Why Not Just Use Voltage and Current?
At low frequencies, Z (impedance) and Y (admittance) parameters work fine because circuits are small compared to wavelength. At RF frequencies, connecting two ports to measure Z₁₂ requires an open circuit — but at 5 GHz, an "open circuit" at the end of a short trace looks like a short circuit after λ/4. The measurement becomes ill-defined and dependent on cable length.
Power Wave Definition
Power waves are defined to give unambiguous, cable-length-independent S-parameter measurements:
a_i = (V_i + Z₀·I_i) / (2·√Z₀) [incident power wave at port i] b_i = (V_i − Z₀·I_i) / (2·√Z₀) [reflected power wave at port i] |a_i|² = incident power at port i |b_i|² = reflected/transmitted power at port i S_ij = b_i/a_j (with a_k=0 for all k≠j → port k matched to Z₀)
Physical Interpretation
| S-Parameter | Physical Meaning | Measurement Condition |
|---|---|---|
| S₁₁ | Fraction of incident power reflected at port 1 | Port 2 terminated in Z₀ |
| S₂₁ | Fraction of incident power at port 1 transmitted to port 2 | Port 2 terminated in Z₀ |
| S₂₂ | Fraction reflected at port 2 | Port 1 terminated in Z₀ |
| S₁₂ | Reverse transmission | Port 1 terminated in Z₀ |
Why Z₀ = 50 Ω Normalization
The choice of Z₀ for the reference termination is what makes S-parameters independent of cable length. As long as the transmission line connecting the VNA to the DUT has characteristic impedance Z₀ = 50 Ω, the S-parameters measured at the VNA ports equal the S-parameters at the DUT ports (after error correction). The "50 Ω" is not a property of the DUT — it's the reference impedance for the wave ratio definition.