Task 3.4: Simulation of fractal structures in the time domain

• Deliverables: D8 T3.4 Final Task Report
• Outputs: Animated time-domain simulations of fractal structures for WP1 and WP4.

Electromagnetic simulation in the time domain is essential for visualization and physical interpretation of electromagnetic phenomena, such as radiation, scattering and diffraction. The results from this workpackage will provide and invaluable feedback to WP1.

a) Time-domain simulation software already developed by partner UGR for wire and planar conventional antennas will be upgraded for the analysis of fractal structures.

b) Animated time-domain simulation of the fractal structures and devices proposed in WP1 and WP4.

Simulations in the time domain allow to isolate interactions using time range (cause and effect can be distinguished providing an easier physical interpretation of the results), to simulate transient phenomena, to visualize the time history of the physical magnitudes and have the possibility of obtaining, in a single program run, broadband information.

UGR group has a home-developed code Method of Moments in the time domain (MoM-TD) code, DOTIG, that is as an excellent tool for the visualization of electromagnetic scattering and radiation phenomena. In order to analyse the complex antennas subject of FRACTALCOMS project, DOTIG has been extended in with:

• Non-uniform segmentation
• Crossing wires and junctions (Fig. 28), with uniform or non-uniform segmentation.
• Ground plane capability in order to reduce the number of unknowns using symmetry.
• The Prony and pencil parameter extraction techniques.

Fig. 28: Pre-fractal antennas with wire junctions can be analysed with DOTIG.

DOTIG is based on the thin-wire approximation of the EFIE. Although thin-wire approximations fail for highly-iterated pre-fractals (see Deliverable D6 – WP3 T3.2 Final Task report), DOTIG results are still useful for visualizing electromagnetic phenomena in the time domain and to draw conclusions about pre-fractal antennas behaviour.

The resulting code has been applied to carry out simulations and numerical experiments to facilitate the understanding of the behaviour of pre-fractal antennas. To this end we have studied the time history of the physical magnitudes such as the current induced in several fractals antennas and the fields created by these currents. As an example, Fig. 29 shows the time evolution of the current (space-time diagram) in a two-iteration Kock (K2) monopole with a Gaussian voltage short-pulse excitation. It is observed that, due to the initial acceleration of the charges at the feed point and at the bends and corners in the wire, almost all the energy is radiated at the beginning and the amplitude of the current pulse decreases very quickly.

Figure 29: Space-time diagram for the current in a K2 monopole excited by a Gaussian short-pulse.

Most time-domain results are based on short-pulse excitations. Since a short pulse contains all the frequency spectrum from 0 up to a given frequency, the input impedance of the antenna can be computed in a large frequency band. In addition, since the pulse is much shorter than the antenna, different parts of the antenna are excited at different times and one can visualize the radiation of these parts separately. For that reason, the short-pulse results have been very useful to visualize the coupling –or shortcut- effect, which is one of the most relevant contributions of the project (see Fig. 6 and 7 in section WP1 Task 1.1).

Other very interesting effect that has been detected thanks to the time-domain space-time diagrams is the coupling between the feeder and the wire segments of a small antenna. This is a very important effect to account for in designing very small antennas that have the lowest possible reactance. Fig. 30a shows the space-time diagram for a K2 monopole excited by a wide Gaussian pulse whose maximum spectral component is such that the monopole is a electrically small antenna at that frequency. The feeder-wire segments coupling can be clearly seen in Fig. 30b, and they play a significant role in the behavior of electrically short pre-fractal antennas. The feeder-shortcut effects take place mainly at segments with a specific orientation tangential to the electric field radiated by the feeder, which are indicated with arrows in Fig. 30b.

Fig 30a: Space time diagram for an electrically small K2 monopole.		Fig. 30b: Wire segments in a K2 monopole that couple with the field radiated by the feeder.

In practice the fractal antennas will work close to arbitrarily inhomogeneous bodies and, consequently, it is useful to study how the antennas parameters are modified in such situation (Fig. 31). However, the total geometry formed by the inhomogeneous body and the antenna is so complex that there is not a single numerical method appropriate to simulate the whole problem. One alternative is to use for each part of the structure the numerical method that best fits to it. In this project we have used a hybrid method combining the method of moments in the time domain (MoMTD) and the Alternating Direction Implicit Finite Difference Time Domain (ADI-FDTD) method to study the performance of fractal antennas in front of an inhomogeneous body. The ADI-FDTD method is based on an implicit-in-space formulation of the FDTD which offers unconditional numerical stability with little extra computational effort. The ADI-FDTD method removes the stability limit for the time increment, making it possible to choose the time increment independently of the space increment.

Figure 31: Hilbert monopole of order two radiating in front of a human head that has been simplified to three concentric spheres with different constitutive parameters. It seems that the presence of the head do not disturb significantly the behaviour of the pre-fractal antennas.

Task conclusion:

In conclusion, the time-domain analysis results have been an invaluable tool for the physical interpretation of the interaction between electromagnetic fields and pre-fractal structures, leading to very important conclusions in workpackage WP1.