Skin Depth Calculator Formula

Understand the math behind the skin depth calculator. Each variable explained with a worked example.

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Formulas Used

Skin Depth

skin_depth_m = 1 / sqrt(pi * frequency_hz * mu * conductivity)

Skin Depth

skin_depth_mm = 1000 / sqrt(pi * frequency_hz * mu * conductivity)

Skin Depth

skin_depth_um = 1000000 / sqrt(pi * frequency_hz * mu * conductivity)

Variables

VariableDescriptionDefault
frequency_hzFrequency(Hz)1000000
conductivityConductivity(S/m)58000000
rel_permeabilityRelative Permeability1
muDerived value= rel_permeability * 4 * pi * 1e-7calculated

How It Works

What is Skin Depth?

Skin depth is the distance into a conductor at which the current density drops to 1/e (about 37%) of its surface value. At high frequencies, current flows mostly near the surface.

Formula

delta = 1 / sqrt(pi x f x mu x sigma)

Where f is frequency, mu is permeability (mu_0 x mu_r), and sigma is conductivity.

Practical Impact

  • At 1 MHz in copper: skin depth is about 0.066 mm
  • At 1 GHz in copper: about 2.1 micrometers
  • Conductors for RF need only be a few skin depths thick

    • Worked Example

    Copper conductor (sigma = 5.8e7 S/m, mu_r = 1) at 1 MHz.

    frequency_hz = 1000000conductivity = 58000000rel_permeability = 1
    1. 01mu = 1 x 4pi x 10^-7 = 1.2566e-6 H/m
    2. 02delta = 1 / sqrt(pi x 1e6 x 1.2566e-6 x 5.8e7)
    3. 03= 1 / sqrt(229.37) = 1 / 15.15 = 0.0660 mm = 66.0 micrometers

    Ready to run the numbers?

    Open Skin Depth Calculator