Fundamental vs 3rd Overtone

Typically when we talk about crystals, we are referring to crystals using the fundamental vibration mode of AT-cut quartz.  Simply stated, “fundamental vibration mode” refers to the crystal resonating at the frequency it is ‘designed’ for.  Fundamental resonant frequency is inversely proportional to thickness, which can cause issues at higher frequencies.  Fundamental-mode crystals at frequencies higher than 50 become very expensive as the quartz blanks are extremely thin and difficult to handle.  This causes the crystal to have a higher rate of breakage in processing.  It is for this reason that at higher frequencies, most crystals will be designed to operate on a crystal’s 3rd overtone.

A 3rd overtone-mode crystal resonates at three times its fundamental frequency.  There are in fact an infinite number of odd number harmonics that exist on the same quartz plate.  The first, third and fifth harmonics are shown in the figure below.  You might notice that there are some anharmonic modes or spurs shown in between, which are by-products of other vibrational states.  These unwanted modes may be suppressed sufficiently by providing a large enough plate diameter to electrode diameter ratio, or by contouring (i.e., generating a spherical curvature on one or both sides of the plate).

spury

As previously discussed, quartz crystals have an equivalent circuit of a series RLC for the fundamental and each harmonic mode, plus a capacitor in parallel representing the capacitance of the electrodes.  The resistance for a third overtone crystal is more than three times that of the fundamental mode, while its capacitance is almost nine times less.  These changes greatly affect the Q and tunability of the crystal.  Third overtone crystals have better stability performance (higher Q), however are significantly more difficult to tune.  This also explains why in oscillators with compensation circuitry (VCXO/TCXO/OCXO) using third overtone and higher crystals are avoided.

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