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In this paper, a same-sense circularly polarized grid-slotted patch antenna with wide axial ratio bandwidth is proposed. The rectangular grid-slotted patch on top and bottom planes are excited through flipped Z-shaped slots pair using a stripline feed to generate same-sense circular polarization with wider axial ratio bandwidth. Characteristic mode analysis is used in the design of the antenna to analyze the desired orthogonal modes. Variations of the resonant frequencies, axial ratio bandwidths and local minimas with the design parameters are discussed. The antenna has a 3 dB axial ratio bandwidth of about 21% from 4.07 GHz to 5.02 GHz, with the realized gain ranging from 2 to 3.5 dBic.

A leapfrog scheme for the unconditionally stable complying-divergence implicit (CDI) finite-difference time-domain (FDTD) method is presented. The leapfrog CDI-FDTD method is formulated to comprise distinctive implicit and explicit update procedures. The implicit update procedures are in the fundamental form with operator-free right-hand sides (RHS), whereas the explicit ones are compatible and correspond to the familiar explicit FDTD method. Using the Fourier (von Neumann) approach, the stability of the leapfrog CDI-FDTD method is analyzed. The eigenvalues of amplification matrix are obtained to prove the unconditional stability. Furthermore, the leapfrog alternating direction implicit (ADI) FDTD and CDI-FDTD methods are discussed and compared, including the RHS floating-point operations (flops) count, for-loops and memory. The leapfrog CDI-FDTD requires merely half the flops of leapfrog ADI-FDTD at RHS while retaining the same left-hand sides (LHS) of implicit update equations and the same number of for-loops without much extra memory. Discussions and numerical results are presented to demonstrate the advantages of leapfrog CDI-FDTD method including unconditional stability, complying divergence, and efficient leapfrog scheme with reduced RHS flops.

A multiple locally 1-D (MLOD) finite-difference time-domain (FDTD) method for inhomogeneous coupled transmission lines and stability analyses are presented. The method is aptly called the MLOD coupled line (CL)-FDTD method. Various split matrices are proposed, and the corresponding update equations are formulated and discussed. All the proposed split matrices yield implicit electric field update equations with tridiagonal or block tridiagonal matrices on the left-hand sides. For more efficiency, the block tridiagonal matrices for implicit electric field may be reformulated and replaced with tridiagonal matrices for implicit magnetic field. The stability analysis is first performed using the von Neumann method in the Fourier domain. It is shown that the von Neumann method alone may not be sufficient to ascertain stability for inhomogeneous media. To include media inhomogeneity, the two-media reduced-matrix stability analysis is proposed. It allows us to efficiently analyze the key stability characteristics in inhomogeneous media and is useful for quick detection of any potential instability that is not apparent via the von Neumann method. The stability characteristics with variation of media parameters are also investigated and discussed. The numerical results are provided to validate the stability and accuracy of the proposed MLOD CL-FDTD method with various split matrices. Accepted version

This article presents the multiple locally one-dimensional (MLOD) finite-difference time-domain (FDTD) method for multiconductor coupled transmission lines. The method is aptly referred to as the MLOD coupled line (CL)-FDTD method, applicable for general asymmetrical multiconductor lines. The differential equations for multiconductor coupled transmission lines are expressed into general compact matrix form and the appropriate set of split matrices are proposed. Utilizing the proposed split matrices, the update procedures and equations of the MLOD CL-FDTD method are provided for general multiconductor lines. The update procedures comprise number of substeps depending on the number of conductor lines while the left-hand side of the implicit update equation constitutes a tridiagonal matrix that can be solved efficiently. The stability analysis is performed using the von Neumann method in the Fourier domain, as well as the two-media reduced-matrix method in the spatial domain for inhomogeneous media. It is found that our proposed method remains stable beyond the Courant time step. Numerical examples demonstrate that the MLOD CL-FDTD method is able to efficiently simulate time domain fields of multiconductor coupled transmission lines at time step larger than the Courant stability limit while maintaining good accuracy.

This article presents the multiple one-dimensional (M1-D) fundamental alternating direction implicit (FADI) finite-difference time-domain (FDTD) method for coupled transmission lines on mobile devices. The method is aptly called the M1-D FADI coupled line (CL)-FDTD method. It is based on the fundamental implicit scheme, which features matrix-operator-free right-hand sides (RHS). The formulations of the M1-D FADI CL-FDTD method and update equations are provided. Various sets of split matrices, including those with self-symmetry, mutual symmetry, and self-mutual separation, are proposed and discussed. Their stability analyses are performed using the Fourier amplification matrix formulated in fundamental form, which is simpler with only one inverse term each without RHS operator. It is found that the sets of split matrices with self-symmetry are unconditionally stable, while those with mutual symmetry and self-mutual separation are not. Using two auxiliary quadratic polynomials along with single necessary and sufficient condition, the analytical proof of unconditional stability is made more convenient and concise. The efficiency of both stable sets of split matrices with self-symmetry is discussed based on the number of RHS terms and floating-point operations count. Numerical results are presented to validate the accuracy of the proposed method at time step larger than the stability limit. Several electromagnetic (EM) simulations of coupled line structures are demonstrated on mobile devices. The CPU time incurred on various platforms is provided for the M1-D FADI CL-FDTD method using both sets of split matrices with self-symmetry. Using mobile devices, the EM simulations can be performed efficiently and ubiquitously anytime, anywhere. MOE (Min. of Education, S’pore) Accepted version

In this article, the notion of teaching and learning electromagnetic (EM) plane wave reflection and transmission using 3D TV is presented. The necessary equipment setup for 3D TV demonstration in a classroom setting is described. The contents of 3D TV, comprising left and right images, are generated in real time by a program on a notebook PC. Projected onto the 3D TV screen, these images combine appropriately to enable stereoscopic view through the use of 3D glasses.

This paper presents the comparison of vector fitting and contour integration methods for pole-zero analysis of microwave filters. Two cases of microwave filters are considered, which include an all-pole classical coupled line filter and a linear phase filter with complex zeros. The poles and zeros obtained using vector fitting method with different chosen number of poles and fitting bandwidth are analyzed. It is found that the poles and zeros may be inconsistent depending on the chosen number of poles and bandwidth. Furthermore, the method may introduce spurious complex zeros that do not satisfy the S parameters unitary conditions, while the poles also do not maintain periodicity between frequency bands for transmission line structures. On the other hand, the poles and zeros obtained using contour integration method are consistent and certain. They also satisfy the unitary conditions and periodicity for transmission line structures.

This paper presents demonstration of electromagnetic (EM) plane wave reflection and transmission on iPad. Based on input by the user, various output parameters related to EM plane wave reflection and transmission are calculated and displayed in real time. Most importantly, the animations of the time domain incident, reflected and transmission waves are shown by the app. The features of the app are demonstrated using several examples, including reflection and transmission in double negative medium. Hence, the app is useful not only for students, but also researchers alike to help them better understand EM plane wave reflection and transmission in various media through visualization.

In this paper, a dual-band omnidirectional planar microstrip antennas are designed using Gielis curves. Gielis curve profiles are used to create antenna prototypes with different patch section lengths to obtain a dual-band. The antenna characteristics of the antenna such as return loss, realized gain and radiation pattern are simulated and are compared with the measured results of the fabricated prototype. The designed antennas have a peak realized gain varying between 1 dB about 4 dB over the two bands.

In this article, we present mobile teaching and learning of coupled-line structures using the multiple-1D coupled-line finite-difference time-domain (M1D CL-FDTD) method. The formulation of the M1D CL-FDTD method applicable for CL structures is provided. The method bypasses the more computationally intensive full-wave 3D method, and it is well suited for implementation on mobile devices. Several mobile apps are developed to provide interactive visualization of electromagnetic (EM) wave propagation in CL structures. These visualizations allow the underlying resonating and coupling mechanisms to be elucidated clearly and improve students' understanding of CL theories. Mobile teaching and learning of various CL structures, including coupled transmission lines, CL bandpass filters, directional couplers, and branch-line couplers, are demonstrated and discussed. Ministry of Education (MOE) Accepted version We gratefully acknowledge the support from the Singapore Ministry of Education Tertiary Education Research Fund (MOE TRF 2015-1-TR15).

This paper presents the application of Belevitch theorem for pole-zero analysis of microwave filters synthesized with transmission lines and lumped elements. The scattering (S) matrix determinant (Δ) based on the Belevitch theorem, aptly called Belevitch determinant, comprises poles and zeros that are separated in different half-plane regions. Using the Belevitch determinant, the poles and zeros of filter transfer functions can be determined separately with certainty, e.g., by applying the contour integration method based on argument principle. Note that the contour integration can be evaluated numerically without requiring complicated overall analytical expressions. The proposed method is able to solve the poles and zeros for filters synthesized with noncommensurate transmission lines and lumped elements, where the transform method and the eigenvalue approach are inapplicable. Several applications are discussed to demonstrate the use of Belevitch theorem and the contour integration method to determine the poles and zeros of various microwave filters on the complex plane. MOE (Min. of Education, S’pore) Accepted version

The wide avai lability of smart handheld and mobile devices has provided educators with another opportunity to aid the teaching of electromagnetics (EM) courses with touchbased interactivity, allowing seamless teaching and learning. This article explores how mobile devices may be used to enhance students' grasp of EM polarization concepts through a special app designed to provide interactive visualization. It also helps instructors to effectively illustrate many wave polarization topics through various interactive features. By using the app, various polarizations can be better explained with two-dimensional (2-D) and three-dimensional (3-D) animations. Users are allowed to input various wave parameters to see, in real time, how they change the polarization ellipse and/or handedness. MOE (Min. of Education, S’pore) Accepted version

This paper presents a novel non-uniform time-step (NUTS) fundamental locally one-dimensional (FLOD) finite-difference time-domain (FDTD) method for multiconductor transmission lines (MTLs) including lumped elements. The NUTS scheme adopts different (non-uniform) time steps for different periods during simulation, in order to reduce the large errors caused by unconditionally stable FDTD methods with uniform time step larger than Courant-Friedrichs-Lewy limit. It is found that NUTS scheme is potentially unstable for alternating-direction-implicit (ADI) FDTD method, but it is stable for LOD-FDTD method or its implementation based on fundamental (FLOD) scheme. The NUTS FLOD-FDTD method is useful to simulate MTLs with lumped elements including resistor, capacitor, and inductor in series and parallel connections. Moreover, the method based on multiple 1-D approach is also extended to incorporate lumped elements in cross connection to model near-field coupling between the MTLs. While the electric current density is commonly used for field-circuit coupling of parallel connected lumped elements, the magnetic current density will be utilized for field-circuit coupling of series and cross-connected lumped elements. Numerical results for MTLs with lumped elements in series, parallel, and cross connections are provided to show the trade-off between efficiency and accuracy of the proposed NUTS FLOD-FDTD method. Compared with the FLOD-FDTD method with uniform time step, the NUTS FLOD-FDTD method may achieve higher accuracy by using smaller time step for certain periods of simulation.

This paper presents the interconnected multi-1-D (IM1-D) fundamental alternating-direction-implicit finite-difference time-domain (FADI-FDTD) and fundamental locally 1-D finite-difference time-domain (FLOD-FDTD) methods for transmission lines with interjunctions. The proposed methods are unconditionally stable and capable of treating multiple main transmission lines and stubs interconnected at various interjunctions using time step larger than Courant–Friedrichs–Lewy limit. Fundamental scheme-based IM1-D FADI- and FLOD-FDTD methods are derived to enhance the efficiency with matrix-operator-free right-hand sides. The methods involve one-step update procedure optimized for simulation of main transmission lines and stubs on mobile device. Using proper treatments at the interjunctions for various interconnection conditions, the electromagnetic fields in all interconnected main transmission lines and stubs can be updated cooperatively and efficiently to solve practical problems. A microstrip line loaded with stubs and a branch-line coupler are simulated to show the accuracy and efficiency of the proposed methods. To extend the applicability for handling the couplings between two transmission lines via gaps, a microstrip circuit with gaps is simulated using the proposed methods incorporated with equivalent circuit models involving capacitances. Real-time simulations of these numerical examples provide much intuitional insight for one to observe the electromagnetic waves propagation in time domain on computer or mobile device.

This paper presents the stability analyses of nonuniform time-step (NUTS) locally one-dimensional finite-difference time-domain (LOD-FDTD) methods for electromagnetic (EM) and thermal simulations. The overall (spatial domain) transition matrix for the whole 3-D computational domain is considered for NUTS, which takes into consideration general inhomogeneous and lossy media. Rigorous stability analyses of NUTS LOD-FDTD methods are provided for both EM and thermal simulations. The analytical proofs of unconditional stability are performed through careful assertion of respective matrix definiteness, along with spectral radius and induced matrix norm analyses. Proper transformations and manipulations are carried out differently for EM and thermal analyses to suit different matrix properties. In each analysis, the fundamental form of the transition matrix is utilized with only one main inverse term, which results in much simpler and concise analysis. It is shown that the NUTS LOD-FDTD methods are unconditionally stable for both EM and thermal simulations. Accepted version

In this paper, a bidirectional linearly polarized grid-slotted patch antenna with Gielis-shaped patch is presented. A coplanar waveguide (CPW) fed slot is used to excite two metasurface layers with Gielis-shaped patch for bi-directional radiation and to reduce the lower cut-off frequency by 4%. The modal significance of the patches are discussed and a prototype with Gielis-shaped patch is fabricated. The simulated and measured antenna characteristics are compared.

This paper presents the simulation of coupled transmission lines on mobile devices using multiple one-dimensional coupled line finite-difference time-domain (M1-D CL-FDTD) methods. The update equations for the M1-D explicit CL-FDTD and the unconditionally stable M1-D alternating direction implicit (ADI) CL-FDTD methods are presented. The methods are well suited to be implemented on mobile devices which may have limited computing resources. This enables EM simulations to be performed anytime, anywhere. The visualization of EM wave propagation along coupled transmission lines on mobile devices is demonstrated.

In this paper, a three-dimensional bandstop frequency-selective structure (FSS) based on Gielis-shaped loop resonator is proposed. A Gielis shape profile for the full and half loop resonator provides a reduction in operating frequency by around 10% compared to a circular profile for a fixed unit cell size. S parameters of an equivalent circuit model for the half Gielis loop unit cell is also discussed.

In this paper, periodic leaky-wave antenna with modified Gielis-shaped patch elements are proposed. Modified Gielis curve profiles are used for the patch elements to enhance the operating bandwidth of the leaky wave antenna. The antenna has an operating bandwidth from around 4 GHz to 8.5 GHz and its characteristics such as return loss, insertion loss, realized gain and radiation pattern are simulated and are compared with the measured results of the fabricated prototype.

This paper presents the numerical stability analysis of multiple one-dimensional locally one-dimensional finite-difference time-domain (M1-D LOD-FDTD) method for inhomogeneous coupled transmission lines. The stability analysis is first performed using the von Neumann method based on Fourier amplification matrix for homogeneous coupled transmission lines. The transition matrix for whole computational domain is next analyzed, which takes into consideration inhomogeneous media. While the M1-D LOD-FDTD method for homogeneous coupled transmission lines is stable based on the von Neumann method, the eigenvalues of transition matrix for inhomogeneous coupled transmission lines may indicate instability. Results show that the stability analysis based on von Neumann Fourier modes alone may not be sufficient to prove stability as it generally assumes homogeneous media.

This paper presents the source-incorporated multiple one-dimensional (M1-D) fundamental alternating direction implicit finite-difference time-domain (FADI-FDTD) method for coupled transmission lines. The update procedures and equations of M1-D FADI-FDTD method including source implementation are formulated based on the fundamental scheme. The scheme features matrix-operator free right-hand sides (RHS) with reduced arithmetic operations and memory indexing. Unlike the conventional stability analysis, the amplification matrix is also derived in the simple fundamental form without RHS matrix operators. It is shown that the M1-D FADI-FDTD method is stable even with time step size larger than that of the stability limit for explicit scheme. Numerical results are presented to validate the proposed method.

This paper presents the numerical stability analysis of multiple one dimensional alternating direction implicit finite-difference time-domain (M1-D ADI-FDTD) method for coupled transmission lines. Two ways of splitting the operator matrices are attempted for the M1-D ADI-FDTD method. It is shown that the direct way of splitting based on self-mutual separation will reduce naturally to the equations for uncoupled transmission lines when the mutual terms are omitted. They also lead to update equations with left-hand sides involving tridiagonal matrices which can be solved efficiently. However, using the split matrices based on self-mutual separation, the resultant M1-D ADI-FDTD method for coupled transmission lines is not unconditionally stable. This is demonstrated through numerical stability analysis based on von Neumann method. Meanwhile, the proposed alternative way of splitting will also lead to update equations with left-hand sides involving tridiagonal matrices. Further numerical stability analysis is complemented to show that the proposed method is capable of treating coupled transmission lines using time step larger than the Courant-Friedrichs-Lewy (CFL) limit.