What Is Normalization?
S-parameters are defined relative to a reference impedance Z₀. The standard is 50 Ω for RF/microwave systems and 75 Ω for video/cable TV. Changing the reference impedance changes all S-parameter values even for the same physical device — the device hasn't changed, only the mathematical reference has.
Re-normalization Formula
To re-normalize from Z₀_old to Z₀_new: For a 2-port device: Γ₀ = (Z₀_new − Z₀_old) / (Z₀_new + Z₀_old) [S_new] = ([S_old] − Γ₀[I]) · ([I] − Γ₀[S_old])⁻¹ For a 1-port (S11 only): S11_new = (S11_old − Γ₀) / (1 − Γ₀·S11_old)
50Ω to 75Ω Renormalization Example
Device measured at Z₀=50Ω: S11 = −20 dB at 0° → |Γ| = 0.100, Γ = 0.100
Renormalize to Z₀=75Ω:
Γ₀ = (75−50)/(75+50) = 25/125 = 0.200
S11_75Ω = (0.100 − 0.200) / (1 − 0.200 × 0.100)
= (−0.100) / (0.980)
= −0.102
→ S11 at Z₀=75Ω = −0.102 → −19.8 dB (slightly different from 50Ω measurement)
When Renormalization Matters
| Situation | Action Required |
|---|---|
| VNA measured at 50Ω, need 75Ω analysis | Renormalize S11 to 75Ω |
| Touchstone file has "R 75" in options line | RF View reads it as 75Ω reference — no action needed |
| Cascade simulation: one device at 50Ω, another at 75Ω interface | Renormalize or use ABCD matrices instead |
| On-wafer measurement with 50Ω probes for 100Ω device | Renormalize to 100Ω after measurement |
RF View: RF View reads the reference impedance (R [value]) from the Touchstone options line and uses it for all Smith chart and impedance calculations. For renormalization, use scikit-rf (Python) or Keysight PLTS. Free on Android for 50Ω analysis.