Moment method solution of double step discontinuities in waveguides

The problem of scattering of a double step waveguide discontinuity is investigated. Two coupled sets of equations in terms of the unknown magnetic current sheets on the apertures are obtained and solved for the electric field distribution using the moment method. The scattering matrix coefficients describing reflection, transmission, and mode conversions at a symmetric double step waveguide discontinuity are obtained and presented graphically for specific junctions.     

Equivalent network approach for guided electron waves obliquelyincident on step discontinuities in planar heterostructures

An equivalent network approach is developed for the analysis of the guided electron wave obliquely incident on step discontinuities in planar heterostructures. Stress is placed on network representations to establish physical pictures of the quantum effects and to yield insight; in addition, a systematic: microwave network approach is employed. A coordinate transformation translates an “eigencoordinate mode” of the guided electron wave propagating at an angle to the step discontinuity into a “structure coordinate mode” propagating normally to the step discontinuity, so that the step can be viewed as a transverse discontinuity and a procedure for the normal incidence can directly be exploited; transmission line equations in the direction normal to the step discontinuity, the mode-matching procedure for the boundary-value problem, and an equivalent network for the guided electron wave obliquely incident on the step discontinuities can be obtained. Using this network, the input admittance formulation is carried out, with which one can easily derive the equations that estimate the scattering and waveguiding characteristics of the guided electron wave obliquely incident on step discontinuities. Numerical examples are presented for a three-layered electron waveguide with a stub, and it is shown that this structure operates as a channel waveguide in addition to an angle filter     

Analysis of a Longitudinal Gyroelectric Discontinuity Inside a Fiber Waveguide

The scattering of guided electromagnetic waves from a finite-length longitudinal gyroelectic discontinuity inside a fiber waveguide is treated analytically. An integral equation approach is employed to formulate the corresponding boundary-value problem. The induced field inside the gyroelectic discontinuity region is expanded into a Fourier-type series in terms of the well-known cylindrical waves M and N plus a purely longitudinal wave Q. Then the method of moments is applied to decouple the basic integral equation. The resulting infinite coupled system of equations is truncated and solved numerically. After determining the field inside the discontinuity, the scattered far field inside the dielectric-rod waveguide is computed by employing a steepest descent integration technique. Numerical results for the scattering coefficients of an incident HE/sub 11/ dominant mode are obtained. Finally, design principles are discussed for practical components based on the treated longitudinal gyroelectric discontinuity.     

Some important properties of waveguide junction generalizedscattering matrices in the context of the mode matching technique

Some important properties for the generalized scattering matrix [S] of waveguide step discontinuities, in the context of the mode matching technique, are derived by considering the conservation of the complex power and self reaction across the discontinuities. Apart from their theoretical significance, these properties are useful for the numerical verification of the mode matching technique when designing waveguide circuits. The properties are shown to apply in the general case of junctions between lossless inhomogeneously filled waveguides, and they are proven to remain valid irrespective of the number of modes retained in the field expansions. During the process of deriving these properties, the mode matching technique for a waveguide step discontinuity is revisited and some subtle theoretical issues are resolved. In this framework, the selection of the appropriate testing modes for enforcing the field continuity conditions across the discontinuity is rigorously justified. In addition, two distinct mode matching formulations corresponding to the two possible orthogonality relations among the eigenmodes of lossless waveguides are proven to be equivalent. Finally, it is shown that the correct application of the held boundary conditions across the step discontinuity implies requirements on the number of modes used to represent the fields, in each waveguide, which are compatible with the relative convergence criterion     

Finite element analysis of MMIC structures and electronic packagesusing absorbing boundary conditions

In this paper, a three-dimensional finite element method (FEM) is employed in conjunction with first and second-order absorbing boundary conditions (ABC's) to analyze waveguide discontinuities and to derive their scattering parameters. While the application of FEM for the analysis of MMIC structures is not new, to the best of the knowledge of the authors the technique for mesh truncation for microstrip lines using the first and higher-order ABC's, described in this paper, has not been reported elsewhere. The scattering parameters of a microstrip discontinuity are computed in two steps. As a first step, the field distribution of the fundamental mode in a uniform microstrip is obtained by exciting the uniform line with the quasi-static transverse electric field, letting it propagate, and then extracting the dominant mode pattern after the higher order modes have decayed. In step two, the discontinuity problem is solved by exciting the structure by using the fundamental mode obtained in step one. The scattering parameters based on the voltage definition are calculated by using the line integral of electric fields underneath the strip. Numerical solutions for several waveguide discontinuities and electronic packages are obtained and compared with the published data     

Iterative Solutions of Waveguide Discontinuity Problems

The method of overlapping regions, together with Schwarz's technique, is applied to waveguide discontinuity problems to illustrate its potential and basic advantages and disadvantages over other methods. The method reasonably corrects an arbitrary initial assumption of field distribution in the plane of discontinuity to the final value in a small number of iterations. The advantages are illustrated for a waveguide bend and dumbbell shaped waveguide as examples of transverse and longitudinal discontinuities, respectively. Numerical results for the case where only the electric field is parallel to the sharp edge discontinuity are presented and compared with available data, while extension to the case where only the magnetic field is parallel to the edge is discussed.     

An effective approach for study of multiple discontinuities oftransmission lines

In this paper, a novel approach for calculation of discontinuities of transmission lines is presented. This approach is flexible, simple and effective. For calculation of multiple discontinuities or to take into account the thickness of the obstacles, it is only necessary to transfer the relationship between the electric and magnetic field components from one discontinuity to another and match them on the last one. The method of transfer may be arbitrary, it may also be realized by using the well-known method of lines or others methods, Both single and multiple waveguide discontinuities are calculated and the computed results are in good agreement with the literature. Examples of finite thickness waveguide discontinuities are also given. The proposed method may be readily used to calculate microstrip discontinuities. Extension to discontinuities of other types of transmission lines can also be performed     

Recurrence model analysis for multiple waveguide discontinuitiesand its application to circular structures

A general formulation for the scattering from multiple waveguide discontinuities is presented. It is based on the modal analysis technique in which the corresponding fields are expanded in terms of vector eigenfunctions and the boundary conditions are imposed at each junction. Analytic expressions for the global scattering matrices are derived using a recurrence procedure that requires substantially less computation than the traditional cascading techniques. The matrix equations are truncated in a manner that satisfies the conditions for a good overall convergence, which is illustrated for step discontinuities in circular waveguides. Numerical results are presented for a thick iris in a circular waveguide and for iris-matched dielectric window designs     

Mode-matching CAD of rectangular or circular multiaperturenarrow-wall couplers

A rigorous and efficient mode-matching computer-aided design (CAD) method for rectangular waveguide H-plane couplers is presented. The couplers employ multiple large rectangular or circular apertures of different sizes and nonuniform distance. The decomposition of the coupler structure into adequate mode-matching key-building blocks, i.e., the T-junction, double-plane step discontinuity, and rectangular-to-circular waveguide transition, together with the homogeneous intermediate waveguide sections of finite lengths yield the desired high flexibility. Both the finite wall thickness and the higher order mode interaction between all discontinuities are accurately taken into account by the combination of the individual building blocks of the generalized scattering matrix technique. Design examples for rectangular and circular aperture provide coupling values of -10.7, -10, -8.1, -5.3, -4.7, -3, -2.6, and -2.3 dB in Ku-band (12-18 GHz), thus demonstrating the flexibility and the efficiency of the method. The theory is verified by excellent agreement with measurements     

Measurement of Two-Mode Discontinuities in a Multimode Waveguide by a Resonance Technique

The deliberate use of two or more propagating modes in a multimode waveguide, and a knowledge of associated control elements, has assumed renewed importance, particularly for millimeter wavelength applications. This paper presents a resonance measurement technique for the precise evaluation of the equivalent network for a lossless shunt discontinuity coupling two nondegenerate modes in a multimode waveguide. The discontinuity structure is placed into a cavity closed by adjustable plungers, and the data consists of those plunger positions which render the cavity resonant in the two modes of interest. This multipoint data is then transformed to permit an analysis of the two-port network in the discontinuity plane by conventional techniques. Computations and experimental results obtained at S band illustrative of the procedure are presented for shunt discontinuities coupling the E/sub 01/ and H/sub 01/ modes in circular waveguide. The accuracy achieved is comparable to that obtained in single mode precision measurements.     

Scattering by Abrupt Discontinuities on Planar Dielectric Waveguides

Two unifying aspects of the problem of scattering by an abrupt discontinuity on a planar dielectric waveguide are considered. The first aspect is concerned with the numerical solution of the scattering problem through consideration of a corresponding bounded waveguide problem in which perfect electric or magnetic conductor bounds with variable locations are introduced. It is shown that the solutions to the bounded problem, when numerically integrated over a range of bound locations defined within half a wavelength, allow the complete mode spectra of the unbounded waveguide to be accurately accounted for. Scattering solutions for both TE- and TM-modes are presented for a wide range of discontinuities and, in the TE-mode case, are in agreement with results obtained using the method due to Rozzi [5]. The second aspect is concerned with the relationship between scattering and "inter-waveguide mode orthogonality." Based on a simple iterative scheme, a meaningful physical interpretation of the scattering process is developed. This allows the scattering to be classified as being of first or higher order, to be explained in terms of the physical characteristics of the mode fields.     

Full-wave characterization of the mode conversion in a coplanarwaveguide right-angled bend

A full-wave algorithm is proposed to analyze thoroughly a 90° bend of coplanar waveguide (CPW). Based on the mixed potential integral equation (MPIE) formulation, the equivalent magnetic current distribution on the apertures is solved by the moment method using overlapping rooftop basis functions and the Galerkln weighting procedure. The matrix pencil approach is then utilized to do the de-embedding procedure and extract both the coplanar and slotline modes scattering off the asymmetric discontinuity. Experiments are performed to measure the scattering parameters and the results verify the accuracy of the present algorithm. The full 4×4 scattering matrix between these two modes is presented from which the occurrence of the mode conversion is investigated. The mode conversion is noticed to become almost complete at certain frequencies, which may be useful in the design of CPW to coupled slotline transition     

On the analysis of single- and multiple-step discontinuities for ashielded three-layer coplanar waveguide

The mode matching procedure is employed to obtain the scattering (S) parameters of the discontinuities. The analysis is validated through a comparison of the calculated S-parameters of a single step discontinuity for a shielded single-layer CPW and those published previously. Calculated S-parameters for various single, double, and triple step discontinuities are presented. Effect of the modal orthogonality criterion on the discontinuity S-parameters is given. Extensive investigation of the numerical convergence of the S-parameters is also described     

New boundary integral equations for CAD of waveguide circuits:guided-mode extracted integral equations

Novel boundary integral equations which are applicable to the analysis of many kinds of waveguide circuits are presented. The new integral equations can treat the waveguide discontinuity problems like the scattering by the isolated finite-sized metallic objects or cavity problems and do not use normal-mode expansion techniques. They are suitable for the basic theory of CAD software for various waveguide circuits. The two-port and H-plane waveguide discontinuity problems which satisfy the single-mode and two-mode conditions are treated. The case of waveguide corner bend is considered as an example. Numerical examples are shown in order to confirm the validity of the new integral equations     

Scattering and transmission matrix representations of multiguidejunctions

The scattering and transmission matrix representations of the mode-matching technique are generalized for multiguide junctions with arbitrarily shaped coupling apertures. A comparison between both representations is given with respect to the CPU time. The relative convergence phenomenon arising in cascaded discontinuities of multiguide junctions is investigated. A numerical criterion for choosing the correct mode ratio among the guides is presented. Also studied is the application to a kind of multiguide junction between a circular waveguide and a coaxial waveguide with hollow inner conductor     

Scattering of the TE/sub 01/ and TM/sub 01/ Modes on Transverse Discontinuities in a Rod Dielectric Waveguide-Application to the Dielectric Resonators

Our purpose is to determine the resonance frequency together with the radiation quality factor of dielectric resonators. To do that, the reflection and the scattering properties of the TE/sub 01/ and TM/sub 01/ modes, incident on an abruptly ended dielectric rod, are analyzed. After the building of the complete mode spectrum on each side of the discontinuity, the continuity relations in the discontinuity plane associated with the orthogonality properties lead to a coupled integral equation system. That one is solved by means of an iterative procedure, providing all the characteristics of the discontinuity (reflection or coupling coefficients, radiation losses). Then, these solutions are used to determine the resonant frequency and the radiation quality factor of cylindrical resonators which are considered as waveguide lengths between two interacting discontinuities.     

Multimode moment method formulation for waveguide discontinuities

A computationally efficient method for analyzing waveguide discontinuities is presented. The method is based on Galerkin's moment method formulation. The generalized scattering matrix of a waveguide discontinuity is derived. A generalized equivalent circuit is constructed which gives physical insight to the problem. The method is found to be several times faster than the well-known mode matching technique. The accuracy of the proposed method is demonstrated by comparing the numerical result with the measured return loss of a multisection iris-coupled filter     

Computations for radiation and surface-wave losses in coplanarwaveguide bandpass filters

A new approach is developed to simulate both radiation and surface-wave losses in general coplanar waveguide (CPW) discontinuity structures. The newly derived formulas are concise, simple, and efficient for computation. Full-wave characterization of CPW filter structures are first accomplished by the mixed-potential integral equation and the method of moments. Given equivalent magnetic-current distributions on the apertures of a CPW, the matrix pencil approach is applied to extract the scattering parameters and the new formulas are employed to obtain the losses and far-field patterns of the space-wave radiation and surface wave. Simulation of the calculated radiation and surface-wave losses by field theory is found to be consistent to the total power loss determined from the scattering parameters by circuit theory, which verifies the correctness of our new expressions     

A Unified Approach to the Analysis of a Category of H-Plane Discontinuities

Based on the mode matching method, the generalized scattering parameters including the fundamental and higher order modes (multi-modes) are obtained for the discontinuity interface of a category of waveguide H-plane discontinuities. Then by using a general port-connection order-decrease method raised by the author, the whole discontinuity including the two interfaces and the intermediate part of finite length or zero length (as is the case for very thin inductive windows or irises) can be combined into one network, and the generalized scattering parameters of this network can be obtained from which the scattering parameters of the fundamental mode can be extracted. If needed, the equivalent circuit parameters can be calculated directly from the scattering parameters. Examples are given to show the validity and versatility of this new method for dielectric filled waveguide, inductive iris and/or window, E-plane metal and/or finline insert, and even the offset E-plane finline insert, etc.. Multiple inserts, windows and irises can also be analysed.     

Analysis of dispersion and series gap discontinuity in shieldedsuspended striplines with substrate mounting grooves

Dispersion and series gap discontinuity of shielded suspended striplines (SSLs) on Duroid substrate (ϵ_r=2.22) are analyzed using the finite-difference time-domain method (FD-TD). Numerical accuracy of better than 0.15% is achieved when the FD-TD is used to calculate the effective dielectric constant (ϵ_reff ) of an air-filled rectangular coaxial transmission line. Data obtained for the frequency-dependent ϵ_reff of uniform SSLs and both scattering and equivalent circuit parameters of various series gap discontinuities are presented. In general, the presence of sidewall mounting grooves causes a nearly frequency-independent small reduction in ϵ_reff. On the other hand, proximity effects of the housing are found to be more important. For the gap discontinuity, coupling across the gap is stronger for wider strips and/or narrower gap width. Irregular transmission behavior is also found when the strip is wide enough to interact strongly with the sidewalls