Stepped Waveguide Research Articles

An Algorithm for Solving Torsional Vibration Problems Based on the Invariant Imbedding Method

In this work the invariant imbedding method has been used to develop an algorithm to study the torsional vibration of non-uniform systems. The algorithm is based on the propagation, reflection, and transmission of waves in a stepped waveguide and is part of a procedure to transform two-point boundary value problems in initial value problems. Based on this approach, a continuous model has been developed and a simple, versatile, and robust algorithm has been constructed to solve torsional vibration problems of non-uniform shafts with circular crosssections. The proposed solution algorithm was extensively evaluated through comparisons with analytical solutions and the finite element method. The results show that the proposed method can provide the exact solution for uniform shafts with concentrated elements and accurate results for a wide variety of torsional vibration problems. Systems with continuously varying geometry may be approximated by stepped shafts. The proposed method can also be used to study the dynamic behaviour of others stepped systems.

Effect of Shape Parameters on the Modal Properties of Stepped Ultrasonic Concentrator

mproving of cutting process is one of the most important requirements that are expected from the machining methods in the recent years. In some machining processes, the positive effect of ultrasonic waves to improve the cutting process is used. The cutting process efficiency depends on the structure of excitation system which generates ultrasonic waves. One of the most important elements of this system is the ultrasonic waveguide. The role of waveguide is the transfer of ultrasonic vibration energy from ultrasonic transducer to the tool cutting edge interacting with the workpiece (ultrasonic assisted machining-UAM). The UAM system performance depends on well-designed ultrasonic waveguide. The most important aspects of waveguide design are a resonant frequency, amplification factor and the determination of waveguide resonant wavelength - usually integer multiple of half wavelength. The effect of geometrical parameters of stepped waveguide on dynamical properties is presented in this paper.

Efficient electromagnetic boundary conditions to accelerate optimization of RF devices

To achieve efficient field formulations and fast numerical computations, the reciprocal relations and equivalence between tangential and normal boundary conditions for electromagnetic fields are discussed in terms of the Maxwell's differential equations. Using the equivalence of each boundary condition, we propose the six essential boundary conditions, which may be applicable to matching electromagnetic discontinuities to efficiently design RF devices. In order to verify our approach, the reflection characteristics of a rectangular waveguide step are compared with respect to six essential boundary conditions.

Polymer-based micromachined rectangular coaxial filters for millimeter-wave applications

In this paper, micromachined devices for millimeter-wave applications at U- and V-bands are presented. These structures are designed using a rectangular coaxial line built of gold-coated SU-8 photoresist layers, where the coaxial center conductor is suspended in air by stubs. The designs include a stepped coplanar waveguide (CPW)-to-coaxial transition at 63 GHz, with an insertion loss of 0.39 dB at 67.75 GHz and a return loss better than −10 dB across the band of operation between 54.7 and 70.3 GHz. Two filters have been designed; one centered at 42 GHz with a 10% bandwidth, and another at 63 GHz with a 5% bandwidth. Measured insertion losses of 0.77 and 2.59 dB were obtained for these filters, respectively. Measured return loss lower than 13.8 dB over the passband was achieved for both designs. The structures presented in this paper involve a low-cost manufacturing process suitable to produce integrated subsystems at millimeter waves.

THREE SECTIONS CIRCULAR WAVEGUIDE APERTURE ANTENNA WITH CONICAL BEAM

A three sections circular waveguide aperture antenna with conical beam is presented. By using two waveguide steps, the aperture distribution of the antenna can be controlled to realize the requirements on the radiation pattern with conical beam including the ∞are angle, gain and the side lobe level. Through optimized design, the impedance bandwidth of 550MHz with i10dB return loss, the gain of 8.1dB and a ∞are angle of 50 degrees have been achieved at the central frequency 35GHz. Good agreement has been observed between simulated results and measured ones. The proposed antenna is easy to be fabricated and suitable for many applications.

A Novel Impedance Matched Mode Generator for Excitation of the TE$_{21}$ Mode in Compact Dual-Mode Circular Waveguide Feeds

A compact dual-mode circular waveguide horn antenna is presented that is fed by the dominant TE <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">$_{11}$</tex> </formula> mode and generates the higher-order TE <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex Notation="TeX">$_{21}$</tex></formula> mode in order to reduce the cross polarization of offset reflectors. To excite the second mode, two blocks and a small discontinuity step are used. These blocks are tangent to the aperture of the second waveguide, as opposed to the traditional case where they are usually located right at the discontinuity step, which results in high reflections. An analytic model is then deployed to extract the mode content factor along with the field tapers of each mode in the principal planes. Other than far-field radiation patterns, emphasis is placed on the scattering parameters of the antenna, and they are compared to the ones for the same antenna with no blocks as well as the traditional case when the blocks are placed right at the discontinuity of the stepped waveguide. It is shown that the proposed feed provides a good impedance match, over a wide frequency band, similar to its counterpart for the single-mode antenna with no blocks. To verify the concept, a prototype antenna is fabricated and tested. There is an excellent agreement between the simulated and measured results.

The Aspects of Practical Application of Ultrafine-Grained Titanium Alloys Produced by Severe Plastic Deformation

The mechanical and physical properties of ultrafine-grained titanium alloys produced by severe plastic deformation are considered. It is found that the formation of ultrafine-grained structure in these materials causes a significant enhancement in their mechanical properties at room temperature and in their resistance to hydrogen embrittlement as well as a change in their acoustic properties. Moreover, superplasticity is realized in these materials at less elevated temperatures relative to the respective coarse grained counterparts. It is shown that the above changes in material properties permit optimization of conditions by the production of items from the titanium alloys, e.g. medical implants having the requisite strength and stepped waveguides having long life even in the high power density conditions of an ultrasound system.

Analysis of far-infrared horns, lightpipes, and cavities containing patterned conductive films

A scheme is described for calculating the scattering parameters of patterned conductive films in waveguide. The films can have non-uniform, non-isotropic, and non-local sheet impedances. Once the scattering parameters are known, they can be combined with the scattering parameters of paths, dielectric slabs, and waveguide steps to build up models of complicated components comprising patterned films in profiled lightpipes and cavities. It is then straightforward to calculate the Stokes fields of the total reception pattern, the natural optical modes to which the component is sensitive, the Stokes fields of the individual natural modes, and the spatial state of coherence. The method is demonstrated by modeling an absorbing pixel in a length of shorted multimode waveguide. The natural optical modes change from being those of the waveguide to those of a free-space pixel as the size of the absorber is reduced.

A NEW HYBRID MM/COMPACT 2-D FDFD METHOD FOR RECTANGULAR RIDGED WAVEGUIDE DISCONTINUITIES

A hybrid mode-matching/compact 2-D finite-difference frequency-domain (MM/compact 2-D FDFD) method is proposed for the analysis of rectangular ridged waveguide discontinuities. In order to apply MM technique, mode spectrum of the ridged waveguide is determined by an improved compact 2-D FDFD method with only two transverse field components at the cutoff frequencies which lead to two independent sets of real symmetric eigenvalue problems for TE and TM modes. Solving these two separate eigenvalue equations, cutoff wave numbers and discrete mode field functions can be obtained respectively from eigenvalues and eigenvectors. Finally, the generalized scattering matrix (GSM) of the rectangular-ridged waveguide step discontinuity can be easily calculated through the transverse field matching procedure. The method is demonstrated at the examples of two waveguide structures, and results are shown to be in excellent agreement with those by the commercial CAD software HFSS.

Modeling of flexible waveguides for ultrasonic vibrations transmission: Longitudinal and flexural vibrations of non-deformed waveguide

The article presents the mathematical model allowing to investigate longitudinal and flexural vibrations of stepped flexible waveguides with transitional section without regard to various vibration modes interaction. The model uses original numerical-analytic calculations based on analytical solutions of the equation of waveguide steps vibrations and their continuous matching with numerical solution of the equation of transitional section vibrations. The proposed model can be considered as an initial approximation to the solution of the problem of flexible waveguides design, which makes it possible to determine and validate effective methods of its addressing. Resonant curves of longitudinal and flexural vibrations of two-step waveguide are traced for the given vibration frequency. Step lengths values providing simultaneous resonance of longitudinal and flexural vibrations for the given frequency are determined. Validity of the proposed model is proved by the results of finite elements method (FEM) modeling using ANSYS ® software. Application of Timoshenko’s model instead of Euler–Bernoulli’s model for description of flexural vibrations enabled reduction of relative deviation of resonant frequencies calculated using ANSYS ® from the value specified during resonant curves tracing down to negligible value (0.17%).

DESIGN OF A BROADBAND TRANSITION USING THE CONSTANT IMPEDANCE STRUCTURE APPROACH

Transitions from circular waveguides to rectangular waveguides are used in many situations. One particular case is between the feed of a circular corrugated horn antenna and following rectangular waveguide structures. Since the field patterns are not the same on both sides the conversion from rectangular to circular waveguide always results in a certain amount of power reflected back in one waveguide. Much effort has been put in designing special converters which reduce this effect. For many designs, reflection is reduced by introducing a certain number of waveguide steps. By adjusting the distance between these steps, one can get destructive interference of the returned signal at specific frequencies. In this paper, an alternative approach, the constant impedance structure (CIS) has been chosen. This eliminates the need to design a waveguide converter for minimum return loss at discrete frequencies. The transition obtained by this approach is compared to a transition based on linear surface interpolation.

FIELD ANALYSIS OF DIELECTRIC WAVEGUIDE DEVICES BASED ON COUPLED TRANSVERSE-MODE INTEGRAL EQUATION-NUMERICAL INVESTIGATION

This is a numerical investigation of a recently proposed for- mulation called coupled transverse-mode integral equation (CTMIE) for analyzing EM fleld properties in general 2-D dielectric waveguide devices. The device is flrst approximated by stack of piece-wise 1-D horizontally layered structures. Transverse fleld components on the in- terface between waveguide slices are unknown functions, which are gov- erned by a coupled integral equation. When unknowns are expanded as a linear combination of given functions, CTMIE is converted to a coupled block matrix equation. We study three waveguide devices, in detail, to understand the relation between modeling parameters and accuracy and convergent rate of the solutions. Examples include a step waveguide junction, a multi-mode interferometer power cross coupler and a linearly tapered waveguide. All results are verifled with inde- pendent calculations using other proven methods.

Coloring of silica glass with silver nanoparticles

The possibility of doping of surface layers of optical fused silica with silver nanogranules upon heating of a thin Ag film on the silica surface by a CO2 laser beam (P ≈ 30 W, λ = 10.6 μm) is established. The effect of exposure time on the doped layer structure has been investigated. The absorption band of the colloidal solution of Ag in silica has been studied. It is shown that this band is homogeneously broadened and its peak (at 420 nm) corresponds to the small volume filling factor (q < 0.1) at an average granule radius of about 3 nm. Based on the measurements of the radial distributions of the reflectance and refractive index over the doped region at λ = 633 nm, it is revealed that the doped layer is an area-irregular asymmetric step waveguide.

Hybrid mode matching and auxiliary sources technique for horn antenna analysis

AbstractA hybrid technique for the analysis of horn antennas is described based on a rigorous description of the horn aperture‐free space discontinuity. The transition from the feeding waveguide to the radiating aperture is analyzed by using the mode matching technique (MMT) employing a stepped‐waveguide approach. The discontinuity between the horn aperture and the free space is modeled by combining the method of auxiliary sources with the MMT for the stepped waveguide section. Results for the input standing wave ratio are given and compared with the available measurements, which demonstrate the very good performance of the method. © 2007 Wiley Periodicals, Inc. Microwave Opt Technol Lett 49: 734–739, 2007; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.22233

Monochromatization of characteristic X-rays using stepped X-ray waveguide

Depending on the X-ray energy, the structure of an X-ray waveguide needs to be varied for greater efficiency. Therefore, a Si/PMMA(polymethyl methacrylate)/Si thin-film structure, whose top Si layer was steplike, was designed as a planar X-ray waveguide on the basis of calculations, and it was fabricated by spin-coating and sputtering. By irradiating white X-rays on two selected areas of a stepped waveguide, the top-layer thicknesses of which were different, W Lβ and Mo Kα lines were effectively guided and monochromatized.

A NOVEL MODELING TECHNIQUE TO SOLVE A CLASS OF RECTANGULAR WAVEGUIDE BASED CIRCUITS AND RADIATORS.

A new methodology has been developed, based on moment method; for analyzing a class of rectangular waveguide based circuits and radiators. The methodology involves in modeling the given structure using tetragonal bricks or cavities and then replacing all the apertures and discontinuities with equivalent magnetic current densities so that the given structure can be analyzed using only the Magnetic Field Integral Equation (MFIE). As it is necessary to use a number of such cavities in order to study these complicated waveguide structures, the present method is named as Multiple Cavity Modeling Technique (MCMT). The major advantage for using the MCMT in rectangular waveguide based structures is the fact that since only the magnetic currents present in the apertures are considered the methodology involves only solving simple magnetic field integral equations rather the coupled integral equation involving both the electric and magnetic currents. Further it is possible to consider both co and cross polarization and also the thickness of the waveguide discontinuities like diaphragm thickness or window thickness in the analysis. Due to this, it is possible to get highly accurate result. It is also possible to extend the method to any number of resonators, cavities or irises regardless of the polarization. To demonstrate, the methodology has been applied to analyze an open end of a waveguide with dielectric plug, both in transmitting and receiving mode, and a waveguide step discontinuity. Even mode and odd mode admittances of interacting identical inductive diaphragms have also been calculated using this methodology. Data obtained using this technique has been compared with measured, CST microwave studio simulation and literature available data. The theory has been validated by the reasonable agreement obtained between experimental data, simulated data and literature available data with numerical data.

Diffraction of H10-Wave by Stepped Rectangular Waveguide Coupling with Impedance Slot Iris

Diffraction of H10-Wave by Stepped Rectangular Waveguide Coupling with Impedance Slot Iris

A Compact and Wide-Band Metallic Reflector Grating in a Rectangular Waveguide

With the use of a generalized transfer-matrix method based on the mode-matching approach for waveguide step discontinuities, reflection properties of metallic waveguide gratings with rectangular grooves are investigated. A proper design for a compact and wide-band reflector grating which can support single-mode operation is also discussed. A waveguide grating with symmetrical and similar cross sections is shown to be of great significance for single-mode support and for constructing a compact reflector. In addition, it is found possible to obtain metallic waveguide gratings which satisfy all the specified requirements by properly adjusting only basic grating parameters.

PadÉ Boundary Conditions for the Finite-Element Modeling of Arbitrary Planar Junctions

Novel boundary conditions based on Pade/spl acute/ approximations for the frequency domain two-dimensional/finite element (2-D/FE) simulation of planar optical junctions of arbitrary geometry and number of accessing waveguides are presented and described in detail. This efficient formulation is straightforwardly implemented within the 2-D/FE framework and also can easily be used in finite difference schemes. Three examples show the applicability and reliability of the present method: a waveguide step discontinuity, waveguide transverse displacement and T-shaped beam splitter.

Efficient analysis of in-line waveguide filters and frequency-selective surfaces with stepped holes

This paper presents a novel method for the analysis of large classes of microwave and mm-wave passive components, including in-line waveguide filters, single- and multi-layer frequency selective surfaces, and open-ended waveguide array antennas. This method is based on the segmentation technique, which permits us to reduce complex components to cascaded waveguide step discontinuities, which are separately characterized through their generalized impedance matrices, as calculated by the integral equation (IE) technique and the boundary integral-resonant mode expansion (BI-RME) method. Some examples demonstrate the flexibility and efficiency of the IE/BI-RME method, and its utility in investigating novel structures not requiring costly fabrication techniques. © 2003 Wiley Periodicals, Inc. Int J RF and Microwave CAE 13: 306–315, 2003.