# Cable Impedance Calculations

### From Open Electrical

This article provides details on the calculation of cable impedances - dc resistance, ac resistance and inductive reactance.

## Contents |

## Cable Resistance

The dc and ac resistance of cable conductors can be calculated based on IEC 60287-1 Clause 2.1.

### DC Resistance

The dc resistance of cable conductors is calculated as follows:

Where is the dc resistance at the conductor operating temperature θ (Ω / *m*)

- is the resistivity of the conductor material at 20
^{o}C (Ω.*m*).- For copper conductors, = 1.7241 x 10
^{-8} - For aluminium conductors, = 2.8264 x 10
^{-8}

- For copper conductors, = 1.7241 x 10

- is the cross-sectional area of the conductor (mm
^{2}) - is the temperature coefficient of the conductor material per K at 20
^{o}C.- For copper conductors, = 3.93 x 10
^{-3} - For aluminium conductors, = 4.03 x 10
^{-3}

- For copper conductors, = 3.93 x 10

- is the conductor operating temperature (
^{o}C)

- is the resistivity of the conductor material at 20

### AC Resistance

The ac resistance of cable conductors is the dc resistance corrected for skin and proximity effects.

Where is the ac resistance at the conductor operating temperature θ (Ω / *m*)

- is the dc resistance at the conductor operating temperature θ (Ω /
*m*) - is the skin effect factor (see below)
- is the proximity effect factor (see below)

- is the dc resistance at the conductor operating temperature θ (Ω /

The skin effect factor is calculated as follows:

Where

- is the dc resistance at the conductor operating temperature θ (Ω /
*m*) - is the supply frequency (Hz)
- is a constant (see table below)

- is the dc resistance at the conductor operating temperature θ (Ω /

Note that the formula above is accurate provided that 2.8.

The proximity effect factor varies depending on the conductor geometry. For round conductors, the following formulae apply.

For 2C and 2 x 1C cables:

For 3C and 3 x 1C cables:

Where

- is the dc resistance at the conductor operating temperature θ (Ω /
*m*) - is the supply frequency (Hz)
- is the diameter of the conductor (mm)
- is the distance between conductor axes (mm)
- is a constant (see table below)

- is the dc resistance at the conductor operating temperature θ (Ω /

Note that the formula above is accurate provided that 2.8.

For shaped conductors, the proximity effect factor is two-thirds the values calculated above, and with:

- equal to the diameter of an equivalent circular conductor of equal cross-sectional area and degree of compaction (mm)
- where is the thickness of the insulation between conductors (mm)

Type of Conductor | Dried and Impregnated? | ||
---|---|---|---|

Copper
| |||

Round, stranded | Yes | 1 | 0.8 |

Round, stranded | No | 1 | 1 |

Round, segmental | - | 0.435 | 0.37 |

Sector-shaped | Yes | 1 | 0.8 |

Sector-shaped | No | 1 | 1 |

Aluminium
| |||

Round, stranded | Either | 1 | 1 |

Round, 4 segment | Either | 0.28 | 0.37 |

Round, 5 segment | Either | 0.19 | 0.37 |

Round, 6 segment | Either | 0.12 | 0.37 |

## Cable Reactance

The series inductive reactance of a cable can be approximated by the following equation:

Where is the conductor inductive reactance (Ω / *k**m*)

- is the supply frequency (Hz)
- is the axial spacing between conductors (mm)
- is the diameter of the conductor, or for shaped conductors, the diameter of an equivalent circular conductor of equal cross-sectional area and degree of compaction (mm)
- is a constant factor pertaining to conductor formation (see below for typical values)

No. of wire strands in conductor | K |
---|---|

3 | 0.0778 |

7 | 0.0642 |

19 | 0.0554 |

37 | 0.0528 |

>60 | 0.0514 |

1 (solid) | 0.0500 |

For 3C and 3 x 1C cables, the axial spacing parameter depends on the geometry of the conductors:

## References

- IEC 60287-1-1, “Electric cables – Calculation of current rating – Part 1: Current rating equations (100% load factor) and calculation of losses – Section 1: General”, 2006
- G.F. Moore, “Electric Cables Handbook”, Third Edition, 1997, an excellent reference book for cables