The Numerical Solution of Some Important Transmission-Line Problems

The generalized numerical solution of Laplace's equation in two dimensions is dealt with, subject to boundary conditions imposed by conducting surfaces and dielectrics which are permitted a limited amount of inhomogeneity. It is shown how this solution may be applied in the determination of the properties of TEM-mode transmission lines including the equivalent circuits of simple obstacles in these lines. The theory is illustrated with a number of examples, certain of which do not appear to have been previously treated theoretically in the literature. While certain of the examples serve mainly to show the power of the technique, others are given very detailed treatment with the production of much new design data.     

The Transmission-Line Matrix Method--Theory and Applications

This paper presents an overview of the transmission-line matrix (TLM) method of analysis, describing its historical background from Huygens's principle to modem computer formulations. The basic algorithm for simulating wave propagation in two- and three-dimensional transmission-live networks is derived. The introduction of boundaries, dielectric and magnetic materials, losses, and anisotropy are discussed in detail. Furthermore, the various sources of error and the limitations of the method are given, and methods for error correction or reduction, as well as improvements of numerical efficiency, are discussed. Finally, some typical applications to microwave problems are presented.     

极坐标系中的B样条有限元法解波导本征值问题

本文提出了用极坐标系中的Ｂ样条有限元法解波导本征值问题，该方法有两个突出优点：（１）避免某些含曲线边界的波导截面的剖分误差；（２）改善尖角波导的计算精度，本文首先建立了极坐标系中Ｂ样条有限元方程，然后通过对圆形，扇形，双脊加圆形和心形波导本征值问题的实际计算，表明方法的有效性和实有价值。     

A Moment Solution for Waveguide Junction Problems

A moment procedure for solving waveguide junction problems is given using the generalized network formulation for aperture problems. As an illustration, the procedure is applied to a transverse planar junction between two uniform cylindrical waveguides. The generalized admittance network representation of the junction is first obtained. Its scattering matrix representation is then deduced from the former representation. A discussion shows that the conservation of complex power technique, which handles the same class of junctions, is, a specialization of the moment procedure.     

Computer Optimization of Inhomogeneous Waveguide Transformers

The problem of designing broadband multisection stepped rectangular waveguide impedance transformers, when the input and output guides have different cutoff frequencies but propagate the same mode, is formulated in general terms for direct optimization by digital computer. The formulation is sufficiently flexible to allow nonideal junction discontinuity effects and mismatched terminations to be taken into account during optimization. Constraints placed on the width, height, or length of any section need be dictated only by considerations for dominant mode propagation and the requirement of small (but not necessarily negligible) junction discontinuities. The objective of the present formulation is a minimax equal-ripple response over a predetermined frequency band satisfying the constraints selected for the particular problem. The ripple search strategy to locate the maximum reflection coefficient within the band and the razor search strategy to minimize it, as described by Bandler and Macdonald in another paper, were employed. Constrained optimum equal-ripple solutions to examples previously published by Young, Matthaei et al. and Riblet are presented. They demonstrate the considerable improvements made possible by the present formulation with regard to performance, reduction in number of sections, and physical size. The approach used in this paper should also find application in the design of broadband microwave matching or equalizing networks consisting of noncommensurate components and for which exact synthesis techniques may be unavailable.     

Three-Dimensional Transmission-Line Matrix Computer Analysis of Microstrip Resonators

A wide range of microwave resonators are analyzed using the same three-dimensional transmission-line-matrix (TLM) computer program. The paper demonstrates the ease of application, versatility, and accuracy of the TLM method. The results presented include the dispersion characteristics of microstrip on dielectric and magnetic substrates and an example of a microstrip discontinuity. The surface-mode phenomenon of microstrip is also investigated.     

A Finite Dilyerence Method For The Solution Of Electromagnetic Waveguide Discontinuity Problems

Finite difference method for the numerical solution of electromagnetic waveguide discontinuity problems is presented. The method of boundary relaxation is applied, using finite difference techniques in the nonuniform section of the waveguide and using a modal representation of the field in the uniform sections of the waveguide. To illustrate the process some two-dimensional diffraction problems in an electromagnetic waveguide with rectangular cross section are solved.     

The Solution of Waveguide Scattering Problems by Application of an Extended Huygens Formulation

The implementation of a recent new hybrid integral-equation/vector finite-element method formulation applicable to inhomogeneous obstacle scattering in hollow waveguide, requiring discretization just of the obstacle, is presented. The integral equation links the given incident modes with the discontinuity-surface electric and magnetic fields. The finite-element equation is expressed in terms of the entire magnetic and surface electric field of the obstacle. Compatible vector finite-element basis function expansions are inserted, resulting in a pair of matrix equations soluble for the unknown electric and magnetic basis coefficients. Corresponding two-port scattering parameters are further derived. Test cases of posts in the$ TE_10$waveguide, with details of the matrix constructions, are described. Numerical results verified against an established commercial code are given. The ability to model inhomogeneous, lossy, and multiple scatterers is demonstrated.     

Numerical Solution of Waveguide Scattering Problems by Finite-Difference Green's Functions

A finite-difference Green's function method for solving time-harmonic wave guide scattering problems involving metallic obstacles of finite size by computer is described. The method is applied to the two-dimensional problem of a TE/sub 10/ mode impinging on cylindrical metallic posts of arbitrary shape in a rectangular waveguide. The equivalent susceptance of a transverse semidiaphragm computed using a 50 point approximation for the induced current distribution is found to be 1.5 percent less than the exact value. The S matrix of a thin bent window versus wavelength is also presented.     

Tri-Band Wilkinson Power Divider Using a Three-Section Transmission-Line Transformer

The analysis and design of a triple-band equal-split Wilkinson power divider are described. The circuit proposed is well matched and isolated at three arbitrary frequencies. The design procedure for the three-section transmission-line transformer based equal-split Wilkinson power divider derived from the ideal transmission-line model is provided. Simulated and experimental results in microstrip technology are presented to verify the idea and the derived equations.     

The Application of a New Class of Equal-Ripple Functions to Some Familiar Transmission-Line Problems

Chevyshev's procedure for determining equal-ripple rational functions with preassigned poles is extended to functions with double-valued singularities. As long as the number of elements is small, design equations for the class of transmission-line filters consisting of shunt-resonant elements spaced a quarter wavelength apart are readily obtained by identifying the unknown coefficients with those of the desired equal-ripple function. This is carried out in some detail for three and four element filters and applied to the design of broad-band stub supports and quarter-wave-spaced broad-band TR tubes. Experimental confirmation is presented.     

Fourier Decomposition Analysis of Anisotropic Inhomogeneous Dielectric Waveguide Structures

In this paper, we extend the Fourier decomposition method to compute both propagation constants and the corresponding electromagnetic field distributions of guided waves in millimeter-wave and integrated optical structures. Our approach is based on field Fourier expansions of a pair of wave equations, which have been derived to handle inhomogeneous mediums with diagonalized permittivity and permeability tensors. The tensors are represented either by a grid of homogeneous rectangles or by distribution functions defined over rectangular domains. Using the Fourier expansion, partial differential equations are converted to a matrix eigenvalue problem that correctly models this class of dielectric structures. Finally, numerical results are presented for various channel waveguides and are compared with those of other literature to validate the formulation.     

Reconstruction of Complex Permittivity of a Longitudinally Inhomogeneous Material Loaded in a Rectangular Waveguide

In this study, an integral equation technique is presented in order to reconstruct the complex permittivity variation of a material loaded in a rectangular cross section waveguide. The problem is first reduced to the solution of a two-coupled integral equations in terms of S-parameters of the system, which contains the Green's function of the empty waveguide. The resulting inverse scattering problem for the unknown complex permittivity of the loading is solved by contrast source inversion (CSI) technique. The validity and reliability of the proposed method has been demonstrated with numerical applications.     

A Quasi-Dynamic Method of Solution of a Class of Waveguide Discontinuity Problems (Short Papers)

It is shown that, if expansion terms of all the modes appearing in the Green's function for the problem are retained, the singular integral equation method can be made to apply by generating a differential equation for this integral. The solution of the differential equation is straightforward, and the inversion of the resulting integral equation then follows standard methods. The process is applied in detail to the case of the capacitive diaphragm, and the results compared to the quasi-static method with correction terms. The results are close for small guide widths, but the present method should give superior results if the guide width permits some overmoding.     

Solution to Waveguide Problems by Successive Extrapolated Relaxation (Short Papers)

A successive extrapolated relaxation (SER) technique has been developed to solve elliptic partial difference equations iteratively. SER is more efficient than optimized successive over-relaxation (SOR) and permits useful solutions of waveguide modes using finite difference methods.     

An Approximate Solution to Some Ferrite Filled Waveguide Problems with Longitudinal Magnetization

An approximate solution for the field structure and propagating modes in parallel plane, circular, and coaxial ferrite filled waveguide is presented. Bundles of plane waves are assumed to propagate in these structures which bounce back and forth along the guide. The solutions are classified into two types depending on the negative or positive equality of the incident and reflected waves. In the case of the circular guide the waves form a cone, and in the coaxial guide they form a frustum of a cone about the axis. The elemental plane waves are also assumed to satisfy Polder's relation and the boundary conditions at the guide walls. Simple relations are obtained with this equivalence for the propagation constant and the field. Comparison to rigorous theory is made in the case of the parallel plane and circular guide. Some experimental verification is presented for the completely filled coaxial waveguide.     

Analytical Solution to a Waveguide Leaky-Wave Filter Structure

Leaky-wave absorption filters have been found advantageous for the suppression of spurious energy of high-power transmitters. However, although there are experimental data of the properties of several specially constructed leaky-wave filters, there are apparently little data relating the effect upon the attenuation of the filters of varying one or more of the possible parameters of their design. In this paper a waveguide leaky-wave filter structure that retains the basic geometry of waveguide leaky-wave filters is analyzed theoretically over a finite frequency range. The complex propagation constant for the least-attenuated leaky-wave mode is obtained by reducing the fundamental integral equation to a transverse resonance equation and solving the reduced equation. The attenuation constant of the least-attenuated mode is obtained for values of 2a//spl lambda/ (i.e., the ratio of waveguide width to one half the freespace wavelength) ranging from 0 to 2. Its dependence on various design parameters of leaky-wave filters, such as main waveguide height, spacing of the coupling slots, width of coupling slots and height of the absorbing waveguides is presented. Good correspondence between theoretically computed curves and experimental data was obtained.