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Capacitance matrix of two conductors transmission line
Elec2: Two conductors transmission line
This is an example of the two conductors transmission line simulation, performed with QuickField software.
Problem Type:
Planeparallel problem of electrostatics.
Geometry:
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.
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 another one.
Self capacitance: C_{11} = C_{22} = Q_{1} / U_{1} ,
Mutual capacitance: C_{12} = C_{21} = Q_{2} / U_{1} ,
where charge Q_{1} and Q_{2} are evaluated on rectangular contours around conductor 1 and 2 away from their edges. We chose the contours for the C_{11} and C_{12} calculation to be rectangles [6<x<0], [0<y<4] and [0 <x<6], [0<y<4] respectively.
Comparison of results
Potential distribution in two conductors transmission line:

C_{11}, F 
C_{12}, 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 QuasiTEM Analysis of Microwave Transmission Lines via the Finite Element Method", Journal of Electromagnetic Waves and Applications, 1990.
Download simulation files: elec2.zip