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TECHNOLOGY BRIEF 19: CRYSTAL OSCILLATORS 423

Technology Brief 19Crystal Oscillators

Circuits that produce well-defined ac oscillations arefundamental to many applications: frequency generatorsfor radio transmitters, filters for radio receivers, andprocessor clocks, among many. An oscillator is acircuit that takes a dc input and produces an acoutput at a desired frequency. Temperature stability, longlifetime, and little frequency drift over time are importantconsiderations when designing oscillators.

A circuit consisting of an inductor and a capacitor willresonate at a specific natural frequency ω0 = 1/

√LC . In

such a circuit, energy is stored in the capacitor’s electricfield and the inductor’s magnetic field. Once energy isintroduced into the circuit (for example, by applying aninitial voltage to the capacitor), it will begin to flow backand forth (oscillate) between the two components; thisconstant conversion gives rise to oscillations in voltageand current at the resonant frequency. In an ideal circuitwith no dissipation (no resistor), the oscillations willcontinue at this one frequency forever.

Making oscillating circuits from individual inductor andcapacitor components, however, is relatively impracti-cal and yields devices with poor reproducibility, hightemperature drift (i.e., the resonant frequency changeswith the temperature surrounding the circuit), and pooroverall lifetime. Since the early part of the 20th century,resonators have been made in a completely different way,namely by using tiny, mechanically resonating pieces ofquartz glass.

Quartz Crystals and Piezoelectricity

In 1880, the Curie brothers demonstrated that certaincrystals—such as quartz, topaz, and tourmaline—become electrically polarized when subjected to mechan-ical stress. That is, such a crystal exhibits a voltageacross it if compressed, and a voltage of oppositepolarity if stretched. The converse property, namelythat if a voltage is applied across a crystal it willchange its shape (compress or stretch), was predicteda year later by Gabriel Lippman (who received the1908 Nobel Prize in physics for producing the firstcolor photographic plate). Collectively, these bidirectionalproperties of crystals are known as piezoelectricity.Piezoelectric crystals are used in microphones to convertmechanical vibrations of the crystal surface, caused byacoustic waves, into electrical signals, and the converse is

used in loudspeakers.Piezoelectricity can also be appliedto make a quartz crystal resonate. If a voltage of theproper polarity is applied across one of the principal axesof the crystal, it will shrink along the direction of that axis.Upon removing the voltage, the crystal will try to restoreits shape to its original unstressed state by stretchingitself, but its stored compression energy is sufficient toallow it to stretch beyond the unstressed state, therebygenerating a voltage whose polarity is opposite of thatof the original voltage that was used to compress it. Thisinduced voltage will cause it to shrink, and the process willcontinue back and forth until the energy initially introducedby the external voltage source is totally dissipated. Thebehavior of the crystal is akin to an underdamped RLCcircuit.

In addition to crystals, some metals and ceramicsare also used for making oscillators. Because theresonant frequency can be chosen by specifying thetype of material and its shape, such oscillators areeasy to manufacture in large quantities, and theiroscillation frequencies can be designed with a highdegree of precision. Moreover, quartz crystals have goodtemperature performance, which means that they canbe used in many applications without the need fortemperature compensation, including in clocks, radios,and cellphones.

(a)

(b)

X1

υcrystal+ _

RS = 50 Ω

υout

LS = 80 mHCS = 1.3 fFCO = 4.5 pF

CO

CSRS LS

+ _

Figure TF19-1: (a) Quartz crystal circuit symbol and (b)equivalent circuit. Values given are for a 5 MHz crystal.

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424 TECHNOLOGY BRIEF 19: CRYSTAL OSCILLATORS

X1

Positive feedback

Negative feedback

+

_

_

+

VCC_ υout

+VCC

gain

FigureTF19-2: Schematic block diagram of an oscillatorcircuit.An oscillator is wired into the positive feedback path,while a negative feedback path is used to control gain.

Crystal Equivalent Circuit and OscillatorDesign

The electrical behavior of a quartz crystal can be modeledas a series RLC circuit (LS, CS, RS) in parallel with a shuntcapacitor (CO). The RLC circuit models the fundamentaloscillator behavior with dissipation. The shunt capacitoris mostly due to the capacitance between the two platesthat actuate the quartz crystal. Figure TF19-1 shows thecircuit symbol, the equivalent circuit with sample values

Figure TF19-3: Schematic (left) and photo (right) of atiny atomic physics package used in a chip-scale atomicclock. (Courtesy of Clark Nguyen, U.C. Berkeley, and JohnKitching, National Institutes of Standards and Technology.

for a commercial 12 MHz crystal along with expressionsand values for the resonant frequencies and Q.

The crystal is, of course, not sufficient to produce acontinuous oscillating waveform; we need to excite thecircuit and keep it running. A common way to do thisis to insert the crystal in the positive feedback path ofan amplifier (Fig. TF19-2). The amplifier, of course, issupplied with dc power (V+

CC and V−CC). Note that no

input signal is applied to the circuit. Initially, the outputgenerates no oscillations; however, any noise at vout thatis at the resonant frequency of X1 will be fed back tothe input and amplified.This positive feedback will quicklyramp up the output so that it is oscillating at the resonantfrequency of the crystal. A negative feedback loop is alsocommonly used to control the overall gain and preventthe circuit from clipping the signal against the op amp’ssupply voltages V+

CC and V−CC.

In order to oscillate continuously, a circuit must meetthe following two Barkhausen criteria: (1) The gain ofthe circuit must be greater than 1. (This makes sense, forotherwise the signal will neither get amplified nor establisha resonating condition.) (2) The phase shift from the inputto the output, then across the feedback loop to the inputmust be 0. (This also makes sense, since if there is non-zero phase shift, the signals will destructively interfere andthe oscillator will not be able to start up.)

Advances in Resonators and Clocks

As good as quartz resonators are, even the best amongthem will drift in frequency by 0.01 ppm per year as aresult of aging of the crystal. If the oscillator is being usedto keep time (as in your digital watch), this dictates howmany seconds (or fractions thereof) the clock will loseper year. Put differently, this drift puts a hard limit onhow long a clock can run without calibration. The samephenomenon limits how well independent clocks can staysynchronized with each other. Atomic clocks provide anextra level of precision by basing their oscillations onatomic transitions; these clocks are accurate to about10−9 seconds per day. Recently, a chip-scale versionof an atomic clock (Fig. TF19-3) was demonstrated bythe National Institute for Standards and Technology(NIST); it consumes 75 mW and was the size of a grain ofrice (10 mm3). Other recent efforts for making oscillatorsfor communication have focused on replacing the quartzcrystal with a type of micromechanical resonator.