Computer Analysis of Latching Phase Shifters in Rectangular Waveguide (Short Papers)

In the statistical literature, several large comparative studies have been conducted on the confidence intervals of proportions. However, few comparative studies have focused on the confidence intervals for extreme event proportions (e.g. zero-failure or all-success events) calculated using exact, approximate, and Bayesian methods. In this study, an extensive simulation with three-level nesting, comprising 980 million parameter space points, was designed based on the relationship between the binomial and beta distributions. After thoroughly examining three evaluation criteria – interval width, coverage, and oscillation – the exact method is recommended for estimating confidence intervals for extreme event proportions. The rationale for this recommendation is explained from four perspectives: exact vs. approximate methods, frequentist vs Bayesian methods, average coverage vs coverage oscillation, and the representativeness of the evaluated methods. Three real-world case studies further demonstrate the validity of this recommendation.

Context. The problem is to systematize and improve the models of a resonance ferrite isolator in the rectangular waveguide for the antenna-feeder devices, generating, receiving, measuring microwave equipment containing ferrite decoupling devices: ferrite isolators and circulators. Objective. The goal of the work is to verify the formula for the losses of the resonant ferrite isolator in the direct and reverse directions, as well as the isolator ratio. Method. The research method of the work is a critical analysis of literary sources, which was carried out, but did not bring the desired results, since it did not allow to verify the correctness of the derivation of the formula [17]. Therefore, a number of hypotheses were put forward, what the formula might mean. The difficulty lay in the presence in the formula of the product of trigonometric functions that can be attributed to frequency properties, which was taken as an initial hypothesis, which was not subsequently confirmed. The check included transformation of formulas using mathematical physics in terms of microwave electrodynamics, trigonometry and algebra. The beginning was the formula of the classics [16], similar to the formula of [18], accepted without proof. As it is known, for the main type of wave in a rectangular waveguide, the components of the magnetic field strength, obtained as a solution to the wave equation under the boundary conditions inherent in a rectangular waveguide. One component of the magnetic field strength is along the direction of wave propagation, and the second one is in the transverse direction in the section of the waveguide are proportional to the trigonometric functions cosine and sine with the same arguments. The equality of the two components of the strengths is traditionally uses to find the plane of circular polarization where to place the ferrite isolator, and so the authors use this proportionality to trigonometric functions in their derivation, namely the formulas of trigonometric functions of a double angle, the basic trigonometric identity sine squared plus cosine squared is equal to one for replacing the propagation constants with trigonometric functions, this allows to get rid of radicals in the formulas, these radicals in the formula are due to the phenomenon of dispersion in a rectangular waveguide. The rest of the manipulations with the formula are the reduction of similar terms. Results. There was obtained analytical expressions for the losses of the resonant ferrite isolator in the forward and reverse directions, as well as the isolator ratio by strict mathematical transformations. There was performed such transformations. The ratios of the longitudinal propagation constant to the transverse propagation constant are replaced by the ratios of the trigonometric functions sine and cosine, since they are continuous as opposed to tangents and cotangents. Such a transformation allows to avoid square roots in the formula for the losses of the ferrite isolator in the forward and reverse directions, which are associated with the presence of dispersion in the waveguide, as in the formula for wavelength in the waveguide. The conversion is based on microwave electrodynamics. The formulas are used for the distribution of fields in a rectangular waveguide for the main type of wave. Further transformations consist in taking the common factor out of brackets and other arithmetic transformations. Conclusions. Тhrer was obtained results partially coincide with the well-known [17], the derivation of the formula [17] was obtained for the first time, the studies carried out allowed us to reject the hypothesis that the product of cosines and sines in the loss formula of a ferrite isolator is a frequency characteristic, it appears as a result of arithmetic transformations. To take into account the frequency range, it is used that there is circular polarization at the middle frequency, there will also be circular polarization at the extreme frequency of the range, but the plane of circular polarization will shift in comparison with the position of the plane of circular polarization at the middle frequency. That is, a peculiar system of two equations is obtained with respect to two positions of the polarization plane relative to the wide side of the rectangular waveguide section. The scientific novelty consists in systematization and generalization of the formulas of the loss of the resonance ferrite isolator, the connection between the formulas from different literature sources, both foreign and domestic, is proved, which saves time for researchers of ferrite isolators for the verification of the formula. The practical significance. It may be useful for teaching purposes and in optimization of the ferrite isolator design.

The behavior of several lower order modes in a sectoral waveguide is investigated. It is shown that their sequence order depends on the flare angle of the sector. It is found that, at an angle smaller than 135°, the waveguide may operate in a single-mode regime with the H 01 mode. The per-unit-length attenuation of the H 01 mode in a sectoral waveguide is analyzed and compared to the attenuation of the H 10 mode in a rectangular waveguide.

An accurate design technique of dual-mode microwave dielectric or air-filled rectangular waveguide filters is described. Dual-mode coupling is realized by a section of rectangular waveguide with square-corner-cut. The unequal couplings between dual-mode pairs of the cavities is provided by a section of evanescent mode waveguide. Rigorous analyses are applied to characterize the microwave junctions and to obtain the design parameters for the filter. The design procedure used to determine the dimensions of the waveguide junctions with a minimum of computational effort is described. The design is demonstrated by four-pole and six-pole dual-mode rectangular waveguide elliptic function filters. Excellent agreement between computer simulation and experimental results with absolutely no tuning justifies the design.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The computer‐aided analysis and design of direct‐coupled and quarter‐wave‐coupled bandpass filters utilizing monomode rectangular waveguides with 1‐dimensional offset discontinuities are described. The equivalent networks of these discontinuities, which consist of a shunt reactance and additional transmission lines connected at both sides, have been derived from the rigorous field‐theoretical investigations of E‐plane and H‐plane displacements in rectangular waveguide. Both network elements are tabulated in terms of geometry and wavelength with fine steps to allow accurate interpolation by means of computational methods, Simple design formulae for the filter geometry as a function of the electrical specifications are given which are based upon narrow‐band approximations. The analytical relationships required for a computer simulation of the filter's wide‐band performance are summarized. The predicted frequency characteristics showed such close agreement with the experimental results obtained on two X‐band filter models that neither tuning elements in the waveguide sections nor final adjustments of the offset widths had to be provided.

A recently developed, rapidly converging moment solution for electromagnetic scattering by a single inductive post in a rectangular waveguide is extended to include the current induced on the past surface. The results are represented by a Fourier series and the first few terms are compared with available data. The excellent agreement demonstrates that this approach can yield an accurate solution. This rather simple procedure is even more attractive when other waveguide obstacles such as thick irises and posts of arbitrary shape, which require, in general, more than just a few Fourier terms for their current representation, are encountered.

Both exact and simplified approximate equations for the current on a pair of conductors above a dissipative Earth are developed. Since, in many practical cases, each conductor consists of a pair of wires, a method for reducing four-wire lines to equivalent two-wire lines is presented. The assumptions used in the approximate expression are that the cross-sectional dimensions of the line (e.g. the distances between conductors but not the height of the conductors above earth) are small compared to the wavelength, that the propagation constant in the Earth is larger than the one in air, and that the conductors are thin compared to the wavelength and any cross-sectional dimension. The first assumption restricts the validity of the equations for the current to below 100 MHz ( lambda =3 m) for typical transmission lines and the second assumption can be met for most practical air-Earth problems. Numerical results for transmission line loss are computed using both the approximate method and the exact method. It is seen that the two results agree well for frequencies less that 100 MHz. The loss is divided into conductor loss and Earth loss and plotted, and physical interpretation of the frequency dependence of each component is given. The results of a parametric study of transmission-line loss are given along with an interpretation.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Generalized quantum master equations (GQMEs) are an important tool in modeling chemical and physical processes. For a large number of problems, it has been shown that exact and approximate quantum dynamics methods can be made dramatically more efficient, and in the latter case more accurate, by proceeding via the GQME formalism. However, there are many situations where utilizing the GQME approach with an approximate method has been observed to return the same dynamics as using that method directly. Here, for systems both in and out of equilibrium, we provide a more detailed understanding of the conditions under which using an approximate method can yield benefits when combined with the GQME formalism. In particular, we demonstrate the necessary manipulations, which are satisfied by exact quantum dynamics, that are required to recast the memory kernel in a form that can be analytically shown to yield the same result as a direct application of the dynamics regardless of the approximation used. By considering the connections between these forms of the kernel, we derive the conditions that approximate methods must satisfy if they are to offer different results when used in conjunction with the GQME formalism. These analytical results thus provide new insights as to when proceeding via the GQME approach can be used to improve the accuracy of simulations.

A new polarization filter with no element inside the circular waveguide is presented. It is realized by the insertion of rectangular waveguide sections in a circular waveguide. The validity of this new design is verified on a prototype model.

Utilization of graphene covered waveguide inserts to form tunable waveguide resonators is theoretically explained and rigorously investigated by means of full-wave numerical electromagnetic simulations. Instead of using graphene-based switching elements, the concept we propose incorporates graphene sheets as parts of a resonator. Electrostatic tuning of the graphene surface conductivity leads to changes in the electromagnetic field boundary conditions at the resonator edges and surfaces, thus producing an effect similar to varying the electrical length of a resonator. The presented outline of the theoretical background serves to give phenomenological insight into the resonator behavior, but it can also be used to develop customized software tools for design and optimization of graphene-based resonators and filters. Due to the linear dependence of the imaginary part of the graphene surface impedance on frequency, the proposed concept was expected to become effective for frequencies above 100 GHz, which is confirmed by the numerical simulations. A frequency range from 100 GHz up to 1100 GHz, where the rectangular waveguides are used, is considered. Simple, all-graphene-based resonators are analyzed first, to assess the achievable tunability and to check the performance throughout the considered frequency range. Graphene–metal combined waveguide resonators are proposed in order to preserve the excellent quality factors typical for the type of waveguide discontinuities used. Dependence of resonator properties on key design parameters is studied in detail. Dependence of resonator properties throughout the frequency range of interest is studied using eight different waveguide sections appropriate for different frequency intervals. Proposed resonators are aimed at applications in the submillimeter-wave spectral region, serving as the compact tunable components for the design of bandpass filters and other devices.

Several RF and microwave radiating devices, such as horn antennas, Fabry–Perot cavity antennas, and aperture-fed focusing devices, are excited through rectangular waveguides. The impedance matching of the overall system (from the waveguide feed to the radiating aperture) is a task of crucial importance that is often addressed by means of brute-force parameter-sweep full-wave analyses or blind optimization algorithms. In both cases, a significant amount of memory and time resources are required. For this purpose, we propose here a simple, yet effective solution, which only requires a single full-wave simulation and a semi-analytical procedure. The former is used to retrieve the antenna input impedance at the end of the waveguide port excitation. The semi-analytical procedure consists in a transmission-line equivalent circuit that models two waveguide discontinuities (namely two capacitive irises) within the waveguide section, whose position and geometric features are finely tuned to obtain a satisfactory impedance matching around the working frequency. The proposed method is shown to be effective in diverse and attractive application-oriented contexts, from the impedance matching of a Fabry–Perot cavity antenna to that of a wireless near-field link between two aperture-fed focusing devices. A remarkable agreement between full-wave simulations and numerical results is found in all cases. Thanks to its versatility, simplicity, and a rather low demand of computational resources, the proposed approach may become an essential tool for the effective design of waveguide-fed antennas.

Rectangular waveguide section with two partial-height transversal inserts located side by side is examined. Such a section acts as a resonator providing two transmission zeros and one transmission resonance located between these zeros simultaneously. Thus, the number of transmission zeros is twice more than the number of waveguide sections. The broadband quarter-wavelength resonator filter using such sections provides two stopbands and one passband simultaneously. Their bandwidths and locations are controlled both by the section geometry and the distance between the sections. Two closely spaced sections providing two independent stopbands are proposed as a perspective block for a filter with complicated frequency response.

The electric field in a waveguide partially filled with a low-loss slab of dielectric in the H plane presents a Circularly polarized component at the air-dielectric interface over a limited frequency range. This effect could be used to improve the performance of nonreciprocal devices utilizing the gyroelectric effect in magnetized semiconductors.

We investigate rotation-induced Fermi resonances in HOCl by the adiabatic rotation (AR), centrifugal sudden (CS), and exact methods, using a highly accurate potential energy surface [Skokov, S.; Peterson, K. A.; Bowman, J. M. Chem. Phys. Lett. 1999, 312, 494]. We focus on the rotationally mediated interaction between the (2,3,3) and (3,2,0) (vOH,vbend,vOCl) states in the K = 4 subband using exact, AR, and CS methods. A simple two-state model is used to analyze the interaction, and interaction parameters are determined and compared with those of the experiment. A similar analysis is done for the high-energy interacting pair of states (4,0,0) and (3,2,1), using the AR method, and good agreement with the experiment is found. The comparison between AR calculations and the experiment for the metastable (6,0,0) and (4,4,2) states in the K = 0 subband shows good agreement for the value of J where zero-order states cross but not for the coupling constant. We also study rotationally mediated coupling in the pairs of states (1,0,2) and (0,3,2), (1,1,1) and (1,4,1), and (3,0,0) and (2,1,3) using exact and approximate methods. These interactions have not been studied experimentally.

Comparison of exact and approximate methods of solving the uncapacitated plant location problem