Skin effect (a-c resistance and internal inductance) calculations

Select appropriate form and input parameters, then click button.

1. Solid circular conductors (internal conductor of coaxial cable)

conductor diameter (d mm)
frequency (Hz)
conductivity (1.0 for soft annealed copper)
permeability (1.0 for vacuum, copper, almium)

2. Tubular conductor

outer diameter (D mm)
inner diameter (d mm)
frequency (Hz)
conductivity (1.0 for soft annealed copper)
permeability (1.0 for vacuum)

Replace outer and inner diameter for outerconductor of coaxial cable.

3. Bimetal conductor (copper clad steel in coaxial cable)

outer copper diameter (D mm)
inner steel diameter (d mm)
frequency (Hz)
conductivity of outer copper layer (1.0 for copper)
permeability of outer copper layer (1.0 for vacuum)
conductivity of innner steel layer (1.0 for copper)
permeability of inner steel layer (1.0 for vacuum)

Commentary

Attenuation of cable is determined from the a-c resistance of conductor, and phase distorsion of cable is determined from the internal inductance of conductor. And these calculations result in eddy current calculation of the conductor considering following factors.

  1. skin effect
  2. proximity effect
  3. eddy current in other sorrounding conductors
Skin effect is the largest of these. But, only few simple cases are calculated analytical method using complex Bessel functions.

Here are simple but impotant cases frequently used in many design.

In fact, isolated single conductor rarely exist. But center conductor of coaxial cable is just this case.

Results of computation are the ratio of AC resistance for DC resistance, DC resistance, AC resistance and internal inductance of the conductor.

Internal inductance is the inductance due to the magnetic field inside the conductor.

In addition, the permeability of the air is 4e-7 * π (H / m), and condctivity of copper is 5.8e7 (G / m)

1999-04-20, Kouichi Hirabayashi