|Angle & Tolerance
The Frequency vs. Temperature characteristic of a quartz crystal is determined by the angle at which the quartz plate is cut from the quartz bar as referenced to the "Theta Angle". The cutting process becomes a simple geometry problem to identify the angle of cut, however the degree of accuracy is very challenging. Angles are measured in degrees, minutes and seconds of arc as referenced to "Theta" and only a measurement using x-ray diffraction is accurate enough to measure angles of the required precision. The actual cutting process is a mechanical process and tool accuracy/precision, wear, cutting rate, etc. all have a bearing on the outcome of the process. Therefore, tolerances come into play and the outcome is a "range" of angles" centered on a nominal. This translates into a group of quartz plates with a "range" of Frequency vs. Temperature characteristics centered around a nominal. Ideally all the plates will meet the desired Frequency vs. Temperature specification. In the case of Doubly rotated AT crystals, DRATs, the angle has to be controlled around two crystallographic axes which is an order of magnitude more challenging then that of a standard AT Cut device.
Adding to the difficulty of maintaining accuracy of the cut angle/stability external mechanical attachments and associated stresses also affect a crystal's temperature characteristics. In crystal design, the phenomenon is known as Angle Rotation and crystal designers utilize techniques to minimize the effect of Angle Rotation.
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