Home > All Issues > PIER
ISSN: 1070-4698

Vol. 80

Front:[PDF file] Back:[PDF file]
Latest Volume
All Volumes
All Issues

2007-12-23 PIER Vol. 80, 477-497, 2008. doi:10.2528/PIER07121106

The m -DSO-ESPRIT Method for Maximum Likelihood DOA Estimation

Leonardo Lizzi, Federico Viani, Manuel Benedetti, Paolo Rocca, and Andrea Massa

The estimation of the directions-of-arrival (DoAs) of multiple signals is a topic of great relevance in smart antenna synthesis and signal processing applications. In this paper, a memory-based method is proposed to compute the maximum likelihood (ML) DoA estimates. Such a conceptually-simple technique is based on the datasupported optimization (DSO) and the estimation of signal parameters via rotational invariance technique (ESPRIT), but fully exploits a memory mechanism for improving the estimation accuracy especially when dealing with critical scenarios characterized by low signal-tonoise ratios (SNR) or/and small number of snapshots. Simulation results assess the potentialities and limitations of the proposed approach that favorably compares with state-of-the-art methods.

2007-12-23 PIER Vol. 80, 461-476, 2008. doi:10.2528/PIER07121503

Improved GA and PSO Culled Hybrid Algorithm for Antenna Array Pattern Synthesis

Wen-Tao Li, Xiao-Wei Shi, Le Xu, and Yong-Qiang Hei

In this paper, a new evolutionary learning algorithm based on a hybrid of improved real-code genetic algorithm (IGA) and particle swarm optimization (PSO) called HIGAPSO is proposed. In order to overcome the drawbacks of standard genetic algorithm and particle swarm optimization, some improved mechanisms based on non-linear ranking selection, competition and selection among several crossover offspring and adaptive change of mutation scaling are adopted in the genetic algorithm, and dynamical parameters are adopted in PSO. The new population is produced through three approaches to improve the global optimization performance, which are elitist strategy, PSO strategy and improved genetic algorithm (IGA) strategy. The effectiveness of the proposed algorithm has been compared with GAs and PSO, synthesizing a circular array, a linear array and a base station array. Results show that the proposed algorithm is able to adapt itself to different electromagnetic optimization problems more effectively.

2007-12-23 PIER Vol. 80, 447-460, 2008. doi:10.2528/PIER07121409

Application of Synthetic Bandwidth Approach in SAR Polar Format Algorithm Using the Deramp Technique

Xin Nie, Dai-Yin Zhu, and Zhao-Da Zhu

The problem of wide bandwidth management in ultra-high resolution SAR systems can be solved by adopting stepped chirps and applying synthetic bandwidth approach. However, high resolution SAR image formation is a non-separable 2-D impulse compression processing, so the synthetic bandwidth procedure should be modified correspondingly with the image formation algorithm adopted. This paper demonstrates the application of synthetic bandwidth approach in SAR Polar Format Algorithm (PFA) using the deramp technique. The problem of motion compensation between the sub-pulses within a burst is discussed, and the signalpro cessing flows are investigated in detail. The presented approach is validated by point target simulation.

2007-12-22 PIER Vol. 80, 431-445, 2008. doi:10.2528/PIER07120502

Photonic Crystals as Infrared Broadband Reflectors with Different Angles of Incidence: a Comparative Study

Narendra Kumar and Sant Ojha

In this communication, we theoretically report the reflection properties of a photonic crystal with alternate layers of air and GaAs for specified values of the lattice parameters. By employing the transfer matrix approach, the reflection spectra of the layered media are obtained for chosen sets of number of unit cells and incident angles. It is observed that the photonic crystals with different number of unit cells completely reflect a wide band in the infrared region of radiation. Also, we find that the reflectivity decreases and the completely reflected bands are shifted towards lower wavelength side with increase in the incident angle. Further, the reflected broadbands in the reflection spectra correspond to the forbidden ranges of wavelength obtained by using the analogy of Kronig-Penney model. It indicates that the completely reflected ranges are forbidden bandgaps, which is considered as an important feature of the proposed photonic crystals.

2007-12-20 PIER Vol. 80, 421-430, 2008. doi:10.2528/PIER07121002

Photonic Crystal Narrow Filters with Negative Refractive Index Structural Defects

Zhuo-Yuan Wang, Xiao-Ming Cheng, Xiao-Qi He, Sheng-Li Fan, and Wen-Zhe Yan

This paper presents a proposal of taking the left-handed material as the structural defects of one-dimensional photonic crystals and uses the transfer matrix method to analyze the band-gap of that structure. The simulation result shows that the structure investigated can be considered as a narrow pass band optical filter. By tuning the refractive index of the left-handed material, the ideal transmission rate in the pass band is as higher as 99.99%, while in the band-gap is lower than 0.01%. In addition, we show that the bandwidth can be increased by reducing the cycle number of the photonic crystals.

2007-12-18 PIER Vol. 80, 409-420, 2008. doi:10.2528/PIER07120302

Towards the Dispersion Relations for Dielectric Optical Fibers with Helical Windings Under Slow- and Fast-Wave Considerations - a Comparative Analysis

Deepak Kumar, Pankaj Choudhury, and Onkar Singh II

The paper presents the electromagnetic (EM) wave propagation in cylindrical optical fibers with helical windings under slow- and fast-wave considerations. Field components are deduced for both the cases, and also, the dispersion relations are obtained by applying the boundary conditions, as modified by the presence of conducting helical windings. Two special cases are considered corresponding to the values of the helical pitch angle as 0 and 90. A comparison of the dispersion relations is presented.

2007-12-18 PIER Vol. 80, 393-408, 2008. doi:10.2528/PIER07120703

A Novel FDTD Approach Featuring Two-Level Parallelization on PC Cluster

Yu Liu, Zheng Liang, and Ziqiang Yang

To improve the parallel efficiency in the case of the finegrained FDTD computing on PC cluster, the concept of "two level parallelization on PC cluster" is presented, and a high performance MPI-OpenMP hybrid FDTD algorithmis developed. In the hybrid algorithm, MPI is used in conjunction with OpenMP multithreading to achieve two level parallelismof the data and tasks at the basis of the domain decomposition FDTD method. Besides, to enhance the flexibility of the parallel FDTD, the interpolation between subspaces is also discussed. The simulation example of a printed antenna for automobile is given. Computations are performed for different numbers of PCs and contrasted with two conventional parallel FDTD algorithms on PC cluster. The results show that with the decrease of the computational granularity on each computer, the novel algorithm is more efficient, and moreover, it can also lessen the influence of the sub-domains virtual topology on the parallel FDTD performance.

2007-12-17 PIER Vol. 80, 381-392, 2008. doi:10.2528/PIER07120902

Numerical Modeling of Active Devices Characterized by Measured S-Parameters in FDTD

Dao Yi Su, De-Min Fu, and Zhi-Hui Chen

A new FDTD modeling approach for active devices characterized by measured S-parameters is presented. This approach applies vector fitting technique and piecewise linear recursive convolution (PLRC) technique to complete modeling process, and does not need to know the equivalent circuits of active devices. It preserves the explicit nature of the traditional FDTD method, and a general updated formula is derived. Furthermore, the main data-processing procedure is directly handled over the frequency band of interest, which avoids the time-domain non-causal error in traditional techniques.

2007-12-17 PIER Vol. 80, 369-380, 2008. doi:10.2528/PIER07120303

The Synthesis of Complex-Angle Zeros for on-Board Antenna Arrays

Gloria Gajardo-Silva and Luis Landesa

Shelkunoff circle synthesis techniques are only effective for equispaced antenna arrays. These techniques are based on reorganizing the zeros on the Shelkunoff circle. We propose a technique based on locating complex-direction zeros to synthesize arbitrary on-board antenna arrays. It is based on the analytical continuation of Green's functions and on a new representation of the complex plane (analogous to the Shelkunoff circle).

2007-12-17 PIER Vol. 80, 349-368, 2008. doi:10.2528/PIER07111503

Mutual External Inductance in Stripline Structures

Marina Koledintseva, James Drewniak, Thomas Van Doren, David Pommerenke, Matteo Cocchini, and David Hockanson

The Method of Edge Currents (MEC) proposed in our previous paper [1] is applied herein for calculating the mutual external inductance associated with fringing magnetic fields that wrap ground planes of a stripline structure. This method employs a quasi-static approach, image theory, and direct magnetic field integration. The resultant mutual external inductance is frequency-independent. The approach has been applied to estimating mutual inductance for both symmetrical and asymmetrical stripline structures. Offset of the signal trace from the centered position both in horizontal and vertical directions is taken into account in asymmetrical structures. The results are compared with numerical simulations using the CST Microwave Studio Software.

2007-12-12 PIER Vol. 80, 337-348, 2008. doi:10.2528/PIER07120202

Frequency and Time Domain Characteristic of a Novel Notch Frequency UWB Antenna

Lida Akhoondzadeh-Asl, Masum Fardis, Ali Abolghasemi, and Gholamreza R. Dadashzadeh

An ultra-wideband (UWB) monopole antenna with a band-notch characteristic is presented which needs only two parameters to tune the notch frequency. The proposed monopole antenna is embedded with a crescent slot, whose length is determined by parametric study. By adjusting the slot length, the notched frequency band within the antenna's operating bandwidth can be easily controlled. Also, the time-domain behaviours are discussed and the fidelity factor is calculated.

2007-12-12 PIER Vol. 80, 321-336, 2008. doi:10.2528/PIER07112804

Prediction of the SAR Level Induced in a Dielectric Sphere by a Thin Wire Dipole Antenna

Nikolaos Kouveliotis and Christos N. Capsalis

The interaction between a dipole antenna,represen ting a simplified model of a mobile terminal,and a homogeneous spherical model of the human head is examined. The Finite Difference Time Domain (FDTD) method is utilized,to calculate the either peak or average value of the Specific Absorption Rate (SAR),corresp onding to different distances between antenna and phantom. The variation of the SAR with the distance between the mobile antenna and the human phantom has gained significant attention in the recent literature and is investigated here. An attempt to correlate the computed SAR values with the basic antenna characteristics,suc h as the standing wave ratio (SWR),rev eals that a precise estimation of the level of the SAR can be achieved regarding data acquired from the mobile terminal.

2007-12-05 PIER Vol. 80, 307-320, 2008. doi:10.2528/PIER07112202

Microwave/Millimeter-Wave Generation Using Multi-Wavelength Photonic Crystal Fiber Brillouin Laser

Guo-Feng Shen, Xian-Min Zhang, Hao Chi, and Xiao-Feng Jin

An all-optical microwave generation using a multiwavelength photonic crystal fiber Brillouin laser is presented. A highly nonlinear photonic crystal fiber with the length of 25m is used as Brillouin gain medium. A Fabry-Perot cavity with two fiber Bragg gratings as reflectors are designed in order to enhance the Brillouin conversion efficiency. The fiber Bragg gratings can be used to selectively excite the jth-order Stokes' wave and suppress other order Stokes' waves. The mechanism for microwave/millimeterwave generation is theoretically analyzed. In the experiment, both 9.788 GHz and 19.579 GHz microwave signals are achieved through mixing the pump wave with the first-order and the second-order Stokes' waves.

2007-12-04 PIER Vol. 80, 295-306, 2008. doi:10.2528/PIER07112706

Empirical Characterization of Wood Surfaces by Means of Iterative Autocorrelation of Laser Speckle Patterns.

Juan-Antonio Martinez-Rojas, Jesus Alpuente-Hermosilla, Estefania Bolivar, Pablo-Luis Lopez-Espi, Santiago Vignote, and Martinez Rojas

A simple and inexpensive method for the qualitative characterization of wood surfaces is presented. It is based on the iterative autocorrelation of laser speckle patterns produced by diffuse laser illumination of the wood surfaces.The method exploits the high spatial frequency content of speckle images. A similar approach with raw conventional photographs taken with ordinary light would be very difficult. A few iterations of the algorithm are necessary, typically three or four, in order to visualize the most important periodic features of the surface. The processed patterns help in the study of surface parameters, to design new scattering models and to classify the wood species.

2007-12-02 PIER Vol. 80, 277-293, 2008. doi:10.2528/PIER07112505

Study on Scintillation Considering Inner- and Outer-Scales for Laser Beam Propagation on the Slant Path through the Atmospheric Turbulence

Zhen-Sen Wu, Hong-Yan Wei, Rui-Ke Yang, and Li-Xin Guo

Based on both the modified Rytov method and the altitude-dependent model of the ITU-R slant atmospheric turbulence structure constant, the uniform model of scintillation index considering inner- and outer-scales is derived form weak to strong fluctuation regions with Gaussian beam propagation on the slant path, and can be degenerated to the result of the horizontal path with atmospheric structure constant is a fixed value. The numerical conclusions indicate the smaller wavelength, the inner-scale has a stronger impact on scintillation than outer-scale. But, in strong fluctuation, the outerscale effect is prominence. Finally, the numerical results are compared and verified with the experimental data.

2007-12-02 PIER Vol. 80, 253-275, 2008. doi:10.2528/PIER07111003

A Novel Design Methodology of Multi-Clad Single Mode Optical Fiber for Broadband Optical Networks

H. Shahoei, Hassan Ghafoori-Fard, and Ali Rostami

In this paper two multi-clad RI- and RII-type optical fiber structures for small dispersion and dispersion slope as well as large bandwidth are considered and novel design strategy for this purpose is presented. The suggested design method uses the Differential Evolution (DE) approach. We put absolute value of dispersion factor as fitness function in differential evolution method. This algorithm successfully introduces a special fiber including so small dispersion and dispersion slope in the predefined wavelength duration. Also, the proposed method can set zero dispersion wavelengths with high accuracy compared other traditional methods. The designed dispersion-shifted RI single-mode fiber has the bandwidth of 600nm and the max amount of 1.36 (ps/km/nm) in that duration which is an ideal result.

2007-11-29 PIER Vol. 80, 241-252, 2008. doi:10.2528/PIER07111701

Nonlinear Stability Analysis of an Oscillator with Distributed Element Resonator

Hamid Vahdati and Abdolali Abdipour

In this paper a complete analysis to the stability of a microwave oscillator with distributed element resonator is presented. In this type of oscillators, the circuit description changes form ordinary differential equations to partial deferential equations. In this paper a Gunn diode oscillator with distributed elements resonator is analyzed. The instability condition of the startup phase and the stability condition of the steady state oscillation is investigated.

2007-11-28 PIER Vol. 80, 225-239, 2008. doi:10.2528/PIER07102101

Combing Multilevel Green's Function Interpolation Method with Volume Loop Bases for Inductance Extraction Problems

Hao-Gang Wang and Barnypok jrxhQLmCnJgUNYcWxfu

In this paper,a fast integral equation method is developed for extracting the inductances in RF ICs,RF MEMs,IC packages,and deep submicron ICs etc. This method combines a recently developed Multilevel Green's Function Interpolation Method (MLGFIM) [1,2] with the volume integral equation discretized using Volume Loop (VL) basis functions. In it,instead of using the filaments model to simulate the currents flowing in the inductors,w e use the conventional SWG basis functions for this kind of basis functions is flexible for problems with complex geometries. The shortest path finding algorithm is also used to find the source loop basis functions. The inductance extractions from the straight line,the spiral inductors,the bump,and the parallel buses in this paper demonstrate the validity and efficiency of this hybrid method.

2007-11-28 PIER Vol. 80, 197-224, 2008. doi:10.2528/PIER07101504

Method of Edge Currents for Calculating Mutual External Inductance in a Microstrip Structure

Marina Koledintseva, James Drewniak, Thomas Van Doren, David Pommerenke, Matteo Cocchini, and David Hockanson

Mutual external inductance (MEI) associated with fringing magnetic fields in planar transmission lines is a cause of socalled "ground plane noise", which leads to radiation from printed circuit boards in high-speed electronic equipment. Herein, a Method of Edge Currents (MEC) is proposed for calculating the MEI associated with fringing magnetic fields that wrap the ground plane of a microstrip line. This method employs a quasi-magnetostatic approach and direct magnetic field integration, so the resultant MEI is frequencyindependent. It is shown that when infinitely wide ground planes are cut to form ground planes of finite width, the residual surface currents on the tails that are cut off may be redistributed on the edges of the ground planes of finite thickness, forming edge currents. These edge currents shrink to filament currents when the thickness of the ground plane becomes negligible. It is shown that the mutual external inductance is determined by the magnetic flux produced by these edge currents, while the contributions to the magnetic flux by the currents from the signal trace and the finite-size ground plane completely compensate each other. This approach has been applied to estimating the mutual inductance for symmetrical and asymmetrical microstrip lines.

2007-11-28 PIER Vol. 80, 179-196, 2008. doi:10.2528/PIER07111504

Enhancement of Directivity Using 2D-Electromagnetic Crystals Near the Band-Gap Edge: a Full-Wave Approach

Lara Pajewski, Lorenzo Rinaldi, and Giuseppe Schettini

A deep analysis of the directivity enhancement, due to the insertion of a simple linear antenna into a dielectric EBG, is presented. The operative frequency is chosen near a band-gap edge. The planewave expansion method is used in order to obtain the Bloch dispersion diagrams of infinite two-dimensional EBGs. A rigorous cylindricalwave approach is used to analyze two-dimensional EBGs with finite size, excited by a line source. We apply these tools to the analysis of different emitting devices, and propose solutions to improve their performances.

2007-11-28 PIER Vol. 80, 161-178, 2008. doi:10.2528/PIER07110105

Automatic Incorporation of Surface Wave Poles in Discrete Complex Image Method

Lei Zhuang, Yunhua Zhang, Weidong Hu, Wenxian Yu, and Guo-Qiang Zhu

Discrete complex image method is introduced to get a closed-form dyadic Green's function by a sum of spherical waves. However, the simulation result by the traditional discrete complex image method is only valid in near-field for several wavelengths. In this paper, we analyze the form of spectral domain dyadic Green's function in the whole kρ plane and the variety of valid range of simulation results by different sampling paths in two-level discrete complex image method. Consequently, for dyadic Green's function, surface wave pole contribution both in spectral domain and spatial domain is clarified. We introduce the automatic incorporation of surface wave poles in discrete complex image method without extracting surface wave poles. The contribution of surface wave poles in spectral domain and spatial domain dyadic Green's function is further confirmed in the new method. Besides, this method can represent dyadic Green's function by spherical waves in the layer where the source and field points are. So it satisfies the splitting requirement and consequently reduces the computational complexity dramatically especially for objects with large scale in direction.

2007-11-27 PIER Vol. 80, 123-160, 2008. doi:10.2528/PIER07111302

Handset Antenna Design: Practice and Theory

Geyi Wen, Qinjiang Rao, Shirook M. Ali, and Dong Wang

In this paper, an attempt is made to present a theory for the design of handset antennas, which results from the long experience that the authors have in the field of handset antenna design. The proposed theory is based on the well-known skin effect and constructs the antenna using a thin wire model that represent the backbone of the final antenna. The analytical solution for the thin wire model is first obtained, and the main properties (such as the return loss and the radiation properties) of the antenna can then be studied using this analytical solution. Once the antenna backbone is constructed, other elements, such as stubs, patches, etc., can be added to optimize the match at the desired frequency bands. A number of numerical and analytical examples are provided throughout the paper to validate the theory. Different antenna types, such as wire antennas and planar antennas, are tested and designed using the thin wire model. The correspondence between the analytical results and those from the numerical simulations using full-wave solvers agree very well in all examples. The authors also present in this paper a novel design of three small antennas for handset applications, which are based on the simple wire monopole, but in a three-dimensional form. The proposed three-dimensional monopole antennas have multi-band and broadband properties that cover most frequency bands being used for the handset device. The antennas feature remarkable properties while occupying a significantly small space, which makes them strong candidates for handset applications and for the future multi-antenna applications too. 1. INTRODUCTION

2007-11-27 PIER Vol. 80, 107-122, 2008. doi:10.2528/PIER07111203

Analysis and Design of Highly Compact Bandpass Waveguide Filter Using Complementary Split Ring Resonators(CSRR)

Hadi Bahrami, Mohammad Hakkak, and Abbas Pirhadi

Split Ring Resonators (SRR) and Complementary Split Ring Resonators (CSRR) are widely used to design metamaterial structures. These structures when excited by suitable electromagnetic fields have resonance behavior and show unusual properties such as negative permeability and permittivity near the resonance frequency region. In this paper, CSRRs are used to design a bandpass waveguide filter in the X-band. The circuit model of these elements in the waveguide is similar to parallel L and C components that are placed in parallel form in a transmission line. Resonance frequency and bandwidth of LC resonance circuit are adjusted by proper choice of the CSRR geometrical dimensions. Then, to design the miniaturized filter these structures are combined with proper admittance inverter. The admittance inverter is designed such that its electric length is very smaller than the conventional λ/4 transmission line. As a result, a filter is compacted about 66% in comparison to the λ/4 transmission line as admittance inverter. Simulation results by Ansoft HFSS (Based on the Finite Element Method) confirm the results of filter circuit model.

2007-11-21 PIER Vol. 80, 77-105, 2008. doi:10.2528/PIER07110803

Computation of EM Field Scattered by an Open-Ended Cavity and by a Cavity Under Radome Using the Iterative Physical Optics

Régis Hémon, Philippe Pouliguen, Hongyang He, Joseph Saillard, and Jean-Francois Damiens

It is always a challenge to predict Radar Cross Section (RCS) of a full scale military platform with a good accuracy. Most of the time antennas and cavities are the main contributors of aircrafts RCS. Several methods have been developed to compute the RCS of cavities such as analytical methods (modal methods) and asymptotic methods (geometrical optics (GO) methods and physical optics (PO) methods). This article presents the Iterative Physical Optics (IPO) method which consists in an iterative resolution of the Magnetic Field Integral Equation (MFIE) to compute the currents on the inner walls of the cavity. This method allows computing arbitrarily shaped cavity with a good accuracy even for cavity with a depth inferior to the wavelength. Comparisons of IPO results with Rays and Finite element methods show a better accuracy of IPO than Rays especially for cross polarization. But computation time represents one of the main limitations of the IPO method. We present here a new formulation of the Segmented IPO method which coupled with the generalized reciprocity theorem decreases significantly the complexity of the method and consequently the computation time. The S-IPO method has been validated by comparisons with Modal method and measurements. We have observed that the repartition of the electric currents density on the inner walls of the cavity is quite the same with IPO and S-IPO computations. Lastly we propose an evolution of the IPO method we have developed to compute the RCSof cavities under radome. This method has been validated by comparison with finite element results.

2007-11-18 PIER Vol. 80, 63-76, 2008. doi:10.2528/PIER07103006

Design of Microstrip Array Antenna by Using Active Element Pattern Technique Combining with Taylor Synthesis Method

Qing-Qiang He and Bing-Zhong Wang

Active element pattern technique is applied for analyzing microstrip array, which divides a large array analysis problem as a superposition of various simplified small array problems and greatly reduces the computation burden. The effects of the mutual coupling and the surrounding array environment are rigorously taken into account in the proposed method. Based on the active element pattern technique, a low side lobe microstrip array is synthesized. The commercial full-wave simulation software, HFSS, is used to simulate the array as a whole and the efficiency of the proposed method is validated.

2007-11-18 PIER Vol. 80, 45-61, 2008. doi:10.2528/PIER07110604

Design and Study of Wideband Single Feed Circularly Polarized Microstrip Antennas

Steven Yang, Kai-Fong Lee, Ahmed Kishk, and Kwai-Man Luk

The performance of single feed truncated corner circularly polarized microstrip antennas with different substrate thickness is studied by simulation and experiment. It is found that the axial ratio bandwidth could be enhanced considerably when a thicker substrate is used, provided that a U-slot and/or L-probe is used to effect impedance matching. One of the configurations attains an axial ratio bandwidth (< 3 dB) of about 14% within the impedance matching band when the substrate thickness is about 0.2λo

2007-11-18 PIER Vol. 80, 29-44, 2008. doi:10.2528/PIER07111205

Fast Analysis of Antenna Characteristics on Electrically Large Composite Objects

Jun Yuan, Yang Qiu, Jing-Li Guo, Yanlin Zou, and Qi-Zhong Liu

Several characteristics of the wire antenna on electrically large composite body are analyzed by an adaptive multilevel fast multipole algorithm (MLFMA). Adaptive MLFMA is applied to the boundary integration of the analysis model. With the basis functions and testing functions expanded with Dirac functions on different position, the calculation of impedance integration can be simplified and all the translation process can be calculated by fast Fourier transformation (FFT). Good agreement between the computed and measured results of antenna characters is obtained.

2007-11-18 PIER Vol. 80, 1-28, 2008. doi:10.2528/PIER07103105

Boundary-Integral Methods for Iterative Solution of Scattering Problems with Variable Impedance Surface Condition

Francis Collino, Florence Millot, and Sebastien Pernet

We present an efficient boundary element method to solve electromagnetic scattering problems relative to an impedance boundary condition on an obstacle of arbitrary shape in the frequency domain. In particular, the technique is based on a Combined Field Integral Equation (CFIE) and is well adapted to treat the partially coated objects. Some methods are then proposed in order to eliminate the magnetic current and to treat correctly the rotation operator n × · (where n is the unit outward normal). After discretization, the final system is solved by an iterative method coupled with the Fast Multipole Method (FMM). Finally, a numerical comparison with a well-tried method to solve this kind of problem proves that we have proposed an attractive technique in terms of memory storage and CPU time.