## When is a Crystal not a ‘Crystal’?: Tuning Forks

Quartz is the material of choice for stable resonators, as it is one of the few piezoelectric crystals that has very high Q and is also highly anisotropic.  Being anisotropic means that the electrical properties of the quartz crystal can vary greatly depending on how the blank for the final finished crystal is cut with respect to the crystallographic axis of a quartz bar shown above.  There is an infinite number of ways quartz can be cut relative to the x, y, and z, axes, and there are several angles of cuts that give properties that are particularly useful.  We will compare the main differences between two different cuts: AT-cut crystals and tuning fork.

AT-cut crystal is the most commonly used cut of crystal in standard applications.  This is a crystal blank cut at 35° 15′ to the Z axis, and can be designed to support frequencies from 0.5MHz to 250MHz through use of overtones.  AT-cut crystals are popular because they have very good temperature stability performance and are fairly easy to produce.  AT-cut crystal’s frequency stability over temperature is represented as a third order polynomial, and they are designed to have zero-temperature coefficients around 25°C.  This makes AT-cut crystals popular for non-ovenized applications (filters, oscillators, TCXOs, etc).

An AT-Cut crystal has a temperature curve that follows a third order polynomial:

$latex \frac{\Delta f}{f} = A(t-t_0)+B(t-t_0)^2+C(t-t_0)^3, t_0=25&s=1$

Tuning forks (sometimes referred to as “wristwatch crystals”) are designed to generate one single frequency: 32.768kHz.  This frequency, which is equal to 215 Hz, makes it easy to generate a 1 Hz signal by a series of divide by two frequency dividers, as needed by the watch industry.  Tuning forks are cut as close to normal to the Z-axis of the wafer, and typically are 2-5° off of the Z axis.  Their frequency stability over temperature is represented as a quadratic function, and they are designed to have a zero-temperature coefficients around 25°C similar to AT-cut crystals.  These wristwatch crystals are sufficiently accurate, usually, while worn as intended, i.e., on someone’s wrist for 16 hours and off the wrist for 8 hours each day.  The accuracies degrade when the watch is off the wrist for extended periods.  The further the storage temperature is from the optimum temperature, the faster the watch loses time.  At temperature extremes, e.g., in a freezer at – 55°C, or at the temperature of boiling water, wristwatches lose about 20 s per day.  The main benefits of a tuning fork is that while limited in frequency, they are significantly cheaper than AT-cut crystals (almost half the price) and require very little power (0.1uW whereas most AT-cut crystals are 10uW).

The tuning fork crystal has a temperature curve that follows a quadratic:

$latex \frac{\Delta f}{f} = A(t-t_0)^2, t_0=25&s=1$

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