Crystal Oscillators

A quartz crystal is piezoelectric: it behaves electrically like an LC circuit with a very high quality factor (Q of 10⁴–10⁶), so its frequency is precise to tens of ppm.

Microcontrollers use a Pierce oscillator: the crystal plus two load capacitors to ground. Calculate them from the crystal's load capacitance $C_L$:

$C_L = \frac{C_1 C_2}{C_1 + C_2} + C_{stray} \quad\Rightarrow\quad C_1 = C_2 \approx 2(C_L - C_{stray})$

with $C_{stray}$ ≈ 2–5 pF. A 32.768 kHz crystal ($2^{15}$ Hz) runs real-time clocks: divide by two 15 times to get exactly 1 Hz.