Enter the magnetic permeability, frequency, conductor radius, and electrical resistivity into the calculator to determine a common dimensionless current-crowding parameter (r/δ). This parameter is often used in skin-effect and proximity-effect loss models; calculating actual proximity-effect loss also requires conductor geometry/spacing.

Proximity Effect Calculator

Enter any 4 of the 5 values to calculate the missing variable

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Proximity Effect (Current-Crowding Parameter) Formula

The following formula calculates a common dimensionless current-crowding parameter (r/δ) used in many AC conductor loss models. Note: the true proximity effect (AC resistance increase due to nearby conductors) also depends on conductor spacing/arrangement, so this parameter alone is not the full proximity-effect loss.

P = r \sqrt{\dfrac{\pi f \mu}{\rho}}

Variables:

  • P is the dimensionless current-crowding parameter (r/δ)
  • μ is the magnetic permeability (H/m)
  • f is the frequency (Hz)
  • r is the conductor radius (m)
  • ρ is the electrical resistivity (Ω·m)

To calculate P, multiply π by the frequency and magnetic permeability, divide by resistivity, take the square root, and then multiply by the conductor radius. (Equivalently: compute skin depth δ = √(ρ/(π f μ)) and then compute P = r/δ.)

What is the Proximity Effect?

The proximity effect is the redistribution of AC current within a conductor caused by the magnetic fields from nearby conductors carrying AC. This interaction tends to crowd current into particular regions (often toward the sides facing or opposing neighboring conductors, depending on geometry and phase), increasing effective AC resistance and losses.

This is different from the skin effect, which is the tendency for AC current to concentrate near the surface of a single isolated conductor at higher frequencies due to the conductor’s own time-varying magnetic field.

How to Calculate Proximity Effect?

The following steps outline how to calculate the parameter P = r/δ used in many proximity-effect/skin-effect models.

  1. Determine the magnetic permeability (μ) in H/m.
  2. Determine the frequency (f) in Hz.
  3. Determine the conductor radius (r) in meters.
  4. Determine the electrical resistivity (ρ) in Ω·m.
  5. Calculate P using P = r √(π f μ / ρ) (equivalently P = r/δ, where δ = √(ρ/(π f μ))).
  6. After inserting the values and calculating the result, check your answer with the calculator above.

Example Problem : 

Use the following variables as an example problem to test your knowledge.

Magnetic Permeability (μ) = 1.2566 x 10^-6 H/m

Frequency (f) = 60 Hz

Conductor Radius (r) = 0.01 m

Electrical Resistivity (ρ) = 1.68 x 10^-8 Ω·m