PIER B | PIER Journals

2014-08-26

PIER B

Vol. 60, 301-315, 2014

download: 628

Ducting and Turbulence Effects on Radio-Wave Propagation in an Atmospheric Boundary Layer

Yung-Hsiang Chou and Jean-Fu Kiang

The split-step Fourier (SSF) algorithm is applied to simulate the propagation of radio waves in an atmospheric duct. The refractive-index fluctuation in the ducts is assumed to follow a two-dimensional Kolmogorov power spectrum, which is derived from its three-dimensional counterpart via the Wiener-Khinchin theorem. The measured profiles of temperature, humidity and wind speed in the Gulf area on April 28, 1996, are used to derive the average refractive index and the scaling parameters in order to estimate the outer scale and the structure constant of turbulence in the atmospheric boundary layer (ABL). Simulation results show significant turbulence effects above sea in daytime, under stable conditions, which are attributed to the presence of atmospheric ducts. Weak turbulence effects are observed over lands in daytime, under unstable conditions, in which the high surface temperature prevents the formation of ducts.

DUCTING AND TURBULENCE EFFECTS ON RADIO-WAVE PROPAGATION IN AN ATMOSPHERIC BOUNDARY LAYER

2014-08-26

PIER B

Vol. 60, 287-300, 2014

doi:10.2528/PIERB14061302

download: 214

A Recursive Approach to Improve the Image Quality in Well-Logging Environments

Yu-Hsin Kuo and Jean-Fu Kiang

A three-stage recursive approach is proposed to improve the recovered distribution of electric parameters in a well-logging environment. The first stage is executed using the conventional linear sampling method (LSM) and the contrast source inversion (CSI) method. In the second stage, the background distribution is updated to better identify the target shape, using the recovered results in the first stage. In the third stage, the background distribution is made closer to the results in stage two, which improves the recovered distribution near the target boundary. The effect of noise is also simulated.

A RECURSIVE APPROACH TO IMPROVE THE IMAGE QUALITY IN WELL-LOGGING ENVIRONMENTS

2014-08-22

PIER B

Vol. 60, 275-285, 2014

doi:10.2528/PIERB14070605

download: 244

Wave Transition and Trapping by Suddenly Created Periodic Plasma

Spencer P. Kuo

Theory, numerical simulation, and experiment on the interaction of electromagnetic wave with suddenly created periodic plasma layers are presented. In the experiment, frequency-downshifted signals of considerably large spectral width and enhanced spectral intensity were detected. Numerical simulation of the experiment, that the plasma has a finite periodic structure and is created much faster than its decay, shows that the frequency downshifted waves have a broad power spectrum and are trapped in this plasma crystal until the plasma frequency drops to become less than the wave frequency. The spectral power increases exponentially with the frequency of the frequency downshifted wave, consistent with the experiment. The simulation reveals that wave trapping results in accumulating the frequency-downshifted waves generated in the finite transition period of plasma creation and decay. Though frequency-upshifted signals were missing in the experimental measurement, it might be attributed to the collision damping of the plasma.

WAVE TRANSITION AND TRAPPING BY SUDDENLY CREATED PERIODIC PLASMA

2014-08-16

PIER B

Vol. 60, 259-274, 2014

doi:10.2528/PIERB14060906

download: 309

Effects of Resonance-Based Phase Shifters on Ka-Band Phased Array Antenna Performance for Satellite Communications

Mehrbod Mohajer , Mohammadsadegh Faraji-Dana and Safieddin Safavi-Naeini

Phase shifters are the key components of phased array systems which provide a low-profile solution for Ka-band satellite communications. In the transmitting mode, it is crucial for the phased array antenna system to meet the standard radiation masks, and any imperfections of phase shifters can yield into radiation mask violation. In this paper, we present the analytical approach to model the non-linear phase-frequency characteristics of Resonance-Based phase shifters, which constitute one of the most widely used class of phase shifters for Ka-band satellite communications. Furthermore, it has been investigated how the phase-frequency response non-linearity affects the phased array radiation patterns, gain, and the beam pointing direction. The simulation results show that, depending on the phase shifter phase-frequency response profile, the radiation mask satisfaction is an important factor in determining the system bandwidth.

EFFECTS OF RESONANCE-BASED PHASE SHIFTERS ON KA-BAND PHASED ARRAY ANTENNA PERFORMANCE FOR SATELLITE COMMUNICATIONS

2014-08-10

PIER B

Vol. 60, 241-258, 2014

doi:10.2528/PIERB14052705

download: 255

Test Dipole Selection for Linear Sampling in Transverse Electric Case

Krishna Agarwal

This paper discusses the problem of choosing an appropriate direction of the test dipole used in linear sampling for the 2-dimensional inverse scattering problem of the transverse electric case. In particular, we propose two approaches, one purely mathematical and the other based on the physics theory of multipole expansion of the scattered magnetic field. It is shown that though the approaches are drawn from different perspectives, they perform similarly and show reasonable reconstruction for several interesting and difficult to reconstruct dielectric scatterers.

TEST DIPOLE SELECTION FOR LINEAR SAMPLING IN TRANSVERSE ELECTRIC CASE

2014-08-10

PIER B

Vol. 60, 227-239, 2014

doi:10.2528/PIERB14051304

download: 291

Efficient Isolation Between Electrically Small Metamaterial-Inspired Monopole Antennas

Nektarios K. Bourgis and Traianos V. Yioultsis

In this paper, a new electrically small metamaterial-inspired monopole antenna is presented. The antenna consists of a simple square-shaped coplanar waveguide (CPW-fed) monopole with an embedded complementary split ring resonator (CSRR). It operates at three distinct frequency ranges with central frequencies around 2.45, 4.2, and 5.8 GHz, exhibiting low return loss and uniform radiation patterns, making it a perfect candidate for modern wireless applications. Furthermore, using this antenna as a primary unit to construct two different 2×2 MIMO system configurations, we achieve systematic minimization of mutual coupling between the radiation elements around 2.45 GHz, using additional single negative (SNG) metamaterial inspired resonators. Mutual coupling is reduced by as much as 27 dB at the aforementioned frequency. The simulated and measured results of all the fabricated antennas are in good agreement.

EFFICIENT ISOLATION BETWEEN ELECTRICALLY SMALL METAMATERIAL-INSPIRED MONOPOLE ANTENNAS

2014-08-04

PIER B

Vol. 60, 215-225, 2014

doi:10.2528/PIERB14070108

download: 255

Design and Analysis of a Compact Triple Band Slotted Microstrip Antenna with Modified Ground Plane for Wireless Communication Applications

Sudipta Das , Partha Pratim Sarkar and Santosh Kumar Chowdhury

A novel single layer, coaxial probe feed compact triple band slotted microstrip patch antenna with modified ground plane for wireless application has been designed and analyzed. The presented antenna, occupying a compact size of 24×22×1.6 mm³, embodies a rectangular slotted patch and a rectangular ground plane modified with open ended step graded slots. The step graded slots are introduced on the ground plane to reduce the size of the antenna by reducing the resonant frequency and also to improve the operating bandwidth of the proposed antenna. The size of the antenna has been reduced by 74% by introducing slots on the ground plane. The measured bandwidths for -10 dB reflection coefficient are 360 MHz (1.72-2.08 GHz) at lower band, 300 MHz (3.36-3.66 GHz) at middle band and 3650 MHz (4.85-8.5 GHz) at upper band which cover the bandwidth requirements of 1.92 GHz PCS, 1.9 GHz PHS, 3.5/5.5 GHz WiMAX, 5.2/5.8 GHz WLAN, 5.2 GHz HisWaNa, 5.5 GHz Wi-Fi 802.11n and 5 GHz HiPERLAN wireless application bands.

DESIGN AND ANALYSIS OF A COMPACT TRIPLE BAND SLOTTED MICROSTRIP ANTENNA WITH MODIFIED GROUND PLANE FOR WIRELESS COMMUNICATION APPLICATIONS

2014-07-17

PIER B

Vol. 60, 195-213, 2014

doi:10.2528/PIERB14031306

download: 1483

Dielectric Resonator Antennas: Designs and Advances

Dipali Soren , Rowdra Ghatak , Rabindra Kishore Mishra and Dipak Poddar

This article presents a comprehensive review of the research carried out on Dielectric Resonator Antennas (DRAs) over the last three decades. Dielectric resonator antennas (DRAs) have received increased attention in various applications due to their attractive features in terms of high radiation efficiency, light weight, small size and low profile. Over last decades, various bandwidth enhancement techniques have been developed for DRAs. In this article, the attention is focused on a type of DRAs that can offer multi-resonance frequencies and these frequencies can be merged into a broad band. In order to effectively review design techniques, DRAs in this article are categorized into three types, broadband, ultra-wideband (UWB) and multiband. The latest developments in DRAs are discussed in the limited scope of this article.

DIELECTRIC RESONATOR ANTENNAS: DESIGNS AND ADVANCES

2014-06-30

PIER B

Vol. 60, 169-193, 2014

doi:10.2528/PIERB14051401

download: 264

Transfer Operator Theory and Inter-Reciprocity of Non-Reciprocal Multiport Antennas

Wolfgang Macher

The present article expounds a formalism for the representation of multi-port non-reciprocal antenna structures in an arbitrary surrounding linear medium. In the most general approach the antenna, the waveguides connected to it, as well as the surrounding medium may contain any distribution of anisotropic magneto-electric media. Furthermore, an arbitrary external field is taken into consideration which need not be of plane wave form. A reciprocally adjoint system is introduced to derive relations which describe the antenna under such general conditions. Since the antenna may contain media which prohibit the use of ordinary scattering, admittance or impedance matrices, an approach by means of generalized scattering matrices, or by a generalized admittance and a generalized impedance matrix, is applied. This leads to an n-port description of the whole waveguide-antenna environment where transfer operators render the interaction between the external field and the state of the ports. These operators are the generalizations of effective length vectors. For its importance the case of reciprocal reflection-symmetric waveguides is treated in detail, including a derivation of the consequences of abstract network reciprocity and complex power relation for voltage-current representations. The formalism is adequate for the description of radar and radio astronomy antennas, in particular when wave polarization plays a crucial role and/or a magnetized plasma environment is present (which is responsible for anisotropy and non-reciprocal conditions).

TRANSFER OPERATOR THEORY AND INTER-RECIPROCITY OF NON-RECIPROCAL MULTIPORT ANTENNAS

2014-06-29

PIER B

Vol. 60, 157-168, 2014

doi:10.2528/PIERB14050101

download: 315

Design of Light Weight Microstrip Patch Antenna on Dielectric and Magnetodielectric Substrate for Broadband Applications in X-Band

Kunal Borah , Arunav Phukan , Satyajib Bhattacharyya and Nidhi Saxena Bhattacharyya

A modification in the structure of substrate has been carried out to reduce weight and improve the performance of microstrip patch antenna in X-band. A step profile is incorporated in the substrate along the radiating edges of the patch. The design is tested on both dielectric and magnetodielectric substrates. Return loss of antenna with varying step riser height and step tread length shows improvement in -10 dB bandwidth to 13.2% for the dielectric and to 12.3% for the magnetodielectric as compared to about 4.8% and 6.9% for unprofiled substrate geometry in dielectric and magnetodielectric respectively. As compared to the unprofiled planar antenna, maximum weight reduction for the stepped antenna on dielectric substrate is 54.75 % and for the magnetodielectric is 58.9% is observed. An equivalent circuit modeling for the stepped structure is carried out for the proposed structure.

DESIGN OF LIGHT WEIGHT MICROSTRIP PATCH ANTENNA ON DIELECTRIC AND MAGNETODIELECTRIC SUBSTRATE FOR BROADBAND APPLICATIONS IN X-BAND

2014-06-25

PIER B

Vol. 60, 141-155, 2014

doi:10.2528/PIERB14041805

download: 265

Overview of Ionospheric Modification by High Frequency (HF) Heaters-Theory

Spencer P. Kuo

The scenarios of achieving effective ionospheric modification are summarized, and the likely physical processes engaging linear and nonlinear mode conversions through plasma inhomogeneity and nonlinearity are revealed. Parametric instabilities, which are the directly relevant processes to achieve effective heating of the ionospheric F region, are formulated and analyzed. The threshold fields and growth rates of instabilities are obtained. The nonlinear Schrodinger equation governing the nonlinear evolution of Langmuir waves is derived and analyzed. The nonlinear periodic and solitary solutions of the equation are obtained. The analyses illustrate the conditions for the generation of Langmuir soliton and nonlinear periodic Langmuir waves.

OVERVIEW OF IONOSPHERIC MODIFICATION BY HIGH FREQUENCY (HF) HEATERS-THEORY

2014-06-24

PIER B

Vol. 60, 125-139, 2014

doi:10.2528/PIERB14050205

download: 239

New High-Rate UWB Scheme for WBAN-Based Healthcare Systems

Zakaria Mohammadi , Rachid Saadane and Driss Aboutajdine

Given the emphasis on increasing wireless network usage for healthcare application, e.g. Wireless Body Area Network (WBAN), the need for high-rate physical layer has become a genuine concern from research and industrial community. The use of the Ultra-Wideband (UWB) is looking especially bright for such systems given its lower energy consumption and performances towards frequency-selective channels. However, the Multi-Band-OFDM-based UWB technique has some inherent limitations as loss in spectral efficiency due to the use of Cyclic-Prefix (CP). In this paper, a new physical layer scheme for high-rate wireless body area networks based on MB-OFDM with Offset Quadrature Amplitude Modulation (OQAM) modulation is presented. The proposed MB-OFDM/OQAM can achieve high spectral and power efficiency than conventional MB-OFDM system. Moreover, the use of the CP Interval in the conventional MBOFDM removes efficiently the Inter-Symbols Interferences (ISI) but remains ineffective towards the Inter-Carriers Interferences (ICI) caused by the channel frequency offset (FO). The performances evaluation of the proposed technique will be carried-out in realistic UWB-WBANs channels with various scenarios, which will be also presented and studied herein.

NEW HIGH-RATE UWB SCHEME FOR WBAN-BASED HEALTHCARE SYSTEMS

2014-06-17

PIER B

Vol. 60, 111-123, 2014

doi:10.2528/PIERB14042205

download: 282

Design of Asymmetric Slot Antenna with Meandered Narrow Rectangular Slit for Dual Band Applications

Raj Kumar , Praveen Naidu and Vivek Kamble

A compact coplanar waveguide (CPW) fed asymmetric slot antenna with dual operating bands is proposed. The slot is modified rectangular in shape and asymmetrically cut in the ground plane. A hexagonal patch fed by a two-step CPW is used to excite the slot. The feed itself is slightly asymmetric (shifted, with unequal ground planes). The asymmetric cuts on the slot together with the feed line asymmetry have helped in obtaining ultra wideband impedance matching. An extra resonance at 2.4 GHz for Bluetooth applications is obtained by cutting an additional meandered narrow rectangular shape slit in the ground plane. The prototype of the proposed antenna has been fabricated and tested. The measured 10 dB return loss bandwidth of the proposed antenna is 200 MHz (2.3-2.5 GHz) for the first band and 12.1 GHz (2.9-15.0 GHz) for the second band. The radiation patterns of the proposed antenna are obtained and found to be Omni-directional in H-plane and bi-directional in E-Plane. The measured and simulated results are in good agreement.

DESIGN OF ASYMMETRIC SLOT ANTENNA WITH MEANDERED NARROW RECTANGULAR SLIT FOR DUAL BAND APPLICATIONS

2014-06-15

PIER B

Vol. 60, 95-110, 2014

doi:10.2528/PIERB14051704

download: 471

Analytical Derivation of Induction Motors Inductances Under Eccentricity Conditions

Hossein Hooshmandi Safa , Mohammad Ebrahimi , Ali Davoudi and Alireza Pouramin

Geometrical modeling of induction machines under eccentricity conditions involves a significant number of self and mutual inductances. These inductances are functions of rotor angular position, and calculating them at each time step requires solving computationally-intensive definite integrals. Conventional techniques use numerical look-up tables, or employ approximated analytical expressions such as limited-term Fourier series expression of turn functions. The former approach needs large memory volume given the size of inductance matrix. Moreover, numerical interpolations are needed upon model execution, which significantly slows down the simulation. The later technique is computationally tasking for a large set of Fourier series terms, or lacks sufficient accuracy if only a few terms are used. Alternatively, computationally efficient closed-form solutions for self- and mutual- inductance expressions are presented here. The step variations of turn functions are considered which streamlines the model formulation. The experimental results validate the proposed model. In particular, the frequency spectrum of the stator current illustrates the ability of proposed technique to detect eccentricity.

ANALYTICAL DERIVATION OF INDUCTION MOTORS INDUCTANCES UNDER ECCENTRICITY CONDITIONS

2014-06-06

PIER B

Vol. 60, 79-93, 2014

doi:10.2528/PIERB14041311

download: 314

Simple Relations Between a Uniaxial Medium and an Isotropic Medium

Saffet Sen

In this article, in a simple way, simple relations are derived between the electric field components of an electrically uniaxial medium and those of an isotropic medium. The permittivity of the isotropic medium is the same as the permittivity of the uniaxial medium that is common to the axes transverse to the optic axis. Using the spectral representation, the vector wave equation for the electric field intensity vector of the uniaxial medium is solved for the x directed, y directed and z directed point sources. For the x directed and y directed point sources, the electric field components transverse to the optic axis are written in terms of the corresponding components of the isotropic medium plus some other terms. Part of these terms are closed forms expressions, and the rest are Sommerfeld type integrals. Elements of each group are related to each other by coordinate transformations. The electric field components parallel to the optic axis are shown to be obtained from the isotropic medium components using coordinate transformations. The relations between the uniaxial medium and isotropic medium field components are verified by comparing the results of a previous study in the literature to the results obtained using the relations in this study. Good agreement is achieved between these results.

SIMPLE RELATIONS BETWEEN A UNIAXIAL MEDIUM AND AN ISOTROPIC MEDIUM

2014-05-26

PIER B

Vol. 60, 63-77, 2014

doi:10.2528/PIERB14040401

download: 291

Hrr Profiles Time-Frequency Non-Negative Sparse Coding for SAR Target Classification

Xinzheng Zhang , Qizheng Wu , Shujun Liu , Jianhong Qin and Wei Song

A new approach to classify synthetic aperture radar (SAR) targets is presented based on high range resolution (HRR) profiles time-frequency matrix non-negative sparse coding (NNSC). Firstly, SAR target images have been converted into HRR profiles. And the non-negative time-frequency matrix for each of the profiles is obtained by using an adaptive Gaussian representation (AGR). Secondly, NNSC is applied to learn target time-frequency basis of the training set. Feature vectors are constructed by projecting each HRR profile time-frequency matrix to low dimensional time-frequency basis space. Finally, the target classification decision is found with support vector machine and nearest neighbor algorithm respectively. To demonstrate the performance of the proposed approach, experiments are performed with Moving and Stationary Target Acquisition and Recognition (MSTAR) public release SAR database. The experimental results support the effectiveness of the proposed technique for SAR target classification.

HRR PROFILES TIME-FREQUENCY NON-NEGATIVE SPARSE CODING FOR SAR TARGET CLASSIFICATION

2014-05-21

PIER B

Vol. 60, 49-62, 2014

doi:10.2528/PIERB14031502

download: 446

An Integral Equation Formulation for TM Scattering by a Conducting Cylinder Coated with an Inhomogeneous Dielectric/Magnetic Material

Ahmed A. Sakr , Ezzeldin A. Soliman and Alaa Abdelmageed

A volume-surface integral equation (VSIE) formulation is developed for determining the electromagnetic TM scattering by a two-dimensional conducting cylinder coated with an inhomogeneous dielectric/magnetic material. The electric field integral equations (EFIEs) are utilized to derive the VSIE. The surface EFIE is applied to the conducting surface, while the volume EFIE is applied to the coating region. By employing the surface and equivalence principles, the problem is reduced into a set of coupled integral equations in terms of equivalent electric and magnetic currents radiating into unbounded space. The moment method is used to solve the integral equations. Numerical results for the bistatic radar cross section for different structures are presented. The well-known exact series-solution for a conducting circular cylinder coated with multilayers of homogeneous materials is used along with the available published data to validate the results. The influence of using coatings with double-positive (DPS) and/or double-negative (DNG) materials on the radar cross section is investigated.

AN INTEGRAL EQUATION FORMULATION FOR TM SCATTERING BY A CONDUCTING CYLINDER COATED WITH AN INHOMOGENEOUS DIELECTRIC/MAGNETIC MATERIAL

2014-05-13

PIER B

Vol. 60, 35-48, 2014

doi:10.2528/PIERB14021003

download: 360

Bistatic RCS Prediction of Composite Scattering from Electrically Very Large Ship-Sea Geometry with a Hybrid Facet-Based Ka and Shadow-Corrected Greco Scheme

Mingyuan Man , Zhen-Ya Lei , Yong-Jun Xie and Xiaofeng Li

This paper presents a hybrid scheme for fast calculation on the bistatic composite scattering from electrically very large ship-sea geometry at high frequencies. Based on the Kirchhoff approximation (KA), we try to break the large-scale sea surface into myriads of plane facets, then derive the Kirchhoff integration analytically on each individual discretized facet. The analytical expression obtained, so-called the ``facet-based Kirchhoff approximation (FBKA)'', is suitable for a quick scattering calculation on the electrically very large sea surface, since it is beyond the intensively refined meshes as the usual Monte Carlo implementation does. Meanwhile, combined with graphical electromagnetic computing method (GRECO) to extract the illuminated and shadow facets in accordance with the incident direction, the conventional physical optics method (PO) is improved by employing current marching technique (CMT) to calculate the currents in the shadow region. The shadow-corrected GRECO is presented in this hybrid model to solve the bistatic scattering from complex and very electrically large perfectly electric conducting (PEC) objects. The accuracy of the shadow-corrected GRECO is confirmed well by exact numerical methods, especially at large scattering angles. The electromagnetic interactions between the ship and sea surface are estimated by the famous ``four-path model'', which has been proved to be valid for ship scattering at relatively calm sea state. Several numerical examples have been presented to demonstrate the efficiency and accuracy of the proposed hybrid method.

BISTATIC RCS PREDICTION OF COMPOSITE SCATTERING FROM ELECTRICALLY VERY LARGE SHIP-SEA GEOMETRY WITH A HYBRID FACET-BASED KA AND SHADOW-CORRECTED GRECO SCHEME

2014-05-12

PIER B

Vol. 60, 15-34, 2014

doi:10.2528/PIERB14022603

download: 369

Design of Multiple Beam Forming Antenna System Using Substrate Integrated Folded Waveguide (Sifw) Technology

Wriddhi Bhowmik , Shweta Srivastava and Laxman Prasad

This paper introduces a novel structure of 4×4 multiple beam forming antenna system using substrate integrated folded waveguide technology. For high speed wireless communication it is necessary to minimize the interferences and multipath fading. Multiple beam forming antenna system is a good solution to these problems. The substrate integrated folded waveguide (SIFW) technology reduces the width of substrate integrated waveguide (SIW) by half. All the basic building blocks required for the antenna array system are designed and simulated individually. They are then combined to form the butler matrix fed antenna array system. The SIFW technology reduces the total width of butler matrix. The radiation performance of the multiple beam forming antenna system is realized by integrating the H-plane SIFW horn antennas with the output ports of the butler matrix. The system is practically realized and good directive multiple beams with symmetric gain (5.8 dB, 5.63 dB, 5.31 dB and 5.9 dB for the beams 1R, 2L, 2R and 1L) have been achieved.

DESIGN OF MULTIPLE BEAM FORMING ANTENNA SYSTEM USING SUBSTRATE INTEGRATED FOLDED WAVEGUIDE (SIFW) TECHNOLOGY

2014-05-12

PIER B

Vol. 60, 1-13, 2014

doi:10.2528/PIERB14022203

download: 312

Interaction of Electromagnetic Waves with a Moving Slab: Fundamental Dyadic Method

Atieh Kashaninejad Rad , Ali Abdolali and Mohammad Mahdi Salary

This paper concerns with the interaction of electromagnetic waves with a moving slab. Consider a homogeneous isotropic slab moving uniformly in an arbitrary direction surrounded by an isotropic medium (free space). In this paper a new simple and systematic method is proposed for analyzing reflection and transmission of obliquely incident electromagnetic waves by a moving slab based on the concept of propagators. In the previous works complex relations were arrived but using this novel method those complexities will not appear thus the method may be extended to more complex structures. In this method, first, electric and magnetic fields are decomposed into their tangential and normal components then each constitutive dyadic is decomposed into a two-dimensional dyadic in transverse plane and two two-dimensional vectors in this plane. Substituting these dyadics into Maxwell's equations gives a first order differential equation which contains fundamental dyadic of the medium. From the solution of this equation, fields inside the slab may be expressed in terms of fields at the front surface of the slab and the propagator matrix which is an exponential function of fundamental dyadic. Using this method the up-going and down-going tangential electromagnetic fields may be obtained at the same time. As a limiting case a slab with vanishing velocity is discussed using this method, and reflection and transmission coefficients of this slab are derived, which ends in Fresnel's equations. At last, several typical examples are provided to exemplify the applicability of the proposed method. Moreover, the results are compared with the method of Lorentz transformation. A good agreement is observed between the results which verifies the validity of the proposed method.