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Microstrip transmission line

QuickField simulation example

A shielded microstrip transmission line consists of a substrate, a microstrip, and a shield.

Problem Type
Plane-parallel problem of electrostatics.


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.
Microstrip transmission line A shielded microstrip transmission line consists of a substrate, a microstrip, and a shield. Strip Ground Air Substrate A B C D E F 10 mm 100 mm 100 mm 10 mm

Model depth Lz = 1 m.

Relative permittivity of air ε = 1;
Relative permittivity of substrate ε = 10.

Determine the capacitance of a microstrip transmission line.

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 = q ² / 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.


Potential distribution in microstrip transmission line:
microstrip transmission line simulation

Theoretical result* (model depth L = 1 m.) C = 178.074 pF.
Approach 1 C = 177.83 pF (99.8%)
Approach 2 C = 178.47 pF (100.2%)
Approach 3 C = 177.33 pF (99.6%)
Approach 4 C = 179.61 pF (100.8%)

See the Elec1_1.pbm and Elec1_2.pbm problems for the 1,3 approaches and the 2,4 approaches respectively.

* Ostergaard, D. F. (1987). Adapting available finite element heat transfer programs to solve 2-D and 3-D electrostatic field problems. Journal of Electrostatics, 19(2), 151–164.