A broad band antenna designed for WLAN applications is simulated in XFdtd^® using a variety of variable mesh configurations and the return loss is compared to measured results.

The antenna simulated, shown in Figure 1, is taken from the IEEE journal paper

T. H. Kim and D. C. Park, “Compact Dual-Band Antenna With Double L-Slits for WLAN Operations,” IEEE Ant. and Wireless Propag. Letters, Vol. 4, pp. 249-252, 2005.

• Figure 1: XFdtd CAD view of broad band Double-L antenna.

The antenna is first simulated in a uniform XFdtd mesh of cell size 0.25mm with a UPML outer boundary on 5 sides and a PEC ground plane as a boundary below the antenna. The computed return loss from XFdtd is shown with the measured and simulated results of the paper authors in Figure 2.

•   Figure 2: XFdtd-computed return loss compared to measured results.

To test the XFdtd variable mesh feature, the antenna will be simulated for the following five cases and the return loss results compared to the uniform results presented in Figure 2. 

• Put plane of antenna (XY slice) in a fixed (0.25mm) mesh and increase the base mesh size
• Put plane of antenna (XY slice) in increasingly finer adaptive mesh and keep base mesh size fixed (0.25mm)
• Put entire antenna in fixed (0.25mm) adaptive mesh and increase base mesh size
• Put entire antenna in increasingly finer adaptive mesh and keep base mesh size fixed (0.25mm)
• Put region of antenna in increasingly finer adaptive mesh and keep base mesh size fixed 

For the first case, the base mesh size is increased up to 4mm resulting in a 16:1 mesh ratio. At this mesh resolution, the 10 cell per wavelength upper frequency limit of XFdtd is 7.5 GHz, or the upper end of the plot shown in Figure 2. One case of the geometry is shown meshed in Figure 3. The return loss for the meshes is shown in Figure 4. It can be seen that with higher mesh ratios, the return loss results vary slightly. This difference is caused by the variations in the feed port which is on the boundary of the variable mesh and changes slightly with each new mesh ratio. While the results are still quite good, this case should be avoided in practice.

• Figure 3: One of the variable mesh geometries simulated for the first case.
• Figure 4: Return loss results for the first variable mesh case compared to the uniform mesh S11.

In the second case, the base mesh size is held constant at 0.25mm but the plane of the antenna is put in a variable mesh region with finer detail. In this case, the feed port and the coaxial line beneath it are changed with each new mesh resulting in slightly different input impedance results. It was found that the impedance of this antenna, particularly around the location of the second null, was quite sensitive to the diameter of the coaxial line, so the changes in the variable mesh impact this. The maximum resolution simulated is 0.05mm which is a ratio of 5:1 with the main grid. Beyond a 5:1 ratio the grid size becomes quite large and is not reasonable to simulate on a PC. One sample of the geometry is shown in Figure 5 and the return loss results in Figure 6.

• Figure 5: A sample geometry of the second variable mesh case.
• Figure 6: Return Loss for second variable mesh cases.

For the third case, the entire antenna is placed in a uniform mesh of 0.25mm and the surround region is meshed in a larger cell size, up to 4mm or a 16:1 ratio. For this case, there are no changes to the input port with each variable mesh, so the input impedance remains identical. One of the cases is shown in Figure 7 and the resulting return loss in Figure 8. Here the results are essentially identical for all mesh ratios.

• Figure 7: One mesh of the third variable mesh case.
• Figure 8: Return loss from third case.

For the fourth case the entire antenna is placed in a variable mesh region that increases in resolution while the base mesh size stays fixed at 0.25mm. In this case, the feed port and coaxial line will change with each variable mesh, altering the input impedance slightly and thus the return loss. A sample of the geometry is shown in Figure 9 and the return loss plots in Figure 10.

• Figure 9: Sample geometry for the fourth variable mesh case.
• Figure 10: Return loss plots for the fourth variable mesh case.

For the fifth case, one detail of the antenna is placed in a variable mesh region with increasing resolution while the base mesh is held constant at 0.25mm. The finer mesh region increases in resolution up to a ratio of 20:1. At this high resolution the very small time step requires a large number of FDTD time steps to reach convergence and in fact the highest resolution case does not reach convergence before the programmed maximum time step is reached. This lack of convergence is seen as a ripple in the return loss plot, especially at the lower frequencies which are the last to converge. A sample geometry is shown in Figure 11 and the return loss plots in Figure 12.

• Figure 11: Sample geometry of the fifth variable mesh case.
• Figure 12: Return loss results from the fifth variable mesh case.

This example has demonstrated the versatility of the XFdtd variable mesh. It also highlights the preferred approach to defining variable mesh regions and indicates some of the issues that may arise when a less desirable mesh region is chosen.