4
25 Differential Position Sensing Example: ADXL-50 Tethers with fixed ends Proof Mass Sense Finger C C Fixed Electrodes V P Suspension Beam in Tension C V o C -V P EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 5
26 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 EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 6
27 Integrator-Based Diff. Position Sensing V P R i o - C F R >> sc (for biasing) C v0 p -V P EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 7
28 Effect of Finite Op Amp Gain V P Total ADXL-50 Sense C ~ 00fF C p C gd - Unity Gain Buffer v 0 -V P EE C45: Introduction to MEMS Design Lecture 5 C. Nguyen /5/08 8
EE C245 ME C218 Introduction to MEMS Design Fall 2011
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