Skin Depth Formula and Calculator for Electromagnetic Waves

Skin effect is a phenomenon that occurs in conductors carrying alternating current (AC) at high frequencies. It describes the tendency of AC current to concentrate near the outer surface, or “skin,” of the conductor, while the inner regions carry less current. This effect is caused by the behavior of electromagnetic waves in conductive materials and has important implications in electrical engineering and transmission line design. This effect is described by the skin depth, which is a measure of how deeply EM fields such as radio waves or alternating current penetrate into a conductor like copper. It is an important parameter in electrical engineering and is dependent on the frequency of the signal passing through the conductor.

The following skin depth formula is used to calculate skin depth in a conductor like copper. It is measured in units of meters, micrometers (µm), or millimeters (mm).

Skin Depth Calculator

A skin depth calculator is a tool or software application that helps engineers and scientists quickly determine the skin depth of a conductor for a given set of parameters, such as the material’s resistivity, permeability, and the frequency of the AC signal or electromagnetic wave.

Skin Depth Calculator:

The following calculator is used to calculate skin depth. Enter values in the INPUT boxes and press the CALCULATE button to check the OUTPUT.

EXAMPLE of skin depth calculator:

• INPUTS:
  • Frequency (MHz) = 2400
  • Conductivity of material = 1.678 x 10^-8 Ohm-meter
  • Relative permeability of material = 0.999994
• OUTPUT:
  • Skin depth (Meters) = 0.00000133079

How to Calculate Skin Depth of Copper

To understand the concept, let’s take the example of copper wire and analyze the effect of frequency. The resistivity of copper at room temperature is 1.678 x 10^-8 Ohm*m, and its relative permeability is 0.999994.

• Case-1: Take an AC frequency of 60 Hz (Enter 60E-6 in calculator), calculate skin depth using the above calculator, which is about 0.00841669 meters (i.e., 8.41 mm).
• Case-2: Take an EM frequency of 3500 MHz, calculate skin depth using the above calculator, which is about 0.000001102 meters (i.e., 1.102 µm).

From skin depth calculations at different frequencies, we can conclude that the skin effect is almost negligible at AC frequencies of 60 Hz in our homes. Moreover, at radio frequencies (RF) with 3.5 GHz (i.e., 3500 MHz), the current also flows only through an extremely thin portion near the surface, which is a few µmeters.

Conclusion

Overall, the skin depth calculator and skin depth formula provide a convenient and efficient way to incorporate the effects of the skin effect into the design and analysis of electrical and electromagnetic systems.