Elec2: Two conductor transmission line

Problem Type:
A plane problem of electrostatics.

Geometry:

The problem's region is bounded by ground from the bottom side and extended to infinity on other three sides.

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

Problem:
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 the 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.

Comparison of Results:

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.

See the Elec2.pbm problem in the Examples folder.