code
Using a PEC half-space in a MoM code will remove the need for meshing the finite plate. This means, for the current measurement configuration, only the antennas and dielectric need to be meshed. This will also aid in more general simulations. In these simulations, the antennas can be replaced by defined sources and the dielectric by a representation of a berm. In this section, hybrid methods are investigated to dramatically reduce simulation time.
Fig. 4.12a shows a FEKO R
simulation using a PEC half-space to simulate the no-dielectric case. This is compared to the benchmark infinite-simulations in CST MWS R
as a control Fig. 4.12b. The infinite ground-plane simulation using FEKO R
took less than 30 minutes on the same machine used for the CST MWS R
simulations. Although the MoM simulation follows the same trend as the FDTD code, a 5 dB difference exists in some areas. In these areas, the MoM code underestimates the coupling. This is most likely due to the difference in feed configuration. In CST MWS R
, the feed is modelled as close as possible to the SMA interface on the bottom of the plate (see Fig. 4.5). Because of the halfspace approximation, the same is not possible for the FEKO R
simulation. In the FEKO R
simulation, the feed is defined as an edge port between the base of the antenna and the halfspace. This will affect how the electric field forms at the base of the antenna as well as the reference phase of the simulation. For practical simulations, the antennas will be replaced by defined sources where this would not be a problem. However, for now simulations will still use this familiar antenna coupling configuration. It will shortly become evident that it is also possible to exploit image theory [52]. This means that the halfspace approximation can be removed by replacing the
CHAPTER 4. COMPUTATIONAL MODELLING AND SCALE MEASUREMENTS 53 (a) FEKO R simulation 0 5 Frequency [GHz]10 15 20 −120 −100 −80 −60 −40 −20 0 S21
Infinite FEKO and CST Comp.
CST Infinite
Feko PEC Halfspace
Feko Mirrored
(b) Simulation Comparison
Figure 4.12: FEKO R
PEC half-space compared to infinite CST MWS R
sim- ulation in (b). The two antennas can be seen on both sides of the image, on top of the infinite PEC halfspace.
monopoles with dipoles around the current ground plane. Consequently, the dielectric is then also mirrored around this surface. A non-dielectric test in this configuration is also compared in Fig. 4.12b.
With the infinite PEC halfspace, a dielectric can be added to test its simula- tion time against the MoM code. As soon as the dielectric is added, simulation time increases to the point where a frequency of 20 GHz becomes unpractical again. Even meshing becomes problematic on a desktop computer above 2 GHz. Consequently, hybrid methods need to be used. These hybrid methods combine the classical MoM with GO, called Ray Launching Geometrical Op- tics (RL-GO). In this hybrid simulation, the MoM will handle small-detailed structures while the asymptotic method handles the larger well approximated structures. These methods are well suited for this problem because of the electrically large dielectric and the small antennas. The problem here how- ever is that an infinite halfspace cannot be used in conjunction with RL-GO. Therefore, the infinite-PEC halfspace is replaced with the previously men- tioned mirror principle. In this case, the dielectric could be solved using GO. At the start, the default ray launching angles were too coarse, this had to be manually changed in the simulation settings. A GO only method would also be possible by replacing antennas with spherical-mode sources. The compari- son between the simulation and measurement of the dielectric can be seen in Fig. 4.13b. Here the measured dielectric on the quasi-infinite plate is com- pared to the mirrored simulation. This figure shows a simulation where the antennas were approximated as line monopoles. The simulation itself finished in the order of minutes. The comparison can be seen to underestimate the measurement at some frequencies. It should be noted that the feeds cannot be accurately modelled in this configuration and is, therefore, partly attributed to the deviation. Also, the FEKO R
CHAPTER 4. COMPUTATIONAL MODELLING AND SCALE MEASUREMENTS 54 (a) FEKO R simulation 2 3 4 Frequency [GHz]5 6 7 8 9 10 −120 −110 −100−90 −80 −70 −60 −50 −40 S21
Infinite Comp. with Dielectric
Measurement
Simulation
(b) Simulation Comparison
Figure 4.13: FEKO R
mirrored simulation including dielectric. Results here are compared to quasi-infinite measurements.
slight rounding of the edges which would significantly decrease diffraction. It should be noted that GO does not directly account for diffraction (GO only accounts for reflection and refraction). However, some relation between RL- GO and physical optics (PO) exists in that elementary Huygens sources are generated on surfaces. Surface currents on the rest of the structure are con- sequently induced by radiation from these sources [69][70]. This approximate PO-like behaviour makes it important to verify the simulation against full- scale real-world measurements. These real-world comparisons can be found in Sec. 6.4.2 where a Multi-copter vehicle is used to do the measurements at this large scale.