Why does a crystal have a lower frequency limit?

Written by on 4/14/2009

The thickness of the crystal determines the frequency. For an AT cut crystal 0.001" (0.0254mm) thick is about a 63MHz fundamental mode resonator. If the thickness is doubled then the resonate frequency would be 0.5 * 63MHz or 31.5MHz.

An 8MHz crystal would be 0.0078" (0.200mm) thick. A 4MHz crystal would be 0.0157" (0.400mm) thick.

Two conditions are encountered that limit the lowest frequency in a particular size of package:

1) The simple condition, the newer low profile ceramic LCC packages will not accept the thicker crystals. Depending on the package, the lower frequency limits range from 8MHz to 12MHz and downward.

2) Remember that a quartz crystal is a vibrating mechanical device. For the best designs, those with lower ESR (CI) and no perturbations (undesired modes of vibration that cause frequency jumps) the vibrating area is intended to be in the center area of the crystal.

When the crystal frequency is lower and the crystal is thicker, the vibrating area is more mechanically coupled to the edges. In this case the perturbations (unwanted resonances) become difficult to nearly impossible to control. The solution is to bevel or contour the crystal (make the crystal look more like a magnifying glass concave shape). This thinning of the edges restricts the vibrating area to the crystals center and allows control of the perturbations.

Unfortunately, restricting the vibrating area increases the ESR significantly. For example at 12MHz:

SM13T 5x7mm crystal ESR maximum is 50 ohms

SM11T 3.2x5mm crystal ESR maximum is 80 ohms

For this example, an SM11T below 12MHz is not practical as the ESR becomes very large.