Tim wrote:

The Pierce logic-gate-biased-active oscillator is pretty reliable to start
and will oscillate somewhere with most crystals from kHz to MHz.

As you found out, it will often come up on one of many overtones.

To reduce chance of coming at an overtone, a series resistor from logic
gate output to the crystal is often enough. If not, a RC low-pass will cut
down even further (although of course adding phase shift.)

The general strategy for discouraging overtone operation and other unwanted modes at frequencies above the crystal fundamental is to design the gain element to have decreasing gain at higher frequencies. The figure attached below (from Hayward's "introduction to RF Design") shows one common implementation.

One of Bernd's papers has some helpful information about low-frequency crystals and oscillator circuits. See pp. 1-3 of:

<www.axtal.com/cms/iwebs/download.aspx?id=71607>

Best regards,

Charles


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