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Main >> Applications >> Sample problems >> PCB hatched ground plane resistance
Problem Type: planeparallel problem of DC conduction.
Geometry:
Plane consists of the copper hexagonal cells with dimensions shown in the picture below. Plane thickness is 35 micrometers.
Given:
Electric conductivity of copper γ = 56e6 S/m;
Task:
DC current is flowing across the rectangular plane 180 mm x 100 mm between the electrodes welded to the diagonal corners. Calculate the electric resistance.
Solution:
Solution is based on the analysis of the currents flowing in the solid plane with equivalent electric conductivity. Task is performed in two steps.
Results:
Step 1 problem:
Solid plate resistance: R = (1/56e6) * 4.8e3 / (4.8e3 * 35e6) = 0.51 mOhm.
Hatched plane resistance: R_ = 0.001 / 0.31 = 3.2 mOhm
Equivalent conductivity of the hatched plane material
γ_ = γ * (R/R_) = 56e6 S/m * (0.51 mOhm / 3.2 mOhm) = 8.9e6 S/m.
Step 2 problem.
Resistance = Voltage drop / Current = 0.054 V / 1 A = 54 mOhm
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