A Microwave Method for the Determination of the Real Parts of the Magnetic and Dielectric Material Parameters of Premagnetized Microwave Ferrites

A microwave method is presented for the determination of the real parts of the magnetic and dielectric material parameters of premagnetized microwave ferrites. It is based on the simultaneous utilization of certain dynamic modes that occur in a cylindrical cavity partly filled with a ferrite sample. Employing the corresponding eigenvalue equations of these modes, the material parameters are computed from the measured resonant frequencies of the cavity. In contrast to other techniques, the described method requires only a single cavity and a single, easily produced sample of the ferrite material to be examined. The evaluation of the measurements can be done with a simple desk-top computer. The material parameters of two different ferrite materials have been measured and found to be in satisfactory agreement with parameters calculated from formulas based on model conceptions.     

A New Method for Measuring Anisotropy at Microwave Frequencies

A method for measuring electric or magnetic anisotropy at microwave frequencies is described. It is based on the effect produced by an anisotropic sample placed inside a square resonant cavity, on two originally degenerate and mutually independent modes. A coupling between the modes is created and, at the same time, the degeneracy is lifted and two distinct resonant frequencies appear. The theory of these effects is presented for the case of uniaxial anisotropic dielectrics. Experiments carried out with samples simulating anisotropy yielded results in good agreement with the theoretical predictions.     

An Automatic System for the Measurement of the Field Distribution in Resonant Cavities

A computer-controlled system for the measurement of the field distribution in microwave cavities is described. Examples of field measurements at various resonant frequencies are given for a cavity with a complex geometry.     

Thickness-shear vibration of an AT-cut quartz resonator with a hyperbolic contour

A theoretical analysis is performed on thicknessshear vibrations of a contoured AT-cut quartz resonator with a hyperbolic thickness variation using the Legendre equation and hypergeometric function. Based on the solution, resonant frequencies and modes are calculated. Strong energy trapping of the modes is observed. The effects of the parameters of the hyperbolic contour on resonant frequencies and modes are examined. A comparison with the conventional contoured resonator in the literature with a quadratic thickness variation is made. The behaviors of the two types of resonators are qualitatively similar, with small but significant quantitative differences.     

单圆柱微波谐振法测量热力学温度的研究

利用氩气的量子力学“从头算”理论和相关实验测量结果,基于圆柱微波谐振法建立了气体折射率热力学温度计实验系统,测量了253~303 K范围内的热力学温度。通过测量圆柱微波谐振腔内4个横磁模式的微波谐振频率,获得了氩气在700 kPa附近的气体折射率,不同微波模式得到的氩气折射率一致性优于1×10^-8,进一步结合氩气的维里状态方程得到热力学温度。热力学温度T和ITS-90国际温标T90差异不确定度为11.6 mK,与国际温度咨询委员会的评估值具有良好的一致性。未来随着氩气理论计算和实验系统压力测量不确定度的深入研究,该方法测定热力学温度的不确定度会进一步改善。     

Modal Coupling in Micromechanical Vibratory Rate Gyroscopes

The authors present modeling approaches to describe the coupling of modes in a resonant vibratory rate gyroscope. Modal coupling due to off-diagonal stiffness and damping terms is considered. Three analytical modeling approaches are presented in the context of a$z$-axis micromechanical vibratory rate gyroscope fabricated in an integrated polysilicon surface-micromachining process. The first approach is based on frequency-response analysis of the gyroscope output. The second approach takes the route of state-space-based system identification to identify the modal-coupling parameters. A third approach based on measured vibration data identifies the coupling parameters due to stiffness and damping. These three methods are then applied to predict the extent of displacement and force coupling between the drive and the sense axes of an existing device as a function of varying degrees of matching between the resonant frequencies associated with the drive and the sense modes. Experimental data show that as the resonant frequencies of the drive and sense modes are brought closer together, an improvement in overall resolution and scale factor of the device is obtained at the expense of an enhanced coupling of forces to displacements between the two axes and the onset of instability for an open-loop sensing implementation.     

Theoretical analysis and experimental measurement for resonant vibration of piezoceramic circular plates

Based on the electroelastic theory for piezoelectric plates, the vibration characteristics of piezoceramic disks with free-boundary conditions are investigated in this work by theoretical analysis, numerical simulation, and experimental measurement. The resonance of thin piezoceramic disks is classified into three types of vibration modes: transverse, tangential, and radial extensional modes. All of these modes are investigated in detail. Two optical techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), are used to validate the theoretical analysis. Because the clear fringe patterns are shown only at resonant frequencies, both the resonant frequencies and the corresponding mode shapes are obtained experimentally at the same time by the proposed AF-ESPI method. Good quality of the interferometric fringe patterns for both the transverse and extensional vibration mode shapes are demonstrated. The resonant frequencies of the piezoceramic disk also are measured by the conventional impedance analysis. Both theoretical and experimental results indicate that the transverse and tangential vibration modes cannot be measured by the impedance analysis, and only the resonant frequencies of extensional vibration modes can be obtained. Numerical calculations based on the finite element method also are performed, and the results are compared with the theoretical analysis and experimental measurements. It is shown that the finite element method (FEM) calculations and the experimental results agree fairly well for the resonant frequencies and mode shapes. The resonant frequencies and mode shapes predicted by theoretical analysis and calculated by finite element method are in good agreement, and the difference of resonant frequencies for both results with the thickness-to-diameter (h/D) ratios, ranging from 0.01 to 0.1, are presented.     

A two-mode microwave cavity method of determining the volume fraction of water in a liquid fuel lubricant

A two-mode microwave cavity method is proposed for determining the volume fraction of water in liquid fuel lubricant materials. The volume fraction of water is determined from the difference between the resonant frequencies for the H₀₁₁ and E₁₁₁ modes. Experimental results are given. __________ Translated from Izmeritel’naya Tekhnika, No. 3, pp. 58–61, March, 2008.     

Automatic Monitor for Microwave Resonators

An instrument was developed to simultaneously measure both the resonant frequency and the bandwidth (which is related to the loaded quality factor) of a resonant microwave cavity under continuous operating conditions. Voltages proportional to both parameters monitored are obtained at the output. The principle of operation, the main causes of error and the accuracy obtained for actual measurements are presented. This instrument could easily be connected to a digital data-acquisition system; it could also be adapted to study resonance phenomena at frequencies other than microwaves.     

Theoretical, numerical, and experimental investigation on resonant vibrations of piezoceramic annular disks

In this study, vibration characteristics of thin piezoceramic annular disks with stress-free boundary conditions are investigated by theoretical analysis, numerical simulation, and experimental measurement. The nonaxisymmetric, out-of-plane (transverse), and axisymmetric in-plane (tangential and radial extensional) vibration modes are discussed in detail in terms of resonant frequencies, mode shapes, and electrical currents. Two optical techniques, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and laser Doppler vibrometer (LDV), as well as the electrical impedance measurement are used to validate the analytical results. Both theoretical and experimental results indicate that the transverse and tangential vibration modes cannot be determined by the impedance analysis; hence, only resonant frequencies of extensional vibration modes are presented from the impedance analyzer. The LDV system is used to measure the resonant frequencies of transverse vibrations. However, both the transverse and extensional vibration modes and resonant frequencies of piezoceramic annular disks are obtained by the AF-ESPI method, and the interferometric fringes are produced instantly by a video recording system. Numerical results obtained by finite-element calculations are compared with those from theoretical analysis and experimental measurements. It is shown that the theoretical predictions of resonant frequencies and the corresponding mode shapes agree well with the experimental results. Good agreement between the predicted and measured electrical impedance also is found. The dependence of resonant frequencies and dynamic electromechanical coupling coefficients on the inner-to-outer radius ratio also is analyzed and discussed in this study.     

Low dispersion surface plasmon-polaritons on deep silver gratings

Surface plasmon modes supported by short-pitch silver gratings with different depths have been characterized by studying the reflectivity as a function of the angle of incidence and the incident wavelength (400–850?nm). Highly non-dispersive ‘flat’ surface plasmon-polariton bands were found corresponding to localized, within the grooves, radiative resonant modes. Experimental reflectivities were compared with model calculations and to help understand the character of each of the modes, the optical magnetic field distributions at the resonant frequencies were explored.     

Experimental measurements and finite element analysis of the coupled vibrational characteristics of piezoelectric shells

Piezoelectric plates can provide low-frequency transverse vibrational displacements and high-frequency planar vibrational displacements, which are usually uncoupled. However, piezoelectric shells can induce three-dimensional coupled vibrational displacements over a large frequency range. In this study, three-dimensional coupled vibrational characteristics of piezoelectric shells with free boundary conditions are investigated using three different experimental methods and finite element numerical modeling. For the experimental measurements, amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) is used to obtain resonant frequencies and radial, lateral, and angular mode shapes. This optical technique utilizes a real-time, full-field, non-contact optical system that measures both the natural frequency and corresponding vibration mode shape simultaneously. The second experimental technique used, laser Doppler vibrometry (LDV), is a pointwise displacement measurement method that determines the resonant frequencies of the piezoelectric shell. An impedance analyzer is also used to determine the resonant frequencies of the piezoelectric shell. The experimental results of the resonant frequencies and mode shapes for the piezoelectric shell are verified with a numerical finite element model. Excellent agreement between the experimental and numerical results is found for the three-dimensional coupled vibrational characteristics of the piezoelectric shell. It is noted in this study that there is no coupled phenomenon at low frequencies over which radial modes dominate. However, three-dimensional coupled vibrational modes do occur at high resonant frequencies over which lateral or angular modes dominate.     

Metamaterial composed of different cells exhibiting a negative refraction property over multiple frequency bands

Experimental measurements are presented of the SSRR-MW (square split resonant ring and metal wire) and CSRR-MW (C split resonant ring and metal wire) samples at microwave frequencies. The geometrical shapes of the metamaterial samples are found to play an important role in determining the resonant frequency. Different cells are chosen to stack into a two-layer or a three-layer metamaterial unit to realize multiple negative passbands. The effective parameters of three one-layer models, a two-layer unit, and a three-layer unit are retrieved from the simulation data. The composed models exhibit two or more negative bands by overlapping the passbands of the original cells, and broaden the negative refraction. The recovered parameters show good agreement with theoretical analysis.     

Spectral analysis of vibrational harmonic motion by use of a continuous-wave CO2 Doppler lidar

Vibrational motion of a harmonic oscillator was investigated with a focused continuous-wave (cw) CO2 Doppler lidar at 9.1-microm wavelength. A continuum of frequencies along with many discrete, equally spaced, resonant frequency modes was observed. The frequency modes are similar in structure to the oscillatory longitudinal modes of a laser cavity and arise because of interference of the natural resonant frequency of the oscillator with specific frequencies within the continuum. Each consecutive resonant frequency mode occurred for a movement of the oscillator much less than the wavelength of incident lidar radiation. For vigorous vibration of the oscillator, the observed spectra may be indicating nonlinear motion.     

Reconstructing design parameters of a rectangular resonator via peak signal-to-noise ratio and global optimization algorithms

This article proposes an approach for reconstructing physical parameters of a sample in a rectangular resonator during microwave radiation, knowing a priori, its electric field distribution. The inverse problem was solved using two global optimization algorithms and the peak signal-to-noise ratio (PSNR) criterion. First, the Self-regulated Fretwidth Harmony Search algorithm (SFHS) identified suitable resonant frequencies for a given configuration. Next, the unified Particle Swarm Optimization (UPSO) optimized said configuration. Together, they became a maximization strategy of the PSNR through a dual optimization process. Results showed the ability of the approach for estimating the height of each sample block and the resonating frequency of the cavity. This process takes longer to finish as a higher PSNR is demanded (mainly due to the aforementioned dual optimization). Even so, it allows for more similar electric field distributions between both, the direct and inverse problems.     

The influence of electrode designs on the resonant vibrations for square piezoceramic plates

In this paper, the resonant vibrations of square piezoceramic plates with four different electrode designs are investigated. Two experimental techniques, the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) and the impedance analysis, are used to access the influence of the electrode arrangement on the resonant characteristics of square piezoceramic plates. Both the out-of-plane and in-plane resonant frequencies and full-field mode shapes of piezoceramic plates with various electrode designs are obtained from the AF-ESPI method. The impedance analyzer is used to measure the resonant and antiresonant frequencies of piezoceramic plates. The dynamic electromechanical coupling coefficient (EMCC), which relates to the ability of conversion between mechanical and electrical energy, is determined from the measured values of resonant and antiresonant frequencies. Experimental results of the resonant vibration characteristics of the square piezoceramic plates are verified by numerical computations based on the finite-element method. Excellent agreement between the experimental and numerical results is found in resonant frequencies and corresponding mode shapes. It is found that the electrode design has important influence on the resonant characteristics of piezoceramic plates. The effect of different designs of electrode is more significant in the in-plane modes than that in the out-of-plane modes.     

A new instrument and technique for diagnosing electromagneticdesign problems in microwave module housings and component packages

A method of measuring the frequencies at which resonances occur and the distribution of the associated electric field intensity at the inside face of the housing or package lid has been developed and tested. The method does not require modification of the connections to the microwave assembly within the housing. It is only necessary that the housing or package have a flat lid and that it be left off so that the item under test can be mounted on an equivalent flat plate on the test instrument. The microwave assembly in the housing or package may be operated normally while resonant field distributions are being measured. The prototype instrument yields results that demonstrate the practical application of this measurement assembly as a diagnostic and design development tool for microwave housings and packages of rectangular metal box basic shape. Resonances in the 8-12 GHz range have been accurately measured and indicate that by scaling dimensions an assembly for use at millimeter wavelengths is feasible     

Experimental measurement and numerical analysis on resonant characteristics of piezoelectric disks with partial electrode designs

Three experimental techniques are used in this study to access the influence of the electrode arrangement on the resonant characteristics of piezoceramic disks. These methods, including the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI), laser Doppler vibrometer-dynamic signal analyzer (LDV-DSA), and impedance analysis, are based on the measurement of full-field displacement, pointwise displacement, and electric impedance, respectively. In this study, one full electrode design and three nonsymmetrical partial electrode designs of piezoelectric disks are investigated. Because the clear fringe patterns measured by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and the corresponding vibration mode shapes are successfully obtained at the same time for out-of-plane and in-plane motions. The second experimental method is the impedance analysis, which is used to measure the resonant and antiresonant frequencies. In addition to these experimental methods, LDV-DSA is used to determine the resonant frequencies of the vibration mode with out-of-plane motion. From the experimental results, the dependence of electrode design on the vibration frequencies and mode shapes is addressed. Numerical computations based on the finite element method are presented, and the results are compared with the experimental measurements. The effect of different designs of electrode is more significant in the in-plane modes than that in the out-of-plane modes.     

Analysis of whispering-gallery superconducting dielectric resonator modes

The whispering-gallery (WG) modes of a superconducting dielectric resonator (SDR) based on a sapphire cylindrical dielectric resonator and a YBa₂Cu₃O_{7 –} shielding cylinder have been studied. A method for the determination of the resonant frequencies and the maximum quality factor of such modes is presented. Calculations have shown that most of the mode energy could be confined between the caustic surface of the WG modes provided the dimensions of the SDR are properly selected, and a magnitude of 10⁹ forQ of the SDR could be estimated. A phenomenal explanation is given to account for such outstanding microwave behavior.     

Vibration characteristics of composite piezoceramic plates at resonant frequencies: experiments and numerical calculations

The experimental measurement of the resonant frequencies for the piezoceramic material is generally performed by impedance analysis. In this paper, we employ an optical interferometry method called the amplitude-fluctuation electronic speckle pattern interferometry (AF-ESPI) to investigate the vibration characteristics of piezoceramic/aluminum laminated plates. The AF-ESPI is a powerful tool for the full-field, noncontact, and real-time measurement method of surface displacement for vibrating bodies. As compared with the conventional film recording and optical reconstruction procedures used for holographic interferometry, the interferometric fringes of AF-ESPI are produced instantly by a video recording system. Because the clear fringe patterns measured by the AF-ESPI method will be shown only at resonant frequencies, both the resonant frequencies and corresponding vibration mode shapes are obtained experimentally at the same time. Excellent quality of the interferometric fringe patterns for both the in-plane and out-of-plane vibration mode shapes are demonstrated. Two different configurations of piezoceramic/aluminum laminated plates, which exhibit different vibration characteristics because of the polarization direction, are investigated in detail. From experimental results, we find that some of the out-of-plane vibration modes (Type A) with lower resonant frequencies cannot be measured by the impedance analysis; however, all of the vibration modes of piezoceramic/aluminum laminated plates can be obtained by the AF-ESPI method. Finally, the numerical finite element calculations are also performed, and the results are compared with the experimental measurements. Excellent agreements of the resonant frequencies and mode shapes are obtained for both results.