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].     

Performance of an array of circular waveguides with strip-loadeddielectric hard walls

An infinite planar periodic antenna array of radiating open-ended circular waveguides is considered. The conducting waveguide walls are covered with dielectric layers loaded with longitudinal conducting strips for providing the hard wall boundary condition. Analysis of the array is carried out by the mode-matching method. The waveguide modes involved in the method are calculated by using the asymptotic strip boundary condition. It is shown that they are split into an independent subsystem of TE modes for the whole cross section and two independent subsystems of TM modes: one is for the central region and another is for the layer region. The calculations show that the operation of the hard waveguides in an array with small element spacing is similar to that of the multimode smooth wall waveguides completely filled with dielectric. For large diameters and element spacing, the hard waveguides have significant advantages over the smooth ones. It is shown that unlike an individual hard waveguide, the aperture efficiency of such a waveguide in the array has a nonmonotonic dependence on the waveguide radius. The results characterizing the behavior of the aperture efficiency and cross-polarization level in a frequency band as well as the contribution of certain waveguide modes in the reflected power are presented and discussed. The examples of the element patterns corresponding to minimal cross polarization are also given     

Generalized Coupled Dielectric Waveguide and its Variants for Millimeter-Wave Applications

The characteristic equations of hybrid TM and TE modes for a generalized coupled dielectric waveguide are derived using the mode-matching technique. From the characteristic equations of the generalized coupled dieketric waveguide, the phase constant, wave impedance, and field distribution can be evaluated. A variety of single and coupled dielectric waveguides can be obtained by assigning proper parameter values to the generalized coupled dielectric waveguide.     

Image theory for the soft and hard surface

Image theory is developed for sources above a planar anisotropic boundary surface, often labeled as soft and hard surface. Realizable with tuned corrugations so that the electric and magnetic field components along the corrugations become zero. The idea pursued is to decompose the original source in two components, giving rise to fields TE and TM to the direction of corrugation, respectively. This makes the problem split into two parts for which the image sources can be easily constructed. For an electric dipole, the image turns out to consist of a rotated dipole in the mirror image point plus a transmission-line current source parallel to the corrugations. The theory is readily applicable to various microwave problems involving a planar soft and hard surface     

Rectangular Waveguides with Impedance Walls

The propagation of guided waves in a rectangular geometry having impedance boundary conditions is investigated. An impedance compatibility relation is derived that must be satisfied in order that a separable modal solution exists for a given impedance configuration. Several new rectangular waveguides are developed; among them are 1) a tall rectangular waveguide operating in a dominant H/sub 10/ mode with no H/sub 0N/ modes; 2) a rectangular waveguide with two parallel anisotropic impedance surfaces; 3) a rectangular waveguide with two parallel walls having isotropic impedance surfaces, the other two walls being anisotropic; 4) a rectangular waveguide supporting only E modes; and 5) rectangular coaxial systems containing impedance surfaces. The modal structure of rectangular waveguides with impedance boundary conditions offers advantages over the conventional waveguide. The potential of oversizing for low-loss and high-power applications is enhanced because of the additional modal control provided by the impedance surfaces. Other applications are suggested.     

A revised formulation of modal absorbing and matched modal sourceboundary conditions for the efficient FDTD analysis of waveguidestructures

A revised formulation of modal absorbing and matched modal source boundary condition is proposed for the efficient analysis of a waveguide circuit with the finite-difference time-domain (FDTD) method. The formulation is based on a suitable translation operator modeling, in time domain, the propagation in a uniform hollow waveguide. By applying this operator, a multimodal absorbing boundary condition is obtained. Moreover, a source algorithm is developed that generates a given incident wave, while absorbing each modal component reflected from a discontinuity. The source is capable of separating incident and reflected waves without requiring any presimulation of long uniform waveguides. The validity and effectiveness of the formulation is verified by means of three numerical experiments. The first two refer to waveguide discontinuities. In these cases, the FDTD results are compared to mode-matching results. The third example is a transition from waveguide to printed circuit transmission line. The numerical simulation is compared with published experimental results. The presented examples show that the generalized scattering matrix of a waveguide circuit can be evaluated accurately in the smallest computational space allowed by the structure     

Modal MRTD approaches for the efficient analysis of waveguidediscontinuities

This paper, the multi-resolution time-domain (MRTD) technique is applied to the waveguide discontinuity problem for fast-scattering parameter computation. To improve the computational efficiency, both three-dimensional (3-D) waveguide regions, including discontinuities, and one dimensional (1-D) homogeneous waveguide region, terminated with the modal absorbing boundary condition (ABC), are simulated in the wavelet domain with the mode composition/expansion algorithm from the modal analysis. A WG-90 rectangular waveguide with a thick asymmetric iris is analyzed and the numerical results are compared with conventional finite-difference time-domain (FDTD) results and mode-matching results     

Rigorous Analysis of the Scattering of Surface Waves in an Abruptly Ended Slab Dielectric Waveguide

The reflection and the scattering properties of even TE and TM surface waves incident in an abruptly ended dielectric slab waveguide are analyzed. The discontinuity is regarded as a junction between two open waveguides namely the dielectric slab waveguide and the free space waveguide. The boundary conditions acting together with the orthogonality provide singular coupled integral equations on the discrete and the continuous wave amplitudes at the discontinuity. These singular coupled intergral equations with Cauchy kernels and infinite limits of integration are solved by iteration via the Neuman series. Numerical results are presented for the reflectivity of the even TE/sub 0/ and TM/sub 0/ fundamental modes, together with their mode conversion on even TE/sub 2/ and TM/sub 2/ in a slab where two guided modes can propagate. Reflectivity and mode conversion of higher order excitations are also investigated     

Transmission Characteristics of Spherical TE and TM Modes in Conical Waveguides (Short Papers)

The transmission properties of spherical TE and TM modes in a perfectly conducting conical waveguide are treated in detail. To start with, an analytically simple and highly accurate digital-computer based iterative algorithm has been employed to evaluate the eigenvalues associated with the spherical TE and TM modes within the guide irrespective of the flare angle (2alpha/sub 0/) of the conical waveguide (theta < 2alpha/sub 0/ < 360/spl deg/). Subsequently, explicit expressions for the attenuation constant, phase constant, phase velocity, and wave impedance are obtained for the spherical modes transmitted within the guide. Accurate eigenvalues obtained numerically are used to study the variation of attenuation constant, phase constant, phase velocity, and wave impedance as a function of the radial distance from the apex with alpha/sub 0/ as a parameter. Measured data on the phase constant of a conical waveguide for the TE/sub 11/ mode have been compared with the analytical results obtained by calculation and an excellent agreement between the two justifies the validity of the analysis presented. Finally, a study of the phase coherence between the dominant spherical TE and TM modes within the guide is presented which may be fruitfully employed in the design of dual-mode conical waveguides.     

An effect of excitation of a transverse magnetic creeping wave when a transverse electric wave crosses the line of the coincidence of propagation constants

Transverse electromagnetic electric (TE) and transverse magnetic (TM) creeping waves on a surface with an anisotropic impedance boundary condition are considered. An asymptotic theory is developed for creeping waves. The theory is valid near the line where the attenuation parameters of two different types of waves coincide and, therefore, standard asymptotics are inapplicable. Asymptotic formulas describing physical effects that occur when a creeping wave propagates across the degeneracy line are derived. It is found that, behind the degeneracy line, a propagating TE wave excites a TM wave with a small amplitude (of order O(k ^−1/6)) and a propagating TM wave excites a TE wave.     

A method of analysis of TE11-to-HE11 modeconverters

An efficient method for the determination of the scattering matrix of TE₁₁-to-HE₁₁ corrugated cylindrical waveguide mode converters has been developed, based on the representation of the fields inside the corrugations by a small number of radial waveguide modes. Numerical results show that the method, when compared to the usual mode-matching techniques, reduces the computation time without loss of accuracy     

1维方形掺杂光子晶体波导中缺陷模的色散特性

为了研究1维方形掺杂光子晶体波导中缺陷模的色散,采用特征矩阵的方法研究了1维方形掺杂光子晶体波导中TE波和TM波缺陷模的变化特征,得到了TE波和TM波的缺陷模随色散强度、色散厚度变化的结果。结果表明,色散强度和色散厚度都会对1维方形掺杂光子晶体波导中TE波和TM波的缺陷模产生明显的影响;利用TE波和TM波的缺陷模随色散强度、色散厚度的变化规律,可以有效地实现对1维方形掺杂光子晶体波导中TE波和TM波各传输模式的有效控制。     

Full-wave analysis of coplanar waveguides for LiNbO3optical modulators by the mode-matching method considering nonidealconductors on etched buffer layers

Rigorous analysis of traveling-wave coplanar waveguide electrodes for LiNbO₃ optical modulator applications is presented by using an extended full-wave mode-matching method. The microwave propagation characteristics under the composite influence of substrate anisotropy, uniform or etched buffer layers, finite electrode thickness and conductivity, and metallization undercutting are accurately assessed by employing a network equivalent formulation. Variations of the coplanar waveguide microwave effective index and the characteristic impedance at low frequencies due to finite electrode conductivity are illustrated, and are important even though the mode is quasi-TEM in nature. The effect of etching the SiO₂ buffer layer is shown to be one possible method for lowering the microwave effective index while keeping the conductor loss at a fixed level     

Electromagnetic transmission of an oblique waveguide array

Transverse magnetic (TM) and transverse electric (TE) wave transmissions of an oblique parallel-plate waveguide array is studied. The scattered wave is represented in terms of continuous and discrete modes based on the Fourier transform and series, respectively. The tangential field continuities at the boundary are enforced to obtain simultaneous equations for the discrete modal coefficients. Residue calculus is utilized to transform the radiation field and reflection coefficient into numerically efficient forms. Numerical computations are performed to illustrate the behavior of wave radiation and reception by an oblique waveguide array.     

Modellization of losses in TE011-mode waveguide bandpassfilters

A mode-matching technique for the analysis of TE₀₁₁ mode waveguide cylindrical bandpass filters including losses is presented. The modes of a lossy radial waveguide are derived and the generalized scattering matrix of the lossy cavity coupled by two rectangular apertures is computed enforcing an impedance boundary condition on the cavity sidewall. Cavity sidewall losses as well as top and bottom wall losses are therefore taken accurately into account. Numerical and experimental results are given for a four cavity filter in Ka band     

Eigenvalues for a Spherical Cavity with an Impedance Wall (Correspondence)

The boundary value solution for the resonance frequencies of a spherical cavity with an impedance wall is presented for the TE and TM cases. It is found that in the TE case with a capacitive cavity surface, a new mode exists and corresponds to the fundamental mode. This is in contrast to the perfectly conducting spherical cavity where a TM mode is the lowest order mode.     

对称单负材料平面波导的波导模

基于经典电磁理论建立了芯层为单负材料的对称三层平板波导的导波方程,采用图解法研究了该波导中的TE和TM波导模,分析了TE波导模和TM波导模会受波导参数μ1/μ2和R的影响,给出TE模和TM模解的横向场分布图.结果显示,在单负材料的对称三层平板波导中只存在慢波导模,TE慢波模只能在磁负材料中传播,TM慢波模只能在电负材料...     

Electrodynamic analysis of eigenmodes in a rectangular waveguide with two L-shaped septa

A technique of electrodynamic calculation and computer-aided simulation of the structure of the electromagnetic fields of TE and TM waves in a rectangular waveguide with two L-shaped ridges and a lossless air filling is presented. The problem is solved by means of the partial domain method with allowance for the edge singularity of the electromagnetic field. Cutoff wave numbers, the structure of the electromagnetic fields of various TE — and TM-wave modes in the cutoff regime, the characteristic impedance, and the breakdown power for the fundamental waveguide mode are calculated.     

Cylindrical cavity-backed suspended stripline antenna-theory andexperiment

The problem of a cylindrical cavity-backed suspended stripline (SSL) antenna is viewed as a transition of the SSL to a circular cylindrical waveguide opening into an infinite ground plane. The fields in the waveguide are expanded in terms of TE and TM modes. The effect of the radiating aperture on the modal expansion of the fields is taken into account by introducing reflection coefficients for each mode. The current on the SSL probe is assumed to have sinusoidal distribution. These simplifications reduce the original problem to that of a known radially oriented current residing on a dielectric sheet inside a circular-cylindrical cavity whose top wall has known impedances corresponding to different modes. The Green's function for this modified structure is found and is used to obtain a general expression for the input impedance. This expression is specialized to the case where the SSL probe and the radiating aperture are coupled through the dominant TE ₁₁ mode only. This input impedance is translated to the measurement plane of the antenna. The computed and measured results are found to be in good agreement     

Oblique scattering by a pair of conducting half planes: TM case

An exact series solution for the oblique scattering by a pair of infinitely long parallel edges of perfectly conducting half planes is formulated for a TM plane wave using the mode-matching technique (MMT). The scattered and guided fields are represented in terms of an infinite series of radial waveguide modes. By applying the appropriate boundary conditions, the coefficients of the scattered field are obtained. The diffraction coefficient of double edges is subsequently derived from the scattered field