Quartz-crystal timing accuracy claim: “In practical electronic timing circuits, achieving more than eight significant digits of timing accuracy can be easily accomplished by using quartz crystals.” Decide whether this statement is valid, considering typical crystal oscillator stability and what “eight significant digits” implies.

Introduction / Context:
Quartz crystal oscillators are the workhorses of timing in digital electronics, used in microcontrollers, communication systems, and test equipment. The statement claims that “more than eight significant digits” of timing accuracy is easily achieved with crystals. This question probes understanding of real-world oscillator accuracy versus stability terms like ppm (parts per million) and ppb (parts per billion).

Given Data / Assumptions:

• “More than eight significant digits” implies relative accuracy better than 1 part in 10^8 (≈ 0.01 ppm).
• Typical crystal oscillators: XO, TCXO, OCXO; ambient conditions vary.
• “Easily achieved” means without specialized disciplining (e.g., GPS, atomic reference) or extensive calibration.
  

Concept / Approach:
Uncompensated crystal oscillators (XO) are commonly 10–50 ppm. Temperature-compensated (TCXO) units are around 0.5–2 ppm, while oven-controlled (OCXO) may reach 0.01–0.1 ppm over short intervals, but long-term aging and environmental factors worsen absolute accuracy. Achieving < 0.01 ppm (1e-8) reliably is the realm of atomic standards or GPS-disciplined oscillators, not “easy” standalone crystals.

Step-by-Step Solution:

Verification / Alternative check:
Datasheets list frequency tolerance at 25°C, stability over temperature, load pulling, aging per day/year. Summing these error sources shows practical absolute accuracy typically well above 1e-8 unless the crystal is disciplined to a higher standard (e.g., GPSDO) or periodically calibrated against an atomic reference.

Why Other Options Are Wrong:

• Correct: Overstates crystal capability; not generally true.
• Only true with atomic disciplining (GPSDO/OCXO): This acknowledges that extra infrastructure is needed; the original claim said “easily” with crystals alone.
• Only true at room temperature: Even then, manufacturing tolerance and aging prevent 1e-8 “easy” accuracy.

Common Pitfalls:
Confusing stability (short-term fluctuation) with absolute accuracy; ignoring aging and load capacitance; assuming OCXO guarantees 1e-8 accuracy without calibration.

Final Answer:
Incorrect