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The recently proposed theory of Maxwellian circuits is demonstrated for applications to linear wire scatterers as well as to linear antennas. It is shown that for each integral equation of thin wire type, there exist coupled linear ordinary differential equations of currents and voltages, the solutions of which are identical to the integral equation, if the same boundary conditions of the integral equation are applied. The subsequence is that the coupled differential equations can be interpreted as equivalent circuit of new type named Maxwellian circuit. The equivalent circuit can provide physical insights to design engineers and computational advantages for broadband calculations. The highlight of this paper is to show both theoretically and numerically that the Maxwellian circuit components depend only on the geometry of the problem, not on the excitation or boundary conditions at the terminals. Index Terms--Generalized transmission line equation, Maxwellian circuits, method of moments (MoM), wire antennas and scatterers.

The main idea of Maxwellian circuits is that any wire structure, such as a thin wire antenna or a microstrip structure, can be represented by equivalent distributed circuits, the solution of which is identical to the solution of Maxwell's equations of that structure. Such circuits are said to be Maxwellian [1]. In this paper, the Maxwellian circuits are implemented into a curved structure, i.e., spiral antennas. Since a spiral antenna has much stronger dispersion and mutual couplings than a straight antenna, the most challenging thing for the spiral antenna is how to realize the broadband equivalent circuits. Numerical results for the two-arm Archimedian spiral antenna show that the solutions of its Maxwellian circuits over a quite wide frequency band are the same as those obtained by the conventional integral equations, but solving the circuits represented by the differential equations is much more efficient than solving the integral equations. Index Terms--Maxwellian circuits, method of moments (MOM), spiral antennas.

Fun impedance matrices of the method of moments (MoM) type have been decomposed into sparse matrices in the application of on-surface measured equation of invariance (OSMEI) [1], [2]. The objectives in [1] and [2] are to find continuous current distributions on scatterers. Thus, the concept of metron and measure is justified under the postulate that the local relation between fields and current densities is an invariant of the excitation. In this paper, we have extended the concept to dipole arrays, where the objective is to find the discrete driving point currents. Numerical results show that using the windowed metrons presented in this paper, the sparsity rate of the sparse matrices can be kept within 1%, while the E- and H-plane patterns are still in good agreement with the MoM results except for the farthest side lobes of the H-plane patterns. Index Terms--Antenna, matrix decomposition, measured equation of invariance.

Frequency band and coupling loss are the two important parameters of leaky coaxial cables with periodic slots, frequency band can be predicted by analyzing the arrangement of the slots on the outer shield of the cable, but the coupling loss is not so easy to determine by classical methods. In this paper, the finite-difference time-domain (FDTD) method is used to calculate the electric field distribution in the slot cut in the outer conductor of the coaxial cable. The dyadic Green's Function is then used to calculate the radiation field of the equivalent surface magnetic current densities. By these two methods, the coupling losses of the leaky coaxial cables with different periods, sizes and shapes of the slots can be accurately obtained. Some results in this paper were verified by the experimental results of the leaky coaxial cables designed for railway mobile communications with a frequency band of 100-500 MHz. Index Terms--Dyadic Green's function, finite-difference time-domain (FDTD) method, leaky coaxial cables, leaky wave antenna, periodic structure, slot array.

In this paper, the formulas of on-surface measured equation of invariance (OSMEI) for wire antennas are derived. The unknowns of each node on the antenna surface are expressed by the vector potential function and surface current density. The unknowns in the vicinity of each node are coupled in a linear equation and the coefficients of the linear equation are determined by the measured equation of invariance (MEI) method. The final impedance matrix obtained by the OSMEI is a highly sparse matrix. It demonstrates that the currents on thin wire antennas may also be solved by a differential equation-based formulation in addition to the conventional integral equations. Index Terms: Absorbing boundary conditions, wire antennas.

Using the conventional method of moment (MOM) calculations, a cylinder of circumferential dimension of 100 wavelengths is considered to be large. Using the measured equation of invariance (MEI) approach, a cylinder of 10000 wavelengths is within the storage capacity and numerical tolerance of a workstation. Although, the MEI has greatly reduced the storage and solution time of the matrix, its overhead to generate the matrix elements is about the same order as that of the MoM. When the target is very large, that overhead can be very time consuming. This paper presents an interpolation and extrapolation technique such that the boundary equations of MEI for high frequencies may be predicted from those of low frequencies. It is demonstrated that in the optical limit the same set of coefficients may be used for all frequencies, which is consistent with the concept of geometric optics where the same rule is applied to all frequencies. Index Terms - Computational time, electromagnetic scattering.

The measured equation of invariance (MEI) is a newly developed computational method which allows finite-difference (FD) or finite-element (FE) mesh to be terminated very closely to objects of interest [1]. In this paper, the authors show how the MEI method may be applied to microstrip antennas and discontinuity problems. The authors demonstrate its use in general full-wave three-dimensional (3-D) microstrip problems, and give results for open-ended microstrip lines and microstrip bends. Sufficient details are included so that a well-versed reader may reproduce the authors' results with much less effort.

Numerical computations of frequency domain field problems or elliptical partial differential equations may be based on differential equations or integral equations. The new concept of field computation presented in this paper is based on the postulate of the existence of linear equations of the discretized nodal values of the fields, different from the conventional equations, but leading to the same solutions. The postulated equations are local and invariant to excitation. It is shown how the equations can be determined by a sequence of 'measures.' The measured equations are particularly useful at the mesh boundary, where the finite difference methods fail. The measured equations do not assume the physical condition of absorption, so they are also applicable to concave boundaries. Using the measured equations, we can terminate the finite difference mesh very close to the physical boundary and still obtain robust solutions. It will definitely make a great impact on the way we apply finite difference and finite element methods in many problems. Computational results using the measured equations of invariance in two and three dimensions are presented.

Since the finite-difference time-domain method was proposed for the solution of Maxwell's equations, various absorbing boundary conditions have been developed to simulate the infinite large space with a finite computation domain. In this paper, we propose a novel technique, which we call 'superabsorption,' to improve absorbing boundary conditions. This method can be applied to every known absorbing boundary condition and yield dramatic reduction on the numerical error caused by the boundary reflection. The principle and analysis of the superabsorption method are presented. Numerical tests are made indicating the improvements on many absorbing boundary conditions by using this technique.

In this paper, a novel fast iteration technique is proposed. The technique is based on the interaction between the matrix decomposition by the measured equation of invariance (MDMEI) and method of moments (MoM). This technique can be used in accelerating MoM iteration process. The numerical example for the scattering of two-dimensional perfect conducting rectangular cylinders with the circumference up to 96 wavelengths shows that the computation speed can be speeded up by 2.5 times. Index Terms--Electromagnetic scattering, matrix decomposition, measured equation of invariance, method of moments.

A study was conducted to analyze the use of discrete periodic wavelengths to measured equation of invariance (MEI) and show that the resolutions of the MEI coefficients are enhanced at high-frequency computations or at geometric extremities. The MEI was utilized at a mesh boundary to determine the terminating equations. Results indicated that the fast discrete period wavelets can support the needed resolution to overcome problems associated with sinusoidal functions.

The domain-decomposed measured equation of invariance (DDMEI) method is proposed for field computation in single and multiple regions. The whole computing domain is partitioned into a cluster of subdomains. For single region problems, this partition splits the computing domain into many subdomains artificially. For multiple regions problems, these subdomains can be taken as those regions separated geometrically. The contribution of sources residing in a subdomain is approximated by a set of sources selected out of these original sources with greatly reduced amounts. The approximation is implemented numerically by the MEI method. The resultant MEI matrices are blocked matrices and each submatrix is highly sparse. Approaches and numerical results are given respectively for the applications of the DDMEI to the scattering of single conducting cylinders, radiation of wire arrays, and capacitance matrix computation for multiconductor transmission lines. The DDMEI proposed in this paper is an improved version of the surface current MEI method (SCMEI). Compared with the SCMEI, the DDMEI improves the sparsity of the MEI matrices and the feasibility of measuring out the MEI coefficients. Furthermore, the DDMEI makes it possible to apply the kind of on-surface MEI methods (OSMEI) to multiple region problems for the first time. Index Terms--Electromagnetic scattering, multiconductor transmission lines, wire arrays.

The main idea of Maxwellian circuits is that any wire structure, such as a thin wire antenna or a microstrip structure, can be represented by equivalent distributed circuits, the solution of which is identical to the solution of Maxwell's equations of that structure. Such circuits are said to be Maxwellian [1]. In this paper, the Maxwellian circuits are implemented into a curved structure, i.e., spiral antennas. Since a spiral antenna has much stronger dispersion and mutual couplings than a straight antenna, the most challenging thing for the spiral antenna is how to realize the broadband equivalent circuits. Numerical results for the two-arm Archimedian spiral antenna show that the solutions of its Maxwellian circuits over a quite wide frequency band are the same as those obtained by the conventional integral equations, but solving the circuits represented by the differential equations is much more efficient than solving the integral equations. [ABSTRACT FROM AUTHOR]

Full impedance matrices of the method of moments (MoM) type have been decomposed into sparse matrices in the application of on-surface measured equation of invariance (OSMEI) [1], [2]. The objectives in [1] and [2] are to find continuous current distributions on scatterers. Thus, the concept of metron and measure is justified under the postulate that the local, relation between fields and current densities is an invariant of the excitation. In this paper, we have extended the concept to dipole arrays, where the objective is to find the discrete driving point currents. Numerical results show that using that windowed metrons presented in this paper, the sparsity rate of the sparse matrices can be kept within 1%, while the E- and H-plane patterns are still in good agreement with the MoM results except for the farthest side lobes of the H-plane patterns. [ABSTRACT FROM AUTHOR]

In this paper, a new analysis for a double step microstrip discontinuity is presented by using generalized transmission line equations [1]. The new analysis is based on a new concept of a finite-length transmission line integrated with its double step discontinuity so that the double step discontinuity is regarded as a finite-length nonuniform transmission line and the generalized equations could be directly implemented. Since the generalized equation coefficients are determined by dynamic numerical methods and the coefficients are invariant with the line excitation and load, the equations are dynamic rather than TEM. The interested discoveries are that the generalized equations for the whole double step structure or a partial double step structure can give us the same results and the generalized equations have broadband frequency characteristics. For the double step structure used in this paper for the analysis, the S-parameters for a frequency band from 0.5 GHz to 10 GH.z can be well calculated by using only two separately generalized equations at frequency of 3 GHz and 8 GHz. [ABSTRACT FROM AUTHOR]

A new numerical model of microstrip transmission line circuits in terms of distributed circuit parameters is here illustrated. Based on full-wave electromagnetic results, the extraction methods of these distributed circuit parameters on different types of microstrip transmission line circuits are introduced. As a preparatory experiment, an improved CAD method using this model is tested on microstrip low-pass filter. Copyright © 2003 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

The online FDTD method derived from general transmission line equations [1] has been introduced in [2, 3]. Following the research on non-uniform transmission lines, we further explore the application of online FDTD in the microstrip cross and T-junction structures. As the theoretic difficulties of modeling the connection of multi-transmission lines have been solved, many microstrip structures that have cross or stub substructures can be easily simulated by online FDTD. Three examples are presented to test the validity of this application. © 2003 Wiley Periodicals, Inc. Microwave Opt Technol Lett 36: 184–187, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10715 [ABSTRACT FROM AUTHOR]

General transmission-line equations based on the theory of differential equations [1] were introduced in [2] and [3]. The equations' dispersion characteristic of a microstrip low-pass filter is studied. The parameters L, C, α, and β of general transmission-line equations are found to be almost invariant to frequency in the passband of the microstrip low-pass filter. By restoring current and voltage distributions with the use of equations in both frequency and time domains, the broadband property of these equations on the microstrip low-pass filter is evident. © 2002 Wiley Periodicals, Inc. Microwave Opt Technol Lett 33: 123–126, 2002; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.10250 [ABSTRACT FROM AUTHOR]

Analyzes a reflector antenna using the finite-difference (FD) method. Calculation of the induced current densities on an axially symmetric parabolic reflector; Effect of the standing wave of current densities on side lobes; Discussion of the occurrence of singularities of FD equations; Results of induced current densities on the surfaces of reflector antennas.

Presents a study that calculated the electric field distribution in the slot cut in the outer conductor of the coaxial cable using the finite-difference time-domain method (FDTD). Discussion on radiation harmonics and resonant points of the leaky coaxial cables; Information on FDTD formulas and radiation field integration; Results of the field distribution in slots.