What is the equation for quality factor?

What is the equation for quality factor?

• A. Quality factor = bandwidth/main frequency
• B. Quality factor = main frequency/bandwidth
• C. Quality factor = bandwidth
• D. Quality factor = main frequency × bandwidth

Answer: (B)

Quality factor measures how sharply a system resonates. It expresses how narrow the resonance is relative to its center frequency. The standard definition is the ratio of the resonant frequency to the bandwidth around that resonance: Q = f0 / Δf. Equivalently, in angular terms, Q = ω0 / Δω. This way of writing it captures the idea that a smaller bandwidth compared with the center frequency yields a higher Q, meaning a more selective, narrower peak. If you tried to use bandwidth alone, or multiply frequency and bandwidth, you’d miss that comparative, dimensionless measure of sharpness. Using the center frequency divided by the bandwidth is the correct, meaningful expression (the inverse arrangement would describe something else).

Quality factor measures how sharply a system resonates. It expresses how narrow the resonance is relative to its center frequency. The standard definition is the ratio of the resonant frequency to the bandwidth around that resonance: Q = f0 / Δf. Equivalently, in angular terms, Q = ω0 / Δω. This way of writing it captures the idea that a smaller bandwidth compared with the center frequency yields a higher Q, meaning a more selective, narrower peak. If you tried to use bandwidth alone, or multiply frequency and bandwidth, you’d miss that comparative, dimensionless measure of sharpness. Using the center frequency divided by the bandwidth is the correct, meaningful expression (the inverse arrangement would describe something else).