Crystal And MEMS Oscillators (XTAL)

BerkeleyCrystal and MEMS Oscillators (XTAL)Prof. Ali M. NiknejadU.C. BerkeleyCopyright c 2014 by Ali M. NiknejadNiknejadAdvanced IC’s for Comm

Crystal ResonatorC0L1C1R1quartzL2C2R2tL3C3R3Quartz crystal is a piezoelectric material. An electric fieldcauses a mechanical displacement and vice versa. Thus it is aelectromechanical transducer.The equivalent circuit contains series LCR circuits thatrepresent resonant modes of the XTAL. The capacitor C0 is aphysical capacitor that results from the parallel platecapacitance due to the leads.NiknejadAdvanced IC’s for Comm

Fundamental Resonant ModeAcoustic waves through the crystal have phase velocityv 3 103 m/s. For a thickness t 1 mm, the delay timethrough the XTAL is given byτ t/v (10 3 m)/(3 103 m/s) 1/3 µs.This corresponds to a fundamental resonant frequencyf0 1/τ v /t 3 MHz 2π 1L C .1 1The quality factor is extremely high, with Q 3 106 (invacuum) and about Q 1 106 (air). This is much higherthan can be acheived with electrical circuit elements(inductors, capacitors, transmission lines, etc). This high Qfactor leads to good frequency stability (low phase noise).NiknejadAdvanced IC’s for Comm

MEMS ResonatorsThe highest frequency, though, is limited by the thickness ofthe material. For t 15 µm, the frequency is about 200 MHz.MEMS resonators have been demonstrated up to GHzfrequencies. MEMS resonators are an active research area.Integrated MEMS resonators are fabricated from polysiliconbeams (forks), disks, and other mechanical structures. Theseresonators are electrostatically induced structures.We’ll come back to MEMS resonators in the second part ofthe lectureNiknejadAdvanced IC’s for Comm

Example XTALSome typical numbers for afundamental mode resonator areC0 3 pF, L1 0.25 H, C1 40 fF,L1R1 50 Ω, and f0 1.6 MHz. Notethat the values of L1 and C1 areC0C1modeling parameters and not physicalR1inductance/capacitance. The value ofL is large in order to reflect the highquality factor.The quality factor is given byQ ωL11 50 103 R1ωR1 C1NiknejadAdvanced IC’s for Comm

XTAL ResonanceRecall that a series resonator has a phase shift from 90 to 90 as the impedance changes from capacitive to inductiveform. The phase shift occurs rapidly for high Q structures.It’s easy to show that the rate of change of phase is directlyrelated to the Q of the resonatorQ ωs dφ2 dωω0For high Q structures, the phase shift is thus almost a “step”function unless we really zoom in to see the details.NiknejadAdvanced IC’s for Comm

XTAL Phase Shift 90 45 L1 0 ω02Q 45 ω 90 C1R1ω0In fact, it’s easy to show that the 45 points are only adistance of ωs /(2Q) apart. ω1 ω0QFor Q 50 103 , this phase change requires an only 20 ppmchange in frequency.NiknejadAdvanced IC’s for Comm

Series and Parallel ModeC0L1C1C0R1L1low resistanceR1high resistanceDue to the external physical capacitor, there are two resonantmodes between a series branch and the capacitor. In theseries mode ωs , the LCR is a low impedance (“short”). Butbeyond this frequency, the LCR is an equivalent inductor thatresonates with the external capacitance to produce a parallelresonant circuit at frequency ωp ωs .NiknejadAdvanced IC’s for Comm

Crystal OscillatorLeffLeffIn practice, any oscillator topology can employ a crystal as aneffective inductor (between ωs and ωp ). The crystal can takeon any appropriate value of Leff to resonate with the externalcapacitance.Topoligies that minmize the tank loading are desirable inorder to minize the XTAL de-Qing. The Pierce resonator isvery popular for this reason.NiknejadAdvanced IC’s for Comm

Clock ApplicationCLKCLKNote that if the XTAL is removed from this circuit, theamplifier acts like a clock driver. This allows the flexbility ofemploying an external clock or providing an oscillator at thepins of the chip.NiknejadAdvanced IC’s for Comm

XTAL TempcoThe thickness has tempco t 14 ppm/ C leading to avariation in frequency with temperature. If we cut the XTALin certain orientations (“AT-cut”) so that the tempco ofvelocity cancels tempco of t, the overall tempco is minimizedand a frequency stability as good as f0 0.6 ppm/ C ispossible.Note that 1 sec/mo 0.4 ppm! Or this corresponds to only0.4 Hz in 1 MHz.This change in thickness for 0.4 ppm is onlyδt 0.4 10 6 t0 0.4 10 6 10 3 m 4 10 10 .That’s about 2 atoms!The smallest form factors available today’s AT-cut crystals are2 1.6 mm2 in the frequency range of 24-54 MHz areavailable.NiknejadAdvanced IC’s for Comm

OCXO ff15ppm 55 C25 C125 CThe typical temperaturevariation of the XTAL isshown. The variation isminimized at roomtemperature by design butcan be as large as 15 ppmat the extreme ranges.15ppmTo minimize the temperature variation, the XTAL can beplaced in an oven to form an Oven Compensated XTALOscillator, or OCXO. This requires about a cubic inch ofvolume but can result in extremely stable oscillator.OCXO 0.01 ppm/ C.NiknejadAdvanced IC’s for Comm

TCXOanalogor digitalIn many applications an oven is not practical. A TemperatureCompenstated XTAL Oscillator, or TCXO, uses externalcapacitors to “pull” or “push” the resonant frequency. Theexternal capacitors can be made with a varactor.This means that a control circuit must estimate the operatingtemperature, and then use a pre-programmed table togenerate the right voltage to compensate for the XTAL shift.This scheme can acheive as low as TCXO 0.05 ppm/ C.Many inexpensive parts use a DCXO, or adigitally-compensated crystal oscillator, to eliminate theTCXO. Often a simple calibration procedure is used to set theXTAL frequency to within the desired range and a simplelook-up table is used to adjust it.NiknejadAdvanced(PCXO)IC’s for Commis a combinedA Programmable CrystalOscillator

XTAL Below ωs11jXc jωCeffωC0C0 Cx ωs 1 jωLxjωCx 11 1 ω 2 Lx CxjωC0 jωCxBelow series resonance, the equivalent circuit for the XTAL isa capacitor is easily derived.The effective capacitance is given byCeff C0 1 NiknejadCx 2ωωsAdvanced IC’s for Comm

XTAL Inductive RegionL effωsωpPast series resonance, the XTAL reactance is inductive ω 2 1sjXc jωLeff jωLx 1 jωC0ωThe XTAL displays Leff from 0 H in the range fromωs ωp .Thus for any C , the XTAL will resonate somewhere in thisrange.NiknejadAdvanced IC’s for Comm

Inductive Region Frequency RangeWe can solve for the frequency range of (ωs , ωp ) using thefollowing equation 2 !ωs1 jωp Lx 1 jωp Leff jωp C0ωpωp ωs.r1 CxC0Example: Cx 0.04 pF and C0 4 pF Since C0 Cx , thefrequency range is very tightωp 1.005ωsNiknejadAdvanced IC’s for Comm

XTAL LossesLeffviroC2′RLRBC1!"# BiasXTAL LossConsider now the series losses in the XTAL. LetX1 1/(ωC1 ) and X2 1/(ωC2 ), and jXc jωLeff .Then the impedance ZL0 is given byZL0 jX1 (Rx jXc jX2 )Rx (jXc jX1 jX2 ) {z} 0 at resonanceNiknejadAdvanced IC’s for Comm

Reflected LossesIt follows therefore that jXc jX2 jX1 at resonance and soZL0 X1jX1 (Rx jX1 ) (X1 jRx )RxRxSince the Q is extremely high, it’s reasonable to assume thatXc Rx and thus X1 X2 Rx , and if these reactances areon the same order of magnitude, then X1 Rx . ThenZL0 X12RxThis is the XTAL loss reflected to the output of the oscillator.NiknejadAdvanced IC’s for Comm

Losses at OvertonesSince X1 gets smaller for higher ω, the shunt loss reflected tothe output from the overtones gets smaller (more loading).The loop gain is therefore lower at the overtones compared tothe fundamental in a Pierce oscillator.For a good design, we ensure that A 1 for all overtones sothat only the dominate mode oscillates.NiknejadAdvanced IC’s for Comm

XTAL Oscillator DesignThe design of a XTAL oscillator is very similar to a normaloscillator. Use the XTAL instead of an inductor and reflect alllosses to the output.A gm RLC1C2RL RL0 RB ro · · ·For the steady-state, simply use the fact that Gm RL CC21 1, orGm /gm 1/A .NiknejadAdvanced IC’s for Comm

XTAL Oscillator SimulationFor a second order system, the poles are placed on the circleof radius ω0 . Since the envelope of a small perturbation growslikev0 (t) Ke σ1 t cos ω0 twhere σ1 1/τ and τ Q 2ω0 A 1 . ωQ0 . ThatFor example if A 3, τmeans that if Q 106 ,about a million cycles of simulation are necessary for theamplitude of oscillation to grow by a factor of e 2.71!NiknejadAdvanced IC’s for Comm

PSS/HB versus TRANSince this can result in a very time consuming transient(TRAN) simulation in SPICE, you can artifically de-Q the tankto a value of Q 10 100. Use the same value of Rx butadjust the values of Cx and Lx to give the right ω0 but low Q.Alternatively, if PSS or harmonic balance (HB) are employed,the steady-state solution is found directly avoiding thestart-up transient.Transient assisted HB and other techniques are described inthe ADS documentation.NiknejadAdvanced IC’s for Comm

Series Resonance XTALNote that the LCRLT RTtank is a lowC1Q(3 20) tuned tothe approximateQ2Q1desired fundamentalRBfrequency of theXTAL (orovertone).The actual frequency selectivity comes from the XTAL, notthe LCR circuit. The LCR loaded Q at resonance is given bythe reflected losses at the tankC2RT0 RT n2 (Rx RB0 )NiknejadRB0 RB Ri DPAdvanced IC’s for Comm

Series XTAL Loop GainAt resonance, the loop gain is given byA Gm RT0RB0C1C1 C2 RB0 RxThe last term is the resistive divider at the base of Q1 formedby the XTAL and the biasing resistor.In general, the loop gain is given byRB0C1A Gm ZT (jω)C C2 RB0 Zx (jω) {z 1} {z}A ,1A ,2The first term A ,1 is not very frequency selective due to thelow Q tank. But A ,2 changes rapidly with frequency.NiknejadAdvanced IC’s for Comm

Series XTAL Fundametal ModeAlAl3-5Aℓ,11Aℓ,2Al 1ω03ω05ω0ω0FundMode3ω05ω0In this case the low Q tank selects the fundamental mode andthe loop gain at all overtones is less than unity.NiknejadAdvanced IC’s for Comm

Series XTAL Overtone ModeAlAlAℓ,23-5Aℓ,11Al 1ω03ω05ω0Al 1ω03ω0OvertoneMode5ω0In this case the low Q tank selects a 3ω0 overtone mode andthe loop gain at all other overtones is less than unity. Theloop gain at the fundamental is likewise less than unity.NiknejadAdvanced IC’s for Comm

Frequency SynthesisLO ( GHz)XTAL ( MHz)For communication systems we need precise frequencyreferences, stable over temperature and process, with lowphase noise. We also need to generate different frequencies“quickly” to tune to different channels.XTAL’s are excellent references but they are at lowerfrequencies (say below 200 MHz) and fixed in frequency. Howdo we synthesize an RF and variable version of the XTAL?NiknejadAdvanced IC’s for Comm

PLL Frequency SynthesisPhase/FrequencyDetectorUPPFDXTAL ReferenceDNLoopCP FilterLO NFrequencyDividerThis is a “phase locked loop” frequency synthesizer. Thestable XTAL is used as a reference. The output of a VCO isphase locked ot this stable reference by dividing the VCOfrequency to the same frequency as the reference.The phase detector detects the phase difference and generatesan error signal. The loop filter thus will force phase equality ifthe feedback loop is stable.NiknejadAdvanced IC’s for Comm

MEMS Resonators The highest frequency, though, is limited by the thickness of the material. For t ˇ15 m, the frequency is about 200MHz. MEMS resonators have been demonstrated up to GHz frequencies. MEMS resonators are an active research area. . Crystal and MEMS Oscillators (XTAL) .