MEMS Real-Time Clocks: small footprint timekeeping. Paolo Frigerio November 15 th, 2018

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1 : small footprint timekeeping Paolo Frigerio November 15 th, 2018

Langfelder Master Thesis on a project about MEMS-based Real-Time

2 Who? 2 Paolo Frigerio paolo.frigerio@polimi.it BSc & MSc in Electronics Engineering PhD with Prof. Langfelder Master Thesis on a project about MEMS-based Real-Time Clocks Collaboration with STMicroelectronics. Focus on temperature compensation of frequency drift

3 Outline 3 Context The MEMS Resonator The Electronic Oscillator System-Level Compensation

Clocks VS Real-Time Clocks 4 A Real-Time Clock (RTC) is a

blocks. Frequency stability is less of a concern.

4 Clocks VS Real-Time Clocks 4 A Real-Time Clock (RTC) is a device that measures the flow of time. Similar to a computer clock, but different in scope CPU Clock Real-Time Clock A CPU Clock synchronizes digital blocks. Frequency stability is less of a concern. A RTC is basically a watch. Frequency stability is of the utmost importance in timekeeping.

5 Where? 5 Smartphones GPS Modules Any embedded systems

Legacy RTCs 6 To produce an accurate and stable frequency,

6 Legacy RTCs 6 To produce an accurate and stable frequency, a frequency selective element is required, that is a narrow-band filter. Historically the resonance of quartz crystals has been exploited. Good thermal stability; Good power handling; Shows little aging. Standard output frequency = Hz (2 15 Hz) Why should one want to replace quartz?

7 MEMS vs Quartz 7 Reduced fabrication costs. More resistant to: Aging; EM disturbances; Mechanical shocks. Smaller area occupation. System-in- Package XT AL Quartz C C MEMS IC MEMS ASIC package

8 Volume [mm 3 ] Why MEMS? 8 Miniaturization is a key requirement in some new fields: IoT Wearables Credit-card-sized applications Portable devices MEMS on the downside, MEMS require an electronic frequency compensation scheme Year

9 Key Requirements 9 Power consumption (< a few µw) Often employed in battery-operated systems. In operation even when the whole system is off. ±10 ppm Frequency Stability (< a few ppm) Temperature/process spread. Young modulus: TCE = 60 ppm/k. Frequency: TCf = 30 ppm/k.

10 Outline 10 Context The MEMS Resonator The Electronic Oscillator System-Level Compensation

11 Requirements 11 Resonance well above 32 khz but as small as possible! Compensation Consumption Large enough stiffness Good resistance to large mechanical shocks Motional resistance as small as possible

12 Scissor-Jack Structure 12 Ultra-small mass: the elastic beam itself is actuated at resonance. k tends to be quite large Large resonance frequency! Parameter Value Units k 3000 N/m m 0.24 nkg f khz ROTOR PP DRIVE PP SENSE

13 Motional Resistance 13 η R m = b η 2 = ω 0m Q η 2 Gaps as small as possible Parallel-Plate Actuation Large displacement not a priority, hence no comb fingers Low-pressure sealing ( 70 ubar) to increase the quality factor Reduced fluid damping There is another different Q-limiting phenomenon b

spring, hence energy dissipation Energy dissipation

14 TED: Thermo-Elastic Damping 14 Local compression/extension produce temperature gradients Compression heats up, extension cools down Temperature gradients produce heat flow across the spring, hence energy dissipation Energy dissipation Q reduction Slots along the rotor hinder heat flow, allowing an increase of Q!

15 Outline 15 Context The MEMS Resonator The Electronic Oscillator System-Level Compensation

16 From Resonators to Oscillators 16 IDEAL RESONATOR i t i t i t P diss P diss OSC i t Power exchanged between reactive elements. i t Oscillation is damped by power losses. i t P in Active circuit supplies power to compensate for losses t t t Stable oscillation!

17 Negative Resistance 17 R C m L m R m The oscillator circuit synthesizes a negative resistance. Ideal component that is able to provide power, instead of burning it. C m L m If R = R m then the series resistors cancel out, leaving an ideal LC-tank. Device losses are compensated.

18 Oscillation Condition 18 The MEMS and the circuit can be described by their corresponding impedances. The MEMS device will oscillate guaranteed that the oscillation condition is satisfied. Oscillation can be sustained if: Z m jω + Z c jω = 0 X m R m MEMS OSCILLATOR X c R c

19 Oscillation Condition 19 The condition can be re-written considering the real and imaginary parts: MEMS OSCILLATOR R Z m = R Z c R m = R c ω equivalent to Barkhausen s condition on the modulus X m X c R c I Z m = I Z c X m ω = X c ω equivalent to Barkhausen s condition on the phase This one provides the oscillation frequency R m

20 Oscillator Topology 20 Requirements: Low power: OTA-based oscillators (as the structure you know for gyros) require more than tens of μw; We want < 1 μa current, that is a few μw; Compact; Limited frequency pulling: Ideally no additional effects w.r.t. the drift caused by spread/temperature in the resonator. Pierce Oscillator

21 The Pierce Oscillator 21 Based on a single active component The equivalent impedance can be evaluated by simple network analysis C 2 Z C c Z c jω = 1 1 jω C 1C 2 C 1 + C 2 g m ω 2 C 1 C 2 C 1 C 2 Capacitance Negative Resistance

22 Equivalent Impedance 22 Z c jω = 1 g m jω C 1C 2 ω 2 C 1 C 2 C 1 + C 2 I BIAS The capacitance "pulls" the resonance frequency ω osc = 1 L m C m C 1 C 2 p = ω osc ω m ω m C m 2C 1 C 2 The negative resistance compensates power losses allowing stable oscillation C 1 g m C 2

23 Stable Oscillation 23 Applying the condition on the real part: g m ω 2 = R m osc C 1 C 2 we conclude that oscillation can be sustained for a very precise ("critical") transconductance value: I BIAS g m = G m,crit = C 1 C 2 ω 2 osc R m C 2 hence a very precise "critical" bias current: g m = I BIAS I nv crit = nv th C 1 C 2 ω 2 osc R m th C 1 g m

24 Oscillation Start-up 24 Actually, in order to guarantee oscillation growth from electronic noise some margin is required gm ω 2 > R m osc C 1 C 2 I BIAS I BIAS > I crit = nv th C 1 C 2 ω 2 osc R m C 2 What happens if the critical value is exceeded? How can we set the required bias current? C 1 g m

25 Amplitude Limitation 25 Purposely set a current larger than necessary and rely on non-linearity V gate t I BIAS I BIAS t f m f m I D (f) I D (f) 0 f 0 f 0 f 0 2f 0 3f 0 f

26 Current Limitation by AGC 26 Different approach: Automatic Gain Control provides a voltage controlled bias current. I BIAS V osc Large enough current to guarantee start-up. V osc AGC senses oscillation amplitude and gradually reduces bias current. C Current close to the critical value I crit at steady state.

27 Low-Power Operation 27 Non-linearity AGC Χ Large enough margin required to guarantee oscillation start-up (e.g. 6 db gain margin). Χ Small effective transconductance value with a large bias current. Large margin required only at start-up. Amplitude limitation mechanism allows operation at minimum current more efficient! Very simple and compact area. Χ Design an auxiliary circuit

28 AGC Schematic 28 Different from the AGC you studied in previous classes. No direct amplitude control mechanism. Current generator that provides large bias at startup. It controls the oscillation amplitude by regulating the oscillator bias point. by exploiting the nonlinearity of MOS transistors. I BIAS AGC

29 Outline 29 Context The MEMS Resonator The Electronic Oscillator System-Level Compensation

30 Why Compensate? 30 The device resonance frequency drifts with temperature. Δf f = TCf 1 ΔT + TCf 2 ΔT2 Typically the linear contribution is dominant, with a coefficient almost equal to 30 ppm/k. Frequency stability within ±1800 ppm.

31 Building a Frequency Stable Clock 31 The idea is to start from a much larger frequency than required (e.g. 500 khz) and reduce it to the standard 32 khz by frequency division. f osc T Hz Such operation needs to track temperature variations and adapt to them: as the frequency drifts, the division factor changes accordingly. f osc N T T = Hz

32 Frequency Division 32 Frequency division schemes are pretty straightforward if the modulus is an integer number. A simple flip-flop can be used as a divide-bytwo circuit. More generally, a digital counter can be used to implement any integer division factor. E ET How can we achieve any real division factor?

33 Fractional Division 33 V osc (t) A fractional division modulus is implemented "on average" by adopting more than one integer modulus. A digital logic determines the sequence of moduli according to temperature, which is monitored by a sensor in real-time (almost ). V osc V out T N(t) V out (t)

34 A Jittery Timing Reference 34 V osc (t) N(t) V out (t) The output waveform is made of cycles having two different durations, depending on the instantaneous division factor. E.g. if you divide 50% of the time by N, and the remaining 50% by N+1 you can implement a fractional modulus equal to the mean value N The resulting average frequency will be a function of how frequently you divide by one or the other modulus. The more frequently you divide by N, the closer the average frequency is to f osc N

35 A Jittery Timing Reference 35 This is not such a big deal If your clock is running 2 seconds fast, but stops for 2 seconds, then the accumulated error would be ideally zero. V osc (t) N(t) The same concept applies here: accumulation of (N)-cycles (shorter than ideal) is compensated by injection of a number of (N+1)-cycles (longer than ideal). Accumulated error is limited, although the error on a single period is huge! V out (t) V ideal out (t) The clock runs fast for a few cycles but a longer cycle allows to compensate the accumulated lead!

36 Frequency Stable Reference 36 ±1800 ppm COMPENSATION ±10 ppm SYSTEM

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

MEMS Clocks: the next big little thing? Giorgio Mussi giorgio.mussi@polimi.it November 14 th, 2017 About me 2 Giorgio Mussi BSc+MSc in Electronics Engineering PhD with Prof. Langfelder I m in my 2 nd year