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Capacitance matrix of two conductors transmission line
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.
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.
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