Main >>Applications >> Sample problems >> PCB hatched ground plane resistance
Problem Type: plane-parallel problem of DC conduction.
Plane consists of the copper hexagonal cells with dimensions shown in the picture below. Plane thickness is 35 micrometers.
Electric conductivity of copper γ = 56e6 S/m;
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 is based on the analysis of the currents flowing in the solid plane with equivalent electric conductivity. Task is performed in two steps.
Step 1 problem:
Solid plate resistance: R = (1/56e6) * 4.8e-3 / (4.8e-3 * 35e-6) = 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