Coax Cable Calculator (Impedance-Inductance-Capacitance)




Impedance (ohms):

Capacitance (pico farads):

Inductance (nano henries):

Cutoff Frequency (GHz):

The Coax Cable Calculator (Impedance–Inductance–Capacitance) is an essential online tool used by electrical engineers, RF professionals, and network installers to compute the fundamental electrical characteristics of coaxial cables. Coaxial cables are widely used in radio frequency transmission lines, CCTV systems, satellite dishes, and high-frequency digital applications. Ensuring these cables meet the desired specifications is critical for system reliability and performance.

This calculator is specifically designed to compute characteristic impedance (Z₀), inductance per unit length (L), and capacitance per unit length (C) based on the geometric and material properties of the cable. The tool provides quick, accurate results that help engineers optimize cable performance and design efficient communication systems.

🛠️ How to Use the Coax Cable Calculator

To use this tool effectively, simply input the required parameters:

  • Inner Conductor Diameter (d) – the diameter of the central wire.
  • Outer Conductor Inner Diameter (D) – the inner diameter of the outer cylindrical shell.
  • Relative Permittivity (εᵣ) – dielectric constant of the insulating material between the conductors.
  • Relative Permeability (μᵣ) – magnetic permeability of the insulating material.

Once these values are entered, the calculator instantly provides:

  • Impedance (Z₀)
  • Inductance (L)
  • Capacitance (C)

📏 Formula Used in the Coax Cable Calculator

Here are the fundamental equations this tool uses, presented in simple, understandable terms:

  1. Characteristic Impedance (Z₀): bashCopyEditZ₀ = (60 / √εᵣ) * ln(D/d)
  2. Inductance per unit length (L): bashCopyEditL = (μ₀ * μᵣ / 2π) * ln(D/d)
  3. Capacitance per unit length (C): bashCopyEditC = (2πε₀ * εᵣ) / ln(D/d)

Where:

  • ln denotes the natural logarithm.
  • ε₀ = 8.854 x 10⁻¹² F/m (permittivity of free space).
  • μ₀ = 4π x 10⁻⁷ H/m (permeability of free space).
  • D = inner diameter of the outer conductor.
  • d = outer diameter of the inner conductor.
  • εᵣ = relative permittivity of the dielectric.
  • μᵣ = relative permeability of the dielectric.

💡 Example Calculation

Let’s consider a practical example using the calculator:

  • Inner Conductor Diameter (d) = 1.0 mm
  • Outer Conductor Inner Diameter (D) = 5.0 mm
  • Relative Permittivity (εᵣ) = 2.3
  • Relative Permeability (μᵣ) = 1

Step-by-step calculation:

  1. Impedance:
    Z₀ = (60 / √2.3) * ln(5 / 1)
    Z₀ ≈ 39.55 * 1.609 = 63.64 ohms
  2. Inductance:
    L = (4π x 10⁻⁷ * 1 / 2π) * ln(5 / 1)
    L ≈ 2 x 10⁻⁷ * 1.609 = 321.8 nH/m
  3. Capacitance:
    C = (2π x 8.854 x 10⁻¹² * 2.3) / ln(5 / 1)
    C ≈ 1.278 x 10⁻¹⁰ / 1.609 = 79.4 pF/m

This example illustrates how quickly and accurately the tool performs key RF calculations.

✅ Benefits of Using the Coax Cable Calculator

  • Saves Time: Instantly delivers accurate impedance, inductance, and capacitance values.
  • Avoids Design Errors: Ensures your coaxial cable meets RF and signal transmission standards.
  • User-Friendly: Intuitive input/output layout makes it suitable for professionals and students alike.
  • Enhances Signal Integrity: Helps in matching impedance to avoid signal loss or reflection.
  • Educational Tool: Great for learning the theoretical relationship between geometry and cable performance.

📚 Additional Insights

🔌 Why Impedance Matters

Impedance matching is critical in RF systems. If the cable’s impedance doesn’t match the system’s requirement (typically 50Ω or 75Ω), signal reflection and power loss occur.

🌐 Applications

  • Television Broadcasts
  • Internet Modems
  • Ham Radio Antennas
  • Satellite Communications
  • Medical Equipment (MRI RF shielding)

🧪 Material Considerations

  • Dielectric Material: Impacts both capacitance and impedance.
  • Conductor Material: While the calculator focuses on geometry, real-world resistive losses can depend on copper vs. aluminum or silver.

🔄 Flexible Design Iteration

Designers can tweak values to optimize their coaxial cable for bandwidth, attenuation, and cost-efficiency by experimenting with diameter and dielectric changes.

❓ 20 Frequently Asked Questions (FAQs)

1. What is the ideal impedance for coaxial cables?
Most RF applications use 50Ω or 75Ω impedance cables for optimal signal performance.

2. Can this tool calculate attenuation?
No, this tool calculates impedance, inductance, and capacitance. Attenuation depends on conductor resistance and dielectric loss.

3. Why does impedance depend on permittivity?
Permittivity affects the electric field inside the cable, changing how signals propagate.

4. What unit should I enter diameters in?
Any consistent unit (e.g., mm or inches) as long as both d and D use the same unit.

5. What if D is less than d?
The calculator will return an error. D must be greater than d for a valid coaxial structure.

6. Can this calculator be used for twin-lead or twisted pair?
No. It’s exclusively for coaxial cable geometry.

7. What happens if εᵣ = 1?
That represents a vacuum or air dielectric, common in some high-frequency applications.

8. Can I use this tool for high-voltage applications?
It helps design geometry but doesn’t consider voltage breakdown of dielectrics.

9. Does temperature affect results?
Temperature changes the dielectric constant slightly, which can affect precision.

10. How accurate is this tool?
It uses standard formulas ideal for initial design and educational use. Practical results may vary slightly.

11. Is permeability important for non-magnetic materials?
For most non-magnetic materials, μᵣ = 1 is appropriate and does not vary.

12. What materials have high permittivity?
Materials like Teflon and polyethylene are commonly used and have εᵣ between 2 and 3.

13. Does this calculator support coax cables with foam dielectrics?
Yes, if you know the dielectric constant, you can enter it manually.

14. Can this be used for underwater cable design?
Only partially. It helps with cable impedance, but waterproofing and pressure ratings are separate considerations.

15. How does inductance affect signal?
Higher inductance can limit bandwidth, especially in high-speed digital systems.

16. Can I calculate propagation delay?
Indirectly, yes. Propagation speed = speed of light / √εᵣ.

17. What’s the effect of increasing the outer diameter?
Increasing D increases impedance and decreases capacitance.

18. What if I don’t know the dielectric constant?
You need to estimate or look it up for the material you plan to use.

19. Is the logarithmic function natural or base 10?
It uses the natural logarithm (ln), which is standard in RF equations.

20. Is this tool suitable for PCB microstrip or stripline?
No, it is tailored specifically for cylindrical coaxial cable design.

🔚 Conclusion

The Coax Cable Calculator (Impedance–Inductance–Capacitance) is a powerful online tool for professionals and students working with RF systems and transmission lines. With just a few inputs—inner and outer diameters and dielectric properties—you get immediate results for the key parameters that dictate your cable’s performance.

Whether you’re designing custom coaxial cables, learning how signal transmission works, or troubleshooting RF interference, this tool provides the precision and speed you need. Make the most of it in your communication system planning and RF projects.