Taper Length Research Articles

Radiation losses of step-tapered channel waveguides

We compute the radiation losses of a rectangular dielectric waveguide (integrated optics channel waveguide) that is tapered so that its wider cross-sectional dimension increases by roughly a factor of three while its narrow dimension remains constant. As the waveguide widens its refractive index decreases to ensure that the waveguide supports only one guided mode. The taper is approximated by a discontinuous staircase curve. A rectangular waveguide taper of 2-microm thickness, tapering from 3- to 10-microm width through fourteen steps of 0.25-microm height, has a minimum loss (at 0.6328-microm wavelength) of 0.13 dB for a 200-microm taper length.

Evaluation of standardized root canal instruments and obturating points

Standardized Kerr root canal reamers, Hedstroem files, and obturating points were selected from seven manufacturers to discover whether their diameter, taper, and blade length conformed to the specifications given by the International Organization for Standardization (ISO). The hot-air tolerance of the identification colors of instrument handles also was tested. Most of the Kerr reamers were manufactured with a satisfactory diameter. Most sizes of Hedstroem files had an acceptable diameter. On the whole, all root canal instruments showed correct taper. All of the gutta-percha points disclosed a considerable lack of accuracy and precision in diameter and taper. One of the two brands of silver points conformed to the specifications of ISO. Identification colors of instruments were resistant to hot-air sterilization. Examination of the length of blades indicated great variations from the requirements of ISO. The manufacturers should focus their attention on producing gutta-percha points in accordance with the specifications of ISO. Standardized Kerr root canal reamers, Hedstroem files, and obturating points were selected from seven manufacturers to discover whether their diameter, taper, and blade length conformed to the specifications given by the International Organization for Standardization (ISO). The hot-air tolerance of the identification colors of instrument handles also was tested. Most of the Kerr reamers were manufactured with a satisfactory diameter. Most sizes of Hedstroem files had an acceptable diameter. On the whole, all root canal instruments showed correct taper. All of the gutta-percha points disclosed a considerable lack of accuracy and precision in diameter and taper. One of the two brands of silver points conformed to the specifications of ISO. Identification colors of instruments were resistant to hot-air sterilization. Examination of the length of blades indicated great variations from the requirements of ISO. The manufacturers should focus their attention on producing gutta-percha points in accordance with the specifications of ISO.

Compliance Characteristics of Angiographic Guidewires

Although the manufacturers' specifications may be identical, brands of widely employed straight, long-paper angiographic guidewires vary considerably in performance. Because guidewire flexibility is a key factor in performance, we investigated the characteristic compliance patterns of similar guidewires (using an apparatus of our own design) from four different manufacturers. The brands were found to differ significantly in compliance at the tip, in rate of change in compliance, and in overall length of taper.

Sonics and ultrasonics : Ranging and data transmission using digital encoded fm-‘chirp’ surface acoustic wave filters Burnsweig, J., Wooldridge, J. SU-20 (April 1973) 190–197

In this report, a novel technique is described for the combination of per-tone equalization (PTEQ) with receiver windowing. The PTEQ is an equalization technique for discrete multitone modulation (DMT) based modems, such as asymmetric digital subscriber line (ADSL) modems and very high bitrate digital subscriber line (VDSL) modems, optimizing the SNR (and thus capacity) of each carrier separately. Windowing functions are very useful in multitone communications systems, to prevent a narrow band noise source from causing wide band interference. Combining both techniques in a windowed PTEQ (referred to as WiPTEQ) leads to a robust communication system. The described technique is especially useful in case of a trapezoidal or raised cosine window, and when the window taper length is large compared to the number of equalizer filter taps.

A Near-Optimum Matching Section without Discontinuities

The optimum tapered matching section requires impedance steps at the taper ends, which exclude in most cases its application for synthesizing waveguide tapers. A new "near" optimum design is described which avoids the impedance steps and yields tapers only a fractional part longer in taper length (or narrower in bandwidth) than the exactly optimum taper. A table of values of a transcendental function has been calculated to simplify the synthesis. An example compares both types of matching sections.

Optimization of Waveguide Tapers Capable of Multimode Propagation

By converting Maxwell's equations, the general case of mode conversion in tapered waveguides is treated by matrix formulation in terms of an infinite set of coupled differential equations with nonuniform coupling coefficients and varying phase constants. An "orthogonalization" or "diagonalization" process is introduced through a nonlinear matrix transformation which is a function of taper length. The general matrix solution of the problem is obtained through a perturbation method in the form of an integral equation of the Volterra type, and the integral equation is solved by an iteration method. In view of the difficulties in finding eigenvalues, the problem is then reduced to the two-mode case, and the mode conversion is obtained in an explicit form revealing certain information which characterizes the choice of "mode-conversion distribution function." Optimization is first obtained through proper choice of the mode-converison distribution function. In an attempt to approximate a Tchebycheff mode-conversion response, further optimization is realized by creating "new zeros" and thereby changing the density of the distribution of zeros in the vicinity of the origin of the mode-conversion curve and the nature of the optimization procedure essentially becomes that of synthesis. Through using the optimized distribution function, a total reduction of about 50 per cent in taper length is realized (when compared with the cosine-squared distribution) for the case of 50-db prescribed-mode discrimination in a taper connecting a 7/8-in ID waveguide to a 2-in ID waveguide operating in the circular electric mode up to 75 kmc.

Electron Trajectories in a Nonuniform Axially Symmetric Magnetic Field

Electrons injected along the flux lines of a spatially varying, axially symmetric magnetic field that is increasing in the direction of electron motion will follow approximately helical trajectories about the flux lines. If the field increases too rapidly, the electrons will not be able to penetrate the magnetic field beyond a certain point and will be turned back by the magnetic mirror formed by the increasing field. For more slowly varying fields, the electrons can penetrate the mirror with a large fraction of their energy in axial velocity. The equations of motion for electrons in a sinusoidally varying magnetic field have been solved on a computer, and the results are presented in graphical form. An application of this field configuration as a device for converging a hollow cylindrical electron beam has been tested, and measured area convergences of 15 to 1 have been obtained by photographing a movable carbon screen collector that is heated by the beam. The beam is started out with a conventional parallel flow gun immersed in the magnetic field. As the beam leaves the first accelerating electrode it enters the region of increasing magnetic field. It then shrinks in diameter and thickness, and hence in area, approximately in proportion to the increase in the magnetic field. The actual area convergence will be less than this increase by an amount depending on the length and rate of the magnetic field taper.

Reflection of a Pyramidally Tapered Rectangular Waveguide

The reflection coefficient Gamma of a pyramidally tapered rectangular waveguide is derived by assuming that the taper impedance is proportional to the height and guide wavelength and inversely proportional to the width of the taper cross section. It is a shown that the loci of Gamma, plotted in the K plane as a function of taper length for some conventional tapers, do not pass through the center of the chart at multiples of a half-guide wavelength as for an exponential line, but instead they converge almost concentrically. The frequency characteristic of the pyramidally tapered waveguide is compared with other types of tapers. Typical 7-kmc experimental results for several tapers differing in length are presented.

Monotonic multi-section tapers for over-moded circular waveguides

The results of a detailed analysis of the propagation of circular electric modes, H0n, is extended, approximated and eventually adapted to the design of monotonic multi-section conical tapers.The formulae and graphs obtained are directly applicable to the calculation of mode conversion loss encountered when two colinear waveguides are connected together by means of a multi-section taper, and the conversion loss is related to the wavelength and the geometry of the structure.The design procedure is illustrated in detail by several numerical examples. It is thereby clearly demonstrated that, for a given mode conversion loss and bandwidth, a considerable reduction in the overall taper length is possible if a multi-section taper of suitable proportions is used in preference to a simple linear taper.

A Transmission Line Taper of Improved Design

The theory of the design of optimal cascaded transformer arrangements can be extended to the design of continuous transmission-line tapers. Convenient relationships have been obtained from which the characteristic impedance contour for an optimal transmission-line taper can be found. The performance of the Dolph-Tchebycheff transmission-line taper treated here is optimum in the sense that it has minim reflection coefficient magnitude in the pass band for a specified length of taper, and, likewise, for a specified maximum magnitude reflection coefficient in the pass band, the Dolph-Tchebycheff taper has minimum length. A sample design has been carried out for the purposes of illustration, and its performance has been compared with that of other tapers. In addition, a table of values of a transcendental function used in the design of these tapers is given.

Note on the taper of connecting-rods

In this study, the stress and stiffness analyses of corner joints with a single corner support, consisting of two plates, one of which plain and the other bent at right angles, have been carried out using the finite element method. It was assume that the plates and adhesive had linear elastic properties. Corner joints without a fillet at the free ends of the adhesive layer were considered. The joint support was analysed under three loading conditions, two linear and one bending moment. In the stress analysis, it was found that for loading in the y-direction and by bending moment, the maximum stresses occurred around the lower end of the vertical adhesive layer/ vertical plate interface; for loading in the x-direction, the maximum stresses occurred around the right free end of the horizontal adhesive layer/vertical plate interface. The effects of upper support length, support taper length and adhesive thickness on the maximum stresses have been investigated. Since the peel stresses are critical for this type of joint, a second corner joint with double corner support (i.e., one in which the horizontal plate is reinforced by a support that is an extension of the vertical plate) was investigated which showed considerable decreases in the stresses, particularly peel stresses. A third type of corner joint with single corner support plus an angled reinforcement member was investigated as an alternative to the previous two configurations. It was found that increasing the length and particularly the thickness of the angled reinforcement reduced the high peel stresses around the lower free end of the adhesive/vertical plate interface, but resulted in higher compressive stresses. In the stiffness analysis, the effects of the geometry of the joints, relative stiffness of adhesive/adherends and adhesive thickness were investigated under three loading conditions. For three types of corner joint, results were compared and recommended designs were determined based on the overall static stiffness of the joints and on the stress analysis.