Crystal oscillator quality factor (Q) — truth test: Do crystal oscillator circuits exhibit a very low Q, or are they characterized by very high Q (narrowband, low-loss resonance)?

Introduction / Context:Oscillator stability, phase noise, and spectral purity are tightly linked to a resonator’s quality factor, Q. Quartz crystals are famous for exceptionally high Q compared with LC or RC networks. This item tests recognition that crystal oscillators are high-Q devices, not low-Q.

Given Data / Assumptions:

• Quartz crystal used as the resonant element.
• Linear small-signal resonator model (motional arm and shunt capacitance).
• Focus on qualitative Q property, not exact numerical values.

Concept / Approach:The quality factor Q measures energy stored versus energy lost per cycle. Crystals have extremely low loss, leading to very high Q (often 10^4–10^6 range depending on cut and frequency). High Q yields a narrow resonance bandwidth and superior frequency stability, which is why crystals dominate timekeeping and reference applications. Therefore the statement “crystal oscillator circuits have a very low Q” is false.

Step-by-Step Solution:

Verification / Alternative check:Compare with RC phase-shift or Wien-bridge oscillators: their Q is modest; LC tanks are higher; crystals are highest among common electrical resonators, which aligns with their ultra-stable performance in clocks and radios.

Why Other Options Are Wrong:

• Correct: Not true; crystals are high-Q.
• Only correct for RC oscillators: RC types are lower-Q than crystals, but the statement concerns crystals.
• Only correct at low temperatures: Temperature affects frequency slightly but does not convert high-Q into low-Q.

Common Pitfalls:Generalizing from RC oscillators to crystals; confusing narrow bandwidth (high Q) with low Q due to terminology.

Final Answer:Incorrect