Skin Depth Calculation, Formula With Example

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Skin Depth
Skin Depth

What is Skin Depth:

Because high frequency signals do not penetrate well into good conductors, the resistance associated with a conductor at these high frequencies will be higher than the dc resistance. This effect is know as the skin effect since the high frequency current flows in a thin layer near the surface of the conductor. The formula to determine the effective skin depth for a conductor is shown below.

In this case, d is the skin depth (in m), f is the frequency of interest (in Hz), m is the permeability of the material (mo, or 1.2566E-6 H/m for most materials),s is the conductivity of the material (in Siemens/m or 1/r where r is the resistivity in ohm-m).

If a circular wire is used with radius a, the effective resistance of the wire can be calculated as shown below where l is the length of the wire and the other variables are defined as above.

The above equation applies for those cases where the skin depth is between 0 and the wire radius, a. If the skin depth is larger than the wire radius, then the equivalent ac resistance of the wire is no different than the dc resistance and is merely determined by the standard formula using the entire wire cross-sectional area. As the frequency approaches zero (dc), the skin depth becomes infinite and as the freqency increases, the skin depth becomes smaller and smaller.

The following table shows how the skin depth varies with some example conductor materials (pure copper and pure aluminum) for typical pulsed power and power conditioning frequencies in the range of 1 kHz to 1 GHz.

Skin Depth Diagram:

Skin Depth Calculator, Calculation With Example

Skin Depth Formula:

Skin Depth Calculator, Calculation With Example

Where

δ = Skin depth in micrometer(μm)

ρ = Resistivity in Microohms(μΩ)

fo = Signal frequency in Hertz

μr = Relativity permeability

μr = Permeability of free space = 4π*10-7

Example For Skin Effect:

To calculate the skin depth. consider the copper conductor which carries 55kHz frequency. Copper has relativity permeability(μr) as constant value = 0.999991 and resistivity (ρ) = 1.78 μm

Let’s apply formula

Skin Depth Calculator, Calculation With Example

Δ = √1.78/3.14*55*0.999991*12.56*10-7

Result:

Δ = 8.791 μm

READ HERE  Circular Waveguide Calculation, Formula, Example

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