The aim of this FET project is basic research on fractal electrodynamics in order to explore the performance limits (both fundamental and technological) of highly innovative fractal shaped miniature devices for future wireless telecommunication systems.
The performance of classical antennas and microwave passive devices of Euclidean geometry is highly sensitive to its size compared to the wavelength. Once these devices have been designed to operate at a particular frequency band, they are not useful at other ones. The possibility of creating fractal multiband antennas, using the self-similarity property of fractal shapes, has already been demonstrated.
Due to the same geometrical electromagnetic constraint of Euclidean geometries, given a particular operating wavelength, classical antennas and microwave devices cannot be made arbitrarily small. However, there is another property of fractal shapes that may lead to a significant size reduction regardless the electromagnetic geometrical constraint: the fractal dimension. A fractal curve enclosed in a finite area or volume has infinite length. In practice, a fractal shaped device will not have infinite length, but it can be made arbitrarily long until the technology limit is reached. This may lead to the design of devices that, having the same length compared to the operating wavelength than their Euclidean counterparts, occupy a smaller volume.
The technological limitations are important here, since fractals are Iterated Function Systems (IFS) that, in theory, require an infinite number of iterations in order to have its unique properties, like the fractal dimension. This leads to structures that have details of infinitely small size, which are obviously impossible to implement in practice. One of the objectives of the research is to study the performance of devices obtained with a finite number of IFS iterations, resulting in a finite smallest size compatible with present technology constraints.
In addition to the technological limitations for the miniaturization of fractal shaped devices, there is also a fundamental limit. This limit establishes the smallest size of a device that can have a given operating bandwidth. In practice, this fundamental limit has never been reached by Euclidean shaped devices. The size limitation depends on how efficiently the device occupies the volume inside the enclosing sphere, and thus fractal shapes are expected to perform much better than Euclidean ones. Another objective of this project is to explore if fractal shaped devices can reach the fundamental limit.
There is another potential limitation of fractal microwave devices that must be investigated: the loss efficiency. It has been shown that in fractal geometries electromagnetic fields and currents concentrate into very small regions. Since the power loss due to Joule effect is proportional to the square of the electric current density integrated along the device surface, current concentration in small areas produce much larger power losses than more uniform current distributions. This effect may result in antennas having much lower gain that the theoretical directivity or microwave filters or resonators having too large insertion losses.
1- Increase the know-how in Fractal Electrodynamics theory and understand better the behavior of electromagnetic fields and electric currents in fractal domains, in order to acquire guidelines for the design of fractal-shaped antennas and microwave devices.
2- Explore if fractal-shaped microwave devices can reach the fundamental miniaturization limit, which has been never reached by Euclidean-shaped devices.
3- Develop a software tool for computer simulation of fractal-shaped microwave devices performance, including time domain visualization of the interaction between geometry and electromagnetic fields, in order to allow a physical interpretation of radiation and resonance of the proposed structures. This tool would allow also the later design and optimization of such devices.4- Explore the impact of the technological limitations on the performance of fractal-shaped microwave devices, including minimum detail size and loss efficiency.
It must be remarked that this is a FET project and therefore the main objective is an increase of knowledge. Fractal antennas are becoming increasingly popular and many European SMEs, driven by the need of offering up-to-date state-of-the-art products, may decide to tackle risks by including them in their production lines. This project should provide answers about the potential interest of fractal antennas, through a careful study of electrical performance vs. technological complexity trade-offs.
The objectives of this project require an interdisciplinary research. In the first place, a progress in the underlying theory for Fractal Electrodynamics is necessary. Recursive mathematical models based on the iteration and scaling of electromagnetic operators must be developed in order to understand the behavior of fractal geometries when excited by electromagnetic fields. This theory will allow both the design of fractal-shaped antennas and microwave devices and the development of the simulation software. The theory is necessary also to predict the parameters of ideal fractal-shaped devices, and explore if they can reach the fundamental miniaturization limit, which has been never reached by Euclidean-shaped devices. The main project workpackage (WP1) will be dedicated to address the items above.
However, the mathematical tools used for the analysis of Euclidean-shaped antennas present many difficulties when applied to fractal domains, and thus a joint effort between researchers specialized in applied mathematics on fractals structures and electromagnetic theorists is necessary in order to obtain the necessary mathematical models. For that reason, there will be a workpackage (WP2) dedicated to electromagnetic field formulation on fractal domains, using fractal vector calculus, an emerging mathematical field in which partner ROME is a leading group.
Numerical simulation is necessary in this project in order to test and predict the performance of many suggested fractal geometries of potential interest. For initially successful geometries, simulation is very important in order to assess the viability of such devices in the frame of present technology constraints. Fractal-shaped devices can be simulated even beyond the technological limitations in order to predict performance in the frame of future technologies. Numerical simulation in the time domain has the added value of providing animated visualization of the interaction between geometry and electromagnetic fields, thus allowing a physical interpretation of radiation and resonance of the proposed structures. Since current numerical modeling methods are not adequate to tackle with fractal devices, a full workpackage (WP3) will be dedicated to develop a complete software simulation package.
The results of numerical simulations, especially in the time-domain, will be an invaluable help to physically understand electromagnetic phenomena on fractal structures, such as radiation, scattering and resonance.
Once the fractal electrodynamics theory has been established in WP1 and the software simulation tool has been developed in WP3, both with the essential support of the vector calculus on fractal domains developed in WP2, it will be possible to suggest fractal structures in which antennas and microwave devices can be based. In the last workpackage (WP4), a few antennas and microwave devices will be designed and the practical technological limitations, including minimum detail size and loss efficiency, will be explored. Prototypes will be constructed and measured, both for experimental validation of the computer model and to test the devices that prove to be most successful in computer simulations.
In summary, the proposed workpackages are:
– WP0: Project Management
– WP1: Theory of fractal electrodynamics
– WP2: Vector calculus on fractal domains
– WP3: Software simulation tool
– WP4: Fractal devices development
An Assessment and Evaluation Workpackage is not considered necessary as this is a basic research project in which the main result will be a increase of knowledge. This knowledge will be materialized in the form of reports (deliverables), publications in refereed journals and conferences and publication in the project web site (dissemination). The quality of deliverables will be assessed and evaluated by the task leaders, workpackage coordinators and the project coordinator, while the quality of publications will be evaluated by journal and conference referees.
Due to the multidisciplinary nature of Fractal Electrodynamics, the consortium includes partners with expertise on different fields, such as electromagnetic theory, fractal mathematics, design of microwave antennas and devices and numerical modeling:
– UPC: Project leader, experts on antennas and microwave devices design and simulation, and early developers of fractal multiband antennas.
– ROME: Experts on vector calculus along fractal curves and surfaces.
– EPFL: Experts on numerical analysis and miniaturization of printed antennas and microwave circuits.
– UGR: Experts on electromagnetic theory and on time domain modeling, with experience on simulation of fractal antennas.
– CIMNE: Experts on efficient adaptive meshing tools for numerical simulation.
The participation of the partners in the project workpackages will be the
following:
