Coaxial Line Geometry and Impedance
A coaxial line consists of an inner conductor (diameter d) surrounded by a dielectric and outer conductor (inner diameter D). The characteristic impedance is:
Z₀ = (138 / √εᵣ) · log₁₀(D/d) [Ω]
For 50 Ω with εᵣ = 1 (air): D/d = 2.303. For polyethylene (εᵣ = 2.25): D/d = 3.48.
Standard Coaxial Impedances
| Impedance | Application | D/d Ratio (air) |
|---|---|---|
| 50 Ω | RF/microwave, test equipment | 2.303 |
| 75 Ω | Cable TV, video, broadcast | 3.495 |
| 93 Ω | High-impedance digital (RG-62) | 6.70 |
Note: 50 Ω is a compromise between minimum attenuation (~77 Ω for air) and maximum power handling (~30 Ω for air).
Attenuation Mechanisms
Total coaxial attenuation has two components:
α_total = α_conductor + α_dielectric α_conductor = (R_s/(2π)) · (1/d + 1/D) / (2·Z₀) [dB/m] α_dielectric = (π · f · √εᵣ · tan δ) / c [dB/m] where R_s = √(π·f·μ/σ) = skin-effect surface resistance
Typical Cable Attenuation (50 Ω, RG-58 vs. LMR-400)
| Frequency | RG-58 (dB/m) | LMR-400 (dB/m) | EchoFlex-10 (dB/m) |
|---|---|---|---|
| 100 MHz | 0.20 | 0.023 | 0.011 |
| 1 GHz | 0.65 | 0.074 | 0.037 |
| 2.4 GHz | 1.10 | 0.120 | 0.060 |
| 5.8 GHz | 1.90 | 0.200 | 0.098 |
| 10 GHz | 2.80 | 0.310 | 0.150 |
Analyzing Coaxial Cable S-Parameters in RF View
A cable measured as .s2p file shows:
- S21 magnitude: negative slope with √f behavior (conductor loss dominant at low f) transitioning to f slope (dielectric loss)
- S11/S22: should be <−25 dB for a well-terminated cable; reflections indicate impedance discontinuities (connectors, kinks)
- S21 phase: linear phase slope → constant group delay indicates a good cable
- Group delay variation: deviation from constant indicates dispersion
RF View's batch SNP processor lets you load S21 data from multiple cable samples or temperature conditions to compare attenuation vs. frequency profiles.