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Two conductors PCB line

QuickField simulation example

This is an example of the two conductors PCB line simulation, performed with QuickField software.

Problem Type
Plane-parallel problem of electrostatics.

Geometry
Two conductors PCB line The region is bounded by ground from the bottom side and extended to infinity on other three sides Conductors Ground Air Dielectric

The problem's region is bounded by ground from the bottom side and extended to infinity on other three sides.
Model depth L = 1 m.

Given
Relative permittivity of air ε= 1;
Relative permittivity of dielectric ε= 2.

Task
Determine self and mutual capacitance of conductors.

Solution
To avoid the influence of outer boundaries, we'll define the region as a rectangle large enough to neglect side effects. To calculate the capacitance matrix we set the voltage U = 1 V on one conductor and U = 0 on another one.

Self capacitance: C11 = C22 = Q1 / U1 ,

Mutual capacitance: C12 = C21 = Q2 / U1 ,

where charge Q1 and Q2 are evaluated on rectangular contours around conductor 1 and 2 away from their edges. We chose the contours for the C11 and C12 calculation to be rectangles [-6<x<0], [0<y<4] and [0 <x<6], [0<y<4] respectively.

Results
Potential distribution in two conductors transmission line:
two conductors transmission line simulation

  C11, F C12, F
Reference* 9.23·10-11 -8.50·10-12
QuickField 9.43·10-11 -8.57·10-12

* Reference: A. Khebir, A. B. Kouki, and R. Mittra, An Absorbing Boundary Condition for Quasi-TEM Analysis of Microwave Transmission Lines via the Finite Element Method, Journal of Electromagnetic Waves and Applications, 1990.