Resonator Q
A resonator's loaded Q combines its intrinsic (unloaded) Q with the external Q set by how tightly it is coupled to the circuit. This tool combines them, gives the resulting 3-dB bandwidth, the coupling coefficient, and the insertion loss a one-port/transmission resonator shows at resonance. Useful for filter, oscillator-tank and cavity design.
Equations & Parameters ▸
\(\dfrac{1}{Q_L}=\dfrac{1}{Q_0}+\dfrac{1}{Q_e} \qquad \text{BW}_{3dB}=\dfrac{f_0}{Q_L} \qquad \beta=\dfrac{Q_0}{Q_e}\)
\(\text{IL}=-20\log_{10}\!\left(1-\dfrac{Q_L}{Q_0}\right)\ \text{dB}\)
\(\text{IL}=-20\log_{10}\!\left(1-\dfrac{Q_L}{Q_0}\right)\ \text{dB}\)
| Q0 | Unloaded quality factor (intrinsic, from resonator losses). |
| Qe | External quality factor (from the coupling to the ports). |
| f0 | Resonant frequency (MHz), optional — gives the 3-dB bandwidth. |
| β | Coupling coefficient Q₀/Qe: <1 undercoupled, 1 critical, >1 overcoupled. |
Reference: D. M. Pozar, Microwave Engineering, 4th ed., Wiley, 2012 (resonators & coupling).
Inputs
Intrinsic
Coupling
MHz
For bandwidthResults
Quality factor
Loaded QL—
Coupling β—
Coupling regime—
Response
3-dB bandwidth—
Insertion loss—
Diagram