Q Factor ⇄ Bandwidth
Loaded Q from bandwidth, or bandwidth from Q, at a center frequency.
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The engineering
Q is selectivity, stored-energy efficiency, and ring-down time in one number. A 10.7 MHz IF filter with 150 kHz bandwidth is Q ≈ 71; a quartz crystal at the same frequency can be Q ≈ 100,000 — which is the whole reason crystals keep time.
High Q rings: the τ row is why struck resonators keep talking after the drive stops.
Where this math comes from
The letter Q was Kenneth S. Johnson's — a Western Electric engineer in the 1920s who needed a symbol for coil quality and, by his own account, picked Q simply because it was unclaimed. The concept (energy stored over energy lost per cycle) predates the letter and runs through every resonant system in physics.
Cavity magnetrons, quartz standards, and superconducting accelerator cells are all the same Q arithmetic at increasingly heroic values.
- 1914Kenneth S. JohnsonCoins Q for coil quality at Western Electric (published usage 1920s).
- 1928Warren MarrisonQuartz crystal clock — Q as a timekeeping technology.
See the full timeline of the math behind every calculator →
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