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Coaxial Cable Characteristic Impedance & Cutoff Calculator

Coaxial cables carry high-frequency radio frequency (RF) signals between transmitters and antennas with minimal radiation loss by maintaining uniform concentric geometry.

Outer diameter of center copper conductor in mm (e.g. RG-58 = 0.90 mm).

Inner diameter of shield braid or outer conductor in mm (RG-58 = 2.95 mm).

Relative permittivity of insulator (Air = 1.0, Foam Polyethylene ≈ 1.5, Solid PE = 2.3, PTFE = 2.1).

Calculated Result
46.91 Ω

Coaxial Cable Impedance (Z₀)

Characteristic Impedance (Z₀)

46.91 Ω

Capacitance per Meter

107.64 pF/m

Inductance per Meter

0.237 µH/m

Propagation Velocity Factor

65.9% of c

Higher-Order TE₁₁ Cutoff

32.71 GHz

Calculation Breakdown

  1. 1. Diameter Ratio & Dielectric FactorD/d = 2.95 mm / 0.9 mm = 3.278. Log₁₀(D/d) = 0.5156, √ε_r = √2.3 = 1.517
  2. 2. Characteristic Impedance FormulationZ₀ = (138 / √ε_r) · log₁₀(D/d) = (138 / 1.517) · 0.5156 = 46.91 Ω
  3. 3. Distributed Capacitance & InductanceC = 24.13 · 2.3 / 0.5156 = 107.64 pF/m, L = 0.46 · 0.5156 = 0.237 µH/m

Impedance vs Shield Diameter D (d = 0.9mm, ε_r = 2.3)

Interactive visualization based on your current inputs

Z₀ (Ω)
0.0193856752.0 mm2.95 mm (RG-58)4.0 mm5.5 mm6.0 mm (75Ω)Shield ID (mm)Impedance Z₀ (Ω)

What Is the Coaxial Cable Characteristic Impedance & Cutoff Calculator?

Characteristic impedance Z0 is the ratio of voltage to current for a wave propagating along a transmission line without reflections.

How Does the Coaxial Cable Characteristic Impedance & Cutoff Calculator Work?

Derived from distributed telegrapher’s parameters Z0 = √(L/C), independent of cable length.

Coaxial Cable Characteristic Impedance & Cutoff Calculator Formula & Variables

The core mathematical equation utilized by this calculator is expressed as:

Z_0 = \frac{138}{\sqrt{\varepsilon_r}} \log_{10}\left(\frac{D}{d}\right), \quad C = \frac{24.13 \cdot \varepsilon_r}{\log_{10}(D/d)} \text{ (pF/m)}, \quad f_c \approx \frac{600}{\pi (D + d) \sqrt{\varepsilon_r}} \text{ (GHz)}

Characteristic impedance is 138 over square root of dielectric constant times log10 of diameter ratio. Capacitance scales with dielectric constant.

How to Use the Coaxial Cable Characteristic Impedance & Cutoff Calculator

  1. Enter center conductor diameter in millimeters.
  2. Enter shield inside diameter.
  3. Specify dielectric insulator relative permittivity.

Step-by-Step Example Calculation

Standard RG-58 50-Ohm Coax (d = 0.90mm, D = 2.95mm, ε_r = 2.3)

Input Values:

innerConductorDiameterMm:0.90
outerShieldInnerDiameterMm:2.95
dielectricPermittivityEr:2.3
Worked Steps: Calculates a 46.94 Ω characteristic impedance, 107.59 pF/m distributed capacitance, 66.0% velocity factor, and 32.7 GHz TE11 cutoff.

Understanding Your Result

Impedance Z0 (Ω): Match to transmitter and antenna to prevent VSWR reflections.

Capacitance (pF/m): Distributed line capacitive loading.

Cutoff Frequency: Upper frequency ceiling before higher-order waveguide modes degrade signal.

Factors That Affect the Result

  • Widening the dielectric gap (higher D/d) raises impedance; denser dielectric lowers velocity of propagation.

When Should You Use This Calculator?

  • Custom RF cable design, SMA/BNC connector impedance matching, and high-speed PCB trace co-planar waveguide modeling.

Assumptions & Limitations

  • Assumes concentric circular cylinders and low-loss dielectric with uniform permittivity.

Frequently Asked Questions

Calculation Accuracy & Reference Note

Standard IEEE microwave transmission line formulation.

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