Coax Impedance Calculator Formula
Understand the math behind the coax impedance calculator. Each variable explained with a worked example.
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_mmVariables
| Variable | Description | Default |
|---|---|---|
outer_diameter_mm | Outer Conductor ID(mm) | 3.5 |
inner_diameter_mm | Inner Conductor OD(mm) | 0.9 |
dielectric_constant | Dielectric 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).
- 01Ratio = 3.5 / 0.9 = 3.889
- 02Z0 = 138 / sqrt(2.3) x log10(3.889)
- 03Z0 = 91.0 x 0.5898 = 53.7 ohms
Frequently Asked Questions
Why 50 ohms?
50 ohms is a compromise between minimum attenuation (77 ohms) and maximum power handling (30 ohms) for air-dielectric coax.
Why 75 ohms for video?
75 ohms minimizes signal attenuation in coax. Video prioritizes signal fidelity over power handling.
What is velocity factor?
Signal speed as a fraction of c. Solid PE: 0.66. Foam PE: 0.78. PTFE: 0.70. Air: 1.0.
Ready to run the numbers?
Open Coax Impedance Calculator