#### What is in this article?:

- Manage Quartz Crystals Under High Vibration
- Characterizing A Source
- Meeting Expectations
- Acceleration Sensitivity
- References

Crystal oscillators can suffer higher-than-expected levels of noise under high vibration.

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Crystal oscillators have long been frequency sources with excellent frequency stability, spectral purity, and low phase noise. Unfortunately, a crystal oscillator’s noise performance can be affected by vibration or other acceleration events in the application environment. Even moderate levels of vibration can significantly affect a low-noise signal. Understanding the behavior of a crystal oscillator under various conditions of vibration and acceleration can help improve the overall performance of an application that must operate under those conditions.

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For a crystal oscillator operating within different mobile platforms, vibration-induced phase noise can be greater than all other noise sources combined.^{1} For many electronic systems, operation in the presence of vibration became an important requirement, as the sensitivity of different components to vibration and acceleration was found to be degrading system performance. Although many components contributed to the problem, in many cases quartz crystal resonators and oscillators were found to be limiting the overall noise performance of these electronic systems.

As a result, it was necessary to improve the dynamic characteristics of quartz crystals and oscillators, as well as to expand the theoretical understanding of quartz and its applications.^{2-4} Some improvements in quartz crystals have developed in the ensuing years, but the intrinsic acceleration sensitivity characteristic of most crystal resonators is still very similar to its state of more than 40 years ago.^{5}

The acceleration sensitivity (also referred to as the “g-sensitivity”) of a well-designed crystal oscillator is primarily a function of the crystal resonator. All quartz crystals have an intrinsic characteristic that causes a small change in resonant frequency when subject to a change in acceleration. This is primarily due to the strain that is applied to the resonator through the mounting and support structure which causes deformation of the quartz.^{6}

Empirical evaluation has shown that the acceleration sensitivity of quartz is vectorial in nature: dependent upon the direction of the applied force. Therefore, the resultant effect of acceleration on the frequency of a given crystal is determined by the instantaneous magnitude of the acceleration as well as the direction in which it is applied. The frequency shift is a maximum when applied in a direction parallel to the force vector.

As shown in **Fig. 1**, as the angle between the force vector and the acceleration sensitivity vector increases from 0 deg. to 90 deg., the effective sensitivity rolls off as the cosine of the angle, approaching 0 at an angle of 90 deg. Therefore, any force that is applied in the plane normal to the vector will have a minimal effect on the crystal. This is depicted in two dimensions by the circles in **Fig. 1**. The bottom circle depicts the positive frequency shift that occurs when the force is applied in the same direction as the Γ vector. (The acceleration sensitivity of a crystal or oscillator is typically denoted by Γ.)

The top circle represents the negative frequency shift of equal magnitude produced when the same force is applied from the opposite direction. This is the case when sinusoidal vibration is applied. As the direction of the acceleration force is constantly shifting 180 deg. at the frequency of vibration, the resonant frequency of the crystal is shifting positively and negatively about the nominal center frequency, effectively applying frequency modulation (FM) to the crystal resonator’s output signal.

When viewed in three dimensions, the Γ circles are rotated about the **Γ** axis to form spheres, as shown in **Fig. 1a**. This model can then be inserted into the oscillator’s frame of reference with the model’s **Γ** vector aligned parallel to the actual **Γ** vector of the oscillator. It is then possible to predict the effective Γ for acceleration force that is applied in any direction.

The frequency during acceleration can then be written in Eq. 1 as the product of two vectors,

f(**a**) = f_{0}(1 + **Γ**·**a**) (1)

where:

f_{0 }= the carrier frequency with no acceleration;

**Γ** = the acceleration sensitivity vector; and

**a** = the acceleration force vector.

The magnitude of Γ is usually linear versus the applied force to greater than 50 g’s.^{4} The frequency response of Γ is also relatively flat. Nonetheless, vibration frequencies of several kHz through mechanical resonances in the blank and mounting structures may cause peaking in some areas, depending upon the type of crystal.

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