Which term is a unitless quantity related to bandwidth?

Which term is a unitless quantity related to bandwidth?

• A. Bandwidth
• B. Impedance
• C. Attenuation
• D. Quality factor

Answer: (D)

Quality factor, often written as Q, is a unitless measure of how sharply a system resonates. In a resonant circuit or filter, Q is defined as the center (resonant) frequency divided by the bandwidth: Q = f0 / Δf. Because both f0 and Δf are in hertz, their ratio has no units, leaving a pure number. This tells you how narrow the resonance is relative to its center frequency—the higher the Q, the narrower and more selective the bandwidth. For example, a circuit resonating at 1 GHz with a bandwidth of 10 MHz has Q = 100. Other terms don’t fit as neatly: bandwidth has units of Hz; impedance has units of ohms; attenuation is a ratio (often in dB) but doesn’t directly quantify how bandwidth relates to a center frequency.

Quality factor, often written as Q, is a unitless measure of how sharply a system resonates. In a resonant circuit or filter, Q is defined as the center (resonant) frequency divided by the bandwidth: Q = f0 / Δf. Because both f0 and Δf are in hertz, their ratio has no units, leaving a pure number. This tells you how narrow the resonance is relative to its center frequency—the higher the Q, the narrower and more selective the bandwidth. For example, a circuit resonating at 1 GHz with a bandwidth of 10 MHz has Q = 100. Other terms don’t fit as neatly: bandwidth has units of Hz; impedance has units of ohms; attenuation is a ratio (often in dB) but doesn’t directly quantify how bandwidth relates to a center frequency.