Vivaldi Antenna Grid Setup – XFdtd

This example demonstrates how to discretize a vivaldi antenna by utilizing the gridding workflow.

Complete the following prerequisite steps during project setup:

Set the project's frequency range of interest.
Import the CAD geometry.
Define materials and assign them to each part.
Apply a modal waveguide excitation to the stripline.
Set the outer boundaries to absorbing.

Next, apply the following grid settings:

The main grid settings are adjusted according to the width of the stripline and the thickness of the substrate, as well as the desired cell size.

Set the minimum cells per wavelength to 25.
Set the minimum feature size for good conductors to 3 mm with 7 cells across.
Set the minimum feature size for poor conductors to 3.17 mm with 6 cells across.

Automatic fixed points are extracted from both the center conductor and substrate.

Finally, apply the following mesh settings:

Apply XACT Accurate Cell Technology® to the three curved conductors.
Apply Dielectric volume averaging to the substrate.

This video includes the following topics:

[0:46] Main grid settings.
[3:18] Grid visualization tools.
[4:58] Automatic fixed points for center conductor and substrate.
[6:41] XACT and dielectric volume averaging mesh settings.
[8:10] Parts list.

Prerequisites

Prior to beginning the gridding steps, the frequency range of interest in the project properties editor is set to the antenna's operating range of 2 GHz to 8 GHz. The antenna includes three conductors—similar conductors on the top and bottom flared toward the outer edge and one in the center flared in the opposite direction. The center conductor includes a 3 mm wide stripline and is embedded in a 3.17 mm thick substrate.

The substrate's dielectric material has a relative permittivity of 2.33 that produces a shorter wavelength than is found in free space, and the three conductors are assigned a copper material definition that generates strong field gradients around their edges. A modal waveguide source is applied at the stripline, and absorbing outer boundaries on all six sides allow for antenna analysis in free space.

Standard Main Grid Properties

The first gridding step is setting the minimum cells per wavelength to 25 in the main grid editor's cell size tab. This generates a more refined grid in both free space and the substrate for increased accuracy. Choosing a specific minimum cells per wavelength value is often based on previous experience in similar projects, so users should determine what value to apply based on their own accuracy needs.

The following steps adjust the minimum feature sizes to the width of the stripline and the thickness of the substrate in order to resolve these geometry features with an adequate number of cells. Users should specify each of these feature sizes as a fixed distance by unchecking the ratio setting and entering the desired value.

For Good Conductors, uncheck the Ratio setting and enter 3 mm with 7 cells across.
For Poor Conductors, uncheck the Ratio setting and enter 3.17 mm with 6 cells across.

The conductors' thickness values are ignored due to the trade-off between accuracy and runtime. At the set frequencies, they have no significant impact on the results so including them only increases RAM and runtime requirements.

Default values in the extents and advanced tabs are sufficient for this example so no additional setting adjustments are necessary in the main grid editor.

Check Grid

A visual inspection of the grid verifies that PrOGrid is applied and incorporating pertinent project settings:

The minimum cells per wavelength in free space and the dielectric are based on the project's frequency range of interest.
Smaller cells appear around the edges of the good conductors where field gradients are strongest.
The number of cells across the stripline and substrate each meet their specified minimum value.

Viewing the geometry along each of the three principle axes shows grid misalignment with both the center conductor and substrate. This must be corrected by adjusting the gridding properties of individual parts.

The grid visualization process continues until no further adjustments are necessary.

Standard Part-Level Properties

Screenshot of the automatic fixed points editor.

By default, PrOGrid is applied to all geometry as it is either imported or created, so no additional steps are required to enable it for the conductors or substrate.

The grid must align with critical pieces of geometry whenever possible in order to improve accuracy. In this project, the three conductors are of interest. The visualization step revealed the following grid misalignment:

Gridlines were not snapped to the center conductor, causing it to be uncentered in the substrate.
Gridlines were not snapped to the six corners of the substrate, causing incorrect sizing and separation between the top and bottom conductors.

The most efficient method for correcting these issues is to enable automatic fixed points on the center conductor and substrate by right-clicking on each part in the Project Tree and selecting Gridding / Meshing, then Gridding Properties to open the editor and select Use Automatic Fixed Points.

Inspecting the grid with these changes applied confirms perfect alignment between the geometry and grid.

Mesh Settings

Meshing is a separate step in the antenna simulation workflow with an impact on CAD geometry discretization.

Enabling XACT for the three conductors more accurately resolves the curved, metal structures than the staircased representation. XACT is enabled by selecting the three conductors in the Project Tree and using the right-click menu to choose Gridding / Meshing, then Enable XACT Mesh.

Dielectric volume averaging (DVA) enhances accuracy at the substrate-air interface beyond XF's standard staircase meshing. DVA is enabled by selecting the Substrate in the Project Tree and using the right-click menu to choose Gridding / Meshing, then Enable dielectric volume averaging.