The Coax Cable Calculator for Impedance, Inductance, and Capacitance helps engineers and professionals design and optimize coaxial cables. Coaxial cables are widely used in telecommunications, networking, and broadcasting. These cables rely on precise impedance, inductance, and capacitance values to maintain signal integrity and minimize losses during transmission. The calculator allows users to compute these electrical properties based on basic physical characteristics of the cable, such as the diameters of the inner and outer conductors and the relative permittivity of the dielectric material.
Key Parameters
To perform the necessary calculations, the following parameters are required:
- D (Outer Conductor Diameter): The outer diameter of the coaxial cable. This diameter affects how the cable interacts with the environment and influences impedance and inductance values.
- d (Inner Conductor Diameter): The inner diameter of the cable, which is the conductor that carries the electrical signal.
- εr (Relative Permittivity): The relative permittivity of the dielectric material between the conductors. This value determines how well the material can store electrical energy and influences capacitance.
Formulas
Here are the formulas used to calculate the key properties of coaxial cables:
Impedance (Z):
Z = 138 * log(D/d) / sqrt(εr)
Inductance per unit length (L):
L = 0.002 * log(D/d)
Capacitance per unit length (C):
C = (7.354 * εr) / log(D/d)
Where:
- Z is the impedance in ohms (Ω)
- L is the inductance in henries per meter (H/m)
- C is the capacitance in farads per meter (F/m)
- D and d are the diameters of the outer and inner conductors, respectively
- εr is the relative permittivity of the dielectric material
Unit Consistency and Notes
To ensure accurate calculations, the diameters (D and d) should be in the same unit, such as millimeters or inches. The units for inductance and capacitance are typically given in henries per meter (H/m) and farads per meter (F/m), respectively. The relative permittivity (εr) is typically a constant value for a given dielectric material, such as polyethylene or Teflon, and should be known for the specific cable in use.
General Reference Table
The table below provides typical values for some coaxial cables to help users quickly find the parameters they need for calculation without having to perform the math each time:
| Outer Diameter (D) | Inner Diameter (d) | Relative Permittivity (εr) | Impedance (Z) | Inductance (L) | Capacitance (C) |
|---|---|---|---|---|---|
| 6 mm | 1 mm | 2.25 | 50 Ω | 0.40 H/m | 78 pF/m |
| 10 mm | 2 mm | 2.35 | 75 Ω | 0.48 H/m | 68 pF/m |
| 12 mm | 3 mm | 2.55 | 100 Ω | 0.52 H/m | 64 pF/m |
Example
Let’s calculate the impedance, inductance, and capacitance for a coaxial cable with the following values:
- Outer diameter (D) = 10 mm
- Inner diameter (d) = 2 mm
- Relative permittivity (εr) = 2.35
Using the formulas provided:
- Impedance (Z):
Z = 138 * log(10/2) / sqrt(2.35)
Z = 138 * log(5) / sqrt(2.35)
Z ≈ 138 * 0.69897 / 1.531
Z ≈ 64.91 Ω - Inductance (L):
L = 0.002 * log(10/2)
L ≈ 0.002 * 0.69897
L ≈ 0.0014 H/m - Capacitance (C):
C = (7.354 * 2.35) / log(10/2)
C ≈ 17.299 / 0.69897
C ≈ 24.74 pF/m
So for this coaxial cable, the impedance is approximately 64.91 ohms, the inductance is 0.0014 H/m, and the capacitance is 24.74 pF/m.
Most Common FAQs
Impedance is a critical factor in ensuring that the cable is properly matched to the connected devices. If the impedance does not match, signal reflections can occur, which can degrade the signal quality and cause interference. Impedance matching is essential for high-quality signal transmission in systems such as television, internet, and radio frequency applications.
The relative permittivity (εr) of the dielectric material plays a crucial role in determining the capacitance of the cable and the speed of the signal. A higher εr value leads to higher capacitance and slower signal transmission speed. Different dielectric materials, such as polyethylene or Teflon, have different εr values, and these affect the overall performance of the coaxial cable.
The diameters of the inner and outer conductors directly influence the impedance, inductance, and capacitance of the cable. A larger outer diameter and a smaller inner diameter typically reduce the impedance, making the cable more suitable for high-frequency applications. A larger inner diameter can also reduce the inductance, while the capacitance increases as the ratio of the conductors changes.