Three Methods to Get Loaded Q
Method 1: 3 dB Bandwidth (most common) Q_L = f₀ / BW₋₃dB Method 2: Phase Slope (one-port) Q_L = f₀ / (f₊₄₅ − f₋₄₅) where f₊₄₅, f₋₄₅ are ±45° phase crossing freqs Method 3: Direct Formula (from S21 at resonance) At resonance, S21 = 1 − 2Q_L/Q_0 (for coupled resonator) Q_L/Q_0 = (1 − |S21_res|) / 2
Method 1 Step-by-Step: 3 dB BW in RF View
- Load filter .s2p → S21 dB view
- Activate BW Marker mode
- RF View automatically finds:
- Peak frequency f₀ (center frequency)
- Left −3 dB crossing frequency f₁
- Right −3 dB crossing frequency f₂
- Bandwidth BW = f₂ − f₁
- Q_L = f₀ / BW (displayed in marker readout)
Method 2: Phase Slope (for matching network resonance)
Load matching circuit simulation S11 → Phase view (S11 phase passes through 0° at resonance — series resonant match) Find frequencies where phase = +45° and −45°: Using delta marker: set reference at 0° crossing → find ±45° crossing freqs Q_L = f₀ / (f₊₄₅ − f₋₄₅) Example: f₀ = 900 MHz (S11 phase = 0°) f₊₄₅ = 912 MHz, f₋₄₅ = 888 MHz Q_L = 900 / (912 − 888) = 900/24 = 37.5
Applications of Q_L in RF Design
| Context | Q_L Meaning | Implication |
|---|---|---|
| BPF qualification | Filter selectivity | Q_L ≥ f₀/BW_spec required |
| Matching network | Bandwidth indicator | Higher Q → narrower BW → check if sufficient |
| Resonator | Energy storage quality | Q_L/Q_0 → coupling efficiency |
| Crystal oscillator | Phase noise, frequency stability | Higher Q_L → better phase noise |
RF View BW Marker: Q_L is automatically computed and displayed when BW Marker is active — no manual calculation needed. Available for all plot types including S21 dB, S11 dB, VSWR, and Group Delay. Free on Android.