PIER M | PIER Journals

2016-09-12

PIER M

Vol. 49, 211-219, 2016

download: 302

Non-Conventional Discretization Grid Based FDTD for EM Wave Propagation in Magnetized Plasma Metallic Photonic Crystal

Mayank Kumar Chaudhari

Photonic band gaps of plasma metallic photonic crystals can be tuned dynamically by subjecting it to external magnetic field leading to variety of applications. Dispersion characteristics of 2D photonic crystals are often studied by Finite Difference Time Domain (FDTD) method based on standard Yee's grid discretization schema, in which x- and y-components of fields are defined on different edges of the Yee's cell. However, finite difference equations for electromagnetic wave propagation in magnetized plasma involve interdependence of polarization currents and electric field in a manner that requires both x- and y-components of fields to be evaluated at the same spatial location. A non-conventional discretization technique is presented in which x- and y-components of fields are evaluated at the same spatial location. In this paper analysis of magnetized plasma metallic photonic crystals (PMPC) is presented using the new grid. However, the proposed discretization scheme can be used to introduce magnetized plasmas in any type of structures that can be studied on the basis of standard Yee's grid. For example, topics such as photonic band gap (PBG) cavities based on PMPC, PBG waveguides involving plasma, meta-materials, etc. can be very effectively studied using the approach presented in this paper. Interesting results are found when PMPC is subject to external magnetic field. Several new bands including two dispersion-less flat bands appear and the existing bands with an exception of first band slightly shift upward when PMPC is subjected to an external transverse magnetic field. The location of flat bands and the location and width of forbidden band gaps can be controlled by external magnetic field as well as plasma parameters. New band gaps appearing for lower r/a for magnetized PMPC can be utilized for several applications such as PBG cavity design for gyrotron devices.

NON-CONVENTIONAL DISCRETIZATION GRID BASED FDTD FOR EM WAVE PROPAGATION IN MAGNETIZED PLASMA METALLIC PHOTONIC CRYSTAL

2016-09-11

PIER M

Vol. 49, 203-209, 2016

doi:10.2528/PIERM16071202

download: 281

Fast Direct Solution of Composite Conducting-Dielectric Arrays Using Sherman-Morrison-Woodbury Algorithm

Yang Zhang , Xinlei Chen , Chao Fei , Zhuo Li and Chang Qing Gu

In this paper, the Sherman-Morrison-Woodbury (SMW) Formula-based algorithm (SMWA) is used to enable the fast direct solution of conducting-dielectric arrays. To speed up the direct solution of the matrix equation, the dense impedance matrix is transformed into a product of several block diagonal matrices via the SMW formula. In the grouping process, the situation that the elements of an array simultaneously belong to two different subgroups at peer level is avoided in order to promote the efficiency. The SMWA conducts the calculation with a respectable reduction in the computational time as well as memory.

FAST DIRECT SOLUTION OF COMPOSITE CONDUCTING-DIELECTRIC ARRAYS USING SHERMAN-MORRISON-WOODBURY ALGORITHM

2016-09-08

PIER M

Vol. 49, 195-202, 2016

doi:10.2528/PIERM16052001

download: 239

A Set of Simple Numerical Pattern Synthesis Algorithms for Anti-Jamming with Superdirective Receiving Array

Huajun Zhang , Huotao Gao , Huaqiao Zhao , Ting Cao and Boya Li

Although a superdirective array can acquire maximum directive gain with electrically small array, in some practical applications, low sidelobe and deep nulls are also important, which can effectively inhibit directional interferences. In this work, a set of simple superdirective pattern synthesis methods are proposed. By introducing diagonal loading factor and adding virtual jamming constraints, they can keep suitable tradeoff among directive gain, efficiency and anti-jamming performance. Besides, easy realization is another good feature of the proposed methods.

A SET OF SIMPLE NUMERICAL PATTERN SYNTHESIS ALGORITHMS FOR ANTI-JAMMING WITH SUPERDIRECTIVE RECEIVING ARRAY

2016-08-30

PIER M

Vol. 49, 181-193, 2016

doi:10.2528/PIERM16052101

download: 1253

Calculation of Force Between Two Ring Magnets Using Adaptive Monte Carlo Technique with Experimental Verification

Tapan Santra , Debabrata Roy and Sotoshi Yamada

This paper represents a new simple technique to calculate force between two ring magnets using adaptive Monte Carlo integration technique. Elementary magnetic force is calculated by discretizing the pole faces of the passive magnets into tiny surfaces. To obtain the resultant force this elementary force equation is integrated over the dimensions of the ring magnets, which incur a multidimensional integration with complicated integral function. This multidimensional integration is solved using adaptive Monte Carlo technique considering singularity treatment and importance sampling. This method is advantageous over existing analytical or quasi analytical methods regarding singularity treatment and computational burden. It is more flexible, especially for using in digital computer. The result of the proposed technique is verified with finite element method and also validated by laboratory experiment. It is observed that the proposed result matches very well with the practical test result, particularly if self demagnetization is considered. So taking into account of simplicity, less computational burden and usefulness, the proposed method may be an alternative choice for magnetic force calculation.

CALCULATION OF FORCE BETWEEN TWO RING MAGNETS USING ADAPTIVE MONTE CARLO TECHNIQUE WITH EXPERIMENTAL VERIFICATION

2016-08-25

PIER M

Vol. 49, 167-179, 2016

doi:10.2528/PIERM16042802

download: 301

Modeling the Effect of Periodic Wall Roughness on the Indoor Radio Propagation Channel

Vincent Adelphe Fono and Larbi Talbi

A deterministic model based on ray tracing and dealing with periodic roughness is developed, for an indoor radio propagation channel and experimentally validated at a frequency of 10 GHz. Two different scenarios are studied, namely a smooth corridor and a corridor having artificial periodic roughness. The periodic roughness consists of a set of conductive semi-cylinders attached to the corridor sidewalls. Two different antenna setups are considered during the measurements, horn-horn antennas and patch-patch antennas, in transmitter-receiver configurations. Excellent agreement is achieved in terms of the received powers versus distance and the power delay profiles. The signal fading is analyzed. The statistical parameters are also generated, and a fair agreement is observed between the simulation and measurement results.

MODELING THE EFFECT OF PERIODIC WALL ROUGHNESS ON THE INDOOR RADIO PROPAGATION CHANNEL

2016-08-23

PIER M

Vol. 49, 153-165, 2016

doi:10.2528/PIERM16061203

download: 285

Statistical Design Centering Optimization of 1D Photonic Crystal Filters

Abdel-Karim S. O. Hassan , Ahmed Sayed Mohamed , Mahmoud M. Taha and Nadia H. Rafat

A statistical design centering approach is introduced, to achieve the optimal design center point of one-dimensional photonic crystal-based filters which are parts of several optoelectronic systems. Up to our knowledge, it is the first time that a design centering approach is applied to such a design problem. The proposed approach seeks nominal designable parameter values that maximize the probability of satisfying the design specifications (yield function). Thus, the achieved optimal design center point is much more robust to unavoidable designable parameter variations, occurring during fabrication process, for example. The yield maximization problem is formulated as an unconstrained optimization problem solved by derivative-free based-algorithm (NEWUOA) coupled with a variance reduction yield estimator to reduce large number of required system simulations. The flexibility and efficiency of the proposed design centering approach are demonstrated by two practical examples: band pass optical filter and spectral control filter. A comparison with Minimax optimization technique is also given.

STATISTICAL DESIGN CENTERING OPTIMIZATION OF 1D PHOTONIC CRYSTAL FILTERS

2016-08-21

PIER M

Vol. 49, 141-151, 2016

doi:10.2528/PIERM16052904

download: 244

An Extension of the Linear Embedding via Green's Operators Method for the Analysis of Disconnected Finite Antenna Arrays

Salman Mokhlespour , Vito Lancellotti and Antonius G. Tijhuis

We describe an extension of the linear embedding via Green's operators (LEGO) method to the solution of finite antenna arrays comprised of disconnected elements in a homogeneous medium. The ultimate goal is the calculation of the admittance matrix and the radiation pattern of the array. As the basic idea is the inclusion of an array element inside a LEGO electromagnetic brick, the first step towards the solution consists of the definition and numerical calculation of hybrid scattering-admittance operators which extend the notion of scattering operators of equivalent currents introduced in the past. Then again, the combination of many bricks involves the usual transfer operators for the description of the multiple scattering between the bricks. Moreover, to reduce the size of the problem we implement the eigencurrents expansion. With the aid of a numerical example we discuss the validation of the approach and the behaviour of the total CPU time as a function of the elements forming the array.

AN EXTENSION OF THE LINEAR EMBEDDING VIA GREEN'S OPERATORS METHOD FOR THE ANALYSIS OF DISCONNECTED FINITE ANTENNA ARRAYS

2016-08-12

PIER M

Vol. 49, 131-140, 2016

doi:10.2528/PIERM16060703

download: 283

A Comparative Study of Flux Cancellation Among Multiple Interconnected Modular Pads in Lumped IPT System

Chun Qiu , Kwok-Tong Chau , Zhen Zhang and Tze Wood Ching

A lumped inductive power transfer system (IPT) with multiple modular pads differs from a stand-alone system. The magnetic coupling between adjacent modules is affected by the flux cancelation which further affects the power transmission. Thus, it is important to investigate the relationship between flux cancelation and system configuration. In this paper, the basic connection and operating mechanism for a modular IPT system are first discussed. Six cases are designed for two scenarios, including single and multiple secondary modules. Performances are compared in various primary excitation modes and secondary connection modes. Results show that the direction of canceled flux is determined by these modes. Matched modes will bring either a higher or a more stable coupling. And unmatched modes between primary and secondary sides tend to have the lowest coupling performance due to severe flux cancelation. Results provide a guidance for system design aiming at different power transfer characteristics.

A COMPARATIVE STUDY OF FLUX CANCELLATION AMONG MULTIPLE INTERCONNECTED MODULAR PADS IN LUMPED IPT SYSTEM

2016-08-10

PIER M

Vol. 49, 117-129, 2016

doi:10.2528/PIERM16051309

download: 333

Curved Space-Time for Light by an Anisotropic Medium: Media with the Variable Optical Axes

Sayed Alireza Mousavi , Rasoul Roknizadeh , Sahar Sahebdivan and Shahram Dehdashti

An optical impedance-matched medium with a gradient refractive index can resemble a geometrical analogy with an arbitrary curved space-time. In this paper, we show that a non-impedance-matched medium with a varying optical axis can also resemble the features of a space of non-trivial metric for light. The medium with a varying optical axis is an engineered stratified slab of material, in which the orientation of the optical axis in each layer slightly differs from the other layers, while the magnitude of refractive index remains constant. Instead of the change in refractive index, the inhomogeneity of such a medium is induced by the local anisotropy. Therefore, the propagation of light depends on the local optical axis. We study the conditions that make the analogy between curved space-time and a medium with a varying optical axis. Extension of the transformation optics to the media with optical axis profile might ease some fabrication difficulties of gradient refractive index materials for particular frequencies.

CURVED SPACE-TIME FOR LIGHT BY AN ANISOTROPIC MEDIUM: MEDIA WITH THE VARIABLE OPTICAL AXES

2016-08-08

PIER M

Vol. 49, 103-115, 2016

doi:10.2528/PIERM16052301

download: 247

Propagation Properties of Partially Coherent Lorentz-Gauss Beams in Uniaxial Crystals Orthogonal to the X-Axis

Guoquan Zhou , Zhiyue Ji and Guoyun Ru

Analytical expressions of the elements of a cross spectral density matrix are derived to describe the partially coherent Lorentz-Gauss beam propagating in uniaxial crystals orthogonal to the x-axis. The intensity and degree of polarization for the partially coherent Lorentz-Gauss beam propagating in uniaxial crystals orthogonal to the x-axis are also presented. The evolution properties of the partially coherent Lorentz-Gauss beam are numerically demonstrated. The influences of the uniaxial crystal and coherence length on the propagation properties of the partially coherent Lorentz-Gauss beam in uniaxial crystals orthogonal to the x-axis are examined. The uniaxial crystal considered here has the property of the extraordinary refractive index being larger than the ordinary refractive index. The partially coherent Lorentz-Gauss beam in the direction along the x-axis spreads more rapidly than that in the direction along the y-axis. With increasing the ratio of the extraordinary refractive index to the ordinary refractive index, the spreading of the partially coherent Lorentz-Gauss beam increases in the direction along the x-axis, but decreases in the direction along the y-axis. Meanwhile, the degree of polarization in the edges of the long and short axes of the beam spot increases. With increasing the coherence length, the beam spot of the partially coherent Lorentz-Gauss beam uniformly becomes less, and the maximum degree of polarization in the edge of the beam spot decreases.

PROPAGATION PROPERTIES OF PARTIALLY COHERENT LORENTZ-GAUSS BEAMS IN UNIAXIAL CRYSTALS ORTHOGONAL TO THE X-AXIS

2016-08-03

PIER M

Vol. 49, 91-101, 2016

doi:10.2528/PIERM16051505

download: 263

Modified GO Solutions for the High Frequency Reflected Wave in the Focal Region of a 3D Elliptical Reflector Placed in Isotropic Chiral Medium

Tariq Rahim , Muhammad Ibrahim , Murad Ali Shah and Jia-Dong Xu

High frequency electromagnetic (EM) fields in the focal region of a 3D elliptical reflector placed in a homogeneous and reciprocal chiral background have been analyzed using geometrical optics (GO) approximation and Maslov's method. The GO solutions becomes invalid at the focal region of a 3D elliptical reflector due to unreal singularities. Therefore, an asymptotic method based on Maslov's theory has been applied to derive high frequency EM fields, which is also valid at the focal points. Moreover, the effect of chirality parameter of the background medium on the position of focal points for both Left circularly polarized wave (LCP) and right circularly polarized (RCP) wave are described by plotting the derived expressions numerically using MATLAB.

MODIFIED GO SOLUTIONS FOR THE HIGH FREQUENCY REFLECTED WAVE IN THE FOCAL REGION OF A 3D ELLIPTICAL REFLECTOR PLACED IN ISOTROPIC CHIRAL MEDIUM

2016-08-02

PIER M

Vol. 49, 81-89, 2016

doi:10.2528/PIERM16051806

download: 372

RF and Microwave Low Power Dielectric Heating Using Parallel Plate Applicator to Control Insect Pests on Tomato Plant

Sandeep Vinayak Gaikwad and Arun N. Gaikwad

This paper focuses on electromagnetic exposure to control insect pests in agriculture using parallel plate applicator. A tomato plant and ``Helicoverpa armigera'' eggs and larvae are exposed to 915 MHz and 2450 MHz. A parallel plate applicator is fabricated and matched with Radio Frequency and Microwave source at 50 Ω. The power up to 250 W was applied to parallel plate applicator in an anechoic chamber to observe the behavior and heating effect on commodities inside the applicator. The rise in temperature of the tomato plant and tomato with insect pest stages were different for different dielectric properties. The reduction in the hatching was observed after the exposure. The first instar to fifth instar larvae erratic movement was observed during exposure. The faster response of heating was observed at the higher side of exposed power. The effect on the heating rate considering the variations in the space between two parallel plates of the applicator is analyzed in this research. The parallel plate capacitor is referred to as an applicator in this paper.

RF AND MICROWAVE LOW POWER DIELECTRIC HEATING USING PARALLEL PLATE APPLICATOR TO CONTROL INSECT PESTS ON TOMATO PLANT

2016-07-20

PIER M

Vol. 49, 69-80, 2016

doi:10.2528/PIERM16030301

download: 391

A Novel Double-Stator Permanent Magnet Generator Integrated with a Magnetic Gear

Shehu Salihu Mustafa , Norhisam Misron , Norman Mariun , Mohammad Lutfi Othman and Tsuyoshi Hanamoto

This paper presents a double-stator permanent magnet generator (DSPMG) integrated with a novel magnetic gear structure which is proposed to be used as a direct drive generator for low speed applications. Torque transmission is based on three rotors consisting of prime permanent magnet poles on the middle rotor and field permanent magnet poles on the inner and outer rotors, respectively. The proposed machine combines the function of a triple rotor magnetic gear and electrical power generator. The operating principle of the generator is discussed, and its performance characteristics are analyzed using 2-dimensional finite-element method (2D-FEM). Analysis results about its magnetic gear ratio, transmission torque, cogging torque and electrical power performance are reported. The 2-D finite element analysis results verify the proposed generator design.

A NOVEL DOUBLE-STATOR PERMANENT MAGNET GENERATOR INTEGRATED WITH A MAGNETIC GEAR

2016-07-18

PIER M

Vol. 49, 61-68, 2016

doi:10.2528/PIERM16051907

download: 256

Preliminary Results on Estimation of the Dispersive Dielectric Properties of an Object Utilizing Frequency-Dependent Forward-Backward Time-Stepping Technique

Shi Wei Ng , Kismet Anak Hong Ping , Shafrida Sahrani , Mohamad Hamiruce Marhaban , Mohd Iqbal Sariphn , Toshifumi Moriyama and Takashi Takenaka

In this paper, a Frequency-Dependent Forward-Backward Time-Stepping (FD-FBTS) inverse scattering technique is used for reconstruction of homogeneous dispersive object. The aim of the technique is to reconstruct the relative permittivity at infinite frequency, static relative permittivity and static conductivity of the homogeneous dispersive object simultaneously. The technique utilizes iterative finite-difference time-domain (FDTD) method for solving inverse scattering problem in time domain. The minimization of the cost functional is carried out utilizing Dai-Yuan nonlinear conjugate-gradient algorithm. The Fréchet derivatives of the augmented cost functional are derived analytically with respect to scatterer properties. Numerical results for reconstruction of two-dimensional homogeneous dispersive illustrate the performance of the proposed technique.

PRELIMINARY RESULTS ON ESTIMATION OF THE DISPERSIVE DIELECTRIC PROPERTIES OF AN OBJECT UTILIZING FREQUENCY-DEPENDENT FORWARD-BACKWARD TIME-STEPPING TECHNIQUE

2016-07-15

PIER M

Vol. 49, 51-60, 2016

doi:10.2528/PIERM16042803

download: 298

Extracting Surface Macro Basis Functions from Low-Rank Scattering Operators with the ACA Algorithm

Vito Lancellotti

The Adaptive Cross Approximation (ACA) algorithm has been used to compress the rank-deficient sub-blocks of the matrices that arise in the numerical solution of integral equations (IEs) with the Method of Moments. In the context of the linear embedding via Green's operator (LEGO) method - a domain decomposition technique based on IEs - an electromagnetic problem is modelled by combining ``bricks'' in turn described by scattering operators which, in many situations, are singular. As a result, macro basis functions defined on the boundary of a brick can be generated by applying the ACA to a scattering operator. Said functions allow compressing the weak form of the LEGO functional equations which then use up less computer memory and are faster to invert.

EXTRACTING SURFACE MACRO BASIS FUNCTIONS FROM LOW-RANK SCATTERING OPERATORS WITH THE ACA ALGORITHM

2016-07-13

PIER M

Vol. 49, 41-50, 2016

doi:10.2528/PIERM16041909

download: 266

Novel Finite Airy Array Beams Generated from Gaussian Array Beams Illuminating an Optical Airy Transform System

Lahcen EZ-ZARIY , Zoubir Hricha and Abdelmajid Belafhal

In this work, a novel family of Finite Airy array beams have been produced by an optical Airy transform system illuminated by Gaussian Array beams. Based on the generalized Huygens- Fresnel integral, an analytical expression is developed to describe the pattern properties of the beam generated at the output plan of the optical system. The well-known Finite Airy beam generated from the fundamental Gaussian beam using an optical Airy transform system is deduced, here, as a particular case of the main result of the actual study. Numerical calculations are performed to show the possibility to create a multitude of Finite Airy array beams with controllable parameters depending on the number of beamlets, the distance between the adjacent modules and the positions and orientations of the beamlets.

NOVEL FINITE AIRY ARRAY BEAMS GENERATED FROM GAUSSIAN ARRAY BEAMS ILLUMINATING AN OPTICAL AIRY TRANSFORM SYSTEM

2016-07-13

PIER M

Vol. 49, 33-39, 2016

doi:10.2528/PIERM16050801

download: 323

Millimeter-Wave Holographic Imaging Algorithm with Amplitude Corrections

Yu-Kun Zhu , Ming-Hui Yang , Liang Wu , Yun Sun and Xiao-Wei Sun

Security detection is becoming extremely important with the growing threat of terrorism in recent years. An effective millimeter-wave (mmw) holographic imaging system is presented in this paper, which can be applied in nondestructive detection such as security detection in airport or other public locations. The imaging algorithm is an extension of the work before as it takes the decay of the amplitude with range into account. The experiment result of an imaging system working at 28-33 GHz frequencies indicates good quality of the algorithm.

MILLIMETER-WAVE HOLOGRAPHIC IMAGING ALGORITHM WITH AMPLITUDE CORRECTIONS

2016-07-10

PIER M

Vol. 49, 21-31, 2016

doi:10.2528/PIERM16050405

download: 539

The Performance Improvement of THz Antenna via Modeling and Characterization of Doped Graphene

Mohammed Taih Gatte , Ping Jack Soh , Hasliza A. Rahim , Raad Badlishah Ahmad and Fareq Malek

The improvement of Terahertz (THz) antenna requires efficient (nano)materials to operate within the millimeter wave and THz spectrum. In this paper, doped graphene is used to improve the performance of two types of patch antennas, a rectangular and an elliptical antenna. The surface conductivity of conventional (non-doped) graphene is first modeled prior to the design and simulation of the two graphene based antennas in an electromagnetic solver. Next, different graphene models and their corresponding surface conductivities are computed based on different bias voltages or chemical doping. These configurations are then benchmarked against a similar antenna based on conventional metallic (copper) conductor to quantify their levels of performance improvement. The graphene based antennas showed significant improvements for most parameters of antenna than that of the conventional antenna. Besides that, the higher chemical potentials resulting from higher biasing voltages also resulted in this trend. Finally, the elliptical patch graphene antenna indicated better reflection performance, radiation efficiency and gain than a rectangular patch operating at the same resonant frequency.

THE PERFORMANCE IMPROVEMENT OF THZ ANTENNA VIA MODELING AND CHARACTERIZATION OF DOPED GRAPHENE

2016-07-07

PIER M

Vol. 49, 9-19, 2016

doi:10.2528/PIERM16042401

download: 367

Coupling of Two Rectangular Waveguides through a Diaphragm with a Dielectric Slab in the Slot

Ludmila P. Yatsuk , Anatoly F. Lyakhovsky , Victor A. Katrich and Andrey A. Lyakhovsky

A scattering problem for two semi-infinite rectangular waveguides coupling through a narrow slot cut in the common end wall of the two waveguides is solved. The slot is partially filled with a dissipative or perfect dielectric insert. A mathematical model based on continuity of tangential components of magnetic field vectors on both surfaces of the diaphragm in the coupling waveguides is proposed. The magnetic field in the slot is represented by a set of slot eigenwaves. The electrical field distribution function is used as a basis function in the Galerkin's procedure allowing to find unknown amplitude coefficients. Simulation and experimental measurement have been carried out. Dependences of scattering parameters upon the wavelength were studied for various geometric parameters, insert position in the slot, and insert material permittivity and losses. A good agreement between simulation results and experimental data is obtained. It was shown that an estimate of the insert permittivity and losses can be done for unknown materials using experimental and simulated data.

COUPLING OF TWO RECTANGULAR WAVEGUIDES THROUGH A DIAPHRAGM WITH A DIELECTRIC SLAB IN THE SLOT

2016-06-30

PIER M

Vol. 49, 1-8, 2016

doi:10.2528/PIERM16043007

download: 406

Cumulative Distributions of Rainfall Rate Over Sumatra

Marzuki Marzuki , Hiroyuki Hashiguchi , Toyoshi Shimomai and Walter L. Randeu

The microwave radio links above 5 GHz suffer from attenuation due to precipitation. The need for employing higher frequencies has therefore encouraged research into rain attenuation due to precipitation. The natural variations of tropical precipitation occur in a wide range of time-scales, so does probably the behavior of radio communication links. This paper examines the variations of cumulative distribution of rainfall in Sumatra from an optical rain gauge measurement with a near continuous record of operation over eleven consecutive years (2002-2012). The worst month statistics were also examined and all results were compared with the ITU-R model. Of some natural variations of rainfall rate investigated, the diurnal variation had the most significant effect on the cumulative distribution of rainfall rate. The ITU-R model overestimated the rainfall rate for the first half of the day (00:00-11:59 LT) whereas it underestimated the rainfall rate until 0.01% of time for the second half of the day (12:00-23:59 LT) before the model starts to overestimate. The ITU model overestimated 52.85% of rainfall rate at 0.01% of time for the first half of the day and underestimates 7.59% for the second half. Considerable differences between the recorded data and the ITU-R model for the annual, seasonal, and intreaseasonal variations are only significant at small time percentage (≤ 0.01%). The relationship of worst month statistics was also slightly different from the ITU-R model. This result reinforces the previous studies on the limitation of the ITU-R model for the tropical region.