Frequency fluctuations

Frequency fluctuations[edit]

Crystals suffer from minor short-term frequency fluctuations as well. The main causes of such noise are e.g. thermal noise (which limits the noise floor), phonon scattering (influenced by lattice defects), adsorption/desorption of molecules on the surface of the crystal, noise of the oscillator circuits, mechanical shocks and vibrations, acceleration and orientation changes, temperature fluctuations, and relief of mechanical stresses. The short-term stability is measured by four main parameters: Allan variance (the most common one specified in oscillator data sheets), phase noise, spectral density of phase deviations, and spectral density of fractional frequency deviations. The effects of acceleration and vibration tend to dominate the other noise sources; surface acoustic wave devices tend to be more sensitive than bulk acoustic wave (BAW) ones, and the stress-compensated cuts are even less sensitive. The relative orientation of the acceleration vector to the crystal dramatically influences the crystal's vibration sensitivity. Mechanical vibration isolation mountings can be used for high-stability crystals.

Phase noise plays a significant role in frequency synthesis systems using frequency multiplication; a multiplication of a frequency by N increases the phase noise power by N². A frequency multiplication by 10 times multiplies the magnitude of the phase error by 10 times. This can be disastrous for systems employing PLL or FSK technologies.

Magnetic fields have little effect on the crystal itself, as quartz is diamagnetic; eddy currents or AC voltages can however be induced into the circuits, and magnetic parts of the mounting and housing may be influenced.

After the power-up, the crystals take several seconds to minutes to "warm up" and stabilize their frequency. The oven-controlled OCXOs require usually 3–10 minutes for heating up to reach thermal equilibrium; the oven-less oscillators stabilize in several seconds as the few milliwatts dissipated in the crystal cause a small but noticeable level of internal heating.^[48]

Drive level[edit]

The crystals have to be driven at the appropriate drive level. Low-frequency crystals, especially flexural-mode ones, may fracture at too high drive levels. The drive level is specified as the amount of power dissipated in the crystal. The appropriate drive levels are about 5 μW for flexural modes up to 100 kHz, 1 μW for fundamental modes at 1–4 MHz, 0.5 μW for fundamental modes 4–20 MHz and 0.5 μW for overtone modes at 20–200 MHz.^[49] Too low drive level may cause problems with starting the oscillator. Low drive levels are better for higher stability and lower power consumption of the oscillator. Higher drive levels, in turn, reduce the impact of noise by increasing the signal-to-noise ratio.^[50]

Crystal cuts[edit]

The resonator plate can be cut from the source crystal in many different ways. The orientation of the cut influences the crystal's aging characteristics, frequency stability, thermal characteristics, and other parameters. These cuts operate at bulk acoustic wave (BAW); for higher frequencies, surface acoustic wave (SAW) devices are employed.

Image of several crystal cuts^[51]

Cut	Frequency range	Mode	Angles	Description
AT	0.5–300 MHz	thickness shear (c-mode, slow quasi-shear)	35°15', 0° (<25 MHz) 35°18', 0°(>10 MHz)	The most common cut, developed in 1934. The plate contains the crystal's x axis and is inclined by 35°15' from the z (optic) axis. The frequency-temperature curve is a sine-shaped curve with inflection point at around 25–35 °C. Has frequency constant 1.661 MHz⋅mm.[52] Most (estimated over 90%) of all crystals are this variant.[53] Used for oscillators operating in wider temperature range, for range of 0.5 to 200 MHz; also used in oven-controlled oscillators.[54] Sensitive to mechanical stresses, whether caused by external forces or by temperature gradients. Thickness-shear crystals typically operate in fundamental mode at 1–30 MHz, 3rd overtone at 30–90 MHz, and 5th overtone at 90–150 MHz;[55] according to other source they can be made for fundamental mode operation up to 300 MHz, though that mode is usually used only to 100 MHz[56] and according to yet another source the upper limit for fundamental frequency of the AT cut is limited to 40 MHz for small diameter blanks.[52] Can be manufactured either as a conventional round disk, or as a strip resonator; the latter allows much smaller size. The thickness of the quartz blank is about (1.661 mm)/(frequency in MHz), with the frequency somewhat shifted by further processing.[57] The third overtone is about 3 times the fundamental frequency; the overtones are higher than the equivalent multiple of the fundamental frequency by about 25 kHz per overtone. Crystals designed for operating in overtone modes have to be specially processed for plane parallelism and surface finish for the best performance at a given overtone frequency.[49]

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