Electromagnetic Potentials and Field Expansions for Plasma Radiation in Waveguides

In order to calculate the raditaion from plasmas placed in waveguides it is necessary to know the field produced by arbitrarily moving charged particles in a waveguide. In this paper modal expansions for the vector and scalar potentials due to arbitrarily moving charged particles in a waveguide are derived and provide the extension of the Lienard-Wiechert potentials to a waveguide environment. In addition, for a plasma filled waveguide, a modal expansion is given of the electric field directly in terms of mode coupling with the charge motion. Expressions for the spectral distribution of the radiation are given, both in general and for cyclotron radiation. Some specific results for the H/sub 10/ mode excited in a rectangular guide by cyclotron motion are also presented.     

Radiation impedance of a dipole printed on periodic dielectric slabs protruding over a ground plane in an infinite phased array

The radiation impedance of a dipole printed on periodic dielectric slabs standing over a ground plane in an infinite phased array is calculated. The calculation is made by means of modal expansions in terms of longitudinal section electric (LSE) and longitudinal section magnetic (LSM) modes. Derivations of these hybrid space modes and development of the modal expansions are presented first. The impedance of the dipole element is then calculated by a method based on the complex power relations with the aid of Poynting's theorem. The results calculated by the present theory in the limiting case of no dielectric slab loading have been compared with the results calculated by the method of ordinary plane wave expansions. A comparison is also made between results calculated by the theory and the experimental data obtained from waveguide simulators or test array. These results are shown to be in good agreement. An outline of steps to formulate the solution of the current distribution on dipole is also given.     

Calculation of the frequency characteristics of the electromagnetic radiation of waveguide-horn antennas

A method for calculation of the frequency characteristics of the electromagnetic radiation of waveguide-horn antennas is proposed. The method is based of frequency expansions of the field of the electromagnetic radiation of the antenna excited by auxiliary finite pulses. This radiation is calculated with the use of the method of nonstationary waveguide equations and the concept of a virtual electromagnetic waveguide. Examples of calculation of the amplitude-phase characteristics of the circuit and radiation patterns at fixed frequencies are presented. It is shown that a high accuracy of determination of frequency characteristics is attainable in rather wide frequency band.     

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].     

Combination of generalized admittance matrices in the form of poleexpansions

This paper describes a novel algorithm for the determination of the wide-band mathematical model of a waveguide component, segmented into elementary blocks of known characteristics. Starting from the Y-matrices of the blocks, given in the form of pole expansions in the frequency domain, the algorithm yields the overall Y-matrix in the same form. Therefore, it can be applied iteratively to find the pole expansion of the Y-matrix of larger and larger waveguide structures. The algorithm is particularly useful if the Y-matrix of the blocks are obtained by the boundary-integral-resonant-mode-expansion (BI-RME) method, which yields the Y-parameters just in the desired form. Two examples show that the joint use of the BI-RME method and of the algorithm described in this paper results in a very accurate and fast numerical code, well-suited for the wide-band modeling of complex waveguide structures     

Circular Waveguide with Sinusoidally Perturbed Walls

Uniform second-order asymptotic expansions are obtained for the propagation of TM waves in a perfectly conducting circular waveguide with sinusoidally perturbed walls using the method of multiple scales. The analysis concerns the interaction of two propagating modes satisfying the resonance condition imposed by the periodicity of the waveguide walls. Two cases of resonance are treated as well as the case of decoupled modes. In the first case resonance occurs whenever the difference between the wavenumbers of the two interacting modes is nearly equal to the wall wavenumber, while in the second case the difference is nearly equal to twice the wall wavenumber. The results of the theory are then applied to the design of a mode coupler.     

Field theoretical treatment of E-plane waveguide junctionswith anisotropic medium

E-plane waveguide junctions containing an anisotropic medium are analyzed. The analysis is based on the equivalence principle and on cavity field expansions. Using the equivalence principle, magnetic surface currents are introduced at the imaginary boundaries chosen between the central region of the junction and the waveguides. The electric displacement D in the junction is expressed in terms of a solenoidal set and an irrotational set. Matching the tangential magnetic field at the imaginary boundaries leads to a matrix equation, the unknown of which are the amplitudes of the scattered waveguide modes. Using this method, the performance of E-plane waveguide junctions with full-height and partial-height ferrite post is analyzed. The influence of the completeness terms G_oq on the numerical results of an empty E-plane Y-junction is shown. The numerical results are compared with previously published experimental and theoretical results     

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     

Accurate modelling of unilateral finline-coplanar waveguide transition

Using the spectral domain technique in conjunction with finite element slot field expansions, the scattering characteristics of the unilateral finline-coplanar waveguide transition are analysed. Flexible rooftop functions varying in both the transverse and longitudinal directions are used instead of a uniform rooftop function as expansion functions to handle arbitrary slot width structures. A typical example is computed. The numerical results for the special case agree well with those available in the literature.<>     

Finite-element coupling matrices

Finite-element coupling matrices are given for hybrid-mode problems in waveguide structures. The matrices refer to Nth-order polynomial expansions of the field, where N = 1, 2, 3, 4 and are antisymmetric and independent of the shape of the element triangle.     

Field theoretical treatment of H-plane waveguide junctionswith anisotropic medium

A method based on the equivalence principle and cavity field expansions is used to analyze an H-plane waveguide junction containing an anisotropic (ferrite or composite ferrite) post. Using the equivalence principle, magnetic surface currents are introduced at the imaginary boundaries chosen between the central region of the junction and the waveguides. The electric displacement in the junction can be completely expressed in terms of a solenoidal set. On the other hand, the magnetic induction in the junction must be expressed in terms of a solenoidal set and an irrotational set. Continuing the tangential magnetic field at the imaginary boundaries leads to a matrix equation, the unknowns of which are the amplitudes of the scattered waveguide modes. Using this method, H-plane waveguide junctions with ferrite and composite ferrite posts are considered. The numerical results show excellent agreement with previously published experimental and theoretical results     

Response of a grounded dielectric slab to an impulse line sourceusing leaky modes

Describes how expansions in leaky (or improper) modes may be used to represent the continuous spectrum in an open radiating waveguide. The technique requires a thorough knowledge of the life history of the improper modes as they migrate from improper to proper Riemann surfaces. The method is illustrated by finding the electric field resulting from an impulsively forced current located in the free space above a grounded dielectric slab     

Perturbation analysis of electromagnetic eigenmodes in toroidalwaveguides

The propagation of electromagnetic waves in a loss-free inhomogeneous hollow conducting waveguide with circular cross section and uniform plane curvature of the longitudinal axis is considered. The explicit solution of Maxwell's equations cannot be given in toroidal waveguides. For small curvature the field equations can, however, be solved by means of an analytical approximation method. In this approximation the curvature of the axis of the waveguide is considered as a disturbance of the straight circular cylinder, and the perturbed torus field is expanded in eigenfunctions of the unperturbed problem. Using the Rayleigh-Schrodinger perturbation theory eigenvalues and eigenfunctions containing first-order correction terms are derived for the full spectrum of all modes, including the degenerate ones. Complicated series expansions are obtained and are represented in closed form by means of the residue theorem     

A Numerical Method for the Solution of the Junction of Cylindrical Waveguides (Short Papers)

In order to solve the waveguide junction problem numerically, we express the fields in the guides by truncated modal expansions and construct an error function which is a measure of the mean-square error in the matching of the boundary conditions at the junction. The minimum of this error leads to a set of linear equations for the modal amplitudes. Offset rectangular waveguides with amplitude and current excitations are studied. A weighting factor which multiplies the error contribution due to the magnetic field is studied, and a criterion for its selection given.     

A general power-series expansion method for exact analysis of the guided modes in an optical fiber

A power-series expansion method for rigorous analysis of the guided modes in a cylindrical, radially inhomogeneous, dielectric waveguide is presented. The method is developed for an arbitrary piece-wise polynomial permittivity profile. The field solutions of the inhomogeneous core are constructed by a sequence of power-series expansions. Convergence is ensured and accuracy maintained by regulating the distance between successive expansion points. The characteristic equation and the cutoff conditions are expressed in a unified manner as a set of functions. The method presented is competitive in terms of accuracy achieved and computing time required.     

Bessel函数与三角函数之积的级数展开及在微波滤波器中的应用

根据对平面波函数运用Fourier-Bessel定理,经过一系列推导并进行反Fourier变换,得到了直角坐标系下Bessel函数与三角函数之积的一种级数展开,该表达式应用到矩-圆波导结的计算中,能解析地推出其广义S参数,得到与文献和HFSS软件较为一致的结果.计算了Ku和Ka频段多种尺寸的有厚度的矩形孔的耦合系数,并与文献、实验数据进行了比较,吻合较好,设计了一个Ku频段6阶类椭圆函数滤波器,实验性能与理论结果一致.     

双指数脉冲在等离子体中传播的二阶渐近展开及其特性

本文用最速下降法推导了等离子体中双指数脉冲传播的一阶和二阶渐近展开式，并进一步推导了基于一阶渐近展开式的幅度和相位的解析表达式。然后讨论了一阶渐近展开式的精度，并基于一阶渐近展开式讨论了双指数脉冲在等离子体中的传输特性，最后通过数值算例与Hosnon方法和支割线积分法的结果进行比较，验证了渐近展开式的正确性。     

Analysis of waveguide discontinuities using edge elements in ahybrid mode matching/finite elements approach

A mode matching (MM)/finite element method (FEM) for the analysis of waveguide discontinuities is presented. The hybrid approach described combines the computational efficiency of the modal analysis with the versatility and flexibility of FEM and enables us to accurately model arbitrary cross section waveguides, where modal expansions cannot be derived analytically. The proposed procedure is based on the edge element expansion of the transverse field components for the direct calculation of the coupling integrals involved in the MM formulation. Numerical and experimental results are presented to show the validity and the accuracy of the method     

Rigorous TE solution to the dielectric wedge antenna fed by a slab waveguide

A rigorous TE solution to the dielectric wedge antenna fed by a slab waveguide of the same material is presented. The method of solution involves modeling the wedge as a sequence of step discontinuities and uses an iterative procedure to track forward and backward partial wave fields, expressed as modal expansions, to obtain the rigorous field solution. Radiation patterns of directive gain are presented. All patterns smoothly decrease from a maximum in the endfire direction and exhibit extremely low side lobe levels. Longer length wedges or smaller dielectric constant materials are shown to produce higher directivity and smaller half-power beamwidths. For slender, gradually tapered wedges, the reflection coefficient of the guided (surface) wave at the input to the wedge is very small indicating a low VSWR for tapered dielectric antennas and there appears to be no gain limitation with antenna length for these antennas.