A shielded microstrip transmission line consists of a substrate, a microstrip, and a shield.
Problem Type:
Plane-parallel problem of electrostatics.
Geometry:
The transmission line is directed along z-axis, its cross section is shown on the sketch.
The rectangle ABCD is a section of the shield, the line EF represents a conductor
strip.
Given:
Relative permittivity of air ε = 1;
Relative permittivity of substrate ε = 10.
Problem:
Determine the capacitance of a transmission line.
Solution:
There are several different approaches to calculate the capacitance of the line:
Both these approaches make use of the equation for capacitance:
C = q / U.
Other possible approaches are based on calculation of stored energy of electric field. When the voltage is known:
C = 2·W / U2,
and when the charge is known:
C = q2 / 2·W.
Experiment with this example shows that energy-based approaches give little bit less accuracy than approaches based on charge and voltage only. The first approach needs to get the charge as a value of integral along some contour, and the second one uses only a local value of potential, this approach is the simplest and in many cases the most reliable.
Results:
Theoretical result: | C = 178.1 pF/m. |
Approach 1: | C = 177.83 pF/m (99.8%). |
Approach 2: | C = 178.47 pF/m (100.2%). |
Approach 3: | C = 177.33 pF/m (99.6%). |
Approach 4: | C = 179.61 pF/m (100.8%). |
The first and third approaches are illustrated in the Elec1_1.pbm problem in the Examples folder, and the Elec1_2.pbm explains the second and the fourth approaches.