# EM.Ferma Tutorial Lesson 8: Modeling 2D Coplanar Waveguide Structures

 Tutorial Project: Modeling 2D Coplanar Waveguide Structures Objective: In this project, you will analyze several coplanar waveguide transmission lines using EM.Ferma's quasi-static simulation engine. Concepts/Features: Fixed-Potential PEC Object Dielectric Object 2D Solution Plane Quasi-Static Analysis Characteristic Impedance Effective Permittivity Variables Parametric Sweep Minimum Version Required: All versions ' Download Link: EMFerma_Lesson8

## What You Will Learn

In this tutorial you will learn how to define and characterize 2D coplanar waveguide structures using quasi-static analysis. You will use a wizard to create the geometry of a CPW line and will later modify its geometry.

## Getting Started

Open the EM.Cube application and switch to EM.Ferma. Start a new project with the following parameters:

 Name EMFerma_Lesson8 Millimeters N/A N/A N/A

## Creating the Coplanar Waveguide Geometry

A coplanar waveguide (CPW) transmission line consists of a center metallic strip located between two wide grounded metallic strips on the two sides. All the three strips are collocated on the same plane. A dielectric substrate is used to support the three metallic strips. The dielectric substrate can be an infinite bottom half-space or a layer of finite thickness. Click on the CPW Wizard button of the Wizard Toolbar or select the menu item Tools → Transmission Line Wizards → Coplanar Waveguide.

 EM.Ferma's wizard toolbar.

The geometry of a coplanar waveguide line appears at the center of the project workspace. The geometry created by the wizard is fully parameterized. Open the variables dialog and change the values of the primary CPW variables according to the table below:

Variable Name Original Definition New Definition
h 0.0015*to_meters 1.5
strip_wid 0.002*to_meters 2
slot_wid 0.002*to_meters 1
 The variables dialog showing the modified definition of some variables.

After the changes, your CPW structure should look like this:

 The CPW geometry created by the wizard in the project workspace.

The geometry created by the wizard consists of four objects belonging to three different material groups as summarized in the table below. The fixed voltage of the "STRIP" PEC group is 1V, while the fixed voltage of the "CONDUCTOR" PEC group is 0V.

 Object Name Object Type Material Group Name Material Group Type ANCHOR Rectangle Strip STRIP Fixed-potential PEC Ground_1 Rectangle Strip CONDUCTOR Fixed-potential PEC Ground_2 Rectangle Strip CONDUCTOR Fixed-potential PEC Substrate Box SUBSTRATE Dielectric material

The domain settings of the CPW line is slightly different than that of the microstrip line you created in the last tutorial lesson. The -Z-offset value for the CPW case is 20mm rather than zero. This is because underneath the substrate of the CPW line there is the free space. So there is an air layer between the substrate and the bottom domain wall. As you can see from the variables list, the parameterization of the CPW line is more complicated than that of the microstrip line because of the constraints on the size and positioning of the two lateral grounds. With the wizard's default settings, the two lateral ground objects, called "Ground_1" and "Ground_2", extend all the ways to the lateral domain walls. You can create a finite ground coplanar waveguide (FGCPW) by setting a smaller width for the lateral grounds so that they don't extend to the edges of the substrate. The table below lists all the domain offset values:

Offset Value
-X 0
+X 0
-Y 0
+Y 0
-Z 20mm
+Z 20mm

Similar to the micrpstrip case, the wizard defined a vertical X-directed field sensor observable called "FS1", which is associated with a 2D solution plane called "SP1". The mesh settings are identical to those of the micrsotrip case, i.e. Δx = Δy = Δz = 0.2mm.

## Running a Quasi-Static Simulation of the CPW Line

Run a quasi-static "Analysis" of your 2D transmission line structure. At the end of the simulation, the output message window reports the computed values of the characteristic impedance and effective permittivity of the CPW transmission line:

Z0: 90.936567 Ohms

Epsilon_Effective: 1.536085

Visualize the electric field and potential distribution on the "Sensor_1" plane. From the vector plot, you can clearly see that the electric fields are confined to the top and bottom surfaces of the two slots.

 The intensity plot of the total electric field distribution of the CPW line in the YZ plane. The vector plot of the total electric field distribution of the CPW line in the YZ plane. The intensity plot of the electric potential distribution of the CPW line in the YZ plane.

If you have installed RF.Spice A/D on your computer, you can verify your results with its Device Manager.

 The CPW line calculator of RF.Spice A/D.

## Simulating a CPW Line with a Conductor-Backed Substrate

If you change the -Z-offset value of the domain box to zero, the bottom PEC wall of the domain box will collapse onto the bottom surface of the dielectric substrate. In that case, you will have a conductor-backed coplanar waveguide (CBCPW) line as shown in the figure below.

 A conductor-backed CPW line with a zero -Z-offset in the domain box.

Run a new quasi-static "Analysis" of your 2D transmission line structure. At the end of the simulation, the output message window reports the computed values of the characteristic impedance and effective permittivity of the conductor-backed CPW transmission line:

Z0: 69.794448 Ohms

Epsilon_Effective: 1.788402

Visualize the electric field and potential distribution on the "Sensor_1" plane. In the vector plot, you can see a large number of electric field lines inside the dielectric region between the center metal strip and the bottom ground besides those extending laterally towards the side grounds above and below the two slots. The modal field profile of this particular CPW transmission line is starting to look more like a microstrip line.

 The intensity plot of the total electric field distribution of the conductor-backed CPW line in the YZ plane. The vector plot of the total electric field distribution of the conductor-backed CPW line in the YZ plane. The intensity plot of the electric potential distribution of the conductor-backed CPW line in the YZ plane.

If you have installed RF.Spice A/D on your computer, you can verify your results with its Device Manager.

 The conductor-backed CPW line calculator of RF.Spice A/D.

## Adding a Shielding Duct Above the CPW Line

The conductor-backed CPW line has a lower characteristic impedance than the one without a bottom ground plane. In this part of the tutorial lesson, you are going to build a more complicated transmission line structure based on the original template geometry the wizard created for you. Activate the PEC group called "CONDUCTOR" in the navigation tree. Under this group, draw a rectangle strip as follows:

Part Name Object Type Group Name Material Type Dimensions Coordinates Rotation Angles
Bridge Rectangle Strip CONDUCTOR Fixed-potential PEC 40mm × 4mm (0, 0, 3mm) (0°, 0°, 0°)

Next, you need to draw the vertical walls to connect the edges of the side grounds to the new "bridge" object. You can draw rectangle strips and rotate them vertically. As an alternative, you will learn here to use CubeCAD's "Bridge Tool". This tool creates a bridge surface between two selected edges of objects. Click the Bridge button of the Tools Toolbar or select the menu item Tools → Transform → Bridge.

 Selecting the bridge tool from the Tools Toolbar.

With the "Bridge Mode" activated, hover your mouse on the right edge of the left side ground object "Ground_2" to highlight that edge as shown in the figure below. If you experience difficulty with mouse-over conflicts from other nearby objects, freeze them as necessary.

 Highlighting the first edge in the bridge process.

Next, hover your mouse on the left edge of the new object "Bridge" to highlight that edge as shown in the figure below. A vertical surface is generated between the two selected edges.

 Highlighting the second edge in the bridge process.

The bridge tool allows you to connect several edges consecutively. To finish the process, you need to press the keyboard's Enter key.

 Completing the bridge process.

Repeat the same process to bridge between the letf edge of the right side ground object "Ground_1" and the right edge of the new object "Bridge".

Note that the objects: Ground_1, Ground_2, Bridge and the two newly added surface objects, all belong to the PEC group "CONDUCTOR" with a zero potential. This means that the top of side of your CPW transmission line is completely shielded and grounded. Therefore, you can bring the top domain wall down comfortably without any concern of field disturbances. A smaller domain box means a smaller mesh, and therefore, faster simulation. Change the domain offset values as follows:

Offset Value
-X 0
+X 0
-Y 0
+Y 0
-Z 0
+Z 2mm

After adjusting the domain size, your new modified CPW structure should look like this:

 The geometry of the modified shielded CPW line.

With a highly reduced computational domain size, you can now afford increasing the mesh resolution. Set

 Defining a very high resolution fixed-cell mesh.

Run a new quasi-static "Analysis" of your 2D shielded transmission line structure. At the end of the simulation, the output message window reports the computed values of the characteristic impedance and effective permittivity of the shielded CPW transmission line:

Z0: 62.059132 Ohms

Epsilon_Effective: 1.594023

Note that the characteristic impedance of the shielded line has dropped to almost half the Z0 value of the original CPW. Visualize the electric field and potential distribution on the "Sensor_1" plane and see how the CPW mode has been restored to some extent.

 The intensity plot of the total electric field distribution of the shielded CPW line in the YZ plane. The vector plot of the total electric field distribution of the shielded CPW line in the YZ plane. The intensity plot of the electric potential distribution of the shielded CPW line in the YZ plane.

## Simulating a Micromachined Shielded CPW Line

In the last part of this tutorial lesson, you are going to construct and simulate a fairy complex micromachined CPW structure. In micromachining fabrication processes, it is possible to remove material from a substrate to create cavities or etch and metallize slanted walls for shielding. First, delete the two surface objects you just created using the bridge tool. Open the property dialog of the rectangle strip object "Bridge" and reduces its width (Y-dimension) from 4mm to 2mm. Make sure the PEC group "CONDUCTOR" is active. Then, use the bridge tool just as you did in the previous part to connect the right edge of the left ground object to the left edge of "Bridge". Similarly, connect the left edge of the right ground object to the right edge of "Bridge". You should get a structure like this:

 Replacing the vertical shield walls with slanted bridges.

To remove part of the dielectric substrate underneath the CPW line, you will draw a pyramid object first and then will subtract is from the substrate box object. Activate the dielectric group "SUBSTRATE" in the navigation tree. Draw a pyramid on a blank space in the project workspace with the following specifications:

Part Name Object Type Group Name Material Type Base Size Top Size Height Coordinates Rotation Angles Top End Cap Bottom End Cap
Pyramid_1 Pyramid Substrate Dielectric 40mm × 8mm 40mm × 4mm 1mm (0, 0, 0) (0°, 0°, 0°) Yes Yes

To draw a pyramid, click the Pyramid button from the Object Toolbar or select the menu item Object → Solid → Pyramid.

 Selecting the Pyramid tool in the object toolbar.
 The property dialog of pyramid.

Your long-base pyramid object with clipped top face should look like this:

 The geometry of the long clipped pyramid object shown while the substrate box and lateral ground objects are in a freeze state.

Then, in the same way as you did in Tutorial Lesson 4, subtract object "Pyramid_1" from the box object called "Substrate". Enable the Subtract Tool and first click on the surface of the object to subtract from, i.e. "Substrate", and then click on the surface of the object to be subtracted, i.e. "Pyramid_1". Complete the process by pressing the Enter key.

 The property dialog of the Boolean subtraction object representing the substrate with removed material.
 The geometry of the completed micromachined shielded CPW structure.

Generate and examine the mesh of the new structure.

 The high resolution fixed-cell mesh of the completed micromachined shielded CPW structure.

Run a quasi-static "Analysis" of your new transmission line structure. At the end of the simulation, the output message window reports the computed values of the characteristic impedance and effective permittivity of the transmission line:

Z0: 69.761433 Ohms

Epsilon_Effective: 1.083085

Note that the effective permittivity has dropped significantly and is very close to 1, i.e. the effective permittivity of an air-filled TEM transmission line. Visualize the electric field and potential distribution on the "Sensor_1" plane. Notice the field lines established between the center metal strip and the slanted shield walls.

 The intensity plot of the total electric field distribution of the micromachined shielded CPW line in the YZ plane. The vector plot of the total electric field distribution of the micromachined shielded CPW line in the YZ plane. The intensity plot of the electric potential distribution of the micromachined shielded CPW line in the YZ plane.