S21 Definition
S21 is the (2,1) element of the scattering matrix — the ratio of the wave emerging from port 2 to the wave incident on port 1, with port 2 terminated in Z₀ = 50 Ω. It represents the forward transmission through the network.
S21 = b₂ / a₁ (with a₂ = 0) |S21| < 1 → insertion loss (passive: filter, cable, connector, matching network) |S21| > 1 → gain (active: amplifier, LNA, PA) Insertion Loss (dB) = −20 · log₁₀|S21| [positive, smaller = less loss] Gain (dB) = 20 · log₁₀|S21| [positive for amplifiers]
Key Filter Parameters from S21
| Parameter | Definition | Typical Spec (LTE BPF) |
|---|---|---|
| Passband IL | −S21 (dB) in passband | < 1.5–2.5 dB |
| Stopband rejection | −S21 (dB) at stop freq | > 30–60 dB |
| 3 dB bandwidth | Freq range where |S21| ≥ −3 dB | 5–20 MHz (LTE channel) |
| Shape factor | BW₋₄₀dB / BW₋₃dB | 1.3–2.0 (SAW/BAW) |
| Passband ripple | Peak-to-peak variation of S21 in passband | < 0.5 dB (Butterworth), ≤ 1 dB (Cheby) |
| Group delay flatness | Δτg across passband | < 5 ns for LTE data |
S21 for Amplifier Characterization
For active two-port networks (LNA, PA), |S21|² represents the available power gain (transducer gain when S11=S22=0). Key specs extracted from S21:
- Gain at f₀: |S21| in dB at the design frequency (e.g., 20 dB LNA gain at 2.4 GHz)
- Gain flatness: variation across the operating band (±0.5 dB typical)
- Gain roll-off: dB/decade slope; sets amplifier bandwidth
- Gain compression (P1dB): frequency where small-signal gain drops 1 dB under large signal — derived from two-tone tests, not from linear S21
S21 Bandwidth Extraction
3 dB BW: frequencies f₁, f₂ where S21(f) = S21_peak − 3 dB Center freq: f₀ = √(f₁ · f₂) [geometric mean for BPF] Fractional BW: FBW = (f₂ − f₁) / f₀ Loaded Q: Q_L = f₀ / (f₂ − f₁)
Typical S21 Values
| Device | S21 Typical |
|---|---|
| LTE SAW/BAW filter (passband) | −1.5 to −3 dB |
| RF cable, 1 m at 2.4 GHz (RG58) | −1.5 to −2 dB |
| SMA connector (to 18 GHz) | −0.1 to −0.3 dB |
| LNA (e.g. 1.5–2.7 GHz) | +14 to +20 dB |
| Power amplifier (PA) | +25 to +35 dB |
| L/C matching network | −0.2 to −1 dB |
RF View: RF View plots S21 from any .s2p file with markers for passband center, 3 dB bandwidth, and stopband rejection. Compare multiple filter files on one chart to evaluate vendors. Group delay is also displayed from the same file.