Coaxial Cable Characteristic Impedance
Characteristic impedance, velocity factor and capacitance per metre of a coaxial line from its diameters and dielectric constant.
Worked example
Input: Outer conductor inner dia. D 3.5 mm, Inner conductor dia. d 1 mm, Dielectric constant εr 2.25
Result: Characteristic impedance Z₀ 50.0543 Ω, Velocity factor 0.666667, Capacitance per metre 99.9132 pF/m
Result: Characteristic impedance Z₀ 50.0543 Ω, Velocity factor 0.666667, Capacitance per metre 99.9132 pF/m
Formula
Z₀ = (138/√εr)·log₁₀(D/d)
C′ = 2π·ε₀·εr / ln(D/d)
How it works
Z₀ = (138/√εr)·log₁₀(D/d). A larger diameter ratio raises the impedance, a higher dielectric constant lowers it. The velocity factor 1/√εr tells you how much the wavelength shrinks inside the cable.
Practical tipFor polyethylene (εr 2.25) coax, 50 Ω needs D/d ≈ 3.5 and 75 Ω needs D/d ≈ 6.5. At equal outer diameter, a 75 Ω cable therefore has a thinner centre conductor.
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Results and summaries are for reference. For certification and test reports use the latest official standard text and calibrated instrument data. Last updated: 2026-10-10