MEMS Clocks: the next big little thing? Giorgio Mussi November 14 th, 2017

Transcription

1 MEMS Clocks: the next big little thing? Giorgio Mussi November 14 th, 2017

2 About me 2 Giorgio Mussi BSc+MSc in Electronics Engineering PhD with Prof. Langfelder I m in my 2 nd year of PhD I work on a project in collaboration with ST Microelectronics about MEMS-based Real-Time Clocks The people I work with are both electronics engineers and mechanical/structural engineers I m an academic but the tight collaboration with the industrial partner gives a quite complete perspective on the state of MEMS & Electronics

3 Outline 3 Context MEMS Topology Electronic Oscillator System-Level Compensation

4 Real-Time Clock (RTC) 4 A real-time clock is a computer clock [ ] that keeps track of the current time. (Wikipedia) CPU Clock Real-Time Clock

5 Applications 5 Smartphones GPS Modules Any embedded systems

6 Legacy RTCs 6 To produce an accurate and stable frequency, you need a frequency selective element Historically, the resonance frequency of a quartz crystal has been used (and is still used!) Good thermal stability Good power handling Shows little aging Standard output frequency = Hz (2 15 Hz) Why does one want to replace quartz? Quartz is failing to fit the requirements in some new fields, mainly those where size matters

7 Why MEMS? 7 Miniaturization is of the utmost importance in some new fields: IoT Wearables Credit-card-sized applications Portable devices in general Volume [mm 3 ] MEMS Quartz Year

8 Miniaturization Footprint 8 A smaller footprint component means Customers can save PCB space Lower cost Easier design No need for external components cheaper bill of materials XT AL Quartz C C IC And so they buy the product! System-in- Package MEMS MEMS ASIC package

9 Key Requirements 9 Power consumption (< a few µw) Often employed in batteryoperated systems RTC often sets the off-consumption of the whole system Frequency Stability (within a few ppm) Main enemy is temperature Young modulus drifts at -60 ppm/k f 0 at -30 ppm/k Frequency Drift [ppm] ±10 ppm Temperature [ C]

10 Outline 10 Context MEMS Topology Electronic Oscillator System-Level Compensation

11 Requirements 11 f 0 much larger than 32 khz (we ll see why) f 0 as low as possible (consumption) Good rejection to external accelerations/vibrations R m as low as possible

12 Scissor-Jack Structure 12 ROTOR PP DRIVE PP SENSE

13 Resonance Frequency 13 The Scissor-Jack structure is suitable to implement a large resonance frequency The mass is the elastic beam itself (ultra-small mm) kk tends to be quite large easily obtainable large f 0 in a quite compact layout ( 400µm x 250µm) Parameter Value Units k 3000 N/m m 0.24 nkg f0 550 khz

14 R m minimization 14 b η Low-pressure sealing ( 70 ubar) to increase the quality factor Fluid damping is reduced Gaps as small as possible Parallel-Plate Actuation Unlike a gyro, large displacement (= comb finger) is not a priority Those are not the only tricks used in this regard! Fluid damping is no more the Q- limiting phenomenon If we want to enhance the Q, we have to act on another physical phenomenon RR mm = bb ηη 2 = ωω 0mm QQ ηη 2 Low Pressure here! Sry jj

15 TED: Thermo-Elastic Damping 15 When a beam is deformed, the material is locally both compressed and extended Compressed spots heat up, Expanded spots cool down A flow of heat takes place all across the beam Energy dissipation Energy dissipation Q reduction If we could hinder the heat flow, Q would benefit from this This is the purpose of the slots all along the rotor!

16 Outline 16 Context MEMS Topology Electronic Oscillator System-Level Compensation

17 Oscillator: basic concept 17 IDEAL RESONATOR LOSSY RESONATOR COMPENSATED LOSSY RESONATOR i(t) i(t) i(t) t t t i(t) LL mm i(t) V(0) CC mm LL mm V(0) CC mm RR mm OSC i(t)

18 Oscillator = Negative Resistor 18 i(t) t i(t) V(0) CC mm LL mm By comparison, the oscillator synthesizes a negative resistance A negative resistance is an ideal component that is able to generate power i(t) t OSC i(t) This component compensates the power dissipated by R m R m represents the frictions happening inside the mechanical device

19 Z m + Z osc = 0 Condition of Oscillation 19 More generally a MEMS (like any resonator) is able to oscillate if: Placed in parallel to an active circuit able to compensate its losses The frequency of oscillation is the one for which the following is satisfied: ZZ mm + ZZ oooooo = 0 RR mm + jjxx mm + RR oooooo + jjxx oooooo = 0 ZZ mm RR oooooo + jjxx oooooo Condition of Oscillation (equivalent to Barkhausen Criterion)

20 Oscillator for RTC: requirements 20 The oscillator should be low power Standard feedback oscillator for gyros burns > tens of µw, we want 2-3 µw The oscillator should not add more frequency drift than the resonator itself I would like to stick to the thermal drift of the f 0 due to the Young modulus drift These requirements are best met by one of the most famous and adopted oscillator topologies: The Pierce Oscillator

21 Pierce Oscillator: Schematic 21 Is the Pierce Oscillator equivalent to a negative resistor? Its equivalent impedance is: vv gg = ii TT /sscc 1 vv dd = vv gg gg mm + ii TT /sscc 2 vv TT = vv gg vv dd CC 1 CC 2 ZZ eeee ss = 1 gg mm ss CC + 1CC 2 ss 2 CC 1 CC 2 CC 1 + CC 2 ii TT vv TT ZZ eeee jjjj = 1 gg mm jjjj CC 1CC 2 ωω 2 CC 1 CC 2 CC 1 + CC 2 YES and NO CC 2 CC 1

22 Pierce Equivalent Impedance Z eq 22 ZZ eeee jjjj = Imaginary part: Equivalent to a capacitance 1 gg mm jjjj CC 1CC 2 ωω 2 CC 1 CC 2 CC 1 + CC 2 Real part: Equivalent to a resistor (negative and frequency dependent) LL mm RR mm CC mm MEMS gg mm ωω 2 CC 1 CC 2 CC 1 CC 2 CC 1 + CC 2 PIERCE Negative Resistance Ability to inject power into the resonator to compensate the losses that damp the oscillation Capacitance side-product of the chosen circuit topology ωω 0 = Considering also the feedthrough cap.: ZZ eeee = ZZ 1ZZ ffff +ZZ 2 ZZ ffff +gg mm ZZ 1 ZZ 2 ZZ ffff ZZ 1 +ZZ 2 +ZZ ffff +gg mm ZZ 1 ZZ 2 LL mm CC mm CC eeee CC mm +CC eeee 1

23 Consumption 23 From the Z eq formula, we can derive how much current we need to burn to compensate the losses: RR eeee = gg mm ωω 0 2 CC 1 CC 2 RR eeee = RR mm gg mm < II BBBBBBBB nnvv ttt II BBBBBBBB > RR mm ωω 0 2 CC 1 CC 2 nnvv ttt

24 Impedance Locus 24 Let s take a look at a useful tool to analyze this structure: the impedance locus Z eq is a complex number. It changes according to gm The circle represents the trajectory of Z eq (g m ) in the complex plane The frequency is fixed! So: Z eq = ZZ eeee gg mm, ωω = ωω 0,MMMMMMMM I{ZZ} gg mm = 0 R{ZZ} gg mm =

25 Oscillation Condition (1) On this plot we can represent the oscillation condition ZZ eeee = ZZ mm Z m is R+L+C Re(Z m ) is constant Im(Z m ) varies with ωω and spans all possible values E.g.: I ZZ mm = 0 ωω = ωω other ω, the distance from the origin (= Z m ) increases dramatically The oscillation condition tells us the only possible working point is the X. ZZ pppppppppppp gg mm RR mm ZZ mm ωω 25 I{ZZ} R{ZZ} gg mm = 0 gg mm =

26 Oscillation Condition (2) 26 The working point is fixed: what does this mean? ZZ pppppppppppp gg mm I{ZZ} gg mm = 0 R{ZZ} ωω = ωω gg mm = gg mm OK, the circuit pulls the f 0 of the MEMS This has a more complex meaning ZZ mm ωω gg mm =

27 Oscillation Condition (3) 27 Re(Z eq ) changes a lot according to gm This is the negative resistance that has to cancel Rm ZZ pppppppppppp gg mm I{ZZ} gg mm = 0 R{ZZ} g m too large R ZZ eeee > RR mm Losses are over-compensated Oscillation amplitude grows in time ZZ mm ωω g m too small R ZZ eeee < RR mm Losses are under-compensated Oscillation amplitude decays in time and dies Oscillation amplitude stable only if gg mm = gg mm gg mm =

28 Oscillation Condition (4) 28 ZZ eeee = ZZ mm GG llllllll jjωω oooooo = 1 gg mm = gg mm GG llllllll = 1 You have seen this as a comparator that, by clamping the signal, adapts its gain to meet the Barkhausen condition on the magnitude In our case, the transistor can as well clamp to reduce its gain (transconductance) in an analogous way

29 Who sets g m? 29 The linear gm you are familiar with depends on the bias current We have 2 options to set the g m : AGC: You build an AGC that: At the startup outputs a large bias current (fast startup of the oscillation) When target amplitude is reached, the current is such that gg mm = gg mm Non-Linearities: You bias the transistor with a large current (gg mm > gg mm ) When the amplitude of oscillation has grown enough, the non-linearity of the transistor will decrease the effective g m

30 AGC helps low-power? 30 Let s return to the main goal: building a (low-power) RTC Is an AGC the more low-power option? AGC Able to operates the oscillator at the minimal current required to reach gg mm = gg mm Adds its own consumption Non-Linearity Need to take margin in setting the bias current (non-minimal current) Very simple, no additional block required Answer: if you really need to spare some power (and we do), an AGC is worth the extra design effort!

31 Pierce + AGC Schematic 31 Notice that this AGC doesn t control the displacement amplitude. It controls the amplitude of the voltage oscillation at the drain node of the oscillator OSCILLATOR AGC If you are curious, you can ask me later how it works!

32 Outline 32 Context MEMS Topology Electronic Oscillator System-Level Compensation

33 Idea 33 Once the oscillator is built How can I compensate its frequency drift? The idea is to start from a high frequency ( 0.5 MHz) and divide it down to 32 khz 0.5 MHz drift with T I track the T-drift with the division factor! Hz = ff MMMMMMMM TT NN dddddddddddddddd TT

34 Frequency Division 34 Given: A high-frequency squarewave Some Silicon How can I get a lower-frequency ( khz if possible) squarewave? DD QQ QQ This is a simple divide-by-2 circuit But it s possible to implement any (integer) division factor!

35 Compensation Machine 35 Multiple frequency dividers The temperature acquisition chain + logic chooses which one to select VV oooooo NN dddddd VV oooooo NN, NN + 1 VV dddddd VV dddddd NN dddddd Temp. Acq. Logic

36 Average Frequency Compensation 36 The effect of this is a high-jitter clock E.g.: Imagine your watch that runs at twice the speed for 1 second, and then stops for 1 second The jitter would be < 1 s VV oooooo VV oooooo NN, NN + 1 NN dddddd VV dddddd But on average it compensates the frequency drift and is able to keep the time If your watch accumulated an error of 1 s at the end of the year, it would be a super-super-stable watch (0.03 ppm drift)! NN dddddd VV dddddd

37 Compensated Clock 37

38 END! 38 Thank you for your attention! Any question?