Also known as: Q, quality factor
The Q factor (quality factor) is a dimensionless measure of how selective and low-loss a resonant system is, defined as its centre frequency divided by its −3 dB bandwidth: Q = f₀ / Δf.1 Equivalently it is 2π times the energy stored per cycle divided by the energy dissipated per cycle. A high Q means a sharp, narrow resonance that rings for many cycles; a low Q means a broad, heavily damped response that dies quickly. Q sets the selectivity of tuned circuits, filters, and oscillators.
How it works
A resonator stores energy and swaps it back and forth between two forms — in an LC circuit, between the inductor’s magnetic field and the capacitor’s electric field. Every cycle a little energy is lost to resistance, radiation, or other damping. Q captures the ratio of what is stored to what is lost:
Q = 2π × (energy stored) / (energy dissipated per cycle)
Because a lightly damped resonator loses little per cycle, it responds strongly only to frequencies very close to resonance, producing a tall, narrow peak — and, viewed in time, it rings for roughly Q cycles after being struck. For a series RLC circuit Q = (1/R)·√(L/C), so lowering the loss resistance R raises Q. The link to bandwidth follows directly: a narrow response equals a high Q, which is why Q = f₀/Δf is the practical measuring recipe.
Loaded versus unloaded Q
Two Q values matter and are often confused:
- Unloaded Q (Qu) is the resonator’s own quality, set only by its internal losses, with nothing drawing power from it. It is the ceiling the component can reach.
- Loaded Q (QL) is what you actually see once the resonator is connected to a source and load, which add their own damping. Coupling to external circuitry always lowers Q, so QL ≤ Qu.
A filter designer trades these deliberately: tighter coupling gives wider bandwidth (lower loaded Q) but lower insertion loss, while loose coupling gives a narrower, sharper response at the cost of more loss. Typical unloaded Q spans a huge range — tens for a simple wire-wound inductor, hundreds to low thousands for a good LC circuit, tens of thousands for a cavity filter, and hundreds of thousands for a quartz crystal resonator.
Relevance to SDR
Q governs how sharply RF hardware can carve the spectrum. Preselector and RF filter stages ahead of an SDR rely on resonators with enough Q to pass the wanted band while rejecting strong out-of-band signals that would otherwise overload the front end. In oscillators, a high-Q resonator (crystal, cavity, or dielectric) narrows the phase noise of the local oscillator, directly improving the purity of the reference the SDR mixes against. High Q is thus a recurring goal wherever frequency selectivity or spectral purity matters.
GopherTrunk performs its channel filtering in software on the IQ stream, where the “selectivity” is set by digital filter design rather than a physical Q. The physical Q of the analog preselector and of the SDR’s reference oscillator still bounds what reaches the ADC, so a clean, well-filtered front end lets GopherTrunk’s digital stages start from better samples. The concept translates: a narrow digital channelizer is the software analogue of a high-Q resonator.