Cable Characteristic Impedance Calculator

Characteristic impedance of a coaxial cable: Z₀ = (138/√ε_r) · log₁₀(D/d)

The characteristic impedance Z₀ of a coaxial cable depends only on geometry and dielectric: Z0 = (138/√εr) · log10(D/d), where D is the shield inner diameter, d the inner conductor diameter, and ε_r the dielectric constant (≈2.3 for polyethylene). For transmission lines in general, Z0 = √(L/C). Standard values: 50 Ω for RF, lab instrumentation and scientific networks (RG-58, RG-213, LMR-400); 75 Ω for cable TV and video distribution (RG-6, RG-59); 93 Ω in legacy computer links. Twisted pair Cat6 carries 100 Ω differential. Example: D = 6 mm, d = 2 mm, ε_r = 2.3 → Z₀ = (138/1.517) · log₁₀(3) ≈ 43.4 Ω. Matching: reflection vanishes when the load equals Z₀; VSWR measures mismatch and the closer to 1:1, the better.

Applications: cable TV, Wi-Fi antennas, Ethernet, ham radio

Characteristic impedance is the basis for sizing cable TV networks (NET, Claro), Wi-Fi antenna feeds, broadcast and ham-radio RF chains, Ethernet twisted-pair (100 Ω), laboratory instrumentation (oscilloscopes, network analyzers) and any link that must avoid reflections.

FAQ

Why 50 Ω in RF and 75 Ω in TV? 50 Ω is the compromise between minimum loss (≈77 Ω) and maximum power-handling (≈30 Ω); 75 Ω minimises loss for video signals.

Does Z₀ depend on cable length? No — it depends only on cross-sectional geometry and the dielectric, not length.

What is VSWR? Voltage Standing Wave Ratio: 1:1 means perfect match, 2:1 already indicates appreciable reflection.

Can I connect 50 Ω to 75 Ω? Only with an impedance transformer (matching network); direct connection causes reflections and power loss.