In this example, the impedance a coplanar conductor-backed waveguide is calculated using the FDE solver’s Power and Impedance Integration tool, and the result is compared with the approximate analytic result from an online impedance calculator [1].

## Simulation Setup

The cross section of the coplanar waveguide is illustrated in the image above.

In this simulation, we use 2D PEC rectangles for the central microstrip and left and right ground planes. The central strip has a width of 2.5 mm with a gap of 1.5 mm between the strip and ground planes on either side.

The dielectric substrate has a thickness of 0.5 mm and permittivity of 4.34001, and the y min boundary condition is set to metal to represent the lower ground plane. A metal boundary is also used for the y max boundary condition and this is possible since the boundary is placed far enough from the structure that there is no coupling between the mode and the y max boundary. PML can also be used for the y max boundary.

A mesh override region is used to make sure that the width of the central strip and the width of the gaps between the central strip and ground planes are accurately resolved.

## Running Simulation and Result Analysis

Run the *coplanar.lms* simulation file and solve for the modes. Select the first mode in the mode list.

Then under the “integrate” drop down menu, select “current” to perform the characteristic impedance calculation. You can specify the region to integrate over by setting the x1, x2, y1, and y2 parameters, or you can also use your mouse to click and drag on the plot on the right-hand side to select the integration region from the plot.

The integration region should be chosen to fully enclose the central conducting strip but not include the ground planes. Since the fields change sharply near the left and right sides of the central conductor, to avoid interpolation error of the fields, it’s best to make sure that the edges of the integration region is a few mesh cells away from the hot spots of the fields. Using the integration region settings shown on the following image, the calculated characteristic impedance is approximately 26.6 ohms. This result is consistent with the results calculated using an online calculator [1] of about 26.7 ohms.

### Related references

[1] http://chemandy.com/calculators/coplanar-waveguide-with-ground-calculator.htm