Analysis of Cable Characteristics and Inductance, Impedance, GMR, and GMD Calculations

1. Cable Construction and Components

Electrical cables consist of several key components that contribute to their performance. Below are the main elements:

• Conductor: The central core of the cable made from conductive materials such as copper (Cu) or aluminum (Al).
• Insulation: A protective layer surrounding the conductor to prevent electrical leakage.
• Shield: Provides electromagnetic interference (EMI) protection and ensures proper grounding.
• Jacket: The outermost layer of the cable, offering mechanical protection and environmental resistance.

Key Parameters Defined:

• Conductor Diameter (D): The diameter of the conducting material.
• Insulation Thickness: The thickness of the insulating layer around the conductor.
• Shield Thickness: The thickness of the shield layer, often composed of metallic or conductive materials.
• Jacket Thickness: The external protective layer's thickness.
• Spacing: The distances between the conductors (A, B, C).

2. Inductance and Impedance Calculations

Electrical parameters such as inductance and impedance significantly influence a cable's performance. Below is a detailed explanation of the calculation methodology.

Inductance Calculation:

The inductance of a cable can be calculated using the formula:
L = 2 * 10^-7 * ln(GMD / GMR) [H/m]

Where:

• GMD (Geometric Mean Distance): The equivalent distance between the phases in a multi-phase system.
• GMR (Geometric Mean Radius): The effective radius of the conductor, accounting for the distribution of current within it.
• ln: Natural logarithm function.

Example Calculation:
For a three-phase system with the following parameters:

• Conductor diameter = 10 mm
• Spacing between conductors (A, B, C) = 30 cm

Step 1: Calculate GMR
GMR = conductor radius * exp(-1/4)
GMR = (10/2 mm) * exp(-1/4)

Step 2: Calculate GMD
For an equilateral triangle configuration:
GMD = (Spacing A * Spacing B * Spacing C)^(1/3)
GMD = (0.3 m * 0.3 m * 0.3 m)^(1/3)

Step 3: Calculate Inductance
L = 2 * 10^-7 * ln(GMD / GMR)

3. Impedance of Cables

Impedance is a combination of resistance (R) and reactance (X), given by:
Z = sqrt(R^2 + X^2) [Ω/m]

Where:

• R: Resistance of the conductor.
• X: Reactance, determined from the inductance.

Reactance (X):
X = 2 * π * f * L

Where:

• f: Frequency in Hz.
• L: Inductance in H/m.

4. Cable Pulling Tensions

When installing cables, tension must be calculated to avoid damaging the cable. The pulling tension is influenced by:

• Cable weight: Heavier cables require higher pulling forces.
• Bend radii: Sharp bends increase the tension significantly.
• Friction coefficients: Affected by the conduit material and lubricant used.

Pulling Tension Formula:
T = W * f + B * (R)

Where:

• T: Pulling tension.
• W: Cable weight.
• f: Friction coefficient.
• B: Bending stiffness.
• R: Bend radius.

5. Braid Coefficient and Cable Shielding

The braid coefficient is used to evaluate the shielding effectiveness of a cable. It depends on the diameter and material of the braid wires.

Formula:
Kb = Shielding coverage % / 100

Applications:

• Electromagnetic interference (EMI) protection.
• Grounding continuity.

6. Conclusion

Proper calculations of inductance, impedance, GMD, and GMR are critical for designing efficient cable systems. Additionally, pulling tension, shielding, and braid coefficients ensure that cables meet operational and safety requirements.

This comprehensive guide combines theoretical knowledge and practical applications to facilitate better cable design and installation practices.