Skin Effect Onset Frequency for a Round Conductor

What is the Skin Effect Formula?

The skin effect describes how alternating current (AC) tends to flow near the surface of a conductor, rather than through its entire cross-section. There isn't one single "skin effect formula," but rather several formulas depending on the conductor's geometry and the desired information (skin depth, AC resistance, etc.).

One example, provided in a reference, gives the onset frequency for the skin effect in a round conductor:

f_skin = 4πμσr²

Where:

• f_skin is the onset frequency.
• μ is the permeability of the conductor material.
• σ is the conductivity of the conductor material.
• r is the radius of the round conductor.

This formula helps determine the frequency at which the skin effect becomes significant. Below this frequency, the current distributes more uniformly. Above this frequency, the current increasingly concentrates near the surface.

Other Relevant Formulas and Considerations

While the above formula is useful, many other formulas exist to calculate parameters related to the skin effect:

• Skin Depth (δ): This represents the depth at which the current density drops to approximately 37% of its surface value. The formula for skin depth varies slightly depending on the assumptions made (e.g., perfectly uniform material). Commonly used is: δ = 1/√(πfμσ), where f is the frequency.

• AC Resistance: The resistance of a conductor at high frequencies increases due to the skin effect. Formulas for calculating this AC resistance depend on the conductor geometry (e.g., round wire, rectangular trace). One reference mentions a formula for a rectangular cross-section PCB trace, but the specific formula isn't provided.

• More Complex Scenarios: For complex geometries or materials with non-uniform properties, numerical methods are often necessary to accurately model the skin effect.

It's crucial to remember that the appropriate formula depends on the specific application and the parameters being calculated. Accurate calculation requires understanding the material properties (conductivity and permeability) and the geometry of the conductor.