Twisted-Pair Impedance Calculation

The diagram illustrates a twisted-pair cable and is related to the calculation of the characteristic impedance of such cables. Twisted-pair cables are widely used in communication systems due to their ability to minimize electromagnetic interference (EMI) and crosstalk.

Formula for Characteristic Impedance:
Z_0 = (120 / √ε_r) * ln(2S / D)

Where:

• Z_0: Characteristic impedance in ohms (Ω).
• ε_r: Relative permittivity (dielectric constant) of the insulation material.
• S: Center-to-center spacing between the two conductors (in mm).
• D: Diameter of each conductor (in mm).
• ln: Natural logarithm.

Steps to Perform the Calculation:

• 1. Determine Conductor Diameter (D): Measure the physical diameter of the conductors in mm.
• 2. Measure Spacing (S): Measure the distance between the centers of the two conductors.
• 3. Find Dielectric Constant (ε_r): Identify the dielectric constant of the insulating material, typically provided by the manufacturer.
• 4. Substitute Values into the Formula: Plug the measured and provided values into the formula to calculate Z_0.

Example Calculation:
Given:

• ε_r = 2.3 (for typical polyethylene insulation),
• S = 2.0 mm,
• D = 0.8 mm,

The characteristic impedance is:
Z_0 = (120 / √ε_r) * ln(2S / D)

First, calculate intermediate values:

• √ε_r = √2.3 ≈ 1.516
• (2S / D) = (2 * 2.0) / 0.8 = 5.0
• ln(5.0) ≈ 1.609

Finally:
Z_0 = (120 / 1.516) * 1.609 ≈ 127.37 Ω

Applications of Twisted-Pair Impedance:

• 1. Communication Systems: Used in Ethernet cables (Cat5, Cat6, etc.) for maintaining signal integrity.
• 2. Transmission Lines: Ensures minimal signal reflection and distortion by matching impedance.
• 3. High-Frequency Applications: Twisted pairs are effective in reducing EMI in high-frequency signal transmissions.

This calculation is critical for designing cables that meet specific requirements for high-speed data transmission.