As mentioned under the frequency section, a relationship exists between quartz plate diameter and thickness. Optimally, an unrestricted vacuum with a D : T =/> 70 : 1 will have minimal impedance. As you restrict and attempt to trap the vibrating energy in the center of the plate, the impedance of the device increases. The increase in impedance is minimal until a D : T of 40 : 1 is reached. At 40 : 1 and smaller, the impedance rises sharply putting the resonator at risk of failing to begin or maintain vibration. Processing steps such as contouring or beveling can mitigate the rise in impedance, however it can not completely eliminate the problem.
Incidental to this phenomenon, holder selection becomes a critical issue since the D : T for a specific design frequency may not allow for the manufacture of a device with an impedance that will allow start-up and vibration over a broad range of drive level.
An example of the criticality of holder selection would be a fundamental mode AT resonator at 2.000 MHz. The approximate thickness of the plate would be 0.033 inches. With a D : T of 40 : 1 the diameter of the plate would be 1.33 inches. Obviously it would not fit into any of the standard metal holders available. This device is a candidate for "energy trapping" by contouring (lense-shaping) the blank. In practice, a designer would choose an HC-36 holder and a 0.600" diameter plate for this design with a D : T of only 18 : 1. Typical Rs would be approximately 55 ohms. Selecting a smaller holder, HC-43 and a 0.350' diameter plate, would result in a resonator with a typical Rs of 350 ohms.
The following chart provides the lower fundamental frequency limit for a specific holder type:
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