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PCB via capacitance
Problem Type: electrostatics.
Geometry: 3D extrusion
All dimensions are in millimeters
Given:
Relative permittivity of dielectric (FR4) ε = 4.7;
Relative permittivity of air ε = 1.
Strip conductor potential V = 1 V.
Task:
Calculate the printed circuit board via capacitance.
Solution:
Capacitance can be calculated as C = 2·W / V^{2}, where W is the electric field energy, V  potential difference.
In 3D problem there is no way to separate the strip electric field from the via electric field. Therefore the total energy is calculated and the resulting capacitance is of the via + strip together.
The 3D problem could be reduced to two 2D problems to calculate the via capacitance and strip conductor capacitance separately.
Results:
Electric potential distribution in the dielectric board (click to view 3D picture):
Electric field energy (3D problem) W = 4.0e13 J
Via and strip combined capacitance
C = 2*4.0e13 / 1^{2} = 8e13 F (0.80 pF).
Via and strip capacitance calculated as a sum of two values form 2D simulations is 0.77 pF, including:
 Via capacitance is 0.33 pF
 Strip capacitance (strip total length is 8.72 mm) is 0.44 pF
Download simulation files.
