Calculate skin depth, required frequency, or shield thickness from frequency, material conductivity, permeability, and attenuation goal.
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Penetration Depth Formula
The following formula is used to calculate penetration depth (skin depth) in a conductor.
d=\frac{1}{\sqrt{\pi f \mu \sigma}}- Where d is the penetration depth (skin depth) (m) (multiply by 1000 to convert to mm)
- f is the test frequency (Hz)
- μ is the magnetic permeability of the material (H/m), where μ = μ0 μr and μ0 = 4π×10⁻⁷ H/m
- σ is the electrical conductivity (S/m) (if using %IACS: σ = (%IACS/100) × 58×10⁶ S/m at 20°C)
To calculate the penetration depth, take the reciprocal of the square root of π multiplied by the frequency, magnetic permeability, and electrical conductivity.
What is Penetration Depth?
Definition:
Penetration depth (also called skin depth) is the characteristic distance an AC electromagnetic field and the associated induced current penetrate into a conductor. At a depth of one skin depth, the field/current amplitude has dropped to 1/e (about 37%) of its value at the surface.
How to calculate Penetration Depth?
Example Problem:
The following example outlines the steps and information needed to calculate a Penetration Depth.
First, determine the test frequency. In this example, the test frequency is 50 Hz.
Next, determine the magnetic permeability. For a non-magnetic conductor, use μr ≈ 1, so μ = μ0 μr = 4π×10⁻⁷ H/m.
Next, determine the electrical conductivity. In this example, assume 100% IACS, so σ = 58×10⁶ S/m (58 MS/m at 20°C).
Finally, calculate the Penetration Depth using the formula above;
d = 1 / √(π f μ σ)
d = 1 / √(π·50·(4π×10⁻⁷)·(58×10⁶))
d ≈ 0.00935 m = 9.35 mm
