Definition
Q = 2π × (Peak energy stored) / (Energy dissipated per cycle) Q = ω₀ · L / R_series [inductor, ω₀ = operating frequency] Q = 1 / (ω₀ · C · R_series) [capacitor] Q = f₀ / BW₋₃dB [resonant circuit bandwidth]
Higher Q means lower loss per cycle, narrower bandwidth, and more frequency-selective behavior. Low-Q components waste energy as heat and broaden the frequency response of resonant circuits.
Typical Q Values for RF Components
| Component | Frequency | Q (typical) | ESR or tan δ |
|---|---|---|---|
| SMD inductor (0402, 10 nH) | 900 MHz | 40–80 | 0.5–1.5 Ω |
| SMD inductor (0402, 10 nH) | 2.4 GHz | 20–50 | 1–3 Ω |
| SMD capacitor C0G/NP0 (10 pF) | 1 GHz | 500–2000 | very low |
| SMD capacitor X7R (100 pF) | 1 GHz | 50–200 | low–moderate |
| Microstrip resonator (50 Ω) | 2.4 GHz | 100–300 | — |
| Ceramic resonator (comb) | 1–10 GHz | 1000–5000 | — |
| SAW resonator | 900 MHz | 1000–4000 | — |
| BAW resonator | 2–6 GHz | 2000–8000 | — |
| Crystal (AT-cut) | 10–50 MHz | 10⁴–10⁶ | — |
Q and Matching Network Insertion Loss
Matching networks with finite-Q components exhibit insertion loss. For an L-network with design Q and component Q_L:
IL ≈ 1 + Q_design / Q_component [linear factor] IL (dB) ≈ 4.34 · Q_design / Q_component [for small IL] Example: Q_design=3, Q_component=50 → IL ≈ 0.26 dB Example: Q_design=5, Q_component=20 → IL ≈ 1.09 dB
This shows why high-Q inductors matter for high-Q matching designs. A 5 nH inductor with Q=60 vs. Q=20 at 2.4 GHz can mean the difference between 0.3 dB and 1.1 dB matching network loss.
Loaded Q vs Unloaded Q
Q_L (loaded Q) = f₀ / BW₋₃dB [observed from S21 of a coupled resonator] Q_0 (unloaded Q) = Q of the resonator alone, without coupling loss Q_ext (external Q) = Q from the coupling structure Relation: 1/Q_L = 1/Q_0 + 1/Q_ext At critical coupling: Q_ext = Q_0 → Q_L = Q_0/2, IL = 6 dB at resonance
RF View Q Calculator: Enter inductor L, ESR, and frequency in the Utilities tab to get Q factor and find the self-resonant frequency. Also supports capacitor Q computation from C and ESR.