Crystal oscillator
Size the load capacitors for a microcontroller's crystal from its load capacitance and the board's stray capacitance, estimate the frequency error of the capacitors you fit, and check the oscillator's gain margin and the crystal's drive level.
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How to use it
Almost every MCU uses a Pierce oscillator: an inverting amplifier with the crystal in the feedback path and a capacitor from each crystal pin to ground.
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Load capacitors — the crystal is cut for a load capacitance CL. The two capacitors appear in series, plus the stray capacitance of the pins and traces: CL = C1·C2/(C1 + C2) + Cstray, so for equal capacitors C = 2·(CL − Cstray).
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Frequency pulling — with the crystal’s motional capacitance, the error from a load that differs from CL: Δf/f ≈ C1m·(CLspec − CL)/(2·(C0 + CLspec)·(C0 + CL)).
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Gain margin — the critical transconductance gm_crit = 4·ESR·(2πf)²·(C0 + CL)²; the MCU’s oscillator gm should be at least five times that for reliable start-up.
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Drive level — DL = ESR·(π·f·(C0 + CL)·Vpp)²/2 against the crystal’s maximum; reduce it with a series resistor if needed.
References: ST AN2867 Oscillator design guide for STM8AF/AL/S, STM32 MCUs and MPUs; Microchip AN826 and AN2648. Related: capacitors, MCU timing.
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