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Main >> Applications >> Sample problems >> 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:
Plane-parallel 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.

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:

 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.

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