Fractal Radiation Research Articles

Critical properties of the optical field localization in a three-dimensional percolating system: Theory and experiment

We systematically study the optical field localization in an active three-dimensional (3D) disordered percolating system with light nanoemitters incorporated in percolating clusters. An essential feature of such a hybrid medium is that the clusters are combined into a fractal radiation pattern, in which light is simultaneously emitted and scattered by the disordered structures. Theoretical considerations, based on systematic 3D simulations, reveal nontrivial dynamics in the form of propagation of localized field bunches in the percolating material. We obtain the length of the field localization and dynamical properties of such states as functions of the occupation probability of the disordered clusters. A transition between the dynamical states and narrow point-like fields pinned to the emitters is found. The theoretical analysis of the fractal field properties is followed by an experimental study of the light generation by nanoemitters incorporated in the percolating clusters. The experimental results corroborate theoretical predictions.

Compact, flexible triple band Sierpinski fractal antenna on a Hilbert patterned ground for W‐WBSN

AbstractWearable Wireless Body Sensor Networks (W‐WBSNs) are the best substitute for traditional healthcare systems by effectively monitoring patients within or remotely from the hospitals. Quite a few tiny sensors linked with one another on the body can efficiently observe the functional status of the human body. The paper introduces a new triple‐band step‐shaped Sierpinski fractal wearable antenna with a Hilbert fractal slot on the partial ground for W‐WBSN applications. It comprises the step‐shaped Sierpinski fractal radiator, situated on the upper side, and a partial ground placed on the lower side of the substrate. A partial ground with a Hilbert fractal slot is used to achieve a compact wearable antenna with improved bandwidth and electromagnetic exposure rate characteristics. The antenna is constructed using a flexible Jeans substrate (permittivity 1.7, loss tangent 0.025) of size 60 × 60 mm2 with a thickness of 2.5 mm as it is a potential candidate. It demonstrates an impedance bandwidth of 6%, 7%, and 10.1%, a gain of 2.57 dBi, 3.608 dBi, and 4.19 dBi, the radiation efficiency of 54.19%, 52.5%, and 54.8% at 3.3 GHz, 5.2 GHz, and 5.8 GHz correspondingly in free space. Also, the peak SAR value of 0.64 W/kg, 0.46 W/kg, and 1.17 W/kg at 3.3 GHz, 5.2 GHz, and 5.8 GHz correspondingly, for 10 g of an average human tissue. The compact, flexible low SAR makes the anticipated antenna a superior contender for wireless wearable network applications.

Rhombus-Inscribed Circular Ring Fractal Array Antenna for Millimeter-Wave 5G Applications

A 1 × 4 planar fractal array antenna is designed and presented for millimeter-wave 5G applications. The array’s top side is made up of a rhombus-inscribed circular ring fractal patch radiator, while the backside is made up of a square notch-loaded partial ground plane. To achieve high gain, a 1 × 4 corporate feeding network is used to excite the array elements. The designed array has an overall size of 28 × 17.75 mm2. From simulations as well as experimental results, it is observed that the designed array offers a wide impedance bandwidth in the frequency range of 22.8–29.2 GHz. Furthermore, a peak gain of 10.7 dBi with a radiation efficiency of > 95% is observed in the operating bandwidth.

4-port UWB MIMO antenna with bluetooth-LTE-WiMax band-rejection and vias-MCP loaded reflector with improved performance

In this article, a 4-port MIMO antenna of dimension 0.46λ0 × 0.46λ0 × 0.01λ0 (λ0 is the lowest operating wavelength at 2.08 GHz) is proposed. It consists of array of fractal radiators sorted orthogonally with 0.05λ0 edge-to-edge separation and contorted feeds perform as impedance transformer. A centered π-shaped inverted-L notch asserts rejection at bluetooth-LTE-WiMax band. The MIMO configuration has common ground plane with no decoupling topology provides an inter-elemental port isolation > 15 dB. There are four vias-Metallic conducting probes (vias-MCP) connected to antenna ground and reflector. The conducting probes enroute the near-field currents from radiators and neutralize into the loaded reflector, with isolation improved > 20 dB and antenna performances are enhanced. The reflector has dimension 0.58λ0 × 0.58λ0 fixed at Hair = 0.07λ0 (≈ 10 mm). The antenna operates from (2.08–10.4) GHz with band rejection at (2.27–3.62) GHz, asserts improved gain characteristics (7–9.57) dBi at pass band and −4 dBi at notched band. This new technique of vias-MCP in the proposed multi-port configuration mitigates mutual interaction of surface wave coupling on radiators, reduces near-field condensed currents and couplate the surface waves into the loaded reflector to improvise impedance matching and gain characteristics for UWB wireless communication systems.

Design of Multi-band Compatible Trigeminal Monopole Array Antenna for Unmanned Aerial Vehicle

Compared with the performance index of UAV system antenna, a compatible trigeminal monopole array antenna is proposed. This antenna uses photosensitive resin as the substrate material, and can be made with UAV shell using 3D printing technology, realizing the integration of the antenna system and UAV. The antenna uses a trigeminal monopole antenna as the basic radiation unit, which is arranged in accordance with the Sierpinski fractal structure to form fractal radiation array. While enhancing the radiation through the array, it ensures that the antenna has a larger working bandwidth. In radiation performance test, the antenna is operating over a frequency spectrum of 1.038-11.916 GHz, and the minimum S11 is -37.92 dB. The proposed antenna has multi-band compatibility, better radiation performance, and greater performance redundancy.

A Modified SWB Hexagonal Fractal Spatial Diversity Antenna With High Isolation Using Meander Line Approach

This manuscript introduces a novel miniaturized super wideband (SWB) hexagonal fractal spatial diversity 2-element multiple-input-multiple-output (MIMO) antenna for broadband applications, as a compact wideband antenna is required for military radio and space communication devices. The designed antenna includes two hexagonal ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1^{st}$ </tex-math></inline-formula> modified Koch iteration) Koch fractal radiators with two linear tapered feedlines (TLTF) and a step tapered slotted ground plane (STSGP) that provides the broad impedance characteristic with miniaturized size in the operating band of 1.78-30 GHz. Moreover, the STSGP is also accountable for enabling the isolation ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S_{12/21}$ </tex-math></inline-formula> ) better than 10 dB. To further meet the isolation higher than 22 dB, a meander line is protruded from the ground plane while maintaining a 6 mm edge-to-edge distance between two antenna elements. Typically, the MIMO antenna with high isolation is beneficial for high-speed data transmission. The experimental outcomes represent that the proposed MIMO antenna is with the advantages of reasonably good diversity gain (nearly 10 dB), stable radiation patterns, high peak gain (almost 6.6 dBi), and moderate radiation efficiency (around 85%) across -10 dB impedance bandwidth. The total active reflection coefficient (TARC) and envelop correlation coefficient (ECC) are less than −25 dB and 0.1 respectively. Due to all these attributes, the proposed 2-element MIMO antenna array can be a potential candidate for military radio, spectrum sensing for cognitive radio, and space communication applications.

Triple band-stop characteristics from an aperture coupled modified Pythagorean tree fractal-based UWB-MIMO antenna integrated with complementary hexagonal spiral defected ground structure

In this manuscript, an aperture-coupled two-port modified Pythagorean tree fractal antenna is modeled and experimentally examined for ultra-wideband applications with triple-band-stop functionality. The proposed array is configured on two 37.5 × 81.5 mm2 FR-4 substrates where the upper substrate incorporates two modified Pythagorean tree fractal radiators and the lower substrate consists a feed network. The notable feature of the proposed Pythagorean tree fractal is the elimination of the base square (0th iteration level) which lowers the total fractal height by 12.11 mm. The multiband response generated by the fractal geometry is extended to a wide operational band by converting the apertures etched from the ground into the hexagonal spiral geometry. The proposed array offers 96.8% fractional bandwidth (3.7–10.64 GHz) with an optimum port-to-port isolation (S21 ≤ −16.1 dB) characteristics. Further, to reject the interfering narrow bands namely downlink C-band satellite communication, WLAN and uplink X-band satellite communication, each feedline is defected with two L-shaped slits, a U-shaped slot and split-ring resonators respectively. Various diversity metrics are investigated which are found to lie within their standard limits. The fabricated prototype (with and without band-notches) is tested and compared with simulated results which show a good similitude, thereby ensuring the feasibility of the proposed array for ultra-wideband and interference rejection operation in a real-world scenario.

Computational analysis of a dual‐port semi‐circular patch antenna combined with Koch curve fractals for ultra‐wideband systems

AbstractThis paper presents a two‐port microstrip‐fed semi‐circular patch antenna integrated with Koch curve fractals and common ground with defected ground structure for the effective implementation in handheld ultra‐wideband (UWB) systems. The proposed array is engraved on a 1.57 mm thick FR‐4 substrate with an overall array size of 30.5 × 47 × 1.64 mm3. The parametric analysis of the proposed array indicates that the two optimized Koch curve fractal (second iteration order) radiators (upper substrate layer) provides an optimum matching performance in a wide operational band (4.395–10.184 GHz, 79.4%) and minimizes the patch area by 41.2% as compared to the conventional circular patch. To realize good port‐to‐port isolation (S21/S12 ≤ −16.8 dB), the reduced ground is slotted and incorporated with a funnel‐shaped decoupling structure at the center. The prototype of the proposed array is fabricated and experimentally tested to justify the simulated S‐parameter results. All diversity metrics like envelope correlation coefficient, diversity gain (DG), mean effective gain, channel capacity loss, and total active reflection coefficient lie within their acceptable limits which affirm a high signal‐to‐noise ratio and the proficiency of the proposed array in the development of high data‐rate UWB communication devices.

UWB aperture coupled circular fractal MIMO antenna with a complementary rectangular spiral defected ground structure (DGS) for 4G/WLAN/radar/satellite/international space station (ISS) communication systems

In this article, a dual-port aperture-coupled circular fractal antenna array is designed, developed and tested for its usage in 4G, WLAN, radar, satellite and ISS communication systems, covering C-band, X-band and Ku-band of frequencies. The proposed array is designed on two FR-4 substrates (with overall dimensions of 34 × 68.7 × 3.245 mm3) where the upper and lower substrate consists of circular fractal radiators (2nd order of iteration) and a feed network respectively. The aperture slots in the ground are transformed into complementary rectangular spiral slots with a tree-shaped DGS, to achieve the desired operational band (4.6–16.8 GHz) with improved matching performance. It provides a maximum gain of 4.57 dB (at 6.6 GHz) and high port-to-port isolation (S21 ≤ −19 dB) performance. The implementation of the proposed array in MIMO systems is validated by various diversity parameters like low ECC, high DG, high MEG, low CCL and stable TARC attributes. An acceptable agreement is achieved between the simulated and experimental results.

Investigation of 2-port UWB MIMO diversity antenna design using characteristics mode analysis

In this research work, a 2-port UWB MIMO diversity antenna is designed to operate from 2.7 to 10.5 GHz with −10 dB impedance bandwidth of 118.18%. The proposed design has a total size of 0.57λ2.7×0.28λ2.7 (λ2.7 is lowest operating wave-length) consists of bi-planar printed fractal radiators whose feeds are contorted in geometry and are diametrically-fed. Characteristics mode analysis (CMA) is introduced to investigate antenna design, feeding technique and modal current distributions. The analysis includes study of modal dynamics, resonance mechanism, bandwidth potentials and modal radiation quality factor. The port-isolation is ⩾−15 dB when ground plane is truncated by rectangular slots via ellipsoid slot. With an end-connected ground thin neutralization lines, mutual coupling is further reduced by 7.5 dB (>−22.5 dB, measured). The diversity performance metrics are evaluated from ECC, CCL, DG, multiplexing efficiency, MEG and TARC. ECC is low <0.17 (from far-field magnitudes) and mean effective gain for both ports are |MEG| < 3 dB with MEG1MEG2 ≊ 1, which is serviceable for UWB multi-standard mobile/wireless/sensor ad-hoc diversity systems. An equivalent circuit model is also designed and the prototype of antenna is fabricated and measured to validate its performance.

Four arm windmill shaped superwideband terahertz MIMO fractal antenna

In this paper, a microstrip line fed windmill shaped antenna for superwideband multiple input multiple output (MIMO) applications at terahertz frequency spectrum is proposed. It comprises a second iterative fractal radiator, tapered microstrip line feeding and partial rectangular ground plane. The antenna element and MIMO configurations are operating from 3.1 THz to more than 60 THz (for S11≤-10 dB). The footprint of spatial and pattern diversity configurations are 110 μm×125 μm and 110 μm×155 μm respectively. Both configurations have isolation more than 30 dB in maximum part of their operating frequency spectrum along with distorted omnidirectional radiation patterns and acceptable values of MIMO performance parameters.

Bandwidth Enhancement of Super Wide Band Fractal Microstrip Patch Antenna for Wireless Applications

In communication system the requirement of bandwidth enhancement is the most necessary requirement. This requirement of bandwidth increment can easily achieve the data rate of the system, so for further development of communication system higher bandwidth is required. Wireless communication already covered most of the frequency range till five giga hertz. In fractal technique structure which is similar in shape are designed for the similar nature of the radiation to increase the radiative power. By fractal radiation area can be increased, is used to achieve the bandwidth of the signal. By fractal technique size of the antenna can also be reduced for miniaturization of the device which is going to be developed. In this paper a different rectangular antenna is presented, consists of dual properties, is fractal and defected ground. This paper shows simulated result and designed hardware result and also shows the comparative result of these. In defective one rectangular slot has been introduced. A higher bandwidth rectangular antenna has been simulated and designed and a comparative analysis of simulated and hardware results compared and analyzed. Simulation done by considering 4 GHz as center frequency. The easily available material FR-4 is used for simulation as well as hardware design. In this substrate thickness will be 1.6mm. Return loss of the given design is achieved less than -10db for almost 11GHz. In future the many applications will use this range of frequency. The value of VSWR is also achieved less than two for 3GHz to 14GHz. Simulation of this design is done by HFSS software. The ground plane is also modified for enhancement of bandwidth.

A Sierpinski Carpet Five Band Antenna for Wireless Applications

A compact Sierpinski Carpet square fractal multiband antenna operating at 3.9 (WiMAX) /6.6 (Satellite TV) /8.1/10.7/11.8 GHz (X-band) is presented. The proposed Microstrip Patch Antenna (MSPA) consists of a Sierpinski Carpet square fractal radiator in which square slots are etched out and a tapered microstrip feed line. The Sierpinski Carpet square fractal patch modifies the current resonant path thereby making the antenna to operate at five useful bands. Impedance matching at these bands are solely achieved by using Sierpinski square slot and tapered feedline, thus eliminating the need of any external matching circuit. The dimensions of the compact antenna is and exhibits S 11 <-10dB bandwidth of about 4.8% (4.01-3.82 GHz), 2.1% (6.62-6.48 GHz), 2.7% (8.24-8.02 GHz), 2.1% (10.77-10.54 GHz) and 21% (12.1-11.60 GHz) with the gain of 7.57/3.91/3.77/6.74/1.33 dB at the operating frequencies 3.9/6.6/8.1/10.7 and 11.8 GHz, respectively under simulation analysis carried out by using HFSS v.13.0.

Determination of complex permittivity of thin dielectric samples based on high-q microstrip resonance sensor

In this paper, a high quality factor microstrip resonator based on modified Minkowski fractal structure sensor is presented for determining the dielectric sample's complex permittivity. A high loaded quality factor value has been achieved by utilizing fractal structure, which is far greater than that of a typical rectangle microstrip antenna. Besides, the modified fractal radiation patch and the feeding section of the sensor result in a highly sensitive area to the tested materials. The sensing principle is implemented by detecting the electric fields perturbation of the resonator when different tested materials are placed over it. The complex permittivity change of the tested materials can be forecasted by transferring the acquired experimental relative resonant frequency shifts (Δf) and loaded QL values of the proposed sensor to a well-developed neural network system. To validate the proposed method, various standard dielectric samples including Teflon, PVC, and others are tested and analyzed. The experimental results are compared with published values with the maximum error of 4.9%.

Analysis and Development of Triangular Gasket Diagonal Slot Embedded Fractal Patch Antenna for Multiband Wireless Applications

This paper presents novel reduced size diagonal slot embedded Triangular Gasket fractal patch antenna for multiband wireless applications. The diagonal slot geometry is embedded in triangular patch antenna for initial size reduction of the basic cell and further miniaturization is achieved by fractalization of the cell upto third order. Three frequency resonances of 2.4, 6.5 and 9.23 GHz are optimized for WiFi, WiMAX and WLAN (Wireless Local Area Network) applications in the S, C and X frequency bands. Size reduction upto 55.32 and 80.74% is achieved in terms of whole antenna area and copper cladding remaining respectively in comparison to triangular patch antenna. Antenna 3D (Three-Dimensional) modeling, simulation and optimization for the desired BW (Bandwidth) and gain requirements are done in HFSS (High Frequency Structure Simulator) and CST (Computer Simulation Technology). Effects of embedding diagonal slot in the basic triangular cell is analyzed in terms of the diagonal slot length and width with corresponding frequency response variations. Microstrip feed line dimensions and ground plane separation from the radiating top layer is optimized for achieving acceptable BWs less than -10 dB for the desired multiple resonances. E-field, H-field, current density and surface current plots are presented to verify the radiations for multiband wireless applications. Proposed slot embedded fractal radiator is fabricated and measured frequency responses and gain patterns are demonstrated in comparison with simulated results for verification of the concept.

An Isolation Enhanced, Printed, Low-Profile UWB-MIMO Antenna with Unique Dual Band-Notching Features for WLAN and WiMAX

Here, a low-profile, printed, ultra-wideband (UWB), multiple-input–multiple-output (MIMO) antenna with unique dual band-notching feature for selective elimination of the interferences from the existing WLAN and WiMAX bands has been investigated. The antenna proposed here consists of two fractal radiators and a defected ground structure. The designed antenna shows an ultra-wide frequency bandwidth of 8.6 GHz (2.0–10.6 GHz). A slot having the shape of the English Letter “U” has been finely etched from the surface of the fractal radiators in order to realize a frequency band-notch, centered at 3.5 GHz (WiMAX). A second band-notch, centered at 5.2 GHz (WLAN) has been obtained by adding horizontal stubs. The prevailing issue of mutual isolation between the adjacent radiating elements has been significantly enhanced by incorporating a vertical decoupling strip at the rear side of the proposed two-port diversity MIMO antenna. The antenna proposed here is compact in shape, having a dimension of 26 × 35 mm2. Simulated and measured results show a good match, justifying its applicability in the modern communication era.

A CSRR-Fed SIW Cavity-Backed Fractal Patch Antenna for Wireless Energy Harvesting and Communication.

This paper presents a novel compact dual-band and dual-polarized complementary split-ring resonator (CSRR)-fed substrate-integrated waveguide (SIW) cavity-backed fractal patch antenna for wireless energy harvesting and communication. The proposed antenna is composed of a Giuseppe Peano fractal radiation patch with a backed SIW cavity. To enhance the bandwidth and minimize the dimensions, the CSRR structure is designed to feed the Giuseppe Peano fractal patch orthogonally. A prototype of the proposed antenna is simulated, fabricated and measured. The proposed antenna exhibits good directionality and high cross-polarization level with especially compact size.

A NOVEL TWO-LAYER STACKED MICROSTRIP ANTENNA ARRAY USING CROSS SNOWFLAKE FRACTAL PATCHES

In this paper, a novel approach was used to design two-layer stacked high-gain microstrip antenna array with improved bandwidth and high aperture e-ciency. Cross Snow∞ake fractal microstrip patches were employed as radiation elements. Varieties of antenna arrays with difierent fractal iterations were optimized by using the Genetic Algorithm (GA) associated with 3D full-wave Finite Element Method (FEM) in order to investigate the in∞uence of the Cross Snow∞ake fractal radiators. As compared with the conventional square patches, the Cross Snow∞ake fractal conflguration provides extremely high ∞exibility to achieve a wideband performance and maintains higher aperture e-ciency at operating frequency band. A prototype antenna with 2£2 Cross Snow∞ake radiators was fabricated and measured. Both simulated and measured results show that the proposed antenna has some promising performances to be more specially, the measured impedance bandwidth is 22.9% (from 5.18GHz to 6.52GHz) when S11 < i10dB; the simulated gain is 12.0dBi and its corresponding aperture e-ciency is up to 87.4% at the working frequency 5.8GHz.

Flexible Sierpinski Carpet Fractal Antenna on a Hilbert Slot Patterned Ground

This paper presents a novel design of fractal antenna on a flexible substrate that operates in UMTS band (universal mobile telecommunication system, 1.92–2.17 GHz). The antenna consists of a Sierpinski carpet fractal radiator, which reduces the overall size of the antenna, and it is realized on top of a Hilbert slot in the ground layer, to achieve required impedance matching. The antenna is compact with the overall dimensions equal to 70 mm × 31 mm × 0.075 mm. Influence that folding has on the initial planar topology is investigated in detail. The obtained results show that the proposed antenna is more tolerant to folding than the conventional patch and that it exhibits relatively stable radiation patterns even when folded in complex manners.

Numerical solution of the Boussinesq equation: Application to the agricultural drainage

Water flow to subterranean drains is described by the Boussinesq equation. To solve this equation, analytical solutions comprising constants, such as the transmissivity and drainable porosity have been developed; however, these solutions assume that free surface of the water falls instantly over the drains. The aim of this investigation is to present a finite difference solution of the differential equation using a drainable porosity variable and a fractal radiation condition. Here, two schemes are presented: the first one, with an explicit head and drainable porosity, both joined by a functional relationship, called mixed formulation; and the second one, called head formulation, with only the head. By using a lineal analytical solution, both methods have been validated and the nonlinear part was stable and brief. The proposed numerical solution is useful for the hydraulic characterization of soils with inverse modelation and to improve the designs of agricultural drainage systems, when taking into consideration that the assumptions of the classical solution have been eliminated. To evaluate the descriptive capacity of the numerical solution, these solutions were used to describe a drainage experiment performed in the laboratory. The results show that the cumulative drained depth is well represented by these solutions with the fractal radiation and the variable drainable porosity. Key words: Fractal radiation condition, variable drainable porosity, analytical solution, mixed formulation, head formulation.