Analysis of narrow wall slots in a rectangular waveguide excited by tilted wires using the virtual cylinder method

Slots in rectangular waveguides are often used at elements in linear array antennas. The polarisation of the radiated energy is usually linear. Circular polarisation can be obtained with compound slots in the broad wall. Experiments have shown that circular polarisation can be obtained from certain I-shaped slots in the narrow wall.

The integral-equation method has been applied along with perturbation theory to investigate the leaky-wave parameters of the fundamental mode in the regular waveguide with a narrow longitudinal slot on its broad wall, opened into shielded semispace. Then, the simple analytical formulas have been derived for the engineering synthesis of radiating elements (REs), which are formed by a nonuniform waveguide section with a nonregular slot on its broad wall. The long slot was cut in the longitudinal direction along certain curved or several connected broken lines, forming small local angles with the waveguide axis. The synthesis of RE's by single-mode approximation has been carried out for the condition of good uniformity of radiating electrical-field distribution along the RE axis near the slot. Good agreement of theoretical and experimental results was obtained.

Over the last decade, several methods [1–8] have been developed to obtain the dyadic Green's functions (DGFs) of layered anisotropic media. The most commonly used methods to find the DGFs are the Fourier transform method with differential formulation [6], the method of eigen-function expansion [7], the matrix formulation [8], and the dyadic decomposition techniques [5, 9–11]. In [8], the dyadic Green's function is formulated based on the tangential electric field and current at the interface, which is not suitable for the problem with z-directed current. The dyadic decomposition techniques as discussed in [5, 9–11] are more general and can provide the complete set of the dyadic Green's functions but only the case when the source is in the free space has been considered. If the source is located in a biaxial slab, then reciprocity theorem for the Green's function can be invoked to obtain the DGFs as in [12]. However, the reciprocity holds true only when the slab is filled with reciprocal medium such as uniaxial medium, biaxial medium, etc. For non-reciprocal medium such as the gyroelectric or gyromagnetic medium, the reciprocity relation for the Green's function no longer holds. The DGFs for source located in a non-reciprocal slab cannot be obtained using the reciprocity theorem.

For of applications of waveguide-slot antennas, it is important to know the radiation characteristics of the slot in a rectangular waveguide wall radiating into a parallel-plate waveguide (PPW). In this work the properties of a longitudinal slot in the narrow wall of a rectangular waveguide radiating into a PPW are investigated. A model of a waveguide-slot radiator is presented and an accurate mathematical analysis provided. It is shown how to improve and optimize the matching of the considered radiators.

A full-wave numerical approach is proposed for analyzing rectangular waveguides with periodic slots. The approach is based on an aperture magnetic field integral equation in one unit cell. The presented technique can analyze both bound and leaky modes on rectangular waveguides with periodic slots that have a rather arbitrary shape on either the broad or narrow wall. Besides, the method can be used for a uniformly slit rectangular waveguide by taking the limit of the period. Using the proposed method, it is found that an air-filled rectangular waveguide with periodic longitudinal slots supports a leaky waveguide mode but no slot mode, while a uniformly slit rectangular waveguide (air-filled) can support a leaky waveguide mode as well as a slot mode. It is also found that an air-filled rectangular waveguide with cross slots supports a surface-wave mode in addition to a leaky waveguide mode.

Recent formulations of the dyadic (or generalized) Green's function describe the relationship between sources (both mechanical stresses and electrical charge) and waves (both mechanical displacements and acoustic potential) on the surface of a substrate. The sixteen elements of the function intrinsically describe all propagation modes, whether Rayleigh or leaky, and are therefore extremely useful in the design of surface acoustic wave devices. While requiring little additional computational effort, the dyadic Green's function thus provides much more information than the traditional effective permittivity function. In this paper, we extend the calculation of the dyadic Green's function to multi-layer substrates. We show that its computation involves a simple cascaded matrix multiplication. The resulting function fully contains the substrate characteristics and, once obtained, can be used to describe the surface behavior with no further regard to the substrate's composition. The dyadic Green's function for a sample multi-layer substrate is presented.

A mathematical representation is constructed for a combined radiating system consisting of a rectangular waveguide with a transverse slot in its broad wall, complemented by impedance monopoles. Two monopoles are arranged externally to the waveguide, while a third is placed inside, forming a configuration equivalent to the well-known Clavin radiator. To analyze this arrangement, a semi-analytical approach is applied, where the system of integral equations is solved using the technique of induced electromagnetomotive forces. The study explores how variations in the geometrical dimensions and electromagnetic properties of the elements provide means to regulate the radiation performance of the structure.

The electric field within a source region is derived by use of a vector form of Green's second identity. The expression obtained is identical to that previously derived1 by a less direct method, but the present approach exposes the need to assume continuity of current density and electric field. The analysis gives the extra dyadic which must be added to the customary superposition integral to take account of the source-point singularity of the electric dyadic Green's function.

The dyadic Green's functions for a parallel-plate chirowaveguide are formulated by using the method of eigenfunction expansion. The eigenfunctions of the chirowaveguide are derived first in terms of two transformed fields. The purely solenoidal magnetic type dyadic Green's function is then expanded by these eigenfunctions. The electric type dyadic Green's function, which is solenoidal as well as longitudinal, is subsequently obtained from the magnetic dyadic Green's function through a simple relationship. It is found that the singular term in the electric dyadic Green's function accounting for the electric field in the source point is established through this latter procedure. The dyadic Green's functions obtained can be used to examine the electric and magnetic fields inside the chirowaveguide and to construct other dyadic Green's functions.

The use of a dyadic layered-medium Green's function as the kernel in a method of moments (MoM) modeling problem greatly reduces the complexity of modeling a stratified medium. Compared to the free-space Green's function, there is an additional cost of having to compute a semi-infinite Sommerfeld integral for each call to calculate the dyadic layered-medium Green's function. This letter discusses a method to tabulate and interpolate the Green's function as a method of reducing the impedance matrix filling time. This method can be used in conjunction with existing methods for increasing the computational speed of the Green's functions.

The convective rates of heat transfer through inclined longitudinal slots is studied for the case where heat is transferred from a lower heated isothermal surface, through the slots, to an upper cooled isothermal surface. Experimental data are given for longitudinal slots having aspect ratios from 6–12, slot heights of 25–60 mm, inclinations from horizontal to vertical, and Ra < 107. Data are also given for a transverse slot of aspect ratio 6, for inclinations from horizontal to vertical, and Ra < 107. It is shown that convective heat transfer rates are essentially independent of slot orientation for inclinations up to 15 deg from the horizontal, but longitudinal slots are more effective in suppressing natural convection than transverse slots with the same aspect ratio, for inclinations from 24 to 75 deg from the horizontal. The difference in heat transfer rates for longitudinal and transverse slots inclined between 24 and 75 deg from the horizontal are shown to be due to different convective flows occurring in each slot. The heat flow measurements are supported by convective flow visualization experiments which demonstrate the modes of convective flow within slots.

We propose a novel excitation technique of an untilted slot in the narrow wall of a rectangular waveguide. The excitation is realized by inserting into the slot a dielectric plate on which there are etched conducting strips. The strip excitation can control the coupling more easily and accurately than a conventional excitation using tilted wires. We analyze the coupling to the slot by using the dyadic Green's function for the waveguide with the dielectric plate, derived by Seki's (1984) virtual cavity method. A double resonance due to the strip and the slot results in large coupling as well as small variation of the phase of the transmitted wave, both over a wide frequency band. Some results are verified by measurements. The coupling can be tuned by varying the distance between the slot and the strip.

The authors proposed a circularly polarized conical beam spherical slot array antenna for applications of low bit rate or low gain/temperature ratio (G/T) land mobile satellite communication and broadcasting services in addition to wireless local area network base stations (see Krairiksh, M. et al., Int. J. Electronics, vol.86, no.7, p.815-23, 1999). The advantage of this antenna is that the structure is simple and suitable for mass production and the feeding structure is also simple. From preliminary results, the radiation pattern appears to be a conical beam (see Phongcharoenpanich, C. et al., IEICE Trans. Electronics, vol.E82-C, no.7, p.1242-7, 1999). This paper presents the theory and experiment of a circularly polarized conical beam spherical slot array antenna. The theoretical result is carried out by means of the method of moments. With the aid of the dyadic Green's function, the integral equations of the unknown currents are solved by using entire domain basis functions and Galerkin's method. The theoretical results of the radiation pattern, elevation angle and directivity, input impedance and axial ratio are illustrated. The experimental results agreed satisfactorily with the theoretical ones.

To characterize electromagnetic waves in complex media has been an important topic because of the useful applications and the scientific significance of the physical mechanism. Dyadic Green's functions, as a mathematical kernel or a dielectric medium response, relate directly the radiated electromagnetic fields and the source distribution. In terms of the vector wave functions in cylindrical coordinates, dyadic Green's functions in an unbounded and a planar, multilayered gyroelectric chiral media are formulated. After a general representation of the Green's dyadics is obtained, the scattering coefficients of the Green's dyadics are determined from the boundary conditions at each interface and are expressed in a greatly compact form of recurrence matrices. In the formulation of the Green's dyadics and their scattering coefficients, three cases are considered, i.e. the current source is impressed in (1) the first, (2) the intermediate, and (3) the last regions, respectively. Although the dyadic Green's functions for an unbounded gyroelectric chiral medium have been reported in the literature, the results are either incorrect or suspicious. As compared to the existing results, the current work basically contributes (1) a correct form of the dyadic Green's function for a unbounded gyroelectric chiral medium, (2) the general representation of the dyadic Green's functions for a multi-layered gyroelectric chiral medium, and (3) a convincing and direct derivation of the irrotational Green's dyadic.

The dyadic Green's functions of the cylindrical chirowaveguide are derived by modal expansion. Bohren's decomposition of the electromagnetic field is used to obtain the vector wave functions. The magnetic dyadic Green's function that is purely solenoidal is first derived and the electric dyadic Green's function is then obtained by manipulating the magnetic dyadic Green's function. The singular term in the expression of the electric dyadic Green's function is reinstated through the manipulation procedure.