Extending the domain of the vector potential in the so-called Hallen's equation, four unknown constants are determined to satisfy the boundary conditions in the same way as the circuit theory, where the vector potential plays the leading role, from which the current density and the current itself are derived. Vanishing of the current density just outside the ends of the antenna is required. For a tube-shaped antenna with walls of infinitesimal thickness, further the current just inside the ends of the antenna should vanish, as a result, the current distribution becomes sinusoidal. Adoption of either the surface current distribution or axial current distribution incurs a crucial effect on the value of the currents calculated from the vector potential. The numerical results of the radiation impedance of a hslf-wave antenna show a tendency of consistency with that relatively newly obtained by employing the exact kernel. The problem on the nonsolvability of Hallen's equation is cleared up. Comments are given on the moment method in relation to the boundary value problems to recommend to add two more undecided constants to Hallen's equation.

Locality in high frequency diffraction is embodied in the Method of Moments (MoM) in view of the method of stationary phase. Local-domain basis functions accompanied with the phase detour, which are not entire domain but are much larger than the segment length in the usual MoM, are newly introduced to enhance the cancellation of mutual coupling over the local-domain; the off-diagonal elements in resultant reaction matrix evanesce rapidly. The Fresnel zone threshold is proposed for simple and effective truncation of the matrix into the sparse band matrix. Numerical examples for the 2-D strip and the 2-D corner reflector demonstrate the feasibility as well as difficulties of the concept; the way mitigating computational load of the MoM in high frequency problems is suggested.

This paper presents a hybrid technique combining the mode-matching method and moment method to analyze various slots cut in the wall of a rectangular waveguide partially filled with a dielectric slab. The waveguide slot structure is decomposed into two parts: a dielectric-loaded waveguide T-junction and an open-ended waveguide radiating into half space. The T-junction is analyzed by the mode-matching method, while the open-ended waveguide is characterized by the moment method with the modal functions in the slot being the full domain basis functions. A new approach for computing multidimensional integrals is proposed in the formulation of the open-ended waveguide, which greatly reduces the computation effort. The T-junction and the open-ended waveguide are then cascaded to obtain the final scattering parameters of the slot structure. Numerical results for different slots on a dielectric-loaded rectangular waveguide calculated by the hybrid method are presented and validated by comparing with measured and simulated data by Ansoft's HFSS. Good agreement is observed for all the cases considered. Parametrical studies are also conducted to examine the effect of the dielectric slab's thickness and relative permittivity on slot antenna's impedance/admittance.

Theoretical analyses are carried out on the height dependence of the antenna factor of an EMI antenna to develop an antenna calibration method that can provide the free-space value of the antenna factor. It is found that the antenna factor in general varies with the antenna height in a quasi-periodic way with a period of about λ/2. Thus, the present paper proposes to take an average of the antenna factors over a height range of about λ/2 to obtain an accurate estimate of the free-space antenna factor. Effective antenna arrangements are also proposed for the antenna calibration. Deviations in the estimate from the free-space antenna factor are less than 0.1 dB for tuned dipoles in the frequency range above 50 MHz. But the errors increase up to 0.3 dB at about 35 MHz. For broadband antennas, the free-space antenna factor can be accurately estimated by taking the average of the antenna factors. Errors are estimated to be less than 0.3 dB in the frequency range from 30 MHz to 1000 MHz.

In many electromagnetic field problems, matrix equations were always deduced from using the method of moment. Among these matrix equations, some of them might require a large amount of computer memory storage which made them unrealistic to be solved on a personal computer. Virtually, these matrices might be too large to be solved efficiently. A fast algorithm based on a Toeplitz matrix solution was developed for solving a bordered Toeplitz matrix equation arising in electromagnetic problems applications. The developed matrix solution method can be applied to solve some electromagnetic problems having very large-scale matrices, which are deduced from the moment method procedure. In this paper, a study of a computationally efficient order-recursive algorithm for solving the linear electromagnetic problems [Z]I = V, where [Z] is a Toeplitz matrix, was presented. Upon the described Toeplitz matrix algorithm, this paper derives an efficient recursive algorithm for solving a bordered Toeplitz matrix with the matrix's major portion in the form of a Toeplitz matrix. This algorithm has remarkable advantages in reducing both the number of arithmetic operations and memory storage.

This paper presents an analysis of electrically large antennas using the adaptive integral method (AIM). The arbitrarily shaped perfectly conducting surfaces are modeled using triangular patches and the associated electric field integral equation (EFIE) is solved for computing the radiation patterns of these antennas. The method of moments (MoM) is used to discretize the integral equations and the resultant matrix system will be solved by an iterative solver. The AIM is employed in the iterative solver to speed up the matrix-vector multiplication and to reduce the memory requirement. As specific applications, radiation patterns of parabolic reflectors and X-band horns are computed using the proposed method.

A method is proposed to compute moments of distributed coupled RLC interconnects. Both uniform line models and non-uniform line models will be developed. Considering both self inductances and mutual inductances in multi-conductors, recursive moment computations formulae of lumped coupled RLC interconnects are extended to those of distributed coupled RLC interconnects. By using the moment computation technique in conjunction with the projection-based order reduction method, the inductive crosstalk noise waveform can be accurately and efficiently estimated. Fundamental developments of the proposed approach will be described. Simulation results demonstrate the improved accuracy of the proposed method over the traditional lumped methods.

There have been significant advances in computational electromagnetics (CEM) in the last decade for a variety of antennas and propagation problems. Improvements in single frequency techniques including the finite element method (FEM), the fast mulitipole moment (FMM) method, and the method of moments (MoM) have led to significant simulation capabilities on basic computing platforms. Similar advances have occurred with time domain methods including finite difference time domain (FDTD) methods, time domain integral equation (TDIE) methods, and time domain finite element (TD-FEM) methods. Very complex radiating and scattering structures in the presence of complex materials have been modeled with many of these approaches. Many commercial products have been made available through the efforts of many individuals. The CEM simulators have enabled virtual EM test ranges that have led to dramatic improvements in our understanding of antennas and propagation in complex environments and to the realization of many of their important applications.

This paper proposes an enhanced RBF network that enhances learning algorithms between input layer and middle layer and between middle layer and output layer individually for improving the efficiency of learning. The proposed network applies ART2 network as the learning structure between input layer and middle layer. And the auto-tuning method of learning rate and momentum is proposed and applied to learning between middle layer and output layer, which arbitrates learning rate and momentum dynamically by using the fuzzy control system for the arbitration of the connected weight between middle layer and output layer. The experiment for the classification of number patterns extracted from the citizen registration card shows that compared with conventional networks such as delta-bar-delta algorithm and the ART2-based RBF network, the proposed method achieves the improvement of performance in terms of learning speed and convergence.

Convergence of the iterative method based on the successive overrelaxation (SOR) method is investigated to solve the matrix equation in the moment analysis of array antennas. It is found this method can be applied to the sub domain method of moments with fast convergence if the grouping technique is applied and the over-relaxation parameter is properly selected, and the computation time for solving the matrix equation can be reduced to be almost proportional to the second power of the number of unknowns.

The theory of the method of moments (MoM), which has been widely used as a numerical technique for analyzing the characteristics of antennas and scatterers, is described. First, the steps of MoM to solve integral equations for conducting wires and planes are presented. It is pointed out that MoM combined with Galerkin's method yields highly accurate results. The importance of ensuring the continuity condition of current on conducting bodies is emphasized and numerical examples for a conducting structure involving junctions of wire segments and planar segments are presented. Finally, MoM for dielectric scatterers including recent developments is described.

A waveguide crossed-slot linear array with a matching element is accurately analyzed and designed by the method of moments using numerical-eigenmode basis functions developed by the authors. The rounded ends of crossed-slots are accurately modeled in the analysis. The initial values of the slot parameters determined by a model with assumption of periodicity of field are modified and refined by the full-wave finite-array analysis for uniform excitation and small axial ratio. As an example, an 8-element linear array is designed at 11.85 GHz, which radiates a circularly polarized wave at a beam-tilting angle of 50 degrees. The radiation pattern, the frequency characteristics of the reflection and the axial ratio are compared between the analysis and the measurement and they agree very well. The calculated and measured axial ratio at the beam direction are 0.1 dB and 1.7 dB, respectively. This method provides a basic and powerful design tool for slotted waveguide arrays.

Recently Azou et al. proposed a method of model reduction for discrete systems based on a new impulse response Gramian. The reduced model was derived by first approximating the low-order impulse response Gramian, and then matching some Markov parameters and time-moments of an original model. In this note a modified method is presented so that the reduced model exactly preserves the low-order impulse response Gramian together with a slightly different set of Markov parameters and time-moments of the original model.

A new moment computation technique for general lumped R(L)C interconnect circuits with multiple resistor loops is proposed. Using the concept of tearing, a lumped R(L)C network can be partitioned into a spanning tree and several resistor links. The contributions of network moments from each tree and the corresponding links can be determined independently. By combining the conventional moment computation algorithms and the reduced ordered binary decision diagram (ROBDD), the proposed method can compute system moments efficiently. Experimental results have demonstrate that the proposed method can indeed obtain accurate moments and is more efficient than the conventional approach.

A new hybrid formulation has been derived for analyzing biological electromagnetic compatibility (Bio-EMC) problems by combining the frequency-domain Method of Moments (MoM) and the Finite-Difference Time-Domain (FDTD) method. This hybrid form is different from, and more direct than, the method previously proposed by Mangoud et al. Some numerical examples are given for the human head exposure field due to a half wavelength dipole and a one-wavelength loop antenna. Our iterative method is found to have fast convergence. In addition, our method works well for cases when the radiation antenna wires are not aligned with the FDTD lattice.

A round-ended wide straight slot cut in the broad wall of a rectangular waveguide is analyzed by the Method of Moments (MoM) using numerical eigenmode basis functions derived by the edge-based finite element method (FEM), referred to as MoM/FEM. The frequency characteristics of the calculated transmission coefficients are compared with the measured ones, and good agreement is observed for a wide variety of antenna parameters. For simpler analysis that does not use MoM/FEM, an equivalent rectangular slot approximation for a round-ended slot is discussed. The resonant frequencies of empirically introduced "equal-area" and "equal-perimeter" slots are compared with those of round-ended slots for a wide variety of parameters such as slot width, wall thickness and dielectric constant inside the waveguide. Based upon MoM/FEM, which can be a reliable reference, it is found that the equal-area slot always gives a better approximation of the order of 1% over that of the equal-perimeter one which is of the order of 5%. For higher accuracy, a new rectangular slot approximation of a round-ended slot is proposed to be a linear combination of equal-area and equal perimeter approximation. The error is around 0.25% for a wide variety of parameters such as slot width-to-length ratio, wall thickness and dielectric constant of the filling material inside the waveguide.

In the process of visual servoing, images are often blurred when the camera is moving. To solve this problem, a visual servoing system is proposed based on image moments of a planar target. According to image moment errors, the system can drive a camera to approach a static target with a 3D translational velocity. In this paper, it was proved that 0- and 1-order image moments are not only image's blur invariants, but also include the information of a target's position relative to the camera. Besides, the state equation of a moving image was deduced, based on which the control structure and an adaptive control strategy of our visual servoing system were designed. At last, some simulation results were presented to demonstrate the validity of the system.

There has recently been considerable interest in research on wearable non-grounded force display. However, there have been no developments for the communication of nonverbal information (ex. tennis and golf swing). We propose a small and lightweight wearable force display to present motion timing and direction. The display outputs a torque using rotational moment and mechanical brakes. We explain the principle of this device, and describe an actual measurement of the torque and torque sensitivity experiments.

A hybrid method-of-moments (MoM) and immittance approach for efficient and accurate analysis of printed slots and strips of arbitrary shape in layered waveguide for various applications has been proposed. An impedance-type MoM is formulated from the electric field integral equation (EFIE) for printed strip case and an admittance-type MoM is formulated from the magnetic field integral equation (MFIE) for the printed slot case, using the Galerkin's technique. Immittance approach has been used to calculate spectral dyadic Green's functions for the layered waveguide. For efficient analysis of large and complex structures, equivalent circuit parameters of a block are first extracted and complete structure is analyzed through cascaded ABCD matrices. The equivalent circuit characterization of printed strip and slot in layered waveguide has been done for the first time. Finite periodic structure loaded with printed strips has been investigated and it shows the electromagnetic bandgap (EBG) behavior. The electromagnetic (EM) program hence developed is checked for its numerical accuracy and efficiency with results generated with High-frequency structure simulator (HFSS) and shows good performance.

Finite-ground microstrip line (FGMSL) open-end discontinuities are characterized via a self-calibrated method of moments (MoM) as a unified circuit model with a fringing capacitance and radiation conductance. By integrating the short-open calibration (SOC) procedure into a determinant MoM, the model parameters are extracted without needing the alternative port impedance. Regardless of non-ideal voltage sources, extracted parameters are observed to achieve a stable convergence as the feeding line is sufficiently extended. After extracted capacitance of a FGMSL open-end with equal strip and finite-ground widths are validated against its traditional MSL counterpart with infinite ground, extensive results are given to originally demonstrate that the capacitance increases as a decelerated function of the finite-ground width and length while the conductance is negligibly small as compared with its imaginary part.