Frequencies Of Higher-order Modes Research Articles

Cutoff frequencies of transmission lines consisting of pair of cylinders

The paper presents a method of evaluation of cutoff frequencies of higher-order modes of transmission line of parallel cylinders by transforming them into a parallel plate configuration using cotangent hyperbolic transformation. Application of the method of finite difference to the weighted Helmholtz equation leads to a set of simultaneous equations. The eigenvalues related to cutoff frequencies are determined from the characteristic equation expressed in terms of matrices obtained from the simultaneous equations. Numerical data are presented.

Headway in cavity design through genetic algorithms

A new code to design the shape of a RF cavity that satisfies user defined characteristics is proposed. The code is based on a genetic algorithm and has proved to be able to generate the shape of a cavity satisfying previously defined characteristics such as fundamental resonant mode frequency, higher order modes frequencies and accelerating field within reasonable computing time. >

Evaluation of cut-off frequencies of higher order modes in eccentric coaxial line

The paper presents a method of evaluation of the cut-off frequencies of higher order modes of transmission lines having eccentric annular cross-section using a combination of conformal transformation and the method of finite difference. The Laplacian operator appearing in the weighted Helmholtz equation resulting from the conformal transformation is represented as a five-point difference operator of unequal arm length along the two axes. The eigenvalues which give cut-off frequencies are evaluated from the characteristic equation expressed in terms of matrices obtained from a set of simultaneous equations satisfying the boundary conditions. Comparison of numerical data is presented.

Finite-element analysis of a triple-TEM cell

The triple-TEM (TTEM) cell offers the possibility of alternative exposures of the electric field on the equipment under test in one setup. Traditional TEM cell design approaches cannot be applied to the TTEM cell because of the special geometric arrangement of the inner conductors. Several important characteristics of the TTEM cell, such as TEM field distributions, characteristic impedance, and cutoff frequencies of higher order modes (TE and TM) are analyzed by using the finite-element method (FEM). The high-frequency performance of the TTEM cell is investigated using a novel FEM approach-the Laplace domain finite-element method (LDFEM). Numerical results obtained thereupon are useful in the engineering design of the TTEM cell. >

Higher order modes in coupled striplines: prediction and measurement

Finite element and resonant cavity methods are used to predict and confirm the cut-off frequencies of higher order modes in stripline. Infinite elements are used to treat open-wall boundaries. Single lines, symmetrically coupled and asymmetrically coupled lines are treated in turn. In the tightly coupled situation the cut-off frequency of the lowest TE mode degenerates to that of an abutted combined linewidth. Established approximation methods for single lines are used where possible. Some practical observations are made and selected finite element field plots are included for completeness.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Effect Of An Internal Flow On The Distribution Of Vibrational Energy In An Infinite Fluid-Filled Thin Cylindrical Elastic Shell

The vibrational energy distribution in an infinite elastic cylinder with an internal uniform flow is investigated. Energy ratios between the power flow in the fluid field and the power flow in the shell are evaluated, using a fully coupled analysis, for a steel and a hard rubber shell of various thicknesses filled with convected water and vibrating in the n = 0, 1, 2 and 3 circumferential modes. The impact of the flow on the dispersion curves is first studied. The effect of the Mach number on the distribution of vibrational energies propagating upstream and downstream is then discussed, and shown to depend upon the branch behaving as either a fluid type or a structural type wave. In general, for downstream propagation, convection increases the power in the structure for structural type waves and decreases it in the structure for fluid type waves. The reverse is true for upstream propagation. Finally, the effect of the flow is shown to be greatest near coincidence or the cut-on frequencies of higher order modes.

Spectral-domain analysis of submillimetre-wave microstrip filters

We consider the cut-off frequencies of high-order modes in boxed submillimetre-wave microstrip filters. It is shown that many of the filters in use at the present time are not cut off in the way that the designers imagine. It is also shown that for ease of manufacture the height of the microstrip channel should be 0.7 times the width and the thickness of the quartz substrate should be 0.5 times the width. This optimum geometry suggests that the upper frequency limit of conventional waveguide components is 1THz.

Resonant frequencies of higher order modes in cylindrical anisotropic dielectric resonators

A method that calculates the frequency of the lowest order mode in a cylindrical isotropic dielectric is extended to higher order modes in a anisotropic crystal. Four different axial match equations are derived depending on whether they are quasi TE or quasi TM, and have an odd or even axial mode number. A general radial match equation is also derived. Combining it with the relevant axial equation forms a set of two coupled transcendental equations that can be solved numerically. The theory is confirmed by room temperature measurements in two sapphire crystals of different aspect ratios, and in cryogenic sapphire resonators used in high stability fixed and tunable oscillators. The sensitivity of mode frequency to dimensional and permittivity perturbations is analyzed. >

Breakdown and Resonance Behaviour of the SRS Waveguide

During the early running of the SRS storage ring the energy was limited to 1.8 GeV because of unexpected electrical breakdown in the waveguide-cavity system. This occurred at roughly 120 kW, half the rated power of the klystron. High power tests showed an unacceptably large amount of third harmonic generated by the klystron, which was found to be produced by a faulty component in the feeder system. Low power investigations indicated that the waveguide-cavity system had a rich resonance spectrum, which could be tuned by changes to any of the movable system components. With the system as initially set, one particular mode could be readily tuned to the third harmonic frequency. The faulty component was replaced and the waveguide system rearranged. With these changes and with the system adjusted to avoid any third harmonic modes, the rf system was immediately able to operate at full power. The SRS has since operated consistently at its design energy of 2 GeV with no rf trips from these effects. The low power tests also revealed that the magic tees only provide good isolation at the 500 MHz operating frequency; the waveguide system thus forms a feedback loop at higher order mode frequencies withmore » the circulating beam and the cavities. This may explain some of the beam instabilities observed in the SRS. This paper delineates the waveguide layout, the parameters of the high and low power tests, and the test results which led to the foregoing conclusions.« less

Higher Order Modes in Square Coaxial Lines

The cutoff frequencies of higher order modes in square coaxial lines are presented and compared with those of circular coaxial lines having the same mean circumference. It is noted that while the characteristics of the dominant TE/sub 10/ mode and the next TE/sub 11/ mode in the square line differ but little from those of their circular counterparts, the same conclusions do not hold in generaI for the remainder of the mode spectrum.

Ray-Optical Analysis of Reflection in an Open-Ended Parallel-Plane Waveguide. I: TM Case

The reflection problem for a TM mode traveling toward the open end of a semi-infinite parallel-plane waveguide, is solved by ray methods. Unlike a previous solution due to Yee, Felsen and Kelley, the present ray-optical solution is a rigorous asymptotic result, i.e., it is identical with the asymptotic expansion of the exact solution when the width of the waveguide is large compared to the wavelength. Numerical results for the modal reflection coefficients are presented and are compared with calculations based on the exact solution. It is found that the agreement between ray-optical and exact values is excellent and even better than in the approach of Yee et al., especially in the vicinity of cutoff frequencies of higher order modes.

Ray-optical analysis of reflection in an open-ended parallel-plane waveguide: II-TE case

The reflection problem for a TE mode traveling toward the end of a semi-infinite parellel-plane waveguide is solved by ray methods. Unlike a previous solution due to Yee et al., the present ray-optical solution is a rigorous asymptotic result, i.e., it is identical with the asymptotic expansion (width of waveguide large compared to wavelength) of the exact solution. Numerical results for the modal reflection coefficients are presented and are compared with calculations based on the exact solution. It is found that the agreement between ray-optical and exact values is excellent and even better than in the approach of Yee et al., especially in the vicinity of cutoff frequencies of higher order modes.

Resonant Frequencies of Higher-Order Modes in Radial Resonators

A summary of the relevant work on radial line discontinuities and radial line resonators is presented. A step-type discontinuity is analyzed using an integral equation formulation and the results are applied to the calculation of the resonant frequencies of a radial resonator. This method is verified by experiment and compared with the foreshortened-line approximation and with the methods of Marcuvitz and Goddard, whose work is satisfactory for the order TM mode. However, the present method is the only one which is equally applicable to the calculation of the resonant frequencies of TM modes possessing higher-order radial variations.