Coaxial Cable Impedance
Z0 = (138/√εr) × log10(D/d)
Quick answer
This calculator solves Z0 = (138/√εr) × log10(D/d) for Outer Conductor ID. With Characteristic Impedance 0.47 kΩ, Dielectric Constant εr 0.5, Inner Conductor OD 22 mm, the result is 5632 mm. It solves in 2 directions, so you can enter the values you have and get the one you need.
Calculator
Formula
Description
The characteristic impedance of a coaxial cable depends on the ratio of the outer conductor inner diameter to the inner conductor outer diameter, and the dielectric constant of the insulating material between them. Standard impedances are 50Ω (used in most RF systems and test equipment), 75Ω (used in video, CATV, and satellite systems), and 93Ω (used in some older data transmission). The 50Ω standard represents a compromise between minimum attenuation (77Ω in air) and maximum power handling (30Ω in air) for the same outer conductor size.
Variables
- Z0 — Characteristic impedance (Ω)
- εr — Relative dielectric constant of the insulating material
- D — Inner diameter of the outer conductor (shield) (mm)
- d — Outer diameter of the inner conductor (center conductor) (mm)
Practical Notes
Common dielectrics: solid PE εr = 2.25, foam PE εr = 1.5, PTFE εr = 2.1, air εr = 1.0. RG-58 (50Ω): d = 0.9mm, D = 2.95mm, PE dielectric. RG-6 (75Ω): d = 1.0mm, D = 4.7mm, foam PE. Lower εr allows faster signal propagation (higher velocity factor) and lower loss.
Symbols and units
| Symbol | Meaning | Default unit | Accepted units |
|---|---|---|---|
| Z0 | Characteristic Impedance | Ω | mΩ, Ω, kΩ, MΩ |
| er | Dielectric Constant εr | — | — |
| D | Outer Conductor ID | mm | mm |
| d | Inner Conductor OD | mm | mm |
Step by step
- 1. What you know: Characteristic Impedance 0.47 kΩ, Dielectric Constant εr 0.5, Inner Conductor OD 22 mm
- 2. The relation: Z0 = (138/√εr) × log10(D/d)
- 3. Substitute: Z0 = 0.47 kΩ, er = 0.5, d = 22 mm
- 4. Result: Outer Conductor ID = 5632 mm
Worked examples
Minimum range
Given: Characteristic Impedance 1 Ω, Dielectric Constant εr 0.025, Inner Conductor OD 0.22 mm
Result: Outer Conductor ID = 0.2206 mm
Low range
Given: Characteristic Impedance 10 Ω, Dielectric Constant εr 0.25, Inner Conductor OD 2.2 mm
Result: Outer Conductor ID = 2.391 mm
Typical
Given: Characteristic Impedance 0.47 kΩ, Dielectric Constant εr 0.5, Inner Conductor OD 22 mm
Result: Outer Conductor ID = 5632 mm
High range
Given: Characteristic Impedance 4.7 Ω, Dielectric Constant εr 8 × 10⁻⁴, Inner Conductor OD 0.22 mm
Result: Outer Conductor ID = 0.2205 mm
Maximum range
Given: Characteristic Impedance 47 Ω, Dielectric Constant εr 0.008, Inner Conductor OD 2.2 mm
Result: Outer Conductor ID = 2.36 mm
Solving for each variable
Solve for Outer Conductor ID
Characteristic Impedance 1 Ω, Dielectric Constant εr 0.025, Inner Conductor OD 0.22 mm → 0.2206 mm
Solve for Inner Conductor OD
Characteristic Impedance 1 Ω, Dielectric Constant εr 0.025, Outer Conductor ID 0.1 mm → 0.09974 mm
How Outer Conductor ID changes with Characteristic Impedance
| Characteristic Impedance (input) | Outer Conductor ID (result) |
|---|---|
| 47 Ω | 38.3 mm |
| 117.5 Ω | 88 mm |
| 0.235 kΩ | 352 mm |
| 0.3525 kΩ | 1408 mm |
| 0.47 kΩ | 5632 mm |
| 0.705 kΩ | 90120 mm |
| 0.94 kΩ | 1.44 × 10⁶ mm |
| 1.88 kΩ | 9.45 × 10¹⁰ mm |
| 3.29 kΩ | 1.59 × 10¹⁸ mm |
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<p><a href="https://vbatpower.com/formulas/cable-impedance/">Coaxial Cable Impedance</a> Calculator by vbatpower.com</p>Frequently asked questions
How do you calculate Coaxial Cable Impedance?
Use Z0 = (138/√εr) × log10(D/d). With Characteristic Impedance 0.47 kΩ, Dielectric Constant εr 0.5, Inner Conductor OD 22 mm, Outer Conductor ID works out to 5632 mm.
How do you calculate calcul attenuation cable coaxial?
Rearrange for Outer Conductor ID: with Characteristic Impedance 10 Ω, Dielectric Constant εr 0.25, Inner Conductor OD 2.2 mm, Outer Conductor ID is 2.391 mm.
What is the formula for Coaxial Cable Impedance?
The formula is Z0 = (138/√εr) × log10(D/d). The characteristic impedance of a coaxial cable depends on the ratio of the outer conductor inner diameter to the inner conductor outer diameter, and the dielectric constant of the insulating material between them.
How do you find Inner Conductor OD when you know the other values?
Rearrange for Inner Conductor OD: with Characteristic Impedance 1 Ω, Dielectric Constant εr 0.025, Outer Conductor ID 0.1 mm, Inner Conductor OD is 0.09974 mm.
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