Acceleration force can alter the performance of a quartz crystal or crystal oscillator. The nature of the effect depends on the type of force that is being applied. Changes in the static gravitational force such as tilting or rotation will cause a step offset in frequency. Time-dependent acceleration or vibration will create frequency modulation in an oscillator. This will generate discrete sidebands in the case of sinusoidal vibration or an increase in the noise floor with random vibration. A shock pulse will cause a sharp temporary perturbation in the output frequency. What follows is an examination of the effects of acceleration force on the performance of quartz crystals and crystal oscillators.

The magnitude of these frequency shifts is a function of the quartz crystal's acceleration or "g-sensitivity" vector and the magnitude and direction of the applied acceleration force. The acceleration sensitivity of quartz crystals is caused by stresses resulting from the mass of the resonator blank reacting against its mounting structure.¹ This sensitivity is determined by many factors such as the type of cut—such as stress compensated (SC) or AT, the design and processing of the quartz blank, the package type, mounting structure and orientation in the holder. The range of typical g-sensitivities for bulk-mode quartz crystals can span several orders of magnitude, from less than 1 × 10^-10 per g for a carefully made precision SC crystal to greater than 1 × 10^-7 per g for a low cost AT crystal.²

Since their magnitudes are relatively small, these effects go undetected in many applications with standard oscillators such as voltage-controlled crystal oscillators (VCXOs). With precision oven-controlled crystal oscillators (OCXOs) or sources designed for severe environmental conditions, the inherent acceleration sensitivity can be very significant. If the oscillator is deployed in a high-vibration environment such as an airborne platform, increased phase noise or discrete spurious components will appear as modulation on the output signal, degrading the performance more than all other sources of noise combined. Even in a benign environment, an OCXO may experience significant frequency shifts due to static g-forces by moving, tilting, or rotating motions.

A crystal oscillator's g-sensitivity is usually characterized by measuring the attributes along three mutually perpendicular axes parallel to the faces of the oscillator package. However, the intrinsic acceleration characteristic of quartz consists of a single vector at some angle that is usually not normal to any of the faces of the package (Fig. 1). Therefore, the resonant frequency during acceleration is a function of the product of the two vectors:

where:

f_o = the center frequency of the resonator with no acceleration,

F(a) = the resonant frequency of the crystal with acceleration,

a = the applied acceleration, and

Γ = the acceleration sensitivity vector of the crystal.³

By measuring the individual mutually orthogonal components in the x, y, and z axes, the magnitude and orientation of the g-sensitivity vector, Γ_max, can be determined. Using the following trigonometric identities, Γ_max can be calculated without any prior knowledge of the crystal itself:

Once the magnitude and angular orientation of Γ_max are known, the expected effect of externally applied acceleration forces in any direction can be determined. When the direction of the applied force is parallel to the axis of Γ_max, it will have the greatest influence on the crystal frequency. As the angle of the applied force moves away from the axis parallel to Γ_max, the resultant effect rolls off as the cosine of the angle α, which is defined as the difference between the direction of applied force and Γmax. For any direction of applied acceleration, the frequency shift is given as the product of the g-sensitivity vector, Γ_max times the applied force (α):

Since the frequency deviation rolls off as the cosine of the angle α between α and Γ_max, a circle is defined as shown in Fig. 2.⁴ If viewed in all three dimensions, this would appear as a sphere with Γ_max along its axis. Therefore, the resultant g-sensitivity of the crystal in any direction as a function of Θ and Φ can be given by:

When the force is applied in the opposite direction, a frequency shift of equal magnitude but opposite sign is produced, defining the second circle in Fig. 2. Because of the vector and cosine nature of the g-sensitivity vector, an interesting attribute of this characteristic is that a plane of zero g-sensitivity is present. This is defined by the plane that is normal to Γ_max. This shows that any force applied to the crystal that is perpendicular to Γ_max will have no effect on the frequency. If the operating environment of the oscillator is such that the most severe acceleration or vibration forces are applied in one known direction, it is possible to orient the oscillator so that frequency shifts will be minimized.

Because of the relatively small frequency shifts that must be measured when characterizing a crystal oscillator's g-sensitivity, specialized test setups and high-resolution instruments are required. One of the most straightforward ways of making basic measurements on a precision oscillator is to use changes in the Earth's gravitational field to cause shifts in the oscillator frequency. This technique is known as the "2-g Tipover" method. The oscillator is placed in a fixture or on a bench and the frequency is monitored until it is stable. The unit is then flipped upside down or rotated 180 deg. and the frequency is once again measured. A unit initially experiencing a gravitational force of 1 g in the downward direction will be subject to a force of 1 g in the opposite direction after beng flipped. The net effect is a change of 2 g. Therefore, the amount of frequency shift measured divided by 2 is the oscillator's g-sensitivity in that axis. The procedure is then repeated for the other two axes. Although conceptually simple, the method requires an extremely stable oscillator to consistently measure the small frequency shifts that occur. Thermally induced short-term drift and modulation due to the connecting cables typically render this method invalid for uncompensated oscillators, although it is used with OCXOs and tightly compensated TCXOs (Fig. 3).