Scattering at Circular-to-Rectangular Waveguide Junctions

A formally exact solution is given for the problem of scattering at a circular-to-rectangular waveguide junction and at a thick diaphragm, with a centered circular aperture, in a rectangular waveguide. The method uses normal TE and TM mode expansions of the waveguide fields and traditional mode matching of the transverse electric and magnetic fields at the junction boundary. Exact closed-form expressions are obtained for the electric field mode-matching coefficients which couple the TE(TM) modes in the rectangular guide to the TE(TM) and TM(TE) modes in the circular guide. Numerical results are presented for the case of TE/sub 10/ mode propagation in the larger rectangular guide with all other modes cutoff. Convergent numerical results for the equivalent shunt susceptances of such junctions are obtained when about 12 modes (eight TE and four TM) are retained in the circular waveguide or in the circular aperture of the diaphragm. The results are graphically compared with formulas and curves due to the quasi-static theory of Bethe and the variational theory given in the Waveguide Handbook [2].     

圆形槽波导到矩形波导结的有限元分析

设计基于圆形槽波导的元件经常会用到圆形槽波导到矩形波导结.应用有限元法(FEM)分析了N端口波导结.采用完全匹配层(PML)将槽波导的开放边界截断为有限区域,然后对圆形槽波导到矩形波导结的散射特性进行了数值计算,得出的散射参量为圆形槽波导振荡器输出结构的优化设计提供了依据.     

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     

Scattering from a cylindrical waveguide with rectangularcorrugations

Electromagnetic scattering from a circular cylindrical waveguide with rectangular corrugations is considered in this paper. An analysis method based on dyadic Green's functions and Fourier transforms is used to get the field in terms of modal currents induced on the corrugation openings. The fields are expressed through a series of modal eigenfunctions in the corrugations, and are integrated to get the unknown expansion coefficients. This analysis method can easily be extended to find the dispersion relations of the corrugated waveguide. The series solution obtained is analytic and suitable for numerical computation. Numerical results are presented to illustrate the scattering behavior of a corrugated cylindrical waveguide in terms of frequency and waveguide geometry     

Scattering at an offset circular hole in a rectangular waveguide

A solution is given for the problem of scattering at an offset circular to rectangular junction and at a thick diaphragm, with an offset circular aperture, in a rectangular waveguide. The method used is mode matching for computing one discontinuity. The difficulty arising from the fact that the eigenmodes of the two waveguides are known in different coordinate systems is overcome by simple transformation for the evaluation of overlap integral between the eigenmodes of each waveguide. Experimental results validate this method     

On Solving TM0n Modal Excitation in a Ka-Band Overmoded Circular Waveguide by the Conservation of Complex Power Technique

To measure the radiation properties of relativistic diffraction generator (RDG) in Ka-band, a TM0n modal excitation model is established, which consists of an overmoded circular waveguide and a coaxial line feeding probe. Using the transverse E-field mode matching and the conservation of complex power technique (CCPT), we deduce the scattering matrix at coaxial line to coaxial line and coaxial line to circular waveguide junctions. Then using the overall cascaded junction scattering matrix, the numerical results for the reflection coefficient of the coaxial line and the power distribution of TM0n multi-modal are presented. The numerical results are in agreement with HFSS simulation results and experimental results. The analysis shows that by choosing the appropriate position of coaxial line probe, the power proportion of the device operating mode excited in circular waveguide could be the largest.     

On Solving TM0n Modal Excitation in a Ka-Band Overmoded Circular Waveguide by the Conservation of Complex Power Technique

To measure the radiation properties of relativistic diffraction generator (RDG) in Ka-band, a TM0n modal excitation model is established, which consists of an overmoded circular waveguide and a coaxial line feeding probe. Using the transverse E-field mode matching and the conservation of complex power technique (CCPT), we deduce the scattering matrix at coaxial line to coaxial line and coaxial line to circular waveguide junctions. Then using the overall cascaded junction scattering matrix, the numerical results for the reflection coefficient of the coaxial line and the power distribution of TM0n multi-modal are presented. The numerical results are in agreement with HFSS simulation results and experimental results. The analysis shows that by choosing the appropriate position of coaxial line probe, the power proportion of the device operating mode excited in circular waveguide could be the largest.     

ANALYSIS AND DESIGN OF MULTIPORT WAVEGUIDE JUNCTIONS WITH ARTIFICIAL INCLUSIONS FORMED OF CONDUCTING STRIPS

A rigorous electromagnetic theory is developed to analyze multiport waveguide junctions with artificial inclusions formed of the conducting strips and dielectric layers. The method is based on the Fourier transform technique combined with the mode matching method technique that takes into account the edge conditions in vicinity of the strip edges. The scattering characteristics of a 3-port junction are discussed with the numerical examples for the SWR maps, the power reflection and transmission coefficients, and the 2D plots of near fields distributions inside the junction area. A strategy of optimize matching properties of the 3-port waveguide junctions is also presented.     

Circular Electric Mode Directional Coupler

This paper describes a circular electric mode directional coupler, composed of two coaxial bifurcations in circular waveguide. The coupling coefficient of the directional coupler depends on the separation between the two bifurcations, and a hybrid junction for the circular electric mode may be obtained at the proper separation. The analysis is carried out in terms of scattering matrix elements characterizing each coaxial bifurcation. The scattering matrix elements were experimentally determined via the Weissfloch tangent method at 5000-Mc band. For convenience, experiments were carried out in sectoral waveguide instead of circular waveguide. Measured characteristics at 9000-Mc band are in good agreement with values determined by circuit calculations employing parameters of the coaxial bifurcation measured at 5000-Mc band. For the case of a hybrid junction, wide-band matching has been accomplished and verified experimentally. Applications of this directional coupler are outlined.     

Conservation of complex power technique for waveguide junctionswith finite wall conductivity

Scattering at the junction of two waveguides with finite wall conductivity is rigorously treated using E-field mode matching and the conservation of complex power technique. At the transverse junction discontinuity between the two waveguides, the complex power absorbed by the junction wall is taken into account along with the usual transfer of complex power from one guide to the other. This leads to a generalized form of the scattering matrix [S] of the lossy junction which incorporates the surface impedance Z_m of the transverse metallic wall, assumed to be a good conductor. The specific case of a copper transverse diaphragm with centered circular iris in an X-band guide is considered and the equivalent TE₁₀ shunt admittance is computed. Numerical results are also given for lossy X-band cavity resonators with circular coupling holes     

Analysis of circular waveguide arrays on cylinders

An analysis is given of the mutual coupling effects in a finite array antenna of circular waveguide elements on a conducting cylinder. The array is described in terms of a scattering matrix and the multimode aperture fields of the elements are solved for by moment methods. Mutual coupling through wave propagation along the surface is treated according to GTD, since for most cases of interest the surface curvature is small in terms of wavelength. Appropriate asymptotic expansions for the magnetic field Green's function are derived for the two basic cases of an axial and a circumferential magnetic current element on the cylinder, the latter being a new case. The method, which allows the array elements to be nonuniformly spaced, applies to cylinders with radii>2lambdaand thus also includes planar arrays. Illustrative numerical examples and comparisons with infinite cylindrical and planar arrays are included.     

Theory of Gyrotron Traveling-Wave Amplifiers

A unified single-mode theory is developed for the gyrotron traveling-wave amplifier (gyro-TWA) at harmonics of electron gyro frequency, both in linear and nonlinear regimes. The theory is applicable to a wide class of waveguide cross sections and waveguide modes; it can also be useful for arbitrary harmonic numbers and with the generalized electron beam model. The waveguide fields are expanded into series of multipoles about the electron guiding centers. A general dispersion equation is derived. Some numerical examples of the gain-frequency curves of gyro-TWA's with out-ridged, magnetron-type, rectangular and circular waveguides are computed by employing the results of kinetic theory.     

On Solving Waveguide Junction Scattering Problems by the Conservation of Complex Power Technique

Normal mode expansions are used to mode match the tangential electric field at the transverse junction of two cylindrical waveguides. Instead of mode matching the tangential magnetic field the principle of conservation of complex power is invoked and leads, without a matrix inversion, to an expression for the junction's input admittance matrix, as seen from the smaller guide. Simple matrix algebra and the reciprocity theorem then provide the generalized scattering matrix of the two-port (with higher order modes included). It is also shown that the solution satisfies the continuity condition for tangential magnetic field in the junction's aperture. Numerical results are given for parallel plate waveguides with TEM, TE/sub 1/, and TM/sub 1/ incident fields, numerical convergence being achieved with about ten modes in the smaller waveguide.     

Matched windows in circular waveguide

Design curves are presented for the matching of a dielectric window in circular waveguide propagating the dominant TE₁₁ mode. The matching is accomplished by thick or thin inductive irises which are in contact with the window on both sides. This configuration gives wide bandwidth and is mechanically convenient, but requires consideration of coupling of the higher-order modes generated by the closely spaced discontinuities. Mode matching and the generalized scattering matrix are utilized     

Narrow wall axial-slot-coupled T junction between rectangular andcircular waveguides

An analysis is presented of a T junction between rectangular and circular waveguides coupled through a long axial slot in the narrow wall of the rectangular waveguide. A moment method with entire orthogonal basis functions is used for deriving expressions for the elements of the scattering matrix. The effect of the wall thickness is taken into account by treating the coupling slot as a short section of a rectangular waveguide and matching the boundary conditions at the interfaces. The conditions satisfied by the scattering matrix of the junction are verified. A comparison between theoretical and experimental results on variation of coupling with frequency is presented     

Characterization of rectangular waveguide with a pseudochiral /spl Omega/ slab

A mode matching approach has been employed for evaluating the matrix S of the section of rectangular waveguide with pseudochiral /spl Omega/ slab. Scattering characteristics for different localizations of the /spl Omega/ slab in the guide are predicted numerically and verified by measurements. Based on the numerical analysis, the scattering properties of the guides are discussed. Scattering parameters are next applied in an optimization procedure to extract constitutive parameters of the /spl Omega/ slab used in experiment.     

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     

Comparison of mode-matching and differential equation techniques inthe analysis of waveguide transitions

The solution of the continuous waveguide transition problem can be obtained by discretizing the boundary and applying mode matching or by using a system of ordinary differential equations. Both approaches involve approximate representations of the boundary. When using the differential equation approach, it is found necessary to consider the transition as several sections in series in order to avoid numerical instabilities. When this is done, one may cascade using a generalized scattering matrix approach or a generalized ABCD matrix method. Results are shown in order to compare the accuracies of the boundary discretization approach and the differential equation approach for the Marie transducer and for linear transitions of various lengths in rectangular waveguides. Experimental results are also given for the Marie transducer     

Analysis of radiation from a horn with a superquadric aperture

This paper presents an analysis of radiation from a horn with a superquadric aperture, modeled using a cascade of superquadric waveguides. Electromagnetic fields within each waveguide are expressed in terms of a set of orthogonal modes derived from polynomial functions based on a Cartesian coordinate system. The scattering matrix at the horn aperture is obtained by calculating the scattering matrix at each of the waveguide junctions using mode matching, and cascading them appropriately. Radiation patterns corresponding to both x- and y-polarizations of the input excitation are then obtained by integrating the aperture field. The computed numerical results are validated by comparing them with the corresponding results obtained from measurements.     

Mode matching analysis of multiple offset coaxial irises in circular waveguide

The step junction between a circular and an eccentric coaxial waveguide is analysed using a rigorous mode matching technique along with the Graff's addition theorem for cylindrical functions. The necessary expressions including the coupling integrals are considered analytically. Based on this analysis the off-centred coaxial iris in a circular waveguide is studied. Its properties are pointed out and the single and dual irises on the same diaphragm features are exploited for the design of bandpass filters.