How do crystal oscillators achieve stability?
A quartz crystal is a piezoelectric resonator with Q from about 104 to 106, giving far better frequency stability than LC circuits. Its Butterworth–Van Dyke model is a series RmLmCm motional branch in parallel with shunt capacitance C0, producing a series resonance fs = 1/(2π√(LmCm)) and a slightly higher parallel (anti-) resonance.[1][2]
What is load capacitance?
Parallel-mode crystals are specified to oscillate at their nominal frequency with a stated load capacitance CL (for a Pierce circuit, roughly the series combination of the two capacitors plus stray). Pulling is approximately Δf/f ≈ Cm/(2(C0 + CL)), so incorrect CL shifts frequency by ppm.
How do XO, VCXO, TCXO and OCXO differ?
| Type | Stability (indicative) | Notes |
|---|---|---|
| XO | ±10 to ±100 ppm over temperature | Uncompensated |
| VCXO | Similar, with ±tens to hundreds of ppm pull | Voltage tuned |
| TCXO | ±0.1 to ±2.5 ppm | Temperature compensated; cellular, GNSS |
| OCXO | ±1 to ±100 ppb | Oven at turnover temperature; instruments, base stations |
Values are typical ranges; check device datasheets.
What cuts and behaviors matter?
AT-cut crystals have a cubic frequency-temperature curve with low slope near room temperature; SC-cut crystals reduce stress sensitivity and are used in OCXOs. Aging (ppm/year), g-sensitivity, drive level dependence and activity dips also matter.[2]
Frequently asked questions
Why do crystals have such high Q?
Quartz has very low internal acoustic loss.
Can I pull a crystal far?
Only by small amounts, typically tens to hundreds of ppm.
What is an MEMS oscillator?
A silicon resonator oscillator competing with quartz in some applications.
See also
References
Online sources accessed October 21, 2026; printed works cited by edition. See all sources.
- “The Design of CMOS Radio-Frequency Integrated Circuits, 2nd ed.”. T. H. Lee, Cambridge University Press. 2004.
- “Characterization of Clocks and Oscillators (NIST Technical Note 1337)”. D. B. Sullivan et al., NIST. 1990.