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Antenna miniaturization, multiband operation and wider operational bandwidth are vital to achieve optimal design for modern wireless communication devices. Using fractal geometries is recognized as one of the most promising solutions to attain these characteristics. The purpose of this paper is to present a unique structure of patch antenna using hybrid fractal technique to enhance the performance characteristics for various wireless applications and to achieve better miniaturization.

In this paper, the authors propose a novel hybrid fractal antenna by combining Koch and Minkowski (K-M) fractal geometries. A microstrip patch antenna (MPA) operating at 1.8 GHz is incorporated with a novel K-M hybrid fractal geometry. The proposed fractal antenna is designed and simulated in CST Microwave studio and compared with existing Koch fractal geometry. The prototype for the third iteration of the K-M fractal antenna is then fabricated on FR-4 substrate and tested through vector network analyzer for operating band/voltage standing wave ratio.

The third iteration of the proposed K-M fractal geometry results in achieving a 20% size reduction as compared to an ordinary MPA for the same resonant frequency with impedance bandwidth of 16.25 MHz and a directional gain of 6.48 dB, respectively. The operating frequency of MPA also lowers down to 1.44 GHz.

Further testing for the radiation patterns in an anechoic chamber shows good agreement to those of simulated results.

A vertically stacked, three layer hybrid Hilbert fractal geometry and serpentine radiator-based patch antenna is proposed and characterized for medical implant applications at the Industrial, Scientific and Medical band (2.4-2.48 GHz). Antenna parameters are optimised to achieve miniaturized, biocompatible and stable transmission characteristics. The paper aims to discuss these issues.

Human tissue effects on the antenna electrical characteristics were simulated with a three-layer (skin, fat and muscle) human tissue model with the dimensions of 180×70×60 mm3 (width×height×thickness mm3). Different stacked substrates are utilized for the satisfactory characteristics. Two identical radiating patches are printed on Roger 3,010 (ε _r=10.2) and Alumina (ε _r=9.4) substrate materials, respectively. In addition, various superstrate materials are considered and simulated to prevent short circuit the antenna while having a direct contact with the metallization, and achieve biocompatibility. Finally, superstrate material of Zirconia (ε _r=29) is used to achieve biocompatibility and long-life. A finite element method is used to simulate the proposed hybrid model with commercially available Ansoft HFSS software.

The antenna is miniaturized, having dimensions of 10×8.4×2 mm3 (width×height×thickness mm3). The resonance frequency of the antenna is 2.4 GHz with a bandwidth of 100 MHz at return loss (S11) of better than −10 dB characteristics. Overall, the proposed antenna have 50 Ω impedance matching, −21 dB far field antenna gain, single-plane omni-directional radiation pattern properties and incident power of 5.3 mW to adhere Specific Absorption Rate regulation limit.

Vertically stacked three layer hybrid design have miniaturized characteristics, wide bandwidth, biocompatible, and stable characteristics in three layer human tissue model make this antenna suitable for implant biomedical monitor systems. The advanced simulation analysis of the proposed design constitutes the main contribution of the paper.

The purpose of this paper is to design an on-chip inductor with high inductance, high-quality factor and high self-resonance frequency for the equivalent on-chip area using fractal curves.

A novel hybrid series stacked differential fractal inductor using Hilbert and Sierpinski fractal curves is proposed with two different layers connected in series using vias. The inductor is implemented in Sonnet EM simulator using 180 nm CMOS standard process technology.

The proposed inductor reduces the parasitic capacitance and negative mutual inductance between the adjacent layers with significant improvement in overall inductance, quality factor and self-resonance frequency when compared with conventional series stacked fractal inductors.

The fractal inductor is used to create high inductance in the single-layer process, but access to multilayers is restricted owing to unusual and expensive fabrication processes.

The proposed inductor can be used in implementation of low noise amplifier, voltage controlled oscillators and power amplifiers.

This paper introduces a combination of two fractal curves to implement a hybrid fractal inductor that enhances the performance of the inductor.

In additive manufacturing (AM) process, the physical properties of the products made by fractal toolpaths are better as compared to those made by conventional toolpaths. Also, it is desirable to minimize the number of tool retractions. The purpose of this study is to describe three different methods to generate fractal-based computer numerical control (CNC) toolpath for area filling of a closed curve with minimum or zero tool retractions.

This work describes three different methods to generate fractal-based CNC toolpath for area filling of a closed curve with minimum or zero tool retractions. In the first method, a large fractal square is placed over the outer boundary and then rest of the unwanted curve is trimmed out. To reduce the number of retractions, ends of the trimmed toolpath are connected in such a way that overlapping within the existing toolpath is avoided. In the second method, the trimming of the fractal is similar to the first method but the ends of trimmed toolpath are connected such that the overlapping is found at the boundaries only. The toolpath in the third method is a combination of fractal and zigzag curves. This toolpath is capable of filling a given connected area in a single pass without any tool retraction and toolpath overlap within a tolerance value equal to stepover of the toolpath.

The generated toolpath has several applications in AM and constant Z-height surface finishing. Experiments have been performed to verify the toolpath by depositing material by hybrid layered manufacturing process.

Third toolpath method is suitable for the hybrid layered manufacturing process only because the toolpath overlapping tolerance may not be enough for other AM processes.

Development of a CNC toolpath for AM specifically hybrid layered manufacturing which can completely fill any arbitrary connected area in single pass while maintaining a constant stepover.

The purpose of this paper is to develop a general mathematic approach to model the microstructures of porous structures produced by additive manufacturing (AM), which will result in fractal surface topography and higher roughness that have greater influence on the performance of porous structures.

The overall shapes of pores were modeled by triply periodic minimal surface (TPMS), and the micro-roughness details attached to the overall pore shapes were represented by Weierstrass–Mandelbrot (W-M) fractal representation, which was integrated with TPMS along its normal vectors. An index roughly reflecting the irregularity of fractal TPMS was proposed, based on which the influence of the fractal parameters on the fractal TPMS was qualitatively analyzed. Two complex samples of real porous structures were given to demonstrate the feasibility of the model.

The fractal surface topography should not be neglected at a micro-scale level. In addition, a decrease in the fractal dimension D_s may exponentially make the topography rougher; an increase in the height-scaling parameter G may linearly increase the roughness; and the number of the superposed ridges has no distinct influence on the topography. Furthermore, the synthesis method is general for all implicit surfaces.

The method provides an alternative way to shift the posteriori design paradigm of porous media to priori design mode through numeric simulation. Therefore, the optimization of AM process parameters, as well as the porous structure, can be potentially realized according to specific functional requirement.

The synthesis of TPMS and W-M fractal geometry was accomplished efficiently and was general for all implicit freeform surfaces, and the influence of the fractal parameters on the fractal TPMS was analyzed more systematically.

The purpose of this paper is to outline the extensive multi-scale and multi-physics challenges when simulating future aircraft and offer strategies to help deal with some of these challenges.

To help with the multi-scale challenges, in a hierarchical, zonal fashion both the handling of turbulence and geometry is considered.

Such modelling of geometry is necessary to help deal with the increasingly coupled nature of many aerodynamic problems more economically and the drive towards considering ever increasing levels of geometrical complexity/scale.

The proposed unified framework could be exploited all the way, through initial fast preliminary design to final numerical test involving various bespoke combinations of hierarchical components.

Application of electromagnetic band gap (EBG) i.e. electromagnetic band gap technique and its use in the design of microstrip antenna and MIC i.e. microwave integrated circuits is becoming more attractive. This paper aims to propose a new type of EBG fractal square patch microstrip multi band fractal antenna structures that are designed and developed. Their performance parameters with and without EBG structures are investigated and minutely compared with respect to the resonance frequency, return loss, a gain of the antenna and voltage standing wave ratio.

The fractal antenna geometries are designed from the fundamental square patch and then EBG structures are introduced. The antenna geometry is optimized using IE3D simulation tool and fabricated on low cost glass epoxy FR4, with 1.6 mm height and dielectric materials constant of 4.4. The prototype is examined by means of the vector network analyzer and antenna patterns are tested on the anechoic chamber.

Combining the square fractal patch antenna with an application of EBG techniques, the gain of microstrip antenna has been risen up and attained good return loss as compared to the antennas without EBG structures. The designs exhibit multi-frequency band characteristics extending in between 1.70 and 7.40 GHz. Also, a decrease in antenna size of 34.84 and 59.02 per cent for the first and second iteration, respectively, is achieved for the antenna second and third without EBG. The experimental results agree with that of simulated values. The presented microstrip antenna finds uses in industrial, scientific and medical (ISM) band, Wi-Fi and C band. This antenna can also be used for satellite and radio detection and range devices for communication purposes.

A new type of EBG fractal square patch microstrip antenna structures are designed, developed and compared with and without EBG. Because of the application of EBG techniques, the gain of microstrip antenna has been risen up and attained good return loss as compared to the antennas without EBG structures. The designs exhibit multi-frequency band characteristics extending in between 1.70 and 7.40 GHz, which are useful for Wi-Fi, ISM and C band wireless communication.

The purpose of this paper is to describe a modified Hilbert‐based fractal antenna for ultra wideband (UWB) wireless applications. Simulation results show excellent multi‐band characteristics for UWB wireless applications.

A Hilbert curve‐based fractal is optimised for self‐replicating, space‐filling and self‐avoiding properties. In the proposed design, the Hilbert curve is applied to a rectangle as an initial iteration and maintained for the later iterations. Additionally, a Yagi‐like strip is removed from the second iteration of the Hilbert patch and a hexagonal portion is removed from the substrate to achieve good optimization. The antenna feed is created through a micro‐strip line with a feeding section. Finally, a partial ground plane technique is used for improved impedance matching characteristics. A finite element method (FEM) is used to simulate the modified Hilbert model with commercially available Ansoft HFSS software.

The proposed antenna is miniaturized (39 mm length×30 mm width) and has multi‐band characteristics. The simulation results show that the antenna has a reflection coefficient characteristic of <−10 dB, a linear phase reflection coefficient, better than 65 percent radiation efficiency, 2.2‐4 dBi antenna gain and nearly omni‐directional radiation pattern properties over the UWB bandwidth (3.1‐10.6 GHz).

The antenna shows promising characteristics for the full 7.5 GHz UWB bandwidth. In addition, the performance is achieved by using laceration techniques on the Hilbert patch and substrate, respectively. A partial ground plane ensures impedance matching of 50 over full UWB bandwidth. The simulation analysis of the modified Hilbert fractal antenna design constitutes the main contribution of the paper.

This paper aims to propose a single element, dual feed, polarisation diversity antenna. The proposed antenna operates from 2.9 to 10.6 GHz for covering the entire ultra-wideband (UWB) frequency range. The antenna is designed for usage in massive multiple input multiple output (MIMO) and closed packaging applications.

The size of the antenna is 24 × 24 × 1.6 mm³. The radiating element of the antenna is derived from the Sierpinski–Knopp (SK) fractal geometry for miniaturization of the antenna size. The antenna has a single reflecting stub placed between the two orthogonal feeds, to improve isolation.

The proposed antenna system exhibits S₁₁ < −10 dB, S₂₁ < −15 dB and stable radiation characteristics in the entire operating region. It also offers an envelope correlation coefficient < 0.01, a diversity gain > 9.9 dB and a capacity loss < 0.4 bps/Hz. The simulated and measured outputs were compared and results were found to be in similarity.

The proposed UWB-MIMO antenna has significant size reduction through usage of SK fractal geometry for radiating element. The antenna uses a single radiating element with dual feed. The stub is between the antenna elements which provide a compact and miniaturized MIMO solution for high density packaging applications. The UWB-MIMO antenna provides an isolation better than −20 dB in the entire UWB operating band.