Wire Over Ground Plane Resistance

Wire Over Ground Plane Resistance

Wire Over Ground Plane Resistance Resistance Calculators

Wire Over Ground Plane Resistance Model
DC resistance of a wire over ground plane is:
ResistanceBiplanarDC
Units: Ohms

AC resistance of a wire over ground plane is:
ResistanceBiplanarACSmallSkinDepth

ResistanceBiplanarACLargeSkinDepth

ResistanceBiplanarACLargeSkinDepth

ResistanceBiplanarACLargeSkinDepth

Units: Ohms

Skin Depth is:
SkinDepthFormula
Units: meters

Description
Resistance calculated using this tool includes both dc and ac resistance of the wire over ground plane. At low frequencies, where skin depth is greater than conductor width and thickness, ac resistance is approximately the same as the dc resistance. As frequency increases, ac resistance increases.

Assumptions and Limitations
Dimensions are in meters.
Conductors are assumed to have equal, uniform circular cross section over their length.
Separation between the conductors is assumed to be large enough that proximity effect may be ignored.
Wire relative permeability: Symbol-muR
Wire relative conductivity: Symbol-sigmaR

Constants
Permeability of free space: Formula, Permeability of Free Space H/m
Conductivity of copper: Symbol-sigma0 = 5.98 x 10 7 S/m (Siemens per meter) at 20-degrees C

Reference: “Inductance Loop and Partial”, C.R. Paul, Wiley, 2010.

WireOverGroundPlane-Dimensioned

Inputs

Wire radius
r
Thickness
t
Length
l
Frequency
f
Relative Conductivity
Relative Permeability

Outputs:

DC Resistance: R = 
2.136e-2 Ohms
AC Resistance: R = 
6.521e-2 Ohms
Skin Depth:  = 
2.058e-4 m