Three Methods to Extract Q from S-Parameters
| Method | S-Parameter | Best For |
|---|---|---|
| 3 dB BW method | S21 resonance | Bandpass/notch resonators, coupled resonators |
| |S11| phase slope | S11 | One-port resonators, resonant matching networks |
| S21 magnitude at resonance | S21 + bandwidth | Coupling coefficient determination |
Method 1: 3 dB Bandwidth from S21
For a bandpass resonator or filter section: Q_L (loaded Q) = f₀ / BW₋₃dB Procedure in RF View: 1. Load resonator .s2p → S21 dB view 2. Activate BW Marker → automatically finds f₀, BW₋₃dB 3. Q_L = f₀ / BW₋₃dB (displayed by RF View as part of BW Marker output) Example: microstrip resonator at 5 GHz, BW₋₃dB = 83 MHz Q_L = 5000 MHz / 83 MHz = 60.2
Method 2: Phase Slope from S11 (One-Port Method)
At series resonance: |S11| has a minimum, phase passes through 0° Q_L = f₀ / (2 × |df/dφ| evaluated near resonance) More precisely: Q_L = f₀ / (f₊₄₅ − f₋₄₅) where f₊₄₅ and f₋₄₅ are frequencies where S11 phase = ±45° Load resonator .s1p → S11 phase view → delta marker at ±45° phase points
Loaded vs Unloaded Q
Q_L (loaded) includes coupling loss and resonator loss Q_0 (unloaded) is the resonator intrinsic Q From S21 at resonance: Coupling factor k = √[(1 − |S21_min|) / |S21_min|] (for single-mode resonator) Q_0 = Q_L × (1 + 2k) (for critically coupled resonator k=1: Q_0 = 3·Q_L) Q_ext = Q_L / k (external Q from coupling structure) For a good resonator: aim for Q_0 >> Q_L
RF View Q Measurement: Load resonator .s2p → BW Marker immediately reads 3 dB bandwidth and Q_L. Switch to Phase view for ±45° phase crossing method. Free on Android.