Engineering
AC & RF Skin Depth formula: delta = SQRT(rho / (pi * f * mu0 * mur))
Estimate skin depth for a good conductor with positive resistivity and a real permeability, keeping the DC case separate.
Skin depth is an attenuation scale, not a sharp current boundary
In the good-conductor, sinusoidal steady-state approximation, delta=SQRT(rho/(PI()*f*mu)) gives the distance over which field/current amplitude falls by a factor e in a planar conductor. Current does not abruptly stop at one skin depth.
The copper example uses rho=1.68E-8 ohm*m and relative permeability 1. Material properties depend on temperature and, for magnetic materials, frequency and field; a constant real permeability is an approximation. Here mu0 is approximated as 4*PI()*1E-7 H/m.
This estimate alone does not select busbar dimensions, plating thickness or winding construction. Geometry, proximity effect, thermal limits and conductor losses also matter. The DC limit is reported as text; negative frequency is invalid, not DC.
| Operating Regime | Frequency f (B3) | Copper Skin Depth delta | PCB / Power Busbar Implication |
|---|---|---|---|
| 60 Hz AC Utility Grid | 60 Hz | 8.42 mm (8,423 um) | Compare depth with geometry; additional loss analysis needed |
| 1 MHz Switching / AM RF | 1,000,000 Hz | 65.23 micrometers | Winding geometry and proximity effects also matter |
| 100 MHz VHF / FM RF | 100,000,000 Hz | 6.52 micrometers | One skin depth does not carry all current |
| 0 Hz Direct Current (DC) | 0 Hz | "Full Cross-Section (DC)" | Infinite skin depth; zero skin effect |
Skin Depth in millimeters (mm) for 50/60 Hz power & kHz inductors
Reports the good-conductor estimate in mm for positive frequency. Both output formulas handle zero frequency consistently.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B2<=0,B3<0,B4<=0),"Invalid inputs",IF(B3=0,"Full Cross-Section (DC)",ROUND(1000*SQRT(B2/(PI()*B3*(4*PI()*0.0000001)*B4)),2))))Skin Depth in micrometers (um) for MHz/GHz RF & PCB traces
Multiplies meters by 1,000,000 to express RF penetration depth in microns.
=IF(COUNT(B2:B4)<>3,"Invalid inputs",IF(OR(B2<=0,B3<0,B4<=0),"Invalid inputs",IF(B3=0,"Full Cross-Section (DC)",ROUND(1000000*SQRT(B2/(PI()*B3*(4*PI()*0.0000001)*B4)),2))))Try the example
Use the original values or change them to test your understanding.