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Coaxial Cable Characteristic Impedance

#coax#impedance#transmission line#characteristic impedance#cable design

Coaxial Cable Characteristic Impedance

The characteristic impedance of a coaxial transmission line depends on the ratio of outer to inner conductor diameters and the dielectric constant of the insulating material. This formula is essential for designing custom coax or understanding commercial cables.

Z0=138εrlog⁡10(Dd)Z_0 = \frac{138}{\sqrt{\varepsilon_r}} \log_{10}\left(\frac{D}{d}\right)

Alternative Forms

Natural Log Form
Z0=60εrln⁡(Dd)Z_0 = \frac{60}{\sqrt{\varepsilon_r}} \ln\left(\frac{D}{d}\right)
Using natural logarithm
Air Dielectric
Z0=138log⁡10(Dd)Z_0 = 138 \log_{10}\left(\frac{D}{d}\right)
For air-insulated coax (εᵣ = 1)

Input Variables

mm

Inner diameter of the outer conductor (shield)(Range: 0.1 – 100 mm)

mm

Outer diameter of the center conductor(Range: 0.01 – 50 mm)

ratio

Dielectric constant of insulating material(Range: 1 – 10 ratio)

Results

Characteristic Impedance (Z_0)
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📖 Example: RG-58 Coaxial Cable

Verify the impedance of standard RG-58 cable

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