DC Resistance of Copper Wires and Traces
[file: resist.mcd]
Conversion formulas included in this spreadsheet:
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Diameter to AWG AWG()
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AWG to diameter DIAMETER()
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Thickness to copper plating weight CPW()
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Copper plating weight to thickness THICKNESS()
Resistance formulas included in this spreadsheet:
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DC resistance of round wires
-
From diameter RROUND()
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From AWG wire size RROUND_AWG()
-
At room temperature only RROUND_RT()
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DC resistance of printed circuit board traces
-
From trace thickness and width RTRACE()
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Using copper plating weight RTRACE_CPW()
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At room temperature only RTRACE_RT()
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DC resistance of power or ground planes
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Using thickness and via diameter RPLANE()
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Using copper plating weight RPLANE_CPW()
Variables used:
r Bulk resistivity of copper
ohm-in.
This coefficient is slightly different from the bulk resistivity of pure copper
(6.58E-07) owing to the annealing process used in making wire, and chemical
imperfections in the copper used for making practical wires.
In practice, the resistance of two wires making up a twisted pair may often be
matched as well as 10%, but almost never as well as 1%.
dr Thermal coefficient of
resistance
per deg. C
If the resistance of a copper wire is R at room temperature, then at a
temperature 1oC higher it will be R(1 +
dr. This coefficient applies to
standard annealed copper wires. The coefficient for pure copper in its bulk
state varies slightly.
Over a temperature range 0-70oC the resistance of copper wires varies 28%.
x Length of wire (in.)
(or separation between contact points on ground plane)
d Diameter of wire (in.)
(or diameter of contact point on ground plane)
AWG American wire gauge (English units)
temp Temperature (°C)
w Width of printed circuit board trace (in.)
t Thickness of printed circuit board trace (in.)
cpw Thickness of printed circuit board traces, in units of copper plating weight
(oz/ft2)
Conversions between American Wire Gauge (AWG) and diameter (in.):
General formula for resistance of a round wire (W):
Resistance of a round wire specified by AWG size instead of diameter (W):
Resistance of a round wire at room temperature (W):
Conversion between thickness, t (in.) and copper plating weight, cpw (oz):
Resistance of a circuit trace (W):
Resistance of a trace specified by plating weight instead of thickness (W):
Resistance of a circuit trace at room temperature (W):
Resistance of a power or ground plane (W):
When using long, skinny traces or wires, the approximations above work extremely
well. Each formula assumes a uniform distribution of current throughout the
conducting body, for which resistance is directly proportional to length.
Currents circulating in a large ground or power plane are not uniform.
Consequently, the resistance measured between two points on a ground or power
plane is not directly proportional to the separation between measurement points.
The following equation models the resistance between two contact points on a
ground plane. This model assumes each contact point touches the ground plane
over some finite area. The approximate diameter of the contact point determines
the overall resistance.
If the contact points lie near any edge of the plane, the resistance between
them may go up by a factor of 2. The resistance near corners may rise even
higher.
-
d1 Diameter of 1st contact point (in.)
-
d2 Diameter of 2nd contact point (in.)
-
t Thickness of plane (in.)
-
cpw Thickness of plane, copper plating weight (oz)
-
x Separation between contact points (in.)
-
temp Temperature (°C)
Resistance of a power or ground plane (W):
Resistance of a power or ground plane specified by plating weight instead of
thickness (W):
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