PIER | PIER Journals

2009-05-20

PIER

Vol. 92, 347-360, 2009

download: 256

Synthesis of Phased Arrays in Complex Environments with the Multilevel Characteristic Basis Function Method

Jaime Laviada-Martinez, Rafael Ayestaran, Marcos R. Pino, Fernando Las Heras Andres and Raj Mittra

The aim of this paper is to present a method to carry out the synthesis of large phased arrays when they are affected by complex environments which can influence the radiation pattern. The synthesis is performed with the help of the Multilevel Characteristic Basis Function Method to calculate a matrix relating input voltages and the far field pattern samples. The method is illustrated with the synthesis of a Secondary Surveillance Radar antenna on a turret containing multiple obstacles.

SYNTHESIS OF PHASED ARRAYS IN COMPLEX ENVIRONMENTS WITH THE MULTILEVEL CHARACTERISTIC BASIS FUNCTION METHOD

2009-05-20

PIER

Vol. 92, 333-346, 2009

doi:10.2528/PIER09041102

download: 603

Numerical Synthesis Design of Coupled Resonator Filters

Shenjie Wen and Lei Zhu

This paper proposes a methodology for numerically synthesizing element values of coupled resonator filters. These element values are compatible in retrieving coupling matrix of a cross-coupled quadruplet structure (also known as the folded structure). Differed from direct synthesis by matrix rotation, numerical solution has been adopted here to its equivalent coupling model. For varied specified return loss, numerical solutions of these element values have been derived and their accuracy is verified with their analytical counterparts to be extended for stringent design requirement. In addition, multiple sets of data are tabulated and categorized for efficient filter synthesis design under different specified pass-band return loss. In the end, an example quadruplet filter is designed, fabricated and measured for validation of the presented synthesis design methodology.

NUMERICAL SYNTHESIS DESIGN OF COUPLED RESONATOR FILTERS

2009-05-19

PIER

Vol. 92, 317-331, 2009

doi:10.2528/PIER09032902

download: 236

Composite Electromagnetic Scattering from the Plate Target Above a One-Dimensional Sea Surface: Taking the Diffraction into Account

Zhen-Sen Wu, Jing-Jian Zhang and Lei Zhao

The properties of composite electromagnetic scattering from a square conducting plate target above a one-dimensional sea surface are discussed with the diffraction of plate edge taken into account. The characteristics of electromagnetic scattering from the sea surface are investigated based on the Kirchhoff Approximation (KA). The backscattering field of a plate target is calculated with the method of higher equivalent edge currents. Besides, the method of equivalent edge currents (MEC), Physical Optics (PO) approximation and the reciprocity theorem method are combined to calculate the composite scattering field from the conducting plate target above a sea surface. The effect of the plate size, inclination, edge diffraction and the frequency of incident wave on the composite scattering field is analyzed.

COMPOSITE ELECTROMAGNETIC SCATTERING FROM THE PLATE TARGET ABOVE A ONE-DIMENSIONAL SEA SURFACE: TAKING THE DIFFRACTION INTO ACCOUNT

2009-05-14

PIER

Vol. 92, 299-315, 2009

doi:10.2528/PIER09040305

download: 775

Realization of Composite Right/Left-Handed Transmission Line Using Coupled Lines

Aya Fekry Abdelaziz, Tamer Mostafa Abuelfadl and Osman Lotfy Elsayed

This paper presents a method to construct composite right/left-handed transmission line using coupled lines. A general procedure to design a composite right/left-handed unit cell is presented. The procedure was used on a specific coupled line configuration, which is the coupled microstrip lines with slotted ground. It is shown that by proper design of the slotted ground, the coupling between the two microstrip lines can be increased dramatically keeping practical dimensions for the coupled line width and spacing. Moreover, with accurate slotted ground design, equal even and odd electrical lengths can be achieved. The performance of this composite right/left-handed line, which is characterized by backward waves with phase advance, is demonstrated by both simulated and measured results and they show good agreement. The realized composite right/left-handed transmission line has a broad bandwidth and small size.

REALIZATION OF COMPOSITE RIGHT/LEFT-HANDED TRANSMISSION LINE USING COUPLED LINES

2009-05-13

PIER

Vol. 92, 281-298, 2009

doi:10.2528/PIER09032003

download: 292

Transient Analysis of Wire Structures Using Time Domain Integral Equation Method with Exact Matrix Elements

Guai-Hong Zhang, Mingyao Xia and Xiao-Min Jiang

A novel time-domain integral equation (TDIE) solver for transient analysis of conducting wires is proposed. It is formulated using the induced electric dipoles as unknown functions. The triangular and B-spline functions are employed as the spatial and temporal basis functions, respectively. By using these basis functions, the matrix elements are found obtainable via exact closed-form formulae, which furnish a robust scheme in terms of stability and accuracy. In addition, to accelerate the matrix filling, a recursive algorithm is introduced. Numerical validations are provided by a dipole antenna, a V-shape antenna and a helical antenna.

TRANSIENT ANALYSIS OF WIRE STRUCTURES USING TIME DOMAIN INTEGRAL EQUATION METHOD WITH EXACT MATRIX ELEMENTS

2009-05-08

PIER

Vol. 92, 267-280, 2009

doi:10.2528/PIER09041409

download: 256

Resistive Sensor for High Power Microwave Pulse Measurement of Te01 Mode in Circular Waveguide

Zilvinas Kancleris, Gediminas Slekas, Vincas Tamosiunas and Milda Tamosiuniene

A resistive sensor (RS) devoted for high power microwave pulse measurement in cylindrical waveguide is considered. The modeling results of the interaction of the TE01 (H01) wave with a semiconductor plate with contacts on sidewalls of the plate placed on a wall of the circular waveguide are presented. A finite-difference time-domain (FDTD) method was employed for the calculation of the electromagnetic field components, reflection coefficient from the semiconductor obstacle, and the average electric field in it. The features of the resonances have been used to engineer the frequency response of the RS. It has been found that such electrophysical parameters of the plate can serve as the prototype of the sensing element (SE) for the circular waveguide RS with flat frequency response.

RESISTIVE SENSOR FOR HIGH POWER MICROWAVE PULSE MEASUREMENT OF TE01 MODE IN CIRCULAR WAVEGUIDE

2009-05-06

PIER

Vol. 92, 255-265, 2009

doi:10.2528/PIER09022301

download: 273

More Accurate Hybrid PO-MoM Analysis for an Electrically Large Antenna-Radome Structure

Bing Hu, Xiao-Wen Xu, Mang He and Ying Zheng

More accurate hybrid PO-MOM process combining physical optics (PO) with method of moment (MOM) is employed to analyze an electrically large antenna-radome structure. The mutual interactions among the antenna, the inner and outer surfaces of the radome are considered through a group of associated integral equations. In the analysis, the antenna surface and the sharp tip part on the radome surface are modeled accurately by using MOM while the rest smooth parts on the radome surfaces are approximated by using PO. Numerical results indicate that the hybrid process presented in this paper is much more accurate than the conventional PO-MOM ones.

MORE ACCURATE HYBRID PO-MOM ANALYSIS FOR AN ELECTRICALLY LARGE ANTENNA-RADOME STRUCTURE

2009-05-01

PIER

Vol. 92, 235-253, 2009

doi:10.2528/PIER09022608

download: 233

High-Order Electromagnetic Modeling of Shortwave Inductive Diathermy Effects

Mauro Parise and Saverio Cristina

A high-order closed-form solution for the specific absorption rate (SAR) distribution induced inside a plane geometry fatmuscle tissue by a shortwave diathermy induction coil is presented. The solution is derived starting from the complete integral expressions for the electromagnetic field components generated by a currentcarrying circular loop located horizontally above a stratified earth. It is valid in a wide frequency range, and is flexible to any multi-turn coil configuration. The spatial distribution of the SAR induced in the muscle tissue by a flat round coil is computed by using the proposed formulation, the zero-order quasi-static one, and the finite difference time domain (FDTD) method. Excellent agreement is demonstrated to exist between the results provided by the new approach and those achieved through FDTD simulations. On the contrary, the performed computations show that the zero-order solution leads to over-estimate the SAR. The performances of the round and figure-eight coil geometries are compared. Despite of what has been argued in previously published papers, it turns out that the figure-eight coil is less energetically efficient than the round one. The work in the present paper is an extension of a previous work.

HIGH-ORDER ELECTROMAGNETIC MODELING OF SHORTWAVE INDUCTIVE DIATHERMY EFFECTS

2009-04-30

PIER

Vol. 92, 223-234, 2009

doi:10.2528/PIER09031809

download: 236

Paraboloidal Reflector in Chiral Medium Supporting Simultaneously Positive Phase Velocity and Negative Phase Velocity

Tariq Rahim, Muhammad Junaid Mughal, Qaisar Naqvi and Muhammad Faryad

Focused high frequency electromagnetic waves reflected from a PEC paraboloidal surface placed in homogeneous, reciprocal and isotropic medium with high chirality parameter are analyzed. The value of the chirality parameter is set such that it simultaneously supports modes of negative and positive phase velocities. Present work is an extension of the previous work, in which the chiral medium supports only positive phase velocity. Using the previous derived expressions, line plots in the focal region are obtained.

PARABOLOIDAL REFLECTOR IN CHIRAL MEDIUM SUPPORTING SIMULTANEOUSLY POSITIVE PHASE VELOCITY AND NEGATIVE PHASE VELOCITY

2009-04-29

PIER

Vol. 92, 209-222, 2009

doi:10.2528/PIER09032704

download: 270

Accuracy Improvement of the Fourier Series Expansion Method for Floquet-Mode Analysis of Photonic Crystal Waveguides

Koki Watanabe and Kiyotoshi Yasumoto

The Fourier series expansion method is a useful tool to approach the problems of discontinuities in optical waveguides, and it applies to analyze the Floquet-modes of photonic crystal waveguides. This paper shows that the Floquet-mode calculation with large truncation order is limited and explains the reason. Furthermore, two techniques of the formulation are presented to relieve this limitation. One of them is a use of the symmetric properties of the Floquet-modes, and another is a use of the Rayleigh quotients to improve accuracy of eigenvalue calculation. They are validated by numerical experiments.

ACCURACY IMPROVEMENT OF THE FOURIER SERIES EXPANSION METHOD FOR FLOQUET-MODE ANALYSIS OF PHOTONIC CRYSTAL WAVEGUIDES

2009-04-28

PIER

Vol. 92, 195-208, 2009

doi:10.2528/PIER09032401

download: 433

A Dual-Band Circularly Polarized Stub Loaded Microstrip Patch Antenna for GPS Applications

Abbas Ali Heidari, Mohammad Heyrani and Mansoor Nakhkash

A single-feed low-profile and easy to fabricate circularly polarized microstrip patch antenna has been developed for GPS applications. For dual frequency operation, four slots are etched near edges of the patch and a crossed slot etched in the center for generating circular polarization. In order to reducing the frequency ratio of two frequency bands of the antenna, the patch is loaded by four short circuit microstrip stubs. The paper reports several simulation results that confirm the desired characteristics of the antenna. Using stub loading, the frequency ratio of two bands of the antenna can be, even, reduced to 1.1.

A DUAL-BAND CIRCULARLY POLARIZED STUB LOADED MICROSTRIP PATCH ANTENNA FOR GPS APPLICATIONS

2009-04-28

PIER

Vol. 92, 181-194, 2009

doi:10.2528/PIER09033105

download: 377

Prediction of Radome Bore-Sight Errors Using a Projected Image of Source Distributions

Haeng-Seon Lee and Haesung Park

In this paper, a calculation method for bore sight error voltages is presented for aperture antennas enclosed in radomes of arbitrary shapes. The method adopts a ray tracing technique frequently used in computer graphics field in constructing two dimensional computer graphics images to obtain a projected image of source distribution, thereby bore sight error voltages and far field radiation patterns are calculated fast and accurately. Besides, the method enables us to use various acceleration schemes used in computer graphics readily. Numerical calculations show that projected source images with a resolution higher than 0.1λ and multiple reflections taken into account produce reliable results. The validity of the method is verified by comparison with results of an analytic solution.

PREDICTION OF RADOME BORE-SIGHT ERRORS USING A PROJECTED IMAGE OF SOURCE DISTRIBUTIONS

2009-04-28

PIER

Vol. 92, 167-180, 2009

doi:10.2528/PIER09040701

download: 411

A Compact X-Band Receiver Front-End Module Based on Low Temperature Co-Fired Ceramic Technology

Zhigang Wang, Ping Li, Rui-Min Xu and Weigan Lin

This letter presents a compact low temperature co-fired ceramic (LTCC) receiver front-end module integrating 9 building blocks. The receiver is a twicefrequency- conversion front-end module with image injection, works at X-band, consists of an X-band embedded image injection band-pass filter (BPF), an L-band multilayer image injection quasi-ellipitc BPF, two monolithic microwave integrated circuit (MMIC) low noise amplifiers (LNAs), two intermediate frequency (IF) amplifiers, two mixers, a IF BPF, and some lumped passive components. All MMICs are mounted into pre-making cavities in the three layers LTCC substrate of the top surface, and the interconnection between MMICs and surface microstrip-line is established by bond wires. A multilayer five-pole Chebyshev interdigital BPF is developed as the first image injection filter, and a four-pole quasi-elliptic BPF composed of stepped-impedance hairpin resonator and miniaturized hairpin resonators that can be coupled through the apertures on the common ground plane is proposed for as the second image injection filter. The developed X-band receiver front-end module is fabricated using twenty layers LTCC dielectric substrate, which has a compact size of 30 × 20 × 20 mm³ (including the metal cavity). The measured receiver gain and noise figure are more than 32 dB and less than 4 dB, respectively. The first and second image injection is better than 28 dB and 40 dB, respectively.

A COMPACT X-BAND RECEIVER FRONT-END MODULE BASED ON LOW TEMPERATURE CO-FIRED CERAMIC TECHNOLOGY

2009-04-22

PIER

Vol. 92, 153-166, 2009

doi:10.2528/PIER09031704

download: 311

Large Phased Arrays Diagnostic via Distributional Approach

Aniello Buonanno, Michele D'Urso, Maurizio Cicolani and Stefano Mosca

A deterministic method for detecting faulty elements in phased arrays is proposed and tested against experimental and numerical data. The solution approach assumes as input the amplitude and phase of the near-field distributions and allows to determine both positions and currents of radiating elements. The corresponding non linear inverse problem is properly solved by exploiting the distributional approach, which allows to cast the initial problem to the solution of a linear one, whose solution is made stable by adopting a proper regularization scheme based on the Truncated Singular Value Decomposition tool. The results fully confirm accuracy of the proposed technique.

LARGE PHASED ARRAYS DIAGNOSTIC VIA DISTRIBUTIONAL APPROACH

2009-04-21

PIER

Vol. 92, 137-151, 2009

doi:10.2528/PIER09031001

download: 267

Equivalent Graphical Solutions of Terminated Conjugately Characteristic-Impedance Transmission Lines with Non-Negative and Corresponding Negative Characteristic Resistances

Danai Torrungrueng and Suthasinee Lamultree

This paper presents the graphical solutions of conjugately characteristic-impedance transmission lines (CCITLs) implemented by periodically loaded lossless transmission lines (TLs), which can exhibit both non-negative (NNCR) and negative characteristic resistances (NCR) with the corresponding propagation constants. The standard T-chart and the extended T-chart are employed to solve CCITL problems with NNCR and NCR cases respectively, depending on the argument of CCITL characteristic impedances. The range of plotting of the standard T-chart and the extended T-chart is always inside or on the unit circle, and always outside or on the unit circle of the voltage reflection coefficient plane, respectively. Two examples of finite periodic TL structures providing both NNCR and NCR cases are given. It is found that both T-charts provide the same input impedance of the corresponding CCITLs as expected, and the standard T-chart is more familiar and easier to deal with.

EQUIVALENT GRAPHICAL SOLUTIONS OF TERMINATED CONJUGATELY CHARACTERISTIC-IMPEDANCE TRANSMISSION LINES WITH NON-NEGATIVE AND CORRESPONDING NEGATIVE CHARACTERISTIC RESISTANCES

2009-04-20

PIER

Vol. 92, 121-136, 2009

doi:10.2528/PIER09030506

download: 347

A Photon Modeling Method for the Characterization of Indoor Optical Wireless Communication

Haeng-Seon Lee

In this paper, an analysis method for optical wave propagation based on photon model is presented for the characterization of optical wireless communication environment. In contrast to radio waves, optical waves have very short wavelengths, so that material properties become important and often cause diffuse reflections. Channel models including diffuse reflections and absorption effects due to material surface textures make conventional electromagnetic wave analysis methods based on ray tracing consume enormous time. To overcome these problems, an analysis method using photon model is presented that approximates light intensity by density of photons. The photon model also ensures that simulation time is within a predictable limit and the accuracy is proportional to the number of total photons used in the simulation.

A PHOTON MODELING METHOD FOR THE CHARACTERIZATION OF INDOOR OPTICAL WIRELESS COMMUNICATION

2009-04-16

PIER

Vol. 92, 103-120, 2009

doi:10.2528/PIER09030904

download: 323

Broadband Measurements of Dielectric Properties of Low-Loss Materials at High Temperatures Using Circular Cavity Method

En Li, Zai-Ping Nie, Gaofeng Guo, Qishao Zhang, Zhongping Li and Fengmei He

We describe a broadband microwave test system that can measure dielectric properties of microwave low-loss materials at high temperatures using circular cavity method. The dielectric constants and loss tangents of samples at different temperatures were calculated from measured shifts of resonant frequencies and unloaded quality factors of the multimode cavity with and without sample. Detailed design and fabrication of the circular cavity capable of working at temperatures up to 1500^οC are discussed. The measurement theory and new calculation method of the radius and length of the cavity at different temperatures are presented. The hardware system was built to measure dielectric properties at wide frequency band from 7 to 18 GHz and over a temperature range from room temperature to 1500^οC. Measurement results of the dielectric properties of quartz samples are given and show a good agreement with the reference values.

BROADBAND MEASUREMENTS OF DIELECTRIC PROPERTIES OF LOW-LOSS MATERIALS AT HIGH TEMPERATURES USING CIRCULAR CAVITY METHOD

2009-04-16

PIER

Vol. 92, 91-102, 2009

doi:10.2528/PIER09030503

download: 280

Directive EM Radiation of a Line Source in the Presence of a Coated PEMC Circular Cylinder

Shakeel Ahmed and Qaisar Naqvi

Electromagnetic scattering of a line source from a perfect electromagnetic conductor (PEMC) circular cylinder coated with double positive (DPS) material or double negative (DNG) material is investigated theoretically. The response of the coated PEMC circular cylinder is observed and it is noted that how the results obtained for this configuration differ from those of a coated perfect electric conductor (PEC) circular cylinder. It is assumed that both the PEMC cylinder and the coating layer are infinite along the cylinder axis. The comparison of directivity of coated PEMC cylinder and coated PEC cylinder is presented.

DIRECTIVE EM RADIATION OF A LINE SOURCE IN THE PRESENCE OF A COATED PEMC CIRCULAR CYLINDER

2009-04-15

PIER

Vol. 92, 79-90, 2009

doi:10.2528/PIER09030302

download: 256

Simulation of Scattered EM Fields from Rotating Cylinder Using Passing Center Swing Back Grids Technique in Two Dimensions

Mingtsu Ho

In this paper, a new numerical technique, passing center swing back grids (PCSBG's) for the resolution of the grid distortion difficulty due to the rotational motion of objects is introduced. This proposed swing-back-grids approach alongside of the method of characteristics (MOC) is developed to solve EM scattering problems featured with rotating objects. The feasibility of such combination is apparent from the fact that MOC defines all field quantities in the centroid of the grid cell. The scattered EM fields from a rotating circular cylinder under the excitation of an EM pulse are predicted in two dimensions and the electric field distributions recorded at several time instances are demonstrated. In order to confirm that the cylinder is rotating and scattering EM fields simultaneously, the circular cylinder is uniformly divided into an even number of slices with one perfect reflector and one non-reflector alternatively since a rotating circular cylinder causes no relativistic effects.

SIMULATION OF SCATTERED EM FIELDS FROM ROTATING CYLINDER USING PASSING CENTER SWING BACK GRIDS TECHNIQUE IN TWO DIMENSIONS

2009-04-15

PIER

Vol. 92, 65-77, 2009

doi:10.2528/PIER09022704

download: 280

Knowledge-Based Support Vector Synthesis of the Microstrip Lines

Nurhan Türker Tokan and Filiz Gunes

In this paper, we proposed an efficient knowledge-based Support Vector Regression Machine (SVRM) method and applied it to the synthesis of the transmission lines for the microwave integrated circuits, with the highest possible accuracy using the fewest accurate data. The technique has integrated advanced concepts of SVM and knowledge-based modeling into a powerful and systematic framework. Thus, synthesis model as fast as the coarse models and at the same time as accurate as the fine models is obtained for the RF/Microwave planar transmission lines. The proposed knowledge-based support vector method is demonstrated by a typical worked example of microstrip line. Success of the method and performance of the resulted synthesis model is presented and compared with ANN results.

KNOWLEDGE-BASED SUPPORT VECTOR SYNTHESIS OF THE MICROSTRIP LINES

2009-04-14

PIER

Vol. 92, 47-64, 2009

doi:10.2528/PIER09030908

download: 304

Signatures of Moving Target in Polar Format Spotlight SAR Image

Xinhua Mao, Dai-Yin Zhu and Zhao-Da Zhu

The synthetic aperture radar (SAR) signatures of moving target are the basis of ground moving target detection and imaging (GMTI&Im). However, previous studies are mainly based on the 2-D separable SAR processing, and little work has been done to investigate the signatures of moving target after the application of a particular fine resolution SAR image formation algorithm. In this paper, the spectrum of moving target after polar format algorithm (PFA) processing is derived. Based on this spectrum, detailed analysis on the SAR signatures of moving target, including the geometric displacement, residual range migration, and the defocusing effect in both range and azimuth dimensions are performed. Simulation results validate the theoretical analysis.

SIGNATURES OF MOVING TARGET IN POLAR FORMAT SPOTLIGHT SAR IMAGE

2009-04-14

PIER

Vol. 92, 33-46, 2009

doi:10.2528/PIER09030906

download: 396

A New Efficient FDTD Time-to-Frequency-Domain Conversion Algorithm

Yan Hui Liu, Qing Huo Liu and Zai-Ping Nie

The time-to-frequency-domain conversion is often required in many applications of the finite-difference time-domain (FDTD) method. This paper presents a new FDTD time-to-frequencydomain conversion algorithm based on the optimization of nonuniform fast Fourier transform (NUFFT) with several redundancy-reduction techniques. The proposed algorithm can perform the FDTD conversion at multiple desired frequencies without the limitation of uniformly spaced frequencies in the fast Fourier transform (FFT). In addition, with a very low storage cost, the algorithm can be much more efficient than other FDTD conversion techniques if a moderate number of frequencies or more are of interest. This algorithm is very useful for some FDTD applications.

A NEW EFFICIENT FDTD TIME-TO-FREQUENCY-DOMAIN CONVERSION ALGORITHM

2009-04-14

PIER

Vol. 92, 17-32, 2009

doi:10.2528/PIER09031606

download: 227

Thickness-Independent Automated Constitutive Parameters Extraction of Thin Solid and Liquid Materials from Waveguide Measurements

Ugur Cem Hasar

The constitutive parameters measurement of thin solid and liquid materials by transmission-reflection methods generally suffers from a) the requirement of the transformation of measured scattering parameters from the reference plane to the end surfaces of the material (measurement plane) and b) inaccurate knowledge on the length of the material, if the material does not fill the entire measurement cell (a waveguide or coaxial-line section). In this research paper, a microwave waveguide method for constitutive parameters determination of these materials is proposed to simultaneously eliminate these problems. There are three main advantages of the proposed method as: a) it explicitly determines the constitutive parameters from measured S-parameters; b) it does not require the knowledge about sample length since it directly measures it as a byproduct of the method; and c) it offers a self-checking feature to trace the performance and accurateness of measurements. This feature does not depend on the constitutive parameters of the sample. We measured the complex permittivity of some thin solid and liquid test samples for validation of the method.

THICKNESS-INDEPENDENT AUTOMATED CONSTITUTIVE PARAMETERS EXTRACTION OF THIN SOLID AND LIQUID MATERIALS FROM WAVEGUIDE MEASUREMENTS

2009-04-14

PIER

Vol. 92, 1-16, 2009

doi:10.2528/PIER09032301

download: 537

Analytical Calculation of Magnetic Field Distribution in Coaxial Magnetic Gears

Linni Jian and Kwok-Tong Chau

Coaxial magnetic gears are a new breed of magnetic devices, which utilize the interaction of permanent magnet fields to enable torque transmission. Apart from using a numerical approach for their magnetic field analysis, an analytical approach is highly desirable since it can provide an insightful knowledge for design and optimization. In this paper, a new analytical approach is proposed to calculate the magnetic field distribution in coaxial magnetic gears. A set of partial differential equations in terms of scalar magnetic potential is used to describe the field behavior, and the solution is determined by considering the boundary constraints. The accuracy of the proposed approach is verified by comparing the field distribution results with those obtained from the finite element method.