How do I calculate the quality factor of a transmission line resonator?
Resonator Quality Factor
The quality factor (Q) of a resonator measures how efficiently it stores energy relative to how much it dissipates per cycle. Q = 2π × (energy stored) / (energy dissipated per cycle). A higher Q means lower loss, sharper resonance, and greater selectivity. For filter and oscillator applications, higher Q enables better performance.
| Parameter | Semi-Rigid | Conformable | Flexible |
|---|---|---|---|
| Loss (dB/m at 10 GHz) | 0.8-2.5 | 1.0-3.0 | 1.5-5.0 |
| Phase Stability | Excellent | Good | Fair |
| Bend Radius | Fixed after forming | Hand-formable | Continuous flex OK |
| Shielding (dB) | >120 | >90 | >60-90 |
| Cost (relative) | 2-5x | 1.5-3x | 1x |
Frequently Asked Questions
How does Q affect filter performance?
Filter insertion loss is inversely proportional to Q: higher Q = lower loss. A 5-pole bandpass filter with 1% bandwidth requires resonator Q > 500 for < 1 dB insertion loss. The same filter on FR4 (Q ≈ 60) would have > 10 dB insertion loss, making it impractical.
What is the highest achievable Q?
Superconducting cavity resonators achieve Q > 10¹⁰ at cryogenic temperatures. At room temperature: metal cavities Q ≈ 5,000-30,000; dielectric resonators Q ≈ 10,000-100,000; sapphire whispering gallery modes Q > 100,000. For PCB-compatible resonators, SIW (substrate integrated waveguide) resonators achieve Q ≈ 200-500.
Does coupling affect measured Q?
Yes. The measured (loaded) Q is always lower than the unloaded Q. To extract Q0 from measurement, use two-port coupling and measure both the loaded Q and the coupling coefficients. Under-coupled measurements (weak coupling, QL ≈ Q0) provide the most accurate Q0 extraction.