Coax Impedance Calculator Formula

Understand the math behind the coax impedance calculator. Each variable explained with a worked example.

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Formulas Used

Characteristic Impedance

impedance_ohm = 138 / sqrt(dielectric_constant) * log10(outer_diameter_mm / inner_diameter_mm)

Velocity Factor

velocity_factor = 1 / sqrt(dielectric_constant)

Diameter Ratio

diameter_ratio = outer_diameter_mm / inner_diameter_mm

Variables

VariableDescriptionDefault
outer_diameter_mmOuter Conductor ID(mm)3.5
inner_diameter_mmInner Conductor OD(mm)0.9
dielectric_constantDielectric Constant (Er)2.3

How It Works

Coaxial Cable Impedance

Formula

Z0 = (138 / sqrt(Er)) x log10(D/d)

Where D is the outer conductor inner diameter, d is the inner conductor outer diameter, and Er is the relative dielectric constant.

Common cables: RG-58 (50 ohm), RG-59 (75 ohm), RG-6 (75 ohm).

Worked Example

RG-58-like: D = 3.5 mm, d = 0.9 mm, PTFE dielectric (Er = 2.3).

outer_diameter_mm = 3.5inner_diameter_mm = 0.9dielectric_constant = 2.3
  1. 01Ratio = 3.5 / 0.9 = 3.889
  2. 02Z0 = 138 / sqrt(2.3) x log10(3.889)
  3. 03Z0 = 91.0 x 0.5898 = 53.7 ohms

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