Crystal Oscillators (XTAL) - University of California ...

1 EECS 142 Crystal Oscillators ( xtal )Prof. Ali M. NiknejadUniversity of California , BerkeleyCopyrightc 2009 by Ali M. NiknejadA. M. NiknejadUniversity of California , BerkeleyEECS 242 p. 1/28 p. 1/28 Crystal ResonatorC0L1C1R1R2R3L2C2L3C3tquartzQuar tz Crystal is a piezoelectric material. An electric fieldcauses a mechanical displacement and vice versa. Thus it is aelectromechanical equivalent circuit contains seriesLCRcircuits thatrepresent resonant modes of the xtal . The capacitorC0is aphysical capacitor that results from the parallel platecapacitance due to the M.

2 NiknejadUniversity of California , BerkeleyEECS 242 p. 2/28 p. 2/28 Fundamental Resonant ModeAcoustic waves through the Crystal have phase velocityv= 3 103m/s. For a thicknesst= 1mm, the delay time throughthe xtal is given by =t/v= (10 3m)/(3 103m/s) = 1/3 corresponds to a fundamental resonant frequencyf0= 1/ =v/t= 3 MHz =12 quality factor is extremely high, withQ 3 106(invacuum) and aboutQ= 1 106(air). This is much higher thancan be acheived with electrical circuit elements (inductors,capacitors, transmission lines, etc). This highQfactor leads togood frequency stability (low phase noise).

3 A. M. NiknejadUniversity of California , BerkeleyEECS 242 p. 3/28 p. 3/28 MEMS ResonatorsThe highest frequency, though, is limited by the thickness ofthematerial. Fort 15 m, the frequency is about200 MHz. MEMS resonators have been demonstrated up to resonators are an active research MEMS resonators are fabricated from polysiliconbeams (forks), disks, and other mechanical structures. Theseresonators are electrostatically induced ll come back to MEMS resonators in the second part of thelectureA. M. NiknejadUniversity of California , BerkeleyEECS 242 p.

4 4/28 p. 4/28 Example XTALC0L1C1R1 Some typical numbers for a fundamen-tal mode resonator areC0= 3pF,L1= ,C1= 40fF,R1= 50 , andf0= Note that the values ofL1andC1are modeling parameters and notphysical inductance/capacitance. Thevalue ofLis large in order to reflect thehigh quality quality factor is given byQ= L1R1= 50 103=1 R1C1A. M. NiknejadUniversity of California , BerkeleyEECS 242 p. 5/28 p. 5/28 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 s easy to show that the rate of change of phase is directlyrelated to theQof the resonatorQ= s2d d 0 For highQstructures, the phase shift is thus almost a step function unless we really zoom in to see the M.

5 NiknejadUniversity of California , BerkeleyEECS 242 p. 6/28 p. 6/28 xtal Phase Shift 0 02Q+90 +45 +0 45 90 L1C1R1In fact, it s easy to show that the 45 points are only a distanceof s/(2Q)apart. 0=1 QForQ= 50 103, this phase change requires an only20ppmchange in M. NiknejadUniversity of California , BerkeleyEECS 242 p. 7/28 p. 7/28 Series and Parallel ModeC0L1C1R1C0L1R1low resistancehigh resistanceDue to the external physical capacitor, there are two resonantmodes between a series branch and the capacitor. In the seriesmode s, theLCRis a low impedance ( short ).

6 But beyond thisfrequency, theLCRis an equivalent inductor that resonateswith the external capacitance to produce a parallel resonantcircuit at frequency p> M. NiknejadUniversity of California , BerkeleyEECS 242 p. 8/28 p. 8/28 Crystal OscillatorLeffLeffIn practice, any oscillator topology can employ a Crystal asaneffective inductor (between sand p). The Crystal can take onanyappropriate value ofLeffto resonate with the that minmize the tank loading are desirable in orderto minize the xtal de-Qing. The Pierce resonator is verypopular for this M. NiknejadUniversity of California , BerkeleyEECS 242 p.

7 9/28 p. 9/28 Clock ApplicationCLKCLKNote that if the xtal is removed from this circuit, the amplifieracts like a clock driver. This allows the flexbility of employing anexternal clock or providing an oscillator at the pins of the M. NiknejadUniversity of California , BerkeleyEECS 242 p. 10/28 p. 10/28 xtal TempcoThe thickness has tempcot 14ppm/ Cleading to a variationin frequency with temperature. If we cut the xtal in certainorientations ( AT-cut ) so that the tempco of velocity cancelstempco oft, the overall tempco is minimized and a frequencystability as good asf0 Cis that1sec/mo = !

8 Or this corresponds to change in thickness only t= 10 6 t0= 10 6 10 3m = 4 10 10. That sabout 2 atoms!The smallest form factors available today s AT-cut crystalsare2 mm2in the frequency range of 24-54 MHz are M. NiknejadUniversity of California , BerkeleyEECS 242 p. 11/28 p. 11/28 OCXO 55 C25 C125 C15ppm ff15ppmThe typical temperaturevariation of the xtal variation isminimized at room temper-ature by design but can beas large as15ppmat theextreme minimize the temperature variation, the xtal can be placedin an oven to form anOven Compensated xtal Oscillator, orOCXO.

9 This requires about a cubic inch of volume but canresult in extremely stable M. NiknejadUniversity of California , BerkeleyEECS 242 p. 12/28 p. 12/28 TCXO analogor digitalIn many applications an oven is not practical. ATemperatureCompenstated xtal Oscillator, or TCXO, uses externalcapacitors to pull or push the resonant frequency. Theexternal capacitors can be made with a means that a control circuit must estimate the operatingtemperature, and then use a pre-programmed table to generatethe right voltage to compensate for the xtal scheme can acheive as low asTCXO inexpensive parts use a DCXO, or adigitally-compensated Crystal oscillator, to eliminate the a simple calibration procedure is used to set the xtal frequency to within the desired range and a simple look-up tableis used to adjust Programmable Crystal Oscillator (PCXO) is a combined PLLA.

10 M. NiknejadUniversity of California , BerkeleyEECS 242 p. 13/28 p. 13/28 xtal Below sC0+Cx sjXc=1j Ceff=1 C0||(1j Cx+j Lx)=1j C0||1j Cx(1 2 LxCx)Below series resonance, the equivalent circuit for the XTALis acapacitor is easily effective capacitance is given byCeff=C0+Cx1 ( s)2A. M. NiknejadUniversity of California , BerkeleyEECS 242 p. 14/28 p. 14/28 xtal Inductive RegionLeff s pPast series resonance, the xtal reactance is inductivejXc=j Leff=1j C0||j Lx(1 ( s )2)The xtal displaysLefffrom0 Hin the range from s foranyC, the xtal will resonate somewhere in M.