PIER B | PIER Journals

2011-04-28

PIER B

Vol. 29, 409-429, 2011

download: 294

Redesign and Optimization of the Paving Algorithm Applied to Electromagnetic Tools (Invited Paper)

Javier Moreno , Ma Jesús Algar , Ivan Gonzalez-Diego and Felipe Catedra

To study any electromagnetic system, the geometry model must be discretized into elements with an appropriate size for the working frequency. The discretization of a system must be transparent to the user of electromagnetic computing tools. A mesher is presented based on the paving algorithm. The algorithm has been modified to allow triangular elements and has been accelerated by distributing the load on multiple processors simultaneously. Also, a multilevel mode has been implemented. With this tool, any geometry defined by NURBS (Non Uniform Rational B-Spline) surfaces can be decomposed into triangular and quadrangular curved elements.

REDESIGN AND OPTIMIZATION OF THE PAVING ALGORITHM APPLIED TO ELECTROMAGNETIC TOOLS (Invited Paper)

2011-04-26

PIER B

Vol. 29, 393-408, 2011

doi:10.2528/PIERB11011109

download: 362

Transient Solution for Lossy Transmission Line by Means of Orthogonal Projection Method

Hengxu Ha , Jing Cai , Zhi-Qian Bo and Bo Chen

A novel electromagnetic transient analysis technique by means of the orthogonal projection method for lossy transmission line is proposed. By employing the proposed method, the traveling waves propagating from one terminal to another can be quickly obtained with less amount of computation at considerably large steps. First of all, the differential function to variable time can be approximated to be the convolution with a fixed vector relates to a certain set of orthogonal basis, e.g. Daubechies' basis. The partial differential telegraph equations related to both variable time t and distance x are then transformed to be differential equations only related to x. The solution of such equations can be obtained accordingly. The discrete coefficients of propagation function for lossy line are obtained as well, by which the propagating traveling waves can be calculated precisely at considerably large sampling periods with less amount of computation.

TRANSIENT SOLUTION FOR LOSSY TRANSMISSION LINE BY MEANS OF ORTHOGONAL PROJECTION METHOD

2011-04-25

PIER B

Vol. 29, 355-392, 2011

doi:10.2528/PIERB10090207

download: 319

Approximate Boundary Relations on Anisotropic Sheets

A. Burak Polat

Approximate boundary relations on general anisotropic sheets of arbitrary shape as well as the special case when they are backed by a perfect electrical conductor are investigated based on a generalization of the procedure introduced by Idemen in 1993 for uniaxially anisotropic planar sheets to general anisotropic and arbitrarily shaped surfaces. The ranges of validity of the approximations in the methodology are also tested numerically for the impedance boundary condition obtained in the case of a PEC backed uniaxially anisotropic sheet.

APPROXIMATE BOUNDARY RELATIONS ON ANISOTROPIC SHEETS

2011-04-22

PIER B

Vol. 29, 339-354, 2011

doi:10.2528/PIERB11030904

download: 278

Multiband Fractal-Like Antennas

Rao Shahid Aziz , Majeed Alkanhal and Abdel-Fattah Sheta

In this paper, new multiband fractal-like antennas are proposed. The proposed multiband antenna design is based on a methodology that utilizes the self transformation principle of fractal-like rectangular profiles to generate multiband operation. The proposed monopole-type antennas are built on a partial ground plane and fed through a microstrip feed line. The analytical design procedures are straightforward and can be applied to any practical antenna structure to operate at multiple preselected bands. The developed methodology has been used to design antennas operating at three, four, and five preselected practical bands. Numerical simulations are utilized to verify the simple design procedures of the proposed multiband antenna structures. The triple-band and the quad-band structures have been realized on FR4 substrate to prove the concept. Simulation and experimental results are in good agreement and demonstrate the performance of the design methodology and the proposed antenna structures.

2011-04-15

PIER B

Vol. 29, 311-338, 2011

doi:10.2528/PIERB11021607

download: 816

Radar Cross Sections of Sea and Ground Clutter Estimated by Two Scale Model and Small Slope Approximation in HF-VHF Bands

Laurent Vaitilingom and Ali Khenchaf

HF-VHF Radars are used in oceanography and sea surveys [1] because they can cover a larger distance than other radars. We can use this kind of radar in sea and ground environments. In these bands, phenomena associated with clutter [2] interfere with radar performance for ship and terrestrial vehicle detection. To improve radar performance, a measure called Radar Cross Section is calculated. We have studied Radar Cross Section in HF-VHF bands with the objective of determining the influence of sea and ground clutter. There are two categories of Radar Cross Section: exact methods [3] and approximate methods [4-8]. We have studied approximate methods because they are faster than exact methods. A common radar configuration is the bistatic configuration where transmitter and receiver are dissociated. The aim of this paper is to study Radar Cross Sections of clutter estimated by approximate models in HF-VHF bands in a bistatic configuration.

RADAR CROSS SECTIONS OF SEA AND GROUND CLUTTER ESTIMATED BY TWO SCALE MODEL AND SMALL SLOPE APPROXIMATION IN HF-VHF BANDS

2011-04-13

PIER B

Vol. 29, 289-309, 2011

doi:10.2528/PIERB11022302

download: 239

An Improved Differential Evolution for Autonomous Deployment and Localization of Sensor Nodes

Subhrajit Roy , Sk. Minhazul Islam , Saurav Ghosh , Swagatam Das and Ajith Abraham

In recent years, Wireless Sensor Networks (WSNs) have transitioned from being objects of academic research interest to a technology that is frequently being employed in real-life applications and rapidly being commercialized. The performance of a WSN is largely affected by high quality deployment and precise localization of sensor nodes. This article deliberates autonomous deployment of sensor nodes from an Unmanned Aerial Vehicle (UAV). This kind of deployment has importance in emergency applications, such as disaster monitoring and battlefield surveillance. The goal is to deploy the nodes only in the terrains of interest, which are distinguished by segmentation of the images captured by a camera on board the UAV. In this article we propose an improved variant of a very powerful real parameter optimizer, called Differential Evolution (DE) for image segmentation and for distributed localization of the deployed nodes. Image segmentation for autonomous deployment and distributed localization are designed as multidimensional optimization problems and are solved by the proposed algorithm. Performance of the proposed algorithm is compared with other prominent adaptive DE-variants like SaDE and JADE as well as a powerful variant of the Particle Swarm optimization (PSO) algorithm, called CLPSO. Simulation results indicate that the proposed algorithm performs image segmentation faster than both types of algorithm for optimal thresholds. Moreover in case of localization it gives more accurate results than the compared algorithms. So by using the proposed variant of Differential Evolution improvement has been achieved both in the case of speed and accuracy.

AN IMPROVED DIFFERENTIAL EVOLUTION FOR AUTONOMOUS DEPLOYMENT AND LOCALIZATION OF SENSOR NODES

2011-04-08

PIER B

Vol. 29, 269-288, 2011

doi:10.2528/PIERB11021904

download: 517

New Techniques for Increasing Antenna Bandwidth with Impedance Loading

Richard Formato

New methods are presented for increasing the bandwidth of wire antennas using impedance loading. This paper extends the seminal Wu-King theory of the internal impedance profile that produces travellingwave only current modes on a center-fed dipole antenna. It also presents a numerical optimization methodology based on Central Force Optimization, a new deterministic multidimensional search and optimization metaheuristic useful for problems in applied electromagnetics. A CFOoptimized loaded monopole antenna is described in detail and compared to the same structure loaded with a fractional Wu-King profile. The CFO monopole generally performs better than other designs using either the full or fractional Wu-King profiles or the extended Wu-King profiles. The methods described in this paper should be useful in any wire antenna design that utilizes impedance loading to increase bandwidth.

NEW TECHNIQUES FOR INCREASING ANTENNA BANDWIDTH WITH IMPEDANCE LOADING

2011-04-07

PIER B

Vol. 29, 251-267, 2011

doi:10.2528/PIERB11022506

download: 368

Modeling of the Human Exposure Inside a Random Plane Wave Field

Franco Moglie , Valter Mariani Primiani and Anna Pia Pastore

The specific absorption rate (SAR) of a human body exposed to a random field inside a reverberation chamber (RC) has been modeled. The exciting field is simulated using the plane wave integral representation which is numerically solved by a superposition of N plane waves randomly generated and repeated M times to reproduce the same statistics of an RC. An experimental validation, carried out by means of known saline solutions, confirms the reliability of this method. The obtained results at various frequencies for the adopted "Visible Human Body" and for some tissues well highlight the absorption percentage. The frequency behavior of the total SAR reveals the resonance of the human body around 75 MHz, in spite of the chaotic source.

MODELING OF THE HUMAN EXPOSURE INSIDE A RANDOM PLANE WAVE FIELD

2011-04-01

PIER B

Vol. 29, 233-250, 2011

doi:10.2528/PIERB11030406

download: 288

Bandwidth Enhancement of Circularly Polarized Square Slot Antenna

Ronald Joseph and Takeshi Fukusako

Bandwidth enhancement technique of circularly polarized square slot antenna is presented in this paper. A square slot antenna with the components of L-probe separated could achieve an axial ratio (AR) bandwidth of 33.84%. Placing Stubs in the slot by studying the electric field behaviour could enhance the AR bandwidth by around 10%. Creating an L-shaped slot on the ground plane, where the electric field rotates in the desired clockwise direction, can further enhance the bandwidth by 7%. A < -10 dB S₁₁ bandwidth of 46.15% and < 3 dB AR bandwidth of 50.35% could be achieved with the present design. Unidirectional patters are obtained by having a cavity at the wide slot of the antenna and shows a measured bandwidth of 41.79% in S₁₁ and 44.97% in AR. Both antennas show a cross polarization discrimination of more than 15 dB on a wide azimuth range. The measured results well comply with the simulated results.

BANDWIDTH ENHANCEMENT OF CIRCULARLY POLARIZED SQUARE SLOT ANTENNA

2011-03-31

PIER B

Vol. 29, 209-231, 2011

doi:10.2528/PIERB11021805

download: 266

Forward and Backward Waves in High-Frequency Diffraction by an Elongated Spheroid

Ivan Viktorovitch Andronov and Daniel Bouche

The asymptotics of induced current of forward and backward waves on a strongly elongated spheroid is constructed by matching the asymptotic representations to exact solution valid in a vicinity of the rear tip of the spheroid. These asymptotic results are compared with numerical computations.

FORWARD AND BACKWARD WAVES IN HIGH-FREQUENCY DIFFRACTION BY AN ELONGATED SPHEROID

2011-03-30

PIER B

Vol. 29, 191-207, 2011

doi:10.2528/PIERB10112209

download: 397

Epsimu, a Tool for Dielectric Properties Measurement of Porous Media: Application in Wet Granular Materials Characterization

Pierre Sabouroux and Doudou Ba

The principal aim of this article is the presentation of EpsiMu, a tool for dielectric properties measurement. This general tool can be used to characterize all types of materials, but in this article we apply it to porous or granular materials. The tool consists of a coaxial cell and dedicated software that allow us to reconstruct the permittivity in almost real-time by a de-embedding process. Dielectric permittivity of soils sample was measured using this microwave tool. So, we can then determine the relationship between the dielectric properties and volumetric water content θ of Fontainebleau sand (center of France) and Dune of Pilat sand (Arcachon Bay area, France). The clay effect on Fontainebleau sand is also studied. We discuss the usefulness of several models that link the permittivity to volumetric water content of soil. It is shown that the soil permittivity model is not directly applicable to Fontainebleau sand and Dune of Pilat sand. We find a good match between our results representing the relative permittivity ε'_r veversus the volumetric water content θ and the Complex Refractive Index model (CRIM) between 600 MHz and 1 GHz. Alternative regression formulae are proposed. The implication of the determination of volumetric water content, θ, is discussed. A linear relation between the dielectric loss tangent and volumetric water content θ of soils is established.

EPSIMU, A TOOL FOR DIELECTRIC PROPERTIES MEASUREMENT OF POROUS MEDIA: APPLICATION IN WET GRANULAR MATERIALS CHARACTERIZATION

2011-03-30

PIER B

Vol. 29, 175-190, 2011

doi:10.2528/PIERB11020802

download: 277

A Proposed Method for Quantifying Uncertainty in RF Immunity Testing Due to Eut Presence

Eduardo Paez , Ciro Tremola and Marco A. Azpurua

Throughout the performance of a RF immunity test according IEC 61000-4-3 there are several factors that should be taken into account to ensure the quality and to estimate the uncertainty associated to the results. One phenomenon that should be considered to calculate uncertainty is the disturbing effect produced by the EUT over the electric field generated within the calibrated uniform field area; nevertheless the mentioned effect is not easily quantifiable because the measuring process using additional antennas or field probes inside the semianechoic chamber could also alter the electric field distribution. An experimental method for quantifying the mentioned uncertainty contribution is presented. The method is based upon the fact that antenna-EUT coupling and reflection effects could be measured through changes in the input impedance of the field generation antenna. A validation procedure for the proposed method is also described. Hence, a relationship between the reflection coefficient at the antenna input port and the electric field strength is derived. The uncertainty contribution is calculated through the maximum relative change in the E-field intensity magnitude for the frequency range of 80-1000 MHz, considering the worst case for several EUT positions.

A PROPOSED METHOD FOR QUANTIFYING UNCERTAINTY IN RF IMMUNITY TESTING DUE TO EUT PRESENCE

2011-03-29

PIER B

Vol. 29, 157-174, 2011

doi:10.2528/PIERB10110810

download: 273

Near Optimal Robust Adaptive Beamforming Approach Based on Evolutionary Algorithm

Rammohan Mallipeddi , Joni Lie , P. N. Suganthan , Sirajudeen Gulam Razul and Chong Meng S. See

The presence of desired signal in the training data for sample covariance matrix calculation is known to lead to a substantial performance degradation, especially when the desired signal is the dominant signal in the training data. Together with the uncertainty in the look direction, most of the adaptive beamforming solutions are unable to approach the optimal performance. In this paper, we propose an evolutionary algorithm (EA) based robust adaptive beamforming that is able to achieve near optimal performance. The essence of the idea is to shape the array beam response such that it has maximum response in the desired signal's angular range and minimum response in the interferences' angular range. In addition, the approach introduces null-response constraints deduced from the array observation to achieve better interference cancelation performance. As a whole, the proposed optimization is solvable using an improved variant of the differential evolution (DE) algorithm. Numerical simulations are also presented to demonstrate the efficacy of the proposed algorithm.

NEAR OPTIMAL ROBUST ADAPTIVE BEAMFORMING APPROACH BASED ON EVOLUTIONARY ALGORITHM

2011-03-28

PIER B

Vol. 29, 139-155, 2011

doi:10.2528/PIERB11021605

download: 254

Analysis and Design of Cruciform Waveguide Junction with a Conducting Diaphragm and a Dielectric Layer in the Main Arm

Faik Bogdanov , Guram Sh. Kevanishvili , Georgi V. Kekelia and Segiy L. Prosvirnin

This paper proposes a rigorous theory of the H-plane four-port (cruciform) waveguide junction with a conducting diaphragm and a dielectric layer in the main (input) waveguide arm. This theory is based on the mode matching method in conjunction with Fourier transform technique and including the edge conditions in vicinity of the diaphragm edges. The numerical analysis of the cruciform waveguide junction is done, and optimal parameters of inclusions are predicted based on the minima of voltage standing wave ratio (VSWR) in the main arm.

ANALYSIS AND DESIGN OF CRUCIFORM WAVEGUIDE JUNCTION WITH A CONDUCTING DIAPHRAGM AND A DIELECTRIC LAYER IN THE MAIN ARM

2011-03-25

PIER B

Vol. 29, 105-138, 2011

doi:10.2528/PIERB10090502

download: 303

A Multiplicative Regularized Gauss-Newton Algorithm and Its Application to the Joint Inversion of Induction Logging and Near-Borehole Pressure Measurements

Faruk Omer Alpak , Tarek Habashy , Aria Abubakar , Carlos Torres-Verdin and Kamy Sepehrnoori

Due to the ill-posed nature of nonlinear inverse problems of borehole geophysics, a parameterization approach is necessary when the available measurement data are limited and measurements are only carried out from sparse transmitter-receiver positions (limited data diversity). A potential remedy is the joint inversion of multi-physics measurements. A parametric inversion approach has desirable attributes for multi-physics measurements with different resolutions. It provides a flexible framework to put the sensitivities of multi-physics multi-resolution measurements on equal footing. In addition, the number of unknown model parameters to be inverted is rendered tractable with parameterization. Consequently, a Gauss-Newton based inversion algorithm taking advantage of the Hessian information can be advantageously employed over inversion approaches that rely only on gradient information. We describe a new dual-physics parametric joint-inversion algorithm to estimate near-borehole fluid permeability and porosity distributions of rock formations from fluid-flow and electromagnetic measurements. In order to accommodate the cases in which the measurements are redundant or lack sensitivity with respect to certain model parameters causing nonuniqueness of the inverted solution, the objective functional to be minimized is regularized with a penalty term. One of the central aspects of this approach is the determination of the regularization parameter. The latter must be chosen in such a way that the relative importance of the misfit between measured and predicted data and the penalty term are effectively balanced over the course of minimization. We propose a new method of adaptively choosing the regularization parameter within a Gauss-Newton method based joint-inversion algorithm using a multiplicative regularization strategy. The multiplicative regularization method is tested against additive regularization in joint-inversion problems involving wireline formation tester transient pressure and induction-frequency electromagnetic logging measurements. The multiplicative regularization method delivers improved convergence rates over additive regularization for all investigated problems. Inversions of relatively more noise-contaminated measurements benefit more from multiplicative regularization.

A MULTIPLICATIVE REGULARIZED GAUSS-NEWTON ALGORITHM AND ITS APPLICATION TO THE JOINT INVERSION OF INDUCTION LOGGING AND NEAR-BOREHOLE PRESSURE MEASUREMENTS

2011-03-24

PIER B

Vol. 29, 83-103, 2011

doi:10.2528/PIERB11020306

download: 344

Derivation of the Effective Nonlinear SchrÖDinger Equations for Dark and Power Law Spatial Plasmon-Polariton Solitons Using Nano Self-Focusing

Sihon H. Crutcher and Abert Osei

An effective Nonlinear Schrödinger Equation for propagation is derived for optical dark and power law spatial solitons at the subwavelength with a surface plasmonic interaction. Starting with Maxwell's Nonlinear Equations a model is proposed for TM polarized type spatial solitons on a metal dielectric interface. Two separate systems are considered in which one metal dielectric interface has a dielectric Kerr medium that has self-defocusing and another similar interface which the dielectric Kerr medium that has self-focusing depending on the modulus of the electric field to some power law variable p. The beam dynamics are analytically studied for these nanowaveguides.

DERIVATION OF THE EFFECTIVE NONLINEAR SCHRÖDINGER EQUATIONS FOR DARK AND POWER LAW SPATIAL PLASMON-POLARITON SOLITONS USING NANO SELF-FOCUSING

2011-03-21

PIER B

Vol. 29, 63-82, 2011

doi:10.2528/PIERB11020204

download: 309

Synthesis of Thinned Planar Concentric Circular Antenna Arrays --- a Differential Evolutionary Approach

Pradipta Ghosh and Swagatam Das

Circular antenna array design is one of the most important electromagnetic optimization problems of current interest. The problem of designing a large multiple concentric planar thinned circular ring arrays of uniformly excited isotropic antennas is considered in this paper. This antenna must generate a pencil beam pattern in the vertical plane along with minimized side lobe level (SLL). In this paper, we present an optimization method based on an improved variant of one of the most powerful real parameter optimizers of current interest, called Differential Evolution (DE). Two sets of different cases have been studied here. First set deals with thinned array design with the goal to achieve number of switched off elements equal to 220 or more. The other set contains design of array while maintaining side lobe level (SLL) below a fixed value. Both set contains two types of design, one with uniform inter-element spacing fixed at 0.5λ and the other with optimum uniform inter-element spacing. The half-power beam width of the synthesized pattern is attempted to maintain fixed at the value equal to that of a fully populated array with uniform spacing of 0.5λ. Simulation results of the designed thinned arrays are compared with a fully populated array for all the cases to illustrate the effectiveness of our proposed method.

SYNTHESIS OF THINNED PLANAR CONCENTRIC CIRCULAR ANTENNA ARRAYS --- A DIFFERENTIAL EVOLUTIONARY APPROACH

2011-03-15

PIER B

Vol. 29, 43-62, 2011

doi:10.2528/PIERB11013105

download: 260

The Renormalization Group Theory Combined to the MS-GEC Method to Study Active Fractal Structures with Incorporated PIN Diodes

Sonia Mili , Chiraz Larbi Aguili and Taoufik Aguili

The renormalization group theory (RGT) is used in this paper to develop an extension of the multi-scale approach (MS-GEC), previously developed by the authors, in order to enable the study of fractal structures at infinite iterations. In this work, we focused on active fractal structures with incorporated PIN diodes but the developed concept can be applied to a wide variety of fractals. The MS-GEC method deals with fractal-shaped objects as a set of scale levels. The processing is done gradually, one scale at each step, from the lowest scale till the highest one. To compute the input impedance of fractal-shaped structures using the MS-GEC method, we demonstrated that the input impedance of any scale level is generated from the input impedance of the previous scale level. When the iteration of fractal tends toward infinity, the structure contains an unknown number of levels. Since the atomic level cannot be defined, a critical point is reached limiting then the scope of the MS-GEC and of the existing classical methods. Based on RGT concepts, if the relation between the input impedances of two consecutive levels can be rewritten independently of the critical parameter (which is in our case the scale level), a transformation called "renormalization group" is generated. Consequently, the input impedance of the infinite active fractal structure approaches the fixed point of the defined transformation independently of the system details at the atomic level. The MS-GEC method combined to the RGT is a very powerful technique since it profits from the advantages (rapidity and reduced memory requirements) of the MS-GEC method and from the ability of the RGT to solve problems at their critical point.

THE RENORMALIZATION GROUP THEORY COMBINED TO THE MS-GEC METHOD TO STUDY ACTIVE FRACTAL STRUCTURES WITH INCORPORATED PIN DIODES

2011-03-15

PIER B

Vol. 29, 23-42, 2011

doi:10.2528/PIERB11011205

download: 410

2.45 GHz (Cw) Microwave Irradiation Alters Circadian Organization, Spatial Memory, Dna Structure in the Brain Cells and Blood Cell Counts of Male Mice, Mus Musculus

Chandra Mohini Chaturvedi , Vineet Prakash Singh , Priyanka Singh , Priyoneel Basu , Muniyandi Singaravel , Ritesh K. Shukla , Alok Dhawan , Atanu Kumar Pati , Ravi Kumar Gangwar and Surya Singh

Present study examines biological effects of 2.45 GHz microwave radiation in Parkes strain mice. Forty-day-old mice were exposed to CW (continuous wave) microwave radiation (2 h/day for 30 days). Locomotor activity was recorded on running wheel for 12 days prior to microwave exposure (pre-exposure), 7 days during the first week of exposure (short-term exposure) and another 7-day spell during the last week of the 30-day exposure period (long-term exposure). Morris water maze test was performed from 17th to 22nd day of exposure. At the termination of the exposure, blood was processed for hematological parameters, brain for comet assay, epididymis for sperm count and motility and serum for SGOT (serum glutamate oxaloacetate transaminase) and SGPT (serum glutamate pyruvate transaminase). The results show that long-term radiation-exposed group exhibited a positive y (phase angle difference) for the onset of activity with reference to lights-off timing and most of the activity occurred within the light fraction of the LD (light: dark) cycle. Microwave radiation caused an increase in erythrocyte and leukocyte counts, a significant DNA single strand break in brain cells and the loss of spatial memory in mice. This report for the first time provides experimental evidence that continuous exposure to low intensity microwave radiation may have an adverse effect on the brain function by altering circadian system and rate of DNA damage.

2.45 GHz (CW) MICROWAVE IRRADIATION ALTERS CIRCADIAN ORGANIZATION, SPATIAL MEMORY, DNA STRUCTURE IN THE BRAIN CELLS AND BLOOD CELL COUNTS OF MALE MICE, MUS MUSCULUS

2011-03-14

PIER B

Vol. 29, 1-22, 2011

doi:10.2528/PIERB11020403

download: 340

Symmetrical Pyramidal Horn Antennas Based on EBG Structures

Irina Khromova , Inigo Ederra , Ramon Gonzalo and Bastiaan P. de Hon

This paper presents a novel pyramidal (EH) horn antenna based on Electromagnetic Band Gap structures (EBGs). The reported pyramidal woodpile-based horn antenna possesses a symmetrical radiation pattern and a wide operating frequency range. Such antennas can substitute metallic horns in certain circumstances, which is especially valuable for millimetre and THz devices. The principle of creating EH-horn antennas in the woodpile structure is explained in detail. In particular, this paper presents the design of a symmetrical woodpile EH-horn antenna operating at frequencies around 110 GHz. The reported antenna exhibits a wide operating bandwidth (more than 10%), while possessing high directivity and radiation efficiency equal to 16.35dBi and -0.55dB (88%) respectively.