Coplanar Resistance

Coplanar Resistance

Coplanar Resistance Resistance Calculators

Coplanar Resistance Model
DC resistance of Coplanar conductors is:
ResistanceBiplanarDC
Units: Ohms

AC resistance of Coplanar conductors is:
ResistanceBiplanarACSmallSkinDepth

ResistanceBiplanarACLargeSkinDepth

Units: Ohms

Skin Depth is:
SkinDepthFormula
Units: meters

Description
Resistance calculated using this tool includes both dc and ac resistance of coplanar conductors. 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

Constant
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.

Coplanar-Dimensioned

Inputs

Width
w
Thickness
t
Length
l
Frequency
f
Relative Conductivity
Relative Permeability

Outputs:

DC Resistance: R = 
1.756e-1 Ohms
AC Resistance: R = 
1.756e-1 Ohms
Skin Depth:  = 
2.058e-4 m