Design of MMICs employing whispering-gallery mode dielectric resonators at microwave and millimeter wave frequencies

A simple theoretical model for predicting the resonant frequencies of the modes of the whispering — gallery (WG) mode dielectric resonators MICs (Microwave Integrated Circuits) at microwave and millimetre wave frequencies is presented. The unsymmetric field distribution for WGE mode in the axial direction is taken into account. The theoretical results are found to be in good agreement with the practical results taken at microwaves C-X bands. In addition, the variation of resonant modes against dielectric resonator's dimensions and dielectric constant is modelled. The effect of the width of dielectric substrate on resonant modes is also illustrated.     

Analysis and modeling of a high-temperature superconducting floating resonant strip in waveguide

A two-gap floating resonant strip is used for characterization of the high-temperature superconductor, YBa₂Cu₃O_7–. The method has the advantages of simplicity, no electrical contact, operation at various resonant frequencies, and of requiring only a small sample. An analysis was devised that allows for the accurate design of the strip dimensions to produce a desired resonant frequency. Experimental measurements in X and Kuband (8–18 GHz) agree well with the calculations. The sensitivities of the circuit to positional errors and size variations of the resonant strip were investigated. The surface resistance was measured and compared favorably with the theory.     

固体板背覆薄层特性的低频超声反演方法研究

研究了应用低频超声的反射频谱对固体板厚度及背覆薄层的各特征参数(包括厚度、声速、密度、衰减、声阻抗率、声时)进行反演的方法。从灵敏度函数、目标函数及误差传递方程的角度,对应用反射频谱的谐振频率或幅度谱反演模型系统的单参数和双参数的方法进行了分析讨论。实验使用中心频率为7MHz的探头检测铝板/聚合物薄层样品,在同样的条件下,谐振频率法和幅度谱法反演的单参数反演效果相当,谐振频率方法的双参数反演效果优于幅度谱方法,前者薄层声阻抗率和声时同时反演的平均误差为3.4%和4.7%,而后者没有得到结果。      

Study on rectangular ultrasonic radiator of flexural resonant vibration in high modes

Based on the theory of coupling vibration and flexural vibration of thin rod of rectangular cross section, the fiexural vibration of rectangular thin plate was studied. The frequency equation was derived under the condition of freeboundaries. The normal modes and the relation between the normal modes and the resonant frequency were obtained. Experiments showed that the calculated resonant frequencies agree well with the measured results, and the rectangular thin plate in flexural vibration has abundant resonant frequencies. The radiator of flexural vibration used in ultrasonic cleaning and other techniques has the advantages of large acoustic radiating area, uniform acoustic field and easy adjustment of resonant frequencies, proving that it is a promising ultrasonic source.     

A study of electrostatic spring softening for dual-axis micromirror

Electrostatic spring softening is an important characteristic of electrostatically actuated dual-axis micromirror, since it lowers the resonant frequencies. This paper presents an approach based on approximating the electrostatic forces by the first-order Taylor's series expansion to investigate this characteristic. The dual-axis micromirror studied in this paper has three motion modes, two torsional (about x- and y-axis, respectively) and one translational (about z-axis). The stiffnesses of all these modes are softened by a DC bias voltage applied to the mirror plate. The resonant frequencies are lowered with the increment of the bias voltage. The relationship of the bias voltage and the resonant frequencies of all the motion modes is derived. The analytical results show that the resonant frequency curves are affected by the capacitor geometries, i.e. the gap between the mirror plate and the electrodes and the electrodes size. The lowering curves drop slowly when the bias voltage is small. While for large bias voltage, the lowering curves drop rapidly. The experiment results are consistent with those obtained by the analytical approach.     

双层粘接板界面的超声非线性谐振特性分析

采用声-力-电类比建立粘接界面非线性力学行为的等效非线性振荡电路,以求解双层粘接板的超声非线性谐振频率。理论上导出非线性谐振频率方程,确定双层粘接板非线性谐振频率与激励幅度、三阶弹性劲度系数的解析关系。双层粘接铝板的超声实验发现:在不良粘接情形下,超声谐振频率发生偏移,其值大于粘接完好区,且激发了较强的三次谐波,但二次谐波幅度变化不大。实验结果表明三次谐波幅度上升,超声谐振频率也显著增大,与理论导出非线性谐振频率变化规律相吻合,且三次谐波与基波、二次谐波的比值反映了非线性谐振频率变化趋势,证实粘接层三阶劲度系数是产生非线性共振频率偏移的主要因素。      

EXPERIMENTAL MEASUREMENTS BY AN OPTICAL METHOD OF RESONANT FREQUENCES AND MODE SHAPES FOR SQUARE PLATES WITH ROUNDED CORNERS AND CHAMFERS

Most of the work done on vibration of plates published in the literature includes analytical and numerical studies with few experimental results available. In this paper, an optical system called the amplitude-fluctuation electronic speckle pattern interferometry for the out-of-plane displacement measurement is employed to investigate the vibration behavior of plates with rounded corners and with chamfers. The boundary conditions are traction free along the circumference of the plate. Based on the fact that clear fringe patterns will appear only at resonant frequencies, both resonant frequencies and corresponding mode shapes can be obtained experimentally using the present method. Numerical calculations by finite element method are also performed and the results are compared with the experimental measurements. Good agreements are obtained for both results. It is interesting to note that the mode number sequences for some resonant modes are changed. The transition of mode shapes from the square plate to the circular plate is also discussed.     

Interpretation of measured data and the resolution analysis of the RTP 4-channel pulsed radar

In the present work, the resolution of a 4-channel pulsed radar being built at Rijnhuisen for RTP tokamak is analyzed. The achievable resolution depends mainly on the accuracy of the time-of-flight measurements and the number of sampling frequencies; since the technological solution and the configuration have already been set, the emphasis is laid on the interpretation of the measured data (inversion problem) and minimization of the overall error. For this purpose, a specific neural network — Multi Layer Perceptron (MLP) — has been successfully applied.The central density in the range 0.2–0.6×10²⁰ m^–3 was considered, i.e., above the critical density for all four frequencies but not too high to restrict the measurements just to the edge of plasma. For a wide class of density profiles, by balancing the inversion error and the time measurement error, the overall error in estimating the reflection point position between 0.72cm (for the lowest frequency) and 0.52cm (for the highest frequency) root mean square was obtained, assuming an RMS error of 70 ps in the time of flight measurements. It is probably much better than what could have been obtained by Abel transform. Moreover, the mapping by MLP is incomparably faster and should be considered for routine multichannel pulsed radar data processing.The author thanks Dr. J. B. Lister for his drawing his attention to the MLP technique.     

Dynamics of a rectangular plate resting on an elastic foundation and partially in contact with a quiescent fluid

In this study, a method of analysis is presented for investigating the effects of elastic foundation and fluid on the dynamic response characteristics (natural frequencies and associated mode shapes) of rectangular Kirchhoff plates. For the interaction of the Kirchhoff plate–Pasternak foundation, a mixed-type finite element formulation is employed by using the Gâteaux differential. The plate finite element adopted in this study is quadrilateral and isoparametric having four corner nodes, and at each node four degrees of freedom are present (one transverse displacement, two bending moments and one torsional moment). Therefore, a total number of 16 degrees-of-freedom are assigned to each element. A consistent mass formulation is used for the eigenvalue solution in the mixed finite element analysis. The plate structure considered is assumed clamped or simply supported along its edges and resting on a Pasternak foundation. Furthermore, the plate is fully or partially in contact with fresh water on its one side. For the calculation of the fluid–structure interaction effects (generalized fluid–structure interaction forces), a boundary element method is adopted together with the method of images in order to impose an appropriate boundary condition on the fluid's free surface. It is assumed that the fluid is ideal, i.e., inviscid, incompressible, and its motion is irrotational. It is also assumed that the plate–elastic foundation system vibrates in its in vacuo eigenmodes when it is in contact with fluid, and that each mode gives rise to a corresponding surface pressure distribution on the wetted surface of the structure. At the fluid–structure interface, continuity considerations require that the normal velocity of the fluid is equal to that of the structure. The normal velocities on the wetted surface of the structure are expressed in terms of the modal structural displacements, obtained from the finite element analysis. By using the boundary integral equation method the fluid pressure is eliminated from the problem, and the fluid–structure interaction forces are calculated in terms of the generalized hydrodynamic added mass coefficients (due to the inertial effect of fluid). To asses the influences of the elastic foundation and fluid on the dynamic behavior of the plate structure, the natural frequencies and associated mode shapes are presented. Furthermore, the influence of the submerging depth on the dynamic behavior is also investigated.     

Free vibration analysis of piezoelectric coupled circular plate with open circuit

A vibration analysis of a circular steel substrate surface bonded by a piezoelectric layer with open circuit is presented. A solution for the electrical potential along the thickness direction of the piezoelectric layer satisfying the open circuit electric boundary condition is developed for the first time. The mechanical model and solutions for the vibration analysis of the piezoelectric coupled circular plate are then established based on the developed electrical potential, the Kirchhoff plate model, and the Maxwell equation. The first four mode shapes and the corresponding resonant frequencies of the plate with two standard boundary conditions are presented in numerical simulations and compared with those of a piezoelectric coupled plate with the closed circuit condition. The simulations show that the resonant frequencies of the open circuit piezoelectric coupled plate are higher than those of the closed circuit piezoelectric coupled plate. Corresponding discussions are thus provided for the higher piezoelectric effect from the open circuit piezoelectric layer.     

Breakdown of a gas in superimposed d.c. and h.f. electric fields

By means of a time resolution it was found that the electric breakdown of air at atmospheric pressure between a charged plate and a spike, on which a torch discharge is burning, gaves rise to comparatively stable ellipsoidal plasma formations — plasmoids. Their dimensions stay within 2÷10 mm, velocity 0÷4 ms, acceleration –210÷1500 ms^–2. Their life time is 10^–2 s in magnitude. They decay either at the spike electrode, or when the actual breakdown takes place, or they desintegrate in the inter-electrode space.     

Measurement of transverse vibrations/visualization of mode shapes in square plate by using digital speckle pattern interferometry and wavelet transform

New filtering scheme is investigated and implemented on digital speckle pattern interferometric fringes to enhance the signal-to-noise ratio (SNR) in the speckle interferograms. To establish the potential of new filtering scheme the experiment was conducted on the vibrating cantilever beam. Experimental results revealed that the new filtering scheme is more powerful than other known filtering schemes (Kumar et al. Opt Laser Eng 2004;41:81–93. Kumar et al. Opt Laser Technol 2001;33:567–571. Shakher et al. Opt Eng 2002;41:176–180. Shakher et al. Proceedings ICICS, Singapore, 9–12 September 1997, p. 953–956. Bowler et al. Proceedings of IEE second international conference on image processing, London, 1986, p. 24–26. Lim. Opt Eng 1981;20:670–678. Devila et al. J Mod Opt 1995;42:1795–1804; Kaufmann et al. Opt Eng 1996;35:9–14). The new scheme reduced the speckle noise and improved SNR in speckle interferograms. Further, the new investigated filtering scheme is implemented to study the mode shapes of square plates under two different boundary conditions. In the first condition all the edges of the square plate were fixed while in the second condition two adjacent edges were fixed and the remaining two edges were free. From the experimental results it is clear that the mode shapes are more distinctly visible with the implementation of the new filtering scheme as compared to other known schemes. Under both the boundary conditions the recorded resonance frequencies were compared with the calculated values of resonance frequencies based on classical theory. The results obtained form DSPI show good agreement with classical theory.     

Microwave transmission through a single subwavelength annular aperture in a metal plate

The resonant transmission of a small annular aperture, with a diameter much smaller than the radiation wavelength, in a thin metal plate is studied at microwave frequencies. It transpires that such an annular aperture supports several resonant guided modes, including those that are not quantized in the azimuthal direction. Such modes have resonant frequencies that are largely independent of the diameter of the annular aperture, thus being supported by annular apertures that tend to zero radius. The transmittance of such a structure at microwave frequencies is detailed and compared with the predictions of a finite element method model.     

Spin — lattice relaxation in chlorofluorocarbon liquids

We have used the spin — echo method to measure spin — lattice relaxation times in liquid chlorofluorocarbons over a wide range of temperatures, frequencies, and molecular weights. Analysis of the experimental data shows that to determine the kinetic parameters of viscous liquids it is necessary to use the theory of nuclear magnetic relaxation by translational diffusion. We describe a method for the computer calculation of these parameters and discuss the results.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 46–51, March, 1976.     

Analysis and Simulation of Reentrant Cylindrical Cavities

Of applications ranging from electron spin resonance to detection of gravitational waves, reentrant circular cylindrical cavities are analyzed on the basis of a mathematically simple formalism extending the range of validity of expressions for resonant frequency and quality factor obtained from lumped RLC constant models. Several cavity configurations in the 1 – 3 GHz range are analytically examined in excellent agreement with frequencies obtained from Superfish code.     

A possible new case of total X-ray reflection

A new and quite simple method is proposed for consideration of multiple scattering of an incident ray by elements of a plane lattice. This method is used to obtain a general expression for the amplitude of coherent scattering of photons on an isolated monatomic layer. It is shown that at incident radiation frequencies coinciding with resonant frequencies of the lattice atoms a new phenomenon can develop: total reflection of photons from the isolated atomic layer, independent of the angle of incidence.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 21–25, April, 1985.The author is indebted to B. M. Bolotovskii for his valuable remarks and to V. L. Vinetstkii for his fruitful evaluation of the study.     

Growth and characterization of delta type Si---SiOx-heterostructures

We present a procedure whereby 2–3nm thick layers of SiO_x are incorporated in (100) Si during molecular beam epitaxial growth. Analysis by Auger electron spectroscopy and transmission electron microscopy shows, that the delta function SiO_x layers with a width of only a few lattice planes are embedded in a monocrystalline Si matrix. Capacitance — voltage measurements and resonant tunneling spectroscopy give evidence that the layers act as sharp potential barriers.     

Resonant transmission of acoustic waves through an elastic plate quasiperiodically corrugated on surfaces

In this work, we study the resonant transmission of acoustic waves through a plate with quasiperiodic surface corrugations. The transmission spectrum shows peculiar transmission peaks, which cannot be simply attributed to the coherent diffraction as recognized previously in structured hard plates (without sustaining internal modes), whereas come from the resonant excitation of the coupled Stoneley surface modes in the elastic plate. The excitation frequencies can be determined by the geometrical structure factor of the quasiperiodic lattice, combining with the dispersion relation of the surface modes.     

Raman studies of nonlinear phenomena in fullerene crystallites

The resonant Raman scattering of C₆₀ crystallites is monitored as a function of excitation intensity at 514.5 nm. At low intensities, a strong line at 1468 cm^–1 is observed. No feature at 1459 cm^–1 is observable. With increasing intensities, the 1468 cm^–1 line shifts continuously and reversibly to lower frequencies. The mode softening is nonlinearly dependent on the input intensity and is accompanied by a nonlinear increase in the Raman intensity. The spectral changes are discussed in terms of a nonlinear reduction in force constant and increase in bond polarisability as a result of an increased intermolecular delocalisation of the -electron cloud. The nonlinear changes are associated with the nonlinear luminescence and photoconductive response observed in fullerenes and are contrasted to the irreversible phototransformation recently discussed.     

Determination of ultrasonic wave velocities and phase velocity dispersion curves of an Inconel 600 plate using resonant ultrasound spectroscopy and leaky Lamb waves

A plate of Inconel 600 was interrogated using the resonant ultrasound spectroscopy (RUS) and the reflected leaky Lamb waves (LLW). It was found that the plate used in the present work has anisotropy in its material properties by the RUS. The longitudinal and the transverse wave velocities of the Inconel 600 plate were determined by the RUS, ultrasonic pulse-echo method and cut-off frequencies of the LLWs. The wave velocities in the direction of thickness determined by the RUS under the assumption of the orthotropic symmetry were quite similar to those obtained by other methods, the pulse-echo method and from cut-off frequencies. The reflected LLW from the plate was measured with varying the incident angle. The dispersion curves obtained from the reflected LLWs show good agreement with the theoretical calculation in general. The mismatches may be caused by anisotropy of the plate.