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2012-09-19
PIER
Vol. 131, 517-533, 2012
download: 151
Zero-Pole Approach to Computer Aided Design of in-Line SIW Filters with Transmission Zeros
Andrzej Jedrzejewski Natalia Leszczynska Lukasz Szydlowski Michal Mrozowski
This paper presents a fast technique for the automated design of pseudo-elliptic lters in in-line topology implemented in substrate integrated waveguide (SIW) technology. The proposed method is based on an optimization routine with cost function involving zeros and poles of scattering parameters. To realize transmission zeros in in-line topology, frequency-dependent couplings were used. Such dispersive couplings were implemented as shorted stubs. The design process starts with the generation of a suitable starting point. To this end, an approximation of SIW as a rectangular waveguide is used and a fast electromagnetic solver based on mode-matching technique is utilized (μWave Wizard). The next step is the optimization process of a lter in a full-wave 3D EM simulator Ansoft HFSS. To increase the speed of convergence, a built-in derivative calculation feature was used and zeros and poles and their derivatives with respect to design parameters were extracted using the vector fitting algorithm. Experimental validation of the method is demonstrated by a third-order filter with asymmetric response and a fifth-order filter with two transmission zeros in addition to an asymmetric response. The experimental results show good agreement between the simulated and measured data.
ZERO-POLE APPROACH TO COMPUTER AIDED DESIGN OF IN-LINE SIW FILTERS WITH TRANSMISSION ZEROS
2012-09-18
PIER
Vol. 131, 495-515, 2012
download: 128
Relay Propagation of Partially Coherent Cosh-Gaussian Beams in Non-Kolmogorov Turbulence
Rumao Tao Lei Si Yanxing Ma Pu Zhou Zejin Liu
The analytical formulas for the average intensity and power in the bucket of the relay propagation of partially coherent cosh-Gaussian (ChG) beams in non-Kolmogorov turbulence have been derived based on the extended Huygens-Fresnel principle. The influences of the beam parameters, relay system parameters and the non-Kolmogorov turbulence parameters on relay propagation are investigated by numerical examples. Numerical results reveal that the relay propagation of the beam is different from that in the case of Kolmogorov turbulence. It is shown that the relay propagation has advantages over direct propagation, and the relay propagation of partially coherent ChG beams depends greatly on the beam parameters, relay system and the generalized exponent α . The focusability of the beam at the target in non-Kolmogorov turbulence increases with larger inner scale, larger relay system radius, smaller outer scale, and smaller generalized structure constant. The results are useful for the practical applications of relay propagation, i.e., free-space communication.
RELAY PROPAGATION OF PARTIALLY COHERENT COSH-GAUSSIAN BEAMS IN NON-KOLMOGOROV TURBULENCE
2012-09-17
PIER
Vol. 131, 477-494, 2012
download: 139
Signal Propagation in Aquaculture Environment for Wireless Sensor Network Applications
Azizi Harun David Lorater Ndzi Mohd F. Ramli Ali Yeon Md. Shakaff Mohd Noor Ahmad Latifah M. Kamarudin Ammar Zakaria Yanyan Yang
This paper presents results of signal propagation studies for wireless sensor network planning in aquaculture environment for water quality and changes in water characteristics monitoring. Some water pollutants can cause widespread damage to marine life within a very short time period and thus wireless sensor network reliability is more critical than in crop farming. This paper shows that network coverage models and assumptions over land do not readily apply in tropical aquaculture environment where high temperatures are experienced during the day. More specifically, due to high humidity caused by evaporation, network coverage at 15 cm antenna height is better than at 5 m antenna heights due to the presence of a super-refraction (ducting) layer. For a 69 m link, the difference between the signal strength measured over several days is more than 7 dBm except under anomaly conditions. In this environment, the two-ray model has been found to provide high accuracy for signal propagation over water where there are no objects in close proximity to the propagation path. However, with vegetation in close proximity, accurate signal variation predication must consider contributions from scattered and diffused components, taking into account frequency selective fading characteristics to represent the temporal and spatial signal variations.
SIGNAL PROPAGATION IN AQUACULTURE ENVIRONMENT FOR WIRELESS SENSOR NETWORK APPLICATIONS
2012-09-17
PIER
Vol. 131, 457-475, 2012
download: 431
Characterization and Modeling of Schottky Diodes Up to 110 GHz for Use in Both Flip-Chip and Wire-Bonded Assembled Environments
Kaoutar Zeljami Jessica Gutierrez Juan Pablo Pascual Tomas Fernandez Antonio Tazón Mohamed Boussouis
This paper presents a wideband model, from Direct Current (DC) to W band, for a single Anode Schottky Diode based on a commercial VDI chip. Different measurements have been performed to obtain a complete large-signal equivalent circuit model suitable for the device under consideration up to 110 GHz, and for its integration in planar circuits. The modeling has been done using a combination of DC, capacitance measurements, and RF scattering measurements. The test structure for on-wafer S-parameter characterization has been developed to obtain an equivalent circuit for Coplanar to Microstrip (CPW-Microstrip) transitions, then verified with 3D Electromagnetic (EM) tools and finally used to de-embed device measurements from empirical data results in W band. 3D EM simulation of the diodes was used to initialize the parasitic parameters. Those significant extrinsic elements were combined with the intrinsic elements. The results show that the proposed method is suitable to determine parameters of the diode model with an excellent fit with measurements. Using this model, the simulated performance for a number of diode structures has given accurate predictions up to 110 GHz. Some anomalous phenomena such as parasitic resistance dependence on frequency have been found.
CHARACTERIZATION AND MODELING OF SCHOTTKY DIODES UP TO 110 GHZ FOR USE IN BOTH FLIP-CHIP AND WIRE-BONDED ASSEMBLED ENVIRONMENTS
2012-09-17
PIER
Vol. 131, 441-455, 2012
download: 145
Full-Wavelength Dipole Antenna on a GaAs Membrane Covered by a Frequency Selective Surface for a Terahertz Photomixer
Truong Khang Nguyen Thi Anh Ho Ikmo Park Haewook Han
An antenna consisting of a full-wavelength dipole on a GaAs membrane covered by a frequency-selective surface is proposed for improved output power from photomixers used as terahertz (THz) sources. The antenna structure reduces the vertical dimension of a typical photomixer antenna using a substrate lens while still exhibiting high total efficiency and high directivity. The resulting antenna after optimization produced an input resistance of 3870 Ω and a radiation efficiency of 60%, corresponding to a total efficiency of approximately 48.3% and a maximum directivity of 20.2 dBi at the resonance frequency of 1.03 THz. The proposed antenna is expected to be a promising alternative THz photomixer design.
FULL-WAVELENGTH DIPOLE ANTENNA ON A GAAS MEMBRANE COVERED BY A FREQUENCY SELECTIVE SURFACE FOR A TERAHERTZ PHOTOMIXER
2012-09-17
PIER
Vol. 131, 425-440, 2012
download: 117
Focusing Properties of Maxwell's Fish Eye Medium
Leonid A. Pazynin Ganna O. Kryvchikova
The existence of drains in the field of the point source both for the spherical cavity with perfectly conducting boundary, filled with a homogeneous medium, and for unbounded Maxwell's fish eye (MFE) are rigorously proved. The existence of all class of generalized Green functions for unbounded MFE medium is established. The Green function describing the perfect focusing is found in this class. The same result for the MFE lens is obtained.
2012-09-17
PIER
Vol. 131, 409-424, 2012
download: 113
Diffraction by Dielectric-Loaded Multiple Slits in a Conducting Plane: TM Case
Dong-Jin Lee Soo-Ji Lee Won-Seok Lee Jong-Won Yu
A new and exact series solution for the scattering and coupling problems by dielectric-loaded multiple slits in a perfectly conducting screen is presented. The case of normal incidence and TM polarization is considered. The scattered and transmitted elds are represented in terms of an in nite series of radial modes. By applying the appropriate boundary conditions, the coecients of scattered and transmitted elds are obtained and some numerical results are given.
DIFFRACTION BY DIELECTRIC-LOADED MULTIPLE SLITS IN A CONDUCTING PLANE: TM CASE
2012-09-17
PIER
Vol. 131, 391-407, 2012
download: 225
A Three Dimensional Analytical Calculation of the Air-Gap Magnetic Field and Torque of Coaxial Magnetic Gears
Yan-Jun Ge Chong-Yang Nie Qiang Xin
In order to solve the defects that the end-effect of magnetic field is ignored in two dimension (2-D) analytical method or 2-D finite element method (FEM); meanwhile, mass computer resource and time for parametric design or optimization are wasted in three dimension (3-D) FEM, a concise and efficient 3-D analytical approach is put forward for the calculation of the air-gap magnetic field and torque of coaxial magnetic gears. Based on the cylindrical coordinates where a coaxial magnetic gear is in, the equivalent current model and vector magnetic potential equation of permanent magnets in high speed permanent magnetic ring are constituted. By superposed magnetic flux density of every tile permanent magnets on high speed permanent magnetic ring in cylindrical coordinates, a air-gap magnetic field 3-D analytical formula is set up without ferromagnetic pole-pieces; in the interest of modulated air-gap magnetic field 3-D analytical formula with ferromagnetic pole-pieces, three types boundary conditions using state equations of contact surfaces between ferromagnetic pole-pieces and air-gap are established by a thorough analysis of the modulate mechanism of ferromagnetic pole-pieces. Finally, magnets of the low speed permanent magnetic ring are reduced to a distribution of equivalent current, which experience the Lorentz force in modulated magnetic field of high speed permanent magnetic ring for torque calculation. The integrals in all aforementioned calculation are axial, so the end-effect is embodied in above analytical model and more precise than 2-D analytical method or 2-D FEM. As the calculation results, the formula is accurate but faster than the 3-D FEM. The analytical model is suited for programmable calculation and that will make the structural and parametric design or optimization of coaxial magnetic gears simple and timesaving.
A THREE DIMENSIONAL ANALYTICAL CALCULATION OF THE AIR-GAP MAGNETIC FIELD AND TORQUE OF COAXIAL MAGNETIC GEARS
2012-09-17
PIER
Vol. 131, 375-390, 2012
download: 136
Novel Phase-Shifting Characteristic of CRLH TL and Its Application in the Design of Dual-Band Dual-Mode Dual-Polarization Antenna
Wen-Quan Cao Bangning Zhang Aijun Liu Tongbin Yu Daosheng Guo Yi Wei
The phase-shifting characteristic of a novel composite right/left handed transmission line (CRLH TL) for two frequency points is analyzed in this paper. Samples of (90˚, 0˚) and (180˚, 0˚) phase-shifting TLs for two frequency points (f1, f2) are deigned and the total length of the CRLH TLs has decreased by more than 77% compared to the conventional microstrip lines. Then a four way power divider made by three Wilkinson power dividers and interconnected with the (90˚, 0˚) and (180˚, 0˚) phase-shifting TLs is designed to feed an antenna with two different operating modes at two different frequency bands. Four radiating patches arranging symmetrically in a loop are printed in an upper substrate and connected with the four outputs of the feed network by four copper pins. When the four rectangular patches are excited by four sources with equal amplitude and phase at f1, metamaterial antenna with conical beam and linear polarization (LP) is achieved; while four sources with equal amplitude but 90˚ phase difference for each adjacent output at f2 leads to wideband antenna with broadside beam and circular polarization (CP). One antenna prototype with dual-band dual-mode dual-polarization property is fabricated and good agreements between simulation and measurement results are obtained. This single-feed patch antenna is valuable in wireless communications for its radiation pattern selectivity and polarization diversity.
NOVEL PHASE-SHIFTING CHARACTERISTIC OF CRLH TL AND ITS APPLICATION IN THE DESIGN OF DUAL-BAND DUAL-MODE DUAL-POLARIZATION ANTENNA
2012-09-16
PIER
Vol. 131, 357-373, 2012
download: 271
Electromagnetic Fields of a Short Electric Dipole in Free Space – Revisited
Gerald Cooray Vernon Cooray
Maxwell's equations specify that electromagnetic fields are generated by accelerating charges. However, the electromagnetic fields of an accelerating charge are seldom used to derive the electromagnetic fields of radiating systems. In this paper, the equations pertinent to the electromagnetic fields generated by accelerating charges are utilized to evaluate the electromagnetic fields of a current path of length l for the case when a pulse of current propagates with constant velocity. According to these equations, radiation is generated only at the end points of the channel where charges are being accelerated or decelerated. The electromagnetic fields of a short dipole are extracted from these equations when r>>l, where r is the distance to the point of observation. The speed of propagation of the pulse enters into the electromagnetic fields only in the terms that are second order in l and they can be neglected in the dipole approximation. The results illustrate how the radiation fields emanating from the two ends of the dipole give rise to field terms varying as 1/r and 1/r2, while the time-variant stationary charges at the ends of the dipole contribute to field terms varying as 1/r2 and 1/r3.
ELECTROMAGNETIC FIELDS OF A SHORT ELECTRIC DIPOLE IN FREE SPACE – REVISITED
2012-09-16
PIER
Vol. 131, 331-355, 2012
download: 340
Slot-Less Torus Solid-Rotor-Ringed Line-Start Axial-Flux Permanent-Magnet Motor
Amin Mahmoudi Solmaz Kahourzade Nasrudin Abd Rahim Hew Wooi Ping Nima Farrokhzad Ershad
This paper presents the design, analysis, and prototyping of a novel axial-flux permanent-magnet (AFPM) motor capable of auto-starting. The preliminary design is a slot-less double-sided solid-rotor line-start AFPM motor with 4 poles for high torque density and stable rotation. One spaced raised ring was added to the inner radii of the rotor disc for smooth line-start motor. The design allows the motor to operate at both starting and synchronous speeds. The basic equations for the solid ring of the rotor of the proposed axial-flux permanent-magnet motor are presented. Non-symmetry of the designed motor led to its 3D time-stepping finite element analysis (FEA) via ANSYS 13.0, which evaluated the design parameters and predicted the transient performance. The designed motor was fabricated and tested, the experimental results showing good agreement with FEA simulation results. The prototype motor showed high starting torque and good synchronization.
SLOT-LESS TORUS SOLID-ROTOR-RINGED LINE-START AXIAL-FLUX PERMANENT-MAGNET MOTOR
2012-09-15
PIER
Vol. 131, 311-329, 2012
download: 115
Signal Model and Moving Target Detection Based on MIMO Synthetic Aperture Radar
Wei Zhou Jian-Tao Wang Hao Wen Chen Xiang Li
Recent years, a new SAR concept based on Multi-Input Multi-Output (MIMO) configuration has demonstrated the potential advantages to simultaneously improve the performance of Synthetic Aperture Radar (SAR) imaging and ground moving target detection by utilizing multiple antennas both at transmission and reception. However, the precise signal model, as well as the effect of ground moving target in image domain and the approaches for moving target indication based on MIMO SAR system are rarely investigated. Our paper has three main contributions. Firstly, we present a detailed signal model for stationary scene and moving target based on a colocated MIMO SAR system, and analyze the motion effect of the moving target. Secondly, we provide an algorithm of phase compensation to combine the multiple virtual channel data in order to enhance the image quality. Thirdly, an adaptive optimal approach is applied for clutter suppression, then the velocity of the moving target is estimated via Delay-and-Sum (DAS) beamforming approach. Finally, several numerical experiments are provided to illustrate the derivation and analysis in this paper.
SIGNAL MODEL AND MOVING TARGET DETECTION BASED ON MIMO SYNTHETIC APERTURE RADAR
2012-09-14
PIER
Vol. 131, 293-310, 2012
download: 128
Design and Implementation of an Ultra-Wideband Six-Port Network
Hao Peng Ziqiang Yang Tao Yang
This paper presents a six-port network over an ultra-wideband (UWB) of 2-8 GHz. Its key component is the six-port junction, which consists of a Wilkinson power divider and three 3-dB quadrature couplers, This six-port junction is accomplished in a low dielectric constant substrate (Rogers RT/duroid 5880). Multi-section impedance transformation is applied in the power divider, and the quadrature coupler is realized by using two 8.34 dB couplers in tandem. An ultra-wideband operation of the six-port junction is verified by full electromagnetic simulations and measurements. The results show that the designed devices exhibit good performance across 2-8 GHz band: the return losses at input ports are higher than 15 dB, the insertion losses from input ports to the remaining ports are 7.2 dB ± 1.7 dB, the isolation between two input ports is greater than 20.5 dB, and the maximum phase difference compared with the theoretical behavior between two test ports is 10°. For the manufactured six-port junction, a six-port phase measurement system and a calibration technique based on support vector regression (SVR) are introduced. Results show that the SVR model can achieve a mean phase error of 1.5274°.
DESIGN AND IMPLEMENTATION OF AN ULTRA-WIDEBAND SIX-PORT NETWORK
2012-09-12
PIER
Vol. 131, 275-292, 2012
download: 130
A Novel Range-Spread Target Detection Approach for Frequency Stepped Chirp Radar
Bo Liu Wenge Chang
This paper presents a novel range-spread target detection algorithm for frequency stepped chirp radar (FSCR) which transmits a chirp-pulse train with frequency stepped carriers. FSCR achieves high range resolution by synthetic wide-band technique, and its process includes intra-pulse matched filtering and pulse-to-pulse inverse discrete Fourier transform (IDFT) or wavelet transform. For FSCR, the high resolution range profile (HRRP) of a target is obtained by target extraction from overlapping HRRPs which is caused by oversampling. During the target extraction (sometimes called de-correlation), some strong scattering points of target echo are discarded, as the result, the signal-to-clutter ratio (SCR) might be reduced and the target detection capability is degraded. To solve this problem for FSCR, a novel detection algorithm without target extraction is addressed. The new algorithm based on the power spectrum of radar echo uses not only the amplitude information, but also the phase information of overlapping HRRPs of a target to improve the SCR, therefore, has significant performance. Moreover, the test statistic and the false alarm probability of the detector are derived, and the implementation procedure and the flow chart of the detection algorithm are designed. Finally, the detection performance is assessed by Monte-Carlo simulation, and the results indicate that the proposed algorithm has about 3 dB detection improvement in SCR compared with the spatial scattering density generalized likelihood ratio test (SSD-GRLT) detector, and at the same condition, is superior to the integrator detector. In addition, the proposed algorithm is robust and easy to implement.
A NOVEL RANGE-SPREAD TARGET DETECTION APPROACH FOR FREQUENCY STEPPED CHIRP RADAR
2012-09-12
PIER
Vol. 131, 259-274, 2012
download: 127
Design of Planar Dual and Triple Narrow-Band Bandstop Filters with Independently Controlled Stopbands and Improved Spurious Response
Huansheng Ning Jun Wang Qingxu Xiong Ling-Feng Mao
A novel design of planar dual and triple narrow-band bandstop filter is presented by adopting the proposed meandered slot defected microstrip structure (MS-DMS) and the simplified spiral microstrip resonator (SSMR). Through this design, the stopbands of the dual- and triple-band bandstop filters can be individually controlled and the improved spurious responses are achieved. First, the fundamental and the first spurious resonances of the MS-DMS and SSMR are analyzed to provide the design rules. Then, by utilizing the prominent stopband of the MS-DMS and the stopband produced by the SSMR coupled to main microstrip line, a dual narrow-band bandstop filter is constructed before its design procedure is outlined. Based on above investigations, a triple narrow-band bandstop filter is implemented by inserting extra SSMRs to another side of the main microstrip line of the dual-band filter to generate a new stopband. To verify the aforementioned design concepts, a dual and triple narrow-band bandstop filter are designed, simulated and tested. Both the simulation and measurement indicate that the fabricated filters exhibit good stopband/passband performance and improved first spurious resonance. Moreover, these filters are simple to design and quite compatible with planar fabrication technique, making them very attractive for practical applications.
DESIGN OF PLANAR DUAL AND TRIPLE NARROW-BAND BANDSTOP FILTERS WITH INDEPENDENTLY CONTROLLED STOPBANDS AND IMPROVED SPURIOUS RESPONSE
2012-09-11
PIER
Vol. 131, 243-258, 2012
download: 120
Interferometric Time Reversal MUSIC for Small Scatterer Localization
Raffaele Solimene Angela Dell'Aversano Giovanni Leone
The problem of localizing small scatterers (in terms of wavelength) by Time Reversal-MUSIC (TR-MUSIC) algorithm is addressed. In particular, we focus on uniqueness problems that might arise for certain far zone configurations when noise corrupts data. These lead to reconstructions affected by ghost targets from which it is difficult to discern actual targets. In order to remedy such a drawback, data obtained at multiple frequencies are employed. In detail, a new multi-frequency version of TR-MUSIC is introduced. It consists in mixing reconstructions obtained at different frequencies. Numerical analysis shows that this method outperforms classical TR-MUSIC as well as its multi-frequency implementation already present in literature.
INTERFEROMETRIC TIME REVERSAL MUSIC FOR SMALL SCATTERER LOCALIZATION
2012-09-09
PIER
Vol. 131, 227-241, 2012
download: 136
An Alternative Range Migration Correction Algorithm for Focusing Moving Targets
David M. Kirkland
This paper presents a method for focusing a moving target in single channel SAR data utilizing a novel technique for range migration correction. The First Order Keystone transform is first applied to remove the range-walk of the moving target signature. A search procedure based on maximizing a contrast cost function is then employed to determine the phase correction which compensates for the remaining range curvature. Finally an adaptive notch filter is used to construct an estimate of the azimuth compression filter necessary to focus the moving target. An experimental result is provided for airborne SAR data to demonstrate the performance of the approach.
AN ALTERNATIVE RANGE MIGRATION CORRECTION ALGORITHM FOR FOCUSING MOVING TARGETS
2012-09-09
PIER
Vol. 131, 211-225, 2012
download: 403
Theory and Experiment of a Compact Waveguide Dual Circular Polarizer
Chao Chang Sarah Church Sami Tantawi Patricia Larkoski Matthew Sieth Kiruthika Devaraj
A new compact and wide-band waveguide dual circular polarizer at Ka-band is presented and tested in this paper. This compact structure is composed of a three-port polarizing diplexer and a circular polarizer realized by a simple pair of large grooves. The polarizing diplexer includes two rectangular waveguides with a perpendicular H-plane junction, one circular waveguide coupled in E-plane. A cylindrical step and two pins are used to match this structure. For a LHCP or RHCP wave in the circular port, only one specific rectangular port outputs power and the other one is isolated. The accurate analysis and design of the circular polarizer are conducted by using full-wave electromagnetic simulation tools. The optimized dual circular polarizer has the advantage of compact size with a volume smaller than 1.5λ³, broad bandwidth, uncomplicated structure, and is especially suitable for use at high frequencies such as Ka-band and above. The prototype of the polarizer has been manufactured and test, the experimental results are basically consistent with the theories.
THEORY AND EXPERIMENT OF A COMPACT WAVEGUIDE DUAL CIRCULAR POLARIZER
2012-09-09
PIER
Vol. 131, 195-210, 2012
download: 170
Miniaturized Dual-Band Matching Technique Based on Coupled-Line Transformer for Dual-Band Power Amplifiers Design
Shun Li Bihua Tang Yuan'an Liu Shulan Li Cuiping Yu Yongle Wu
This study presents a novel miniaturized dual-band coupled-line impedance transformer. This dual-band matching technique uses the characteristics of coupled-line and dual-band stubs to realize matching arbitrary complex impedance to arbitrary complex impedance at two arbitrary uncorrelated frequencies. Especially, it satisfies the demand of dual-band matching at two relatively closed operating frequencies (n= f2 / f1 ≤ 1.2), and occupy a very small circuit area with inherent DC-Block function. The proposed synthesis approach is validated by the design and fabrication of a 30 W gallium nitride (GaN)-based class-AB power amplifier (PA) for GSM and WCDMA at 1800 MHz and 2140 MHz. The PA's output matching network based on the proposed structure can accurately match 50 Ω to the ideal load impedances of the transistor at two designed frequency simultaneously and has 20% and 15% bandwidth for which the reflection coefficient magnitudes are less than 0.1, respectively.
MINIATURIZED DUAL-BAND MATCHING TECHNIQUE BASED ON COUPLED-LINE TRANSFORMER FOR DUAL-BAND POWER AMPLIFIERS DESIGN
2012-09-09
PIER
Vol. 131, 185-194, 2012
download: 110
Investigation of Bandwidth Enhancement in Volumetric Left-Handed Metamaterials Using Fractals
Teofilo Max De la Mata Luque Naga Ravi Kanth Devarapalli Christos Christodoulou
Volumetric left-handed metamaterials made up of an array of split-ring resonators (SRRs) and wires exhibit negative index of refraction in a very narrow bandwidth due to the resonant nature of SRRs. We investigate the possible bandwidth enhancement by adding resonances to the system using fractals. The operating bandwidth of the system is increased when the additional resonances are placed close enough to each other. The Sierpiński-carpet fractal pattern is chosen as the distribution for the SRRs. The principle is demonstrated through simulations, and prototypes are fabricated and tested to verify consistency with simulations.
INVESTIGATION OF BANDWIDTH ENHANCEMENT IN VOLUMETRIC LEFT-HANDED METAMATERIALS USING FRACTALS