Crystal Q, quality factor

  • Dec 13,2022

The Q or quality factor is an important aspect of quartz crystal resonance. Crystals offer very high levels of Q, sometimes in excess of 100 000.

Accordingly it is necessary to be able to calculate the level of Q to be able to determine other constraints and design considerations for the circuit in which it is to operate.

A straightforward equation is available to be able to calculate the value of Q for a given crystal.

Q=12 π Fs R C1Q=12 π Fs R C1

From this it can be seen that the series capacitance has a major effect on the Q. Lowering the series capacitance increases the Q in direct proportion for a given frequency.

Quartz crystal resonators are a complex linkage between the electrical md mechanical domains. Although in theory it appears that theory operation appears quite straightforward, in practice many effects work together and they may link in unexpected manners. It is not unknown for quartz crystal resonators to be excited by a different mode in a particular circuit and hence operate on an incorrect frequency. Understanding how quartz crystal resonators work can help identify these issues in the unlikely event they may occur. Often adding a broadly resonant circuit to the oscillator to ensure that it can only operate in the required mode suffices in this instance.

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