EE C245 - ME C218 Introduction to MEMS Design Fall Today s Lecture

Transcription

1 EE 45 ME 8 ntroduction to MEMS Design Fall 003 Roger Howe and Thara Srinivasan Lecture 6 Micromechanical Resonators EE 45 ME 8 Fall 003 Lecture 6 Today s Lecture ircuit models for micromechanical resonators Microresonator oscillators: sustaining amplifiers, amplitude limiters, and noise Resonant inertial sensors: accelerometers and gyroscopes EE 45 ME 8 Fall 003 Lecture 6

2 Reading/Reference List. T.. Nguyen, h.d. Thesis, Dept. of EES, U Berkeley, 994. T. A. Roessig, R. T. Howe, A.. isano, and J. H. Smith, Surfacemicromachined resonant accelerometer, Transducers 97, hicago, ll., June 69, 997, pp A. A. Seshia, R. T. Howe, and S. Montague, An integrated microelectromechanical resonantoutput gyroscope, EEE MEMS 00, Las egas, Nevada, January 00. net lecture. T.. Nguyen, Transceiver frontend architectures using vibrating micromechanical signal processors, Topical Meeting on Silicon Monolithic ntegrated ircuits in RF Systems, Sept. 4, 00, pp. 33. J. Wang, Z. Ren, and. T.. Nguyen, Selfaligned.4 GHz vibrating radialmode disk resonator, Transducers 03, Boston, Mass., June 8, 003, pp B. Bircumshaw, et al, The radial bulk annular resonator: towards a 50Ω RF MEMS filter, Transducers 03, Boston, Mass., June 8, 003. M. U. Demirci, M. A. Abdelmoneum, and. T.. Nguyen, Mechanically cornercoupled square microresonator array for reduced series motional resistance, Transducers 03, Boston, Mass., June 8, 003, pp Kaaakari, et al, Squareetensional mode singlecrystal silicon micromechanical RFresonator, Transducers 03, Boston, Mass., June 8, 003, pp EE 45 ME 8 Fall 003 Lecture 6 3 ombdrive Lateral Resonator Anchor connects ground plane and resonator Typical bias: O 0 D voltage across drive and sense electrodes to resonator EE 45 ME 8 Fall 003 Lecture 6. T.. Nguyen, h.d. Thesis, EES Dept., U Berkeley, 994 4

3 The Lateral Resonator as a Twoort EE 45 ME 8 Fall 003 Lecture 6. T.. Nguyen, h.d. Thesis, EES Dept., U Berkeley, nput urrent nput current i t is the derivative of the charge q v D dv i t v dt d dt D D The capacitance has a D component and a timevarying component due to the motion of the structure t o m m t t linearized case t Substitute to find the input current: vd t v t v t dv dv i t o m v dt dt t t EE 45 ME 8 Fall 003 Lecture 6 i t 6 3

4 4 7 EE 45 ME 8 Fall 003 Lecture 6 nput Motional Admittance Y w hasor form of the motional current i : X Y The displacementtovoltage ratio can be reepressed in terms of the drive force F d The input motional admittance inverse of impedance is the ratio of the phasor motional current to the ac drive voltage: X F F X Y d d F F X Y d d 8 EE 45 ME 8 Fall 003 Lecture 6 nput Admittance ont. The electrostatic force component at the drive frequency is: t v t v t f D d, The mechanical response of the resonator is Lecture 9: F d o o d Q k F X / / The input admittance is: Q k o o / / o o Q k / /

5 Series LR Admittance The current through an LR branch is: L / o R o L R Match terms in motional admittance find equivalent elements EE 45 ME 8 Fall 003 Lecture 6 9 Equivalent ircuit for nput ort A series LR circuit results in the identical epression find equivalent values L,, and R m L η η k km R η Qη electromechanical coupling coefficient o L R At resonance, the impedances of the inductance and the capacitance cancel out R EE 45 ME 8 Fall 003 Lecture 6 0 5

6 6 EE 45 ME 8 Fall 003 Lecture 6 Output ort Model onsider first the current due to driving the input set v 0 t t t i n phasor form, / / Q k X o o and are related by the forward current gain φ : φ model by a currentcontrolled current source EE 45 ME 8 Fall 003 Lecture 6 Twoort Equivalent ircuit v 0 L R o φ 0

7 omplete Twoort Model L L o φ φ o R R Symmetry implies that modeling can be done from port, with port shorted superimpose the two models EE 45 ME 8 Fall 003 Lecture 6 3 Equivalent ircuit for Symmetrical Resonator f f. T.. Nguyen, h.d., U Berkeley, 994 EE 45 ME 8 Fall 003 Lecture 6 4 7

8 455 khz ombdrive Resonator alues L assumes vacuum not small huge! mindboggling! EE 45 ME 8 Fall 003 Lecture 6. T.. Nguyen, h.d., U Berkeley, DoubleEnded Tuning Fork Resonators i 0 urrent through structure more resistance decreases Q more feedthroughto substrate EE 45 ME 8 Fall 003 Lecture 6 T. Roessig, h.d.,me, U Berkeley,

9 deal Tuning Fork Twoort Response hase change of 80 o at resonance pins the frequency, with drifts in the feedback amplifier having little effect Response assumes no feedthroughcapacitance between input and output ports EE 45 ME 8 Fall 003 Lecture 6 T. Roessig, h.d.,me, U Berkeley, Tuning Fork Response with apacitive Feedthrough f Feedthroughcapacitance results in a null in the amplitude response and an added sense current which increases with frequency and which can obscure the resonance entirely! R int drive v d int f R eq L eq eq o o structure node EE 45 ME 8 Fall 003 Lecture 6 R int int i s Net lecture: f and its control sense T. Roessig, h.d.,me, U Berkeley,

10 Microresonator Oscillator EE 45 ME 8 Fall 003 Lecture 6. T.. Nguyen and R. T. Howe, EEE J. SolidState ircuits, 34, urrenttooltage or Transresistance Amplifier R f i in i 0 v out R f i in The feedback resistor can be implemented using a MOSFET biased in the triode region EE 45 ME 8 Fall 003 Lecture 6 0 0

11 Microresonator Oscillator Schematic Transresistance amplifier: M 3 implements a variable resistance R f M M implement a simple inverting amplifier M 6 M 7 implement a second amplifying stage EE 45 ME 8 Fall 003 Lecture 6. T.. Nguyen and R. T. Howe, EEE J. SolidState ircuits, 34, ntegrated 6.5 khz Microresonator Oscillator MOS with tungsten metallization olysi lateral resonator. T.. Nguyen and R. T. Howe, EEE J. SolidState ircuits, 34, EE 45 ME 8 Fall 003 Lecture 6 Erratic chaotic behavior observed for high D biases in this and other MEMS oscillators was later eplained by Kim Turner h.d. ornell, 999, now USB

12 ierce Oscillator Schematic crystal doubleended tuning fork Advantage over transr configuration: capacitive impedances determine loop gain lower noise, higher gain EE 45 ME 8 Fall 003 Lecture 6 A. A. Seshia, et al, MSM0, San Juan, uerto Rico 3 TuningFork Oscillator Neararrier Spectrum ierce Topology output power dbc/hz Measured rmsnoise thermal electronic noise A. A. Seshia, et al, EEE MEMS0. EE 45 ME 8 Fall 003 Lecture 6 frequency 0 5 Hz 4

13 Differential Resonant Accelerometer nertial force is coupled from a proof mass through a leverage system to two DETF oscillators in a pushpull manner tension compression EE 45 ME 8 Fall 003 Lecture 6 T. Roessig, h.d.,me, U Berkeley, Leverage Mechanism DETF oscillators are etremely stiff to forces along their length, which makes mechanical amplification feasible n the ideal case of a perfect pivot, Archimedes F out / F in r in / r out EE 45 ME 8 Fall 003 Lecture 6 T. Roessig, h.d.,me, U Berkeley,

14 Resonant Accelerometer erformance Fractional RA measures instability of an oscillator as a function of integration time. RA min at τ sec for 70 khz DETF oscillators f min Hz. Sensitivity 45 Hz/g a min 90 µg EE 45 ME 8 Fall 003 Lecture 6 T. Roessig, h.d.,me, U Berkeley, ResonantOutput Rate Gyroscope frame suspension outer frame direction of motion tuning fork oscillator proof mass oscillator lever arm tuning fork oscillator F c Ω z z fied free y drive fleure EE 45 ME 8 Fall 003 Lecture 6 sense direction A. A. Seshia, h.d. Thesis EES Dept., U Berkeley May

15 ResonantOutput Gyro: Mechanical Element reference resonator proof mass fleure tuning fork force sensor tuning fork force sensor proof mass error correction outer frame EE 45 ME 8 Fall 003 Lecture 6 selftest electrodes lever arm A. A. Seshia, et al, EEE MEMS0. 9 ResonantOutput Gyroscope Die Shot Tuning Fork Drive Electronics roof Mass Drive Electronics Mechanical Structure 4.5 mm EE 45 ME 8 Fall 003 Lecture 6 z y A. A. Seshia, et al, EEE MEMS0. Sandia MEMS MEMSfirst process 30 5

16 Oscillator output power dbm Sideband Modulation by oriolis Force DETF oscillator output oriolis offset Nominal peak Frequency 0 5 Hz oriolis offset EE 45 ME 8 Fall 003 Lecture 6 sideband output in presence of an applied deg/sec rotation rate at 6 Hz. Output sideband power dbµ Output sideband power dbµ Rotation rate signal Offset Frequency offset from carrier Hz A. A. Seshia, et al, EEE MEMS0. sideband output in the absence of rotation Frequency offset from carrier Hz 3 6