Artificial Magnetic Materials Using Fractal Hilbert Curves

Electr. & Comput. Eng. Dept., Univ. of Waterloo, Waterloo, ON, Canada
IEEE Transactions on Antennas and Propagation (Impact Factor: 2.18). 09/2010; 58(8):2614 - 2622. DOI: 10.1109/TAP.2010.2050438
Source: IEEE Xplore


Novel configurations based on Fractal Hilbert curves are proposed for realizing artificial magnetic materials. It is shown that the proposed configuration gives significant rise to miniaturization of artificial unit cells which in turn results in higher homogeneity in the material, and reduction in the profile of the artificial substrate. Analytical formulas are proposed for design and optimization of the presented structures, and are verified through full wave numerical characterization. The electromagnetic properties of the proposed structures are studied in detail and compared to square spiral from the point of view of size reduction, maximum value of the resultant permeability, magnetic loss, and frequency dispersion. To validate the analytical model and the numerical simulation results, an artificial substrate containing second-order Fractal Hilbert curve is fabricated and experimentally characterized using a microstrip-based characterization method.

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    • "The most important advantage of this structure is its simple fabrication. In spite of most metamaterial structures, such as SRR where numerous PCB boards, each containing a unit cell, are stacked together to provide an effective medium [2] [3] [4] [5] [6] [7], 3-dimemtional short wires can be fabricated easily by using standard multi-layer PCB fabrication. All short wires are made on two sides of one PCB board and in this way fabrication will be much easier, especially at higher frequencies [8] [9]. "
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    ABSTRACT: Short wire metamaterial is a kind of metamaterial, which has a very simple manufacturing process. In spite of regular metamaterials whose fabrication requires compressing and stacking of several printed circuit boards (PCBs), short-wire metamaterials can be fabricated using standard multi-layer PCB fabrication. These metamaterials have already been introduced and modeled; however, the reported analytical models have a big deviation from simulation and measurement results. Here; we propose an accurate analytical model for prediction of the resonant frequency of these metamaterials. The analytical model has been verified through comparison with previously reported measurement results.
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    • "–[5], gradient-index MTMs for high directivity [6], transmission line (TL) MTMs for beam scanning [7], LH MTMs for bandwidth enhancement [8], magnetic MTMs for antenna's surface wave suppression [9], controllable LH MTMs for steerable antennas [10], and even the most recently reported electric or magnetic MTMs for suppression of antenna's mutual coupling [11]–[13]. The mushroom structure which was initially researched as a high-impedance surface [14] is an important EM MTM element . "

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    • "Currently, fractals combined with LH MTMs have become a heated topic, for instance, fractal perturbation in CSRRs results in a significant lower resonance [7] [8], multiband behavior [9], and broadband performance [10] of the LH cell. Others also proposed Hilbert curve inclusions for the engineered artificial magnetic materials [11], and the authors even exploited fractal concept in UWB filter for elevation of passband performance [12]. Up to now, most research focuses on the double negative MTMs issue, few literatures are reported concerning the use of single negative-ε or negative-μ to improve the selectivity [5] [6]. "
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    ABSTRACT: Novel single negative metamaterial (MTM) transmission lines (TLs) are presented and studied in microstrip technology. They consist of a host TL in the conductor strip and a fractal-shaped complementary ring resonator (CRR) etched in the ground plane. Two types of fractal-shaped CRR are involved including the Moore and Hilbert. It is found that fractal perturbation in CRR results in lower and more transmission zeros in comparison with conventional CRR using nonfractal geometries. The single negative-permeability or -permittivity of these MTM TLs which associated with the resultant multitransmission zeros occurs by turns and should benefit devices with high selectivity requirement. Potential application of these MTM cells are illustrated by two examples, one is the microstrip stepped-impedance transformers (SIT) operating at 3.5 GHz with two edged attenuation poles to introduce selectivity; the other one is the Hi-Lo microstrip low-pass filter (LPF) with cutoff frequency 2.5 GHz exhibiting improved selectivity (77.3 dB/GHz). By constructing the low-impedance sections as hybrid prefractal shape and crown square, both the SITs and LPF obtained additional bandwidth enhancement and good matching. Consistent results between simulation and measurement have confirmed the design concept.
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