Example copper skin depth

Skin depth is 66.1 / sqrt(f) millimeters with f in hertz. 2.4 GHz is 2.4e9 Hz.

Worked example

Er is the substrate relative permittivity. It is not a length.
H is the substrate height from ground to the trace, in the selected length unit.
W is the drawn trace width. The wide or narrow equation uses W/H.
S is the edge gap between two traces, in the same unit as H.
Effective width is optional. Blank means Z0 uses W. This page does not calculate a correction.

Characteristic impedance 51.002 ohm

Wide or narrow Hammerstad equation. eta_0 = 376.73 ohm. Branch uses W/H.

Effective permittivity 3.0669

Er_eff = (Er+1)/2 + ((Er-1)/2) * (1 + 12*H/W)^(-0.5)

Differential impedance 83.257 ohm

Z_diff = 2 * Z0 * (1 - 0.48 * exp(-0.96 * S/H))

Delay 148.368 ps/inch

t_pd = 84.72 * sqrt(Er_eff) ps/inch

Delay per millimeter 5.841 ps/mm

ps/mm = (84.72 * sqrt(Er_eff)) / 25.4

Phase velocity 1.7118e8 m/s

V_p = 2.9979e8 / sqrt(Er_eff) m/s

Copper skin depth 1.3493 um

delta = 66.1 / sqrt(f_Hz) mm for annealed copper

Z0 uses the trace width. No thickness correction is applied.

Dielectric loss is not shown. The written loss product does not state whether frequency is hertz or gigahertz.