Crystal & Resonator

A crystal, short for quartz crystal, is a piezoelectric component that vibrates at one very precise mechanical resonant frequency when an AC voltage is applied to its electrodes, so it is used as an accurate frequency reference for clocks and timing. A resonator is any component that resonates at a set frequency; in electronics the term usually means a ceramic resonator, a lower-cost and lower-accuracy piezoceramic alternative to a quartz crystal that often has its load capacitors built in. Both are used to set the clock frequency of an oscillator.

A quartz crystal works by the piezoelectric effect. A thin slice of quartz is placed between two electrodes; when a voltage is applied, the quartz mechanically deforms, and when it springs back it generates a voltage. Driven by an AC signal it vibrates, and it vibrates most strongly at one sharp mechanical resonant frequency set mainly by the thickness and cut of the plate. Because quartz is very stable and has an extremely high quality factor, this resonance gives an accurate, stable frequency reference.

A quartz crystal is far more accurate and stable, typically tens of parts per million, and is used where timing matters, such as USB, Ethernet, radios and real-time clocks. A ceramic resonator uses a piezoceramic element, is cheaper and smaller, usually has its two load capacitors built in so it needs fewer external parts, and starts up faster, but its accuracy is only about half a percent. Use a crystal for precise timing and a ceramic resonator for low-cost microcontroller clocks that do not need tight accuracy.

A quartz crystal has two closely spaced resonant frequencies. At the series resonant frequency fs the motional arm of the crystal is purely resistive and the impedance is at its minimum. At the slightly higher parallel or anti-resonant frequency fp, the motional arm resonates with the shunt capacitance C0 and the impedance is at its maximum. Between fs and fp the crystal looks inductive, and this narrow band is where a crystal oscillator operates. A datasheet specifies whether a part is a series-mode or a parallel-mode (load-capacitance) crystal.

Load capacitance CL is the capacitance the parallel-mode crystal expects to see across its terminals to oscillate at its marked frequency. In a Pierce oscillator it is set by the two load capacitors C1 and C2 to ground plus the stray capacitance Cstray of the pins and board. The two capacitors appear in series to the crystal, so CL is approximately C1 times C2 divided by C1 plus C2, plus Cstray. With equal capacitors this gives C1 = C2 = 2 times (CL minus Cstray). For example, for a CL of 12 pF with about 3 pF of stray, use two 18 pF capacitors.

The Pierce oscillator is the standard crystal oscillator circuit built into almost every microcontroller. It uses an inverting amplifier, a large feedback resistor of about one megohm that biases the amplifier into its linear region, the quartz crystal connected between the two clock pins XTAL1 and XTAL2, and two load capacitors from those pins to ground. The crystal operates in its inductive region and, with the load capacitors, forms a resonant feedback network that sustains a stable oscillation at the crystal frequency.

32.768 kHz is exactly 2 to the power 15, so a simple 15-stage binary counter divides it down to exactly one pulse per second, which is ideal for keeping time. These tuning-fork quartz crystals are small, extremely low power, and accurate enough for clocks and watches, which is why the 32.768 kHz crystal is the standard timekeeping crystal in real-time clock chips, watches, microcontrollers and appliances.

ppm means parts per million, a way of expressing how far the frequency can deviate; 1 ppm of a 10 MHz crystal is 10 Hz. Frequency tolerance is the allowed error at room temperature, set by manufacturing. Frequency stability is the extra drift over the operating temperature range, and there is also aging, a slow drift over years. A datasheet lists these separately, for example plus or minus 10 ppm tolerance and plus or minus 20 ppm stability, and the total error is their sum.

ESR is the equivalent series resistance, the motional resistance Rm of the crystal at resonance; a lower ESR is easier for an oscillator to start and sustain. Drive level is the power actually dissipated in the crystal while it oscillates. Too high a drive level ages the crystal quickly or can damage it, especially a tiny 32.768 kHz tuning fork, while too low a drive level can prevent reliable start-up, so the oscillator design must keep the drive level within the datasheet limit.

Aging is the slow, gradual change of a crystal's frequency over months and years, caused by stress relief in the mounting, mass transfer of contamination onto the quartz surface, and material changes. It is usually specified in ppm per year and is largest in the first year. Good sealing, a suitable cut, and a low drive level reduce aging, which matters most in precision timing such as clocks, instruments and communications.

The AT-cut is the most common way of slicing a quartz crystal, at about a 35 degree angle to the crystal axis. It vibrates in the thickness-shear mode and has an excellent, nearly flat frequency-versus-temperature curve around room temperature, which is why AT-cut crystals dominate the megahertz range used for microcontrollers, USB and radios. The 32.768 kHz timekeeping crystal instead uses a tuning-fork cut that vibrates by flexing.

A crystal is just the passive quartz element and needs an external oscillator circuit, such as the Pierce circuit in a microcontroller, to make it oscillate. A crystal oscillator module, or XO, packages the crystal and the oscillator circuit together and outputs a ready-made clock signal. A TCXO adds temperature compensation for much better stability, a few parts per million, and an OCXO keeps the crystal in a temperature-controlled oven for parts-per-billion stability used in GPS, telecom and instrumentation.

They are used wherever an accurate clock or timing reference is needed: the 32.768 kHz crystal in real-time clocks, watches and timers; megahertz quartz crystals for microcontrollers, USB, Ethernet, Bluetooth, GPS and radio transmitters and receivers; ceramic resonators for low-cost microcontroller clocks; and TCXO and OCXO oscillators for precision communications and test equipment. Almost every digital and radio system contains at least one crystal or resonator.