Investigations of complex modes in a generalized bilateral finlinewith mounting grooves and finite conductor thickness

A generalized bilateral finline with mounting grooves and finite conductor thickness is analyzed by a full-wave mode-matching method. The final nonstandard eigenvalue equation is derived from the unknown coefficients in the slot regions to reduce the size of the matrix equation. The convergence studies of the mode-matching method is first studied for the fundamental mode of a symmetric bilateral finline. Both the propagation constant and the characteristic impedance as defined by the power-voltage relationship are analyzed and compared to the existing data. Excellent agreement is obtained. The effects of metallization thickness and mounting grooves are discussed. The accurate results obtained for the fundamental mode by the mode-matching method with respect to both relative and absolute convergence were also obtained for the complex modes of the finline. The dispersion characteristics of the fundamental, higher order, evanescent, and complex modes are presented for an asymmetric bilateral finline. The effects of mounting grooves and metallization thickness on the complex mode propagation constants are investigated and discussed     

A simplified formulation to analyze inhomogeneous waveguides withlossy chiral media using the finite-element method

In this paper, an efficient finite-clement formulation is presented for the analysis of the propagation characteristics in arbitrarily shaped lossy inhomogeneous waveguides loaded with chiral media. It is a simplified form of the one proposed for the bi-anisotropic media. In this formulation, showing no spurious modes, the frequency or the propagation constants may be treated as eigenvalues of a resulting sparse quadratic eigenproblem. However, in order to handle losses easily and to facilitate computation of complex modes, the frequency is specified as an input parameter and the eigensystem is solved for the complex propagation constant as the eigenvalue. This sparse eigensystem is further transformed into a generalized one, thus maintaining the sparse properties of the matrices. New numerical finite-element results are presented     

A scalar variational conformal mapping technique for weakly guiding dielectric waveguides

A novel approach of combining the finite-element method with the conformal mapping technique is proposed for solving the scalar variational formulas for weakly guiding dielectric waveguides. This approach avoids spurious modes and gives satisfactory results even for modes near cutoff, requiring less computer memory and time. Various specific dielectric structures, such as the rectangular guide, channel guide, and rib guide, are considered to estimate the error associated with the scalar formulation relative to the vectorial formulation. The efficiency of this approach is demonstrated with an analysis of a directional coupler whose coupling properties are described by means of numerical results such as propagation constants, field distributions, etc.     

鳍线阻抗不连续性的混合模散射特性

本文用混合模展开鳍线中的本征场,并应用谱域法确定主模和高次模的传播常数和谱域中的本征场,然后结合模匹配法分析鳍线阻抗不连续性的混合模散射特性。文中给出计算的单鳍前30个模,双鳍前20个模的传播常数和阻抗不连续性的主模散射参数,计算结果与文献发表的结果一致。有关数值收敛性问题亦在文中进行了讨论。     

Coupled mode analysis of a finline

A theoretical analysis of a unilateral finline loaded with arbitrary inhomogeneous lossy dielectric material is presented. The rigorous coupled-mode approach is used. The electromagnetic field in the line is expressed in terms of the modes of a ridged waveguide, and the problem is transformed to a matrix eigenvalue equation. Approximate expressions are derived for investigating the properties of the fundamental mode in finlines loaded with dielectric slabs. Dispersion characteristics, the characteristic impedance, and the attenuation due to dielectric losses and the finite conductivity of the metal coating are computed for various line configurations. The numerical results are compared to data obtained by means of the spectral-domain method, proving the validity and usefulness of the proposed approach     

On the validity of the effective-index method for rectangulardielectric waveguides

The effective-index method (EIM) for rectangular dielectric waveguides is derived as an approximation from an exact equivalent-network formulation. It is explained why EIM gives accurate results for the fundamental modes in near cutoff region as well as for all the guided modes in well-guiding region. As a direct improvement on EIM a simple eigenvalue equation is presented, which takes into account the shape of the predominant slab-waveguide mode. It is shown that EIM overestimates propagation constants compared to the improved results     

Complex modes in boxed microstrip

A method is described for obtaining the propagation coefficients and field patterns of a large number of modes for microstrip with a minimum of computational effort. The method uses a discrete space-domain formulation to calculate a large number of higher-order modes in a way which leads to their fast location and which ensures that node modes are missed. This includes those pairs of modes with complex conjugate propagation constants of the type reported for finline, as well as the normal evanescent modes. In addition, the characteristic impedance of microstrip is efficiently calculated. The results presented are obtained using the generally accepted power-current definition and are in agreement with other published results     

On the mode-coupling formation of complex modes in a nonreciprocalfinline

This paper studies and models the mechanism for forming the complex modes commonly found in boxed quasi-planar or planar guided-wave structures. To illustrate the fact that the mode-coupling among the various forms of modes is closely related to the formation of complex modes, the dispersion characteristics of the complex propagation constants (or the so-called mode spectrum) of a nonreciprocal unilateral finline are obtained by the rigorous full-wave SDA (spectral-domain approach). It is found that in the mode spectrum of the nonreciprocal finline, a forward wave and a backward wave interact to produce a pair of complex modes. The interactions between two forward (backward) traveling waves, between a forward wave and a backward wave, and between two complex waves (modes) are modeled by applying the mode-coupling theory. The concept of hypothetical modes is introduced in the model. These hypothetical modes are obtained by applying mode-coupling theory to the mode spectrum previously obtained. The approximate values obtained for the propagation constants of the three types of wave interactions using the model presented in the paper are in close agreement with those given by the full-wave SDA     

A New Technique for the Analysis of the Dispersion Characteristics of Microstrip Lines

Dispersion characteristics of shielded microstrip lines are investigated using a new technique. The method utilizes the well-known singular integral equation approach for deriving an alternate form of eigenvalue equation with superior convergence properties. It is shown that accurate numerical results may be obtained from this eigenvalue equation using only a 2x2 matrix equation. In comparison, the conventional formulation of the problem requires the use of matrices that are much larger in size. Aside from the numerical efficiency, the simplicity of the method makes it possible to conveniently extract higher order modal solutions for the propagation constants that affect the high-frequency application of microstrip lines. Even though the derivation of the determinantal equation requires some intricate mathematical manipulations, the user may bypass these completely and use the final eigenvalue equation which is programmable on the computer.     

Application of the method of lines to cylindrical inhomogeneous propagation structures

The method of lines is applied to the Helmholtz equation in cylindrical co-ordinates to analyse cylindrical inhomogeneous propagation structures such as finlines in circular waveguide housings. The numerical results for the frequency dependent propagation characteristics and the dominant mode characteristic impedance for the finline structures are presented.<>     

Calculating the Characteristic Impedance of Finlines by Transverse Resonance Method

The characteristic impedance of finlines with up to three slots is calculated by a rigorous hybrid-mode analysis which includes the finite metallization thickness and finite depth of the mounting grooves. The transverse resonance principle utilized reduces considerably the order of the involved matrix eigenvalue problem. The propagation constants for the fundamental HE/sub 1/ mode (and EH/sub 0/ mode at related structures), as well as for the higher order modes (up to HE/sub 7/), and the characteristic impedances for the fundamental modes are computed as a function of frequency for the bilateral and unilateral finline, as well as for the unilateral finline with two coupled slots, and an additional slot on the opposite side of the substrate surface. The finite metallization thickness and mounting groove depth considered show significant influence on the behavior of the characteristic impedance.     

A simple technique for calculating the propagation dispersion ofmulticonductor transmission lines in multilayer dielectric media

A multiconductor transmission line in a multilayer dielectric medium is complicated and therefore is frequently analyzed by the simple quasi-TEM (transverse electromagnetic) approach. Unlike the full wave eigenvalue approach, the quasi-TEM approach does not give the propagation dispersion characteristics of the line. This work overcomes this problem by first obtaining the solution of each multiconductor mode from the quasi-TEM approach. Then these solutions are used as both basis and testing functions in a variational formulation of the full wave eigenvalue analysis. The result is high accuracy in the dispersive propagation constants of the multiconductor modes. By solving only for high frequency eigenvalues, not for the high frequency eigenvectors, the method is simpler and faster than the conventional full wave dispersion analyses     

Theoretical of and Experimental Investigation Finline Discontinuities

The dominant and the first-five higher order modes in a unilateral finline are precisely described from a thorough spectral-domain approach. Then, using the modal analysis, coupling coefficients between eigenmodes at a discontinuity that have to be introduced into the scattering matrix formulation are directly computed in the spectral-domain, and, consequently, the equivalent circuit parameters of the discontinuity are determined. Finafly, finline discontinuities often used for impedance transformation are investigated and a good agreement between theoretical and experimental results is reported.     

Finite-Difference Analysis of Rectangular Dielectric Waveguide Structures

A class of dielectric waveguide structures using a rectangular dielectric strip in conjunction with one or more layered dielectrics is analyzed with a finite-difference method formulated directly in terms of the wave equation for the transverse components of the magnetic field. This leads to an eigenvalue problem where the nonphysical, spurious modes do not appear. Moreover, the analysis inclndes hybrid-mode conversion effects, such as complex waves, at frequencies where the modes are not yet completely bound to the core of the highest dielectric constant, as well as at frequencies below cutoff. Dispersion characteristic examples are calculated for structures suitable for millimeter-wave and optical integrated circuits, such as dielectric image lines, shielded dielectric waveguides, insulated image guides, ridge guides, and inverted strip, channel, strip-slab, and indiffused inverted ridge guides. The numerical examples are verified by results available from other methods.     

A Nonlinear Finite-Element Leaky-Waveguide Solver

A novel hybrid finite-element method for the analysis of leaky-waveguide structures is presented. The possibly radiating structure is enclosed within a fictitious circular contour-C in order to truncate the infinite solution domain. The field in the unbounded domain, outside contour-C, is expressed as a superposition of transverse electric and magnetic modes. Their radial dependence is expressed in terms of Hankel functions, which satisfy the radiation condition at infinity. The bounded area is discretized using hybrid node/edge elements for an accurate and efficient handling of the electric field vector wave equation. The transparency of the fictitious contour is ensured by enforcing the field continuity conditions according to the principles of a vector Dirichlet-to-Neumann mapping. The whole procedure yields a nonlinear eigenvalue problem for the complex axial propagation constant (beta). The nonlinearity is due to the appearance of beta within the argument of the Hankel functions. The final nonlinear problem is solved by employing a matrix Regula-Falsi algorithm. Initial guesses for the Regula-Falsi algorithm and a fast estimation of the eigenvalues spectrum are provided by a linear formulation based on a second-order approximation (beta/k_o)² Lt 1. The proposed method is validated against published numerical and experimental results for both leaky and surface wave modes.     

Analysis of higher order modes on unilateral finlines with arbitrarily located slots

In this paper a rigorous method is presented which allows a complete calculation of all modes existing on a unilateral finline with an arbitrarily located slot. Also an investigation of the field distribution is possible. Hereby the behaviour of the different modes can be explained. This method also permits the determination of the propagation properties of higher order modes; thus information is needed for the calculation of finline discontinuities.     

Analysis of Finline with Finite Metallization Thickness (Short Papers)

In this paper, we present a method for analyzing finline structures with finite metallization thickness. The method is based on a hybrid mode formulation but it by-passes the lengthy process of formulating the determinantal equation for the unknown propagation constant. Some numerical results are presented to show the effect of the metallization thickness for unilateral and bilateral finlines.     

A mixed spectral-domain approach for dispersion analysis ofsuspended planar transmission lines with pedestals

A mixed spectral-domain analysis is used to derive dispersion characteristics of domain modes in a class of planar transmission lines with a pedestal. Equivalent structures are constructed in which magnetic surface currents are identified as the unknowns at the aperture separating two different regions. Spectral dyadic Green's functions are derived for these structures using the spectral-domain immittance approach. The characteristic equations resulting from the application of the spectral Galerkin method involve mixing two different spectral domains, which exist on the two sides of the pedestal support. The present method allows one to retain the simplicity and numerical efficiency of the conventional spectral-domain immittance approach, which cannot be applied directly to the present structures. Numerical data are provided for the dispersion characteristics of dominant modes in a pedestal-supported stripline and finline     

Broadside coupled strip inset dielectric guide and its directionalcoupler application

A theoretical and numerical method is presented for the analysis of broadside-coupled strip inset dielectric guide. The method of analysis is based on an integral equation formulation and Galerkin's procedure. Besides propagation constants for two fundamental and higher order modes, the characteristic impedances for the two fundamental modes are calculated using the total propagating power and the longitudinal strip currents. The propagation characteristics of the two fundamental modes are then used to compute 4-port circuit parameters that are essential for accurate analysis and design of coupled line circuits. The effects of various structural parameters on the S-parameters are investigated and it is found that this broadside coupled strip IDG structure is useful for the realization of the directional couplers. Examples of strong and weak directional couplers are given. Furthermore, the propagation constants and S-parameters of coaxially excited coupled strips are measured, and are in good agreement with the theoretical analysis     

Calculation of Propagation Constants and Cutoff Frequencies of Radially Inhomogeneous Optical Fibers

Based on the finite-difference technique, an efficient numerical method that can treat both the propagation constants and cutoff frequencies of optical fibers with arbitrary permittivity profiles is developed in the rigorous vector form. Such a propagation problem is formulated in transverse fields so that the proposed method does not suffer from spurious modes. The associated boundary conditions including those at cntoff are derived in a novel way. Thereafter, numerical results of the cutoff frequency and propagation constant of a fiber with the parabolic profile are presented.