Coupling Coefficients Of Resonators Research Articles

Calculation of coupling coefficients for diamond micro-ring resonators

We deduce equations to calculate coupling coefficients of diamond micro-ring resonators. The equations can be used universally at any wavelength but not limited to the transmission peaks/valleys, and can be adapted with triangular cross-sections and tapered waveguides. Consequently, we build three models in accordance to different diamond processing technologies. These models deal with ring resonators with either rectangular cross sections, or triangular cross sections, or with tapered bus for triangular cross sections. The calculated coupling coefficients can be well fitted by exponential decay functions of gap d. Due to geometrical limitations, triangular-cross-sectional diamond resonators are shown to have much smaller (factor 20) coupling coefficients than those of rectangular-cross-sectional resonators. A tapered bus is shown to be beneficial to increase the coupling coefficient. Besides the calculation of coupling coefficients, the method presented in the paper can also be used to calculate the bending loss of micro-ring resonators, as a complement to the existing methods.

A Design Method of Transmission-Type Metasurfaces Using Circuit Synthesis Theory of Microwave Bandpass Filters

In this paper, we applied the circuit synthesis theory of filters to the design of transmission-type metasurface cells and arbitrarily designed the amplitude and phase of the transmission and reflection by adjusting the resonant frequency and coupling coefficient. In addition, we successfully designed the phase of the unit cell by using the frequency conversion of filter theory. Moreover, we designed a refractive transmission-type metasurface plate with a novel cell structure that reacts to both polarizations. The prototype operated at the desired refraction angle, confirming the design theory.

Investigation of electrode pitch on resonant and capacitive characteristics in X-cut LiNbO3 membrane-based laterally-excited bulk acoustic resonator

The laterally-excited bulk acoustic resonators (XBARs) have been gaining attention for their use as radio frequency filters due to their ability to resonate at high frequencies (>5 GHz) and wide fractional bandwidth. However, the limited cognition about the resonant characteristics of XBARs remains an obstacle for its commercial application. In this paper, the influence of electrode pitch () on resonant frequency (), quality factor () and effective electromechanical coupling coefficient () in X-cut LiNbO3 membrane-based resonators are investigated for both the XBAR mode and first-order asymmetry mode (). The XBAR mode with above 8 GHz was excited at a metallization ratio () less than 0.5 when was within 5 to 10 , as well as less than 0.6 when was within 15 to 20 . Meanwhile, we revealed that increasing had negligible effect on the of XBAR mode but did produce a positive improvement on its and . In contrast, both and of the mode gradually declined with increasing . In addition, we have demonstrated the disparity between simulated and calculated as a function of , varying with , to achieve a more accurate prediction of capacitance behavior in resonators. Overall, this work has demonstrated the complex relationship of resonant and capacitance properties of X-cut membrane-based resonators on the electrode pitch, which will aid in optimal designing of high-performance filters.

Development of a 6 MeV electron beam energy Linac for fruit sterilization

Treatment of fresh fruits, meat, and food with ionizing radiation has been frequently chosen to destroy harmful pathogenic microorganisms and oriental fruit flies. Electron beam linear accelerator (Linac) is commonly used as the source of irradiation to produce photons and electrons in megavolt energy. A 6 MeV Linac designed for medical therapy has been developed for fresh fruit sterilization at Synchrotron Light Research Institute (SLRI). Some physical design and beam dynamic results of the electron gun and 6 MeV Linac will be presented in this paper. Testing of each subsystem and installation of the 6 MeV Linac with major auxiliary systems will be described in this paper. It is the first system designed, fabricates, and tested in-house for the fruit sterilization application at SLRI. Measurement results of the Linac properties are presented as a resonant frequency and coupling coefficient at low power called a cold test. The Linac system with all sub-systems and the auxiliary systems will be installed and tested before x-rays production. During commissioning some electron beam parameters out of the electron gun and the Linac exit will be measured.

Resonance prediction and inverse design of multi-core selective couplers based on neural networks.

Resonance analysis and structural optimization of multi-channel selective fiber couplers currently rely on numerical simulation and manual trial and error, which is very repetitive and time consuming. To realize fast and accurate resonance analysis and calculation, we start with dual-core structures and establish forward classification and regression neural networks to classify and predict different resonance properties, including resonance types, operating wavelength, coupling coefficient, coupling length, 3dB bandwidth, and conversion efficiency. The pre-trained forward neural networks for dual-core fibers can also realize accurate and fast prediction for multi-core fibers if the mode energy exchange occurs only between one surrounding core and the central core. For the inverse design, a tandem neural network has been constructed by cascading the pre-trained forward neural network and the inverse network to solve the non-uniqueness problem and provide an approach to search for appropriate and desired multi-core structures. The proposed forward and inverse neural networks are efficient and accurate, which provides great convenience for resonance analysis and structural optimization of multi-channel fiber structures and devices.

A Real-Time Calibrated Adaptive-ZVS Class-D Power Amplifier for 6.78 MHz Wireless Power Transfer System

This brief presents a class-D power amplifier (PA) with an adaptive zero-voltage switching (A-ZVS) technique for 6.78 MHz resonant wireless power transfer (R-WPT) system. In R-WPT operation, the loading impedance of a PA can be varied by the process tolerance of the LC resonant components or WPT environments, such as the resonant topology, coupling coefficient, and loading condition of the receiver. In particular, the commonly used series-parallel resonant topology suffers from resonant point deviation of primary LC tank, resulting in hard switching of the PA. Consequently, efficiency degradation and electromagnetic interference can occur under multi-MHz operation. The proposed A-ZVS feedback loop calibrates the equivalent resonant capacitance in real-time to achieve ZVS by adjusting the loading impedance to be slightly inductive. The proposed PA was fully integrated except for one switched capacitor used as the tuning element and fabricated in a TSMC 0.18 <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mu \text{m}$ </tex-math></inline-formula> BCD process. The measurement results demonstrated robust ZVS operation with a peak system efficiency of 52.7 % and an enhanced maximum transmitting power of 107 %.

FEM Analysis of the Effect of Polarization on the Electromechanical Coupling Factor of Resonators with a Wrap-Around Electrode

The efficiency of electromechanical conversion in piezoelectric elements is assessed according to the magnitude of the electromechanical coupling coefficient. For power applications of piezoelectric elements, it is desirable that the efficiency of electrical to mechanical energy conversion be as high as possible. In case of resonators with electrodes incompletely covering their bases, an inhomogeneous electric field is generated, which results in inhomogeneous polarization of the resonator. The resonator will be polarized in some places either in a direction other than the desired one or not polarized at all. The degree of polarization of the resonator is one of the factors affecting the electromechanical coupling coefficient. The aim of this work is to analyze the magnitude of the electromechanical coupling coefficient of resonators with electrodes incompletely covering the bases and to compare the results with the electromechanical coupling coefficient of resonators with fully electroded bases. The physical description is given by the linear piezoelectric equations, the Gaussian equation for the electric field, and by Newton’s law of force. On this basis, a FEM model is developed and used to analyze the electromechanical coupling coefficient. The result of the calculation of the electromechanical coupling cofficient is that for resonators with a wrap-around electrode in studied shape and dimensions there will be a decrease in the electromechanical coupling coefficient compared to a fully electroded resonator of identical dimensions. The presented conclusions are compared with analytically and experimentaly achieved results.

Analysis of high electromechanical coupling coefficient zinc oxide Lame’ mode resonators and a design technique for spurious mode mitigation

This paper presents an exhaustive analysis on Zinc Oxide based modified Lame’ mode resonators. Extensive analytical study describing the operating principles of the resonator is presented and comparisons with finite element (FE) simulation results show excellent agreement. Subsequently, the effect of electrode configuration, type of metal used for electrode, electrode coverage ratio and electrode thickness on the effective electromechanical coupling coefficient (Keff2) is analyzed from which electrode configurations that can offer best values for Lame’ modes on rectangular plates are suggested. On this basis, a remarkably high coupling coefficient (i.e. about 14.5% simulated) is achieved. In addition, a method of mitigating in-band spurious modes without causing a significant change on the resonant frequency and coupling coefficient is demonstrated. In this setting, the simulated results offered a spurious free resonance with a sufficient suppression of spurious modes without inducing a performance degradation on the main mode.

Pressure-induced Fermi resonance between fundamental modes in phthalic anhydride

In situ high-pressure Raman spectra of phthalic anhydride (PA) have been measured up to 16 GPa through diamond anvil cell technique. The results show that all the Raman bands are blue-shifted with the increase of pressure, accompanied by appearance of some new bands. A Fermi resonance phenomenon of the two Raman fundamental modes of PA at 773 cm−1 and 801 cm−1 is proposed at pressures above 6.6 GPa, where a possible first-order phase transition occurs. The pressure-induced changes of Fermi resonance parameters, e.g., intensity ratio, coupling coefficient and frequency gap of unperturbed transition, are discussed.

Active and selective manipulation of dual transparency windows in hybrid graphene-vanadium dioxide metamaterial

Active and selective manipulation of dual–spectral electromagnetically induced transparency (EIT) metamaterial constructed by three graphene strips and vanadium dioxide (VO2) layer is proposed and demonstrated numerically. Simulation results illustrate that the dual-spectral EIT-like effect are induced by adjacent graphene strips acted as bright and bright mode and excited opposite-phase electric field distributions. One or two of EIT-like windows can be modulated by selectively varying graphene strip’s Fermi energy. Meanwhile, the Fermi energies of three graphene strips are varying simultaneously, the position of dual transparency windows as a whole obviously exhibit blue shift. Moreover, the amplitude of dual–spectral EIT windows can be simultaneously manipulated while frequency remain rough constant during the phase transition process of VO2. The physical mechanism underneath the phenomenon of actively and selectively tunable EIT, which is revealed by theoretically calculated results based on the classical three-oscillator model, can be attributed to the variation of resonance frequency, coupling coefficient and losses of the resonators caused by varying Fermi energy of graphene strips and conductivity of VO2.

A study of a new hybrid vibration energy harvester based on broadband-multimode

To improve the energy conversion efficiency and working frequency bandwidth of a single frequency piezoelectric vibration energy harvester, a new type of hybrid vibration energy harvester is developed which is combined with the mechanism of piezoelectric and electromagnetic energy conversion. The system comprises of a PZT cantilever beam, an elastic suspended magnetic mass, a magnet block attached to the end of the cantilever beam and a resonator. The addition of resonator can not only increase the mode, but also adjust the frequency of harvester flexibly. Nonlinear magnetic force of magnet block not only broadens the frequency band and improves the output performance of the system, but also changes the resonant frequency to make the harvester have better adjustable performance. On this basis, an improved electromechanical coupled analytical model of continuum is proposed which can be solved by the Runge-Kutta algorithm and the influence of different factors (the mass and spring stiffness of the resonator, as well as the electromechanical coupling coefficient, electromagnetic coupling coefficient, magnet mass and magnetic flux) on the output are analyzed. According to the prototype of the vibration energy harvester developed, an experimental system was built. The performance of the independent and hybrid energy harvesters is evaluated by experimental and analytical methods. The peak output voltage of the piezoelectric part was about 4 times that of the electromagnetic part. The peak output current of the electromagnetic part is about 30 times that of the piezoelectric part. The study results show that the proposed new hybrid vibration energy harvester can achieve a wider frequency range and multimodal vibration energy harvesting. In addition, the bandwidth and power of the harvester can be dynamically adjusted by changing the resonator or electromechanical coupling coefficient, and the bandwidth of the harvester can also be adjusted by changing the quality and characteristics of the magnet.

MUTUAL COUPLING COEFFICIENTS OF ROTATING RECTANGULAR DIELECTRIC RESONATORS IN CUT-OFF RECTANGULAR WAVEGUIDE

Background. A further increase in the speed of information transfer is determined by more stringent requirements for the elements of communication devices. One of the most important components of such devices is various filters, which are often made on the basis of dielectric resonators. Calculation of the parameters of multi-section filters is impossible without further development of the theory of their design. The development of filter theory is based on electrodynamic modelling, which involves calculating the coupling coefficients of dielectric resonators in various transmission lines.&#x0D; Objective. The aim of the research is to calculate and study the coupling coefficients of rectangular dielectric resonators with a rectangular metal waveguide when their axes rotate. Investigation of new effects to improve the performance of filters and other devices based on them.&#x0D; Methods. Methods of technical electrodynamics are used to calculate and analyse the coupling coefficients. The end result is to obtain new analytical formulas for new structures with rectangular dielectric resonators, which make it possible to analyse and calculate their coupling coefficients.&#x0D; Results. New analytical expressions are found for the coupling coefficients of dielectric resonators with the rotation of their axes in a rectangular waveguide.&#x0D; Conclusions. The theory of designing filters based on new structures of dielectric resonators with rotation of their axes in metal waveguides has been expanded. New analytical relationships and new patterns of change in the coupling coefficients are found.&#x0D; Keywords: dielectric filter; rectangular dielectric resonator; rotation; coupling coefficients.

Intermolecular Interactions at the Silica-Liquid Interface Modulate the Fermi Resonance Coupling in Surface Methanol.

The buried solid/liquid interface between hydrophilic fused silica and binary solvent mixtures of acetonitrile (MeCN) and methanol (MeOH) was studied with vibrational sum-frequency generation (vSFG) spectroscopy. Our data showed that at high relative concentrations of methanol, the Fermi resonance peak in the vSFG spectrum is greatly suppressed, and it progressively gains intensity as methanol is diluted with perdeuterated acetonitrile. This phenomenon is quantified by the Fermi resonance coupling coefficient, W, extracted using a two-level model, as well as the experimental intensity ratio, R, of the methyl Fermi resonance band to that of the symmetric stretch. At a 1.0 MeOH mole fraction, W and R values were 10 ± 10 cm-1 and 0.01 ± 0.02, respectively, whereas at a 0.1 mole fraction, W and R increased to 46 ± 4 cm-1 and 0.43 ± 0.16, respectively. This indicates that solvation with acetonitrile effectively tunes the Fermi coupling of methanol vibrations at the silica/liquid interface.

COUPLING COEFFICIENTS OF ROTATING RECTANGULAR DIELECTRIC RESONATORS WITH RECTANGULAR WAVEGUIDE

Background. A further increase in the speed of information transfer is determined by more stringent requirements for the elements of communication devices. One of the most important components of such devices is various filters, which are often made on dielectric resonators. Calculation of the parameters of multi-section filters is impossible without further development of the theory of their design. The development of filter theory is based on electrodynamic modeling, which involves calculating the couplingcoefficients of dielectric resonators in various transmission lines.Objective. The aim of the research is to calculate and study the coupling coefficients of rectangular dielectric resonators with a rectangular metal waveguide when their axes rotate. Investigation of new effects to improve the performance of filters and other devices based on them.Methods. Methods of technical electrodynamics are used to calculate and analyze the coupling coefficients. The end result is to obtain new analytical formulas for new structures with rectangular dielectric resonators, which make it possible to analyze and calculate their coupling coefficients.Results. New analytical expressions are found for the coupling coefficients of dielectric resonators with the rotation of their axes in a rectangular waveguide.Conclusions. The theory of designing filters based on new structures of dielectric resonators with rotation of their axes in metal waveguides has been expanded. New analytical relationships and new patterns of change in the coupling coefficients are found.

The Simulation of Resonant Mode and Effective Electromechanical Coupling Coefficient of Lithium Niobate Crystal with Different Orientations

At present, the proportion and role of thin film bulk acoustic wave (FBAR) filters in mobile communication products are becoming more and more obvious due to its higher work frequency and smaller size. As a commonly used piezoelectric material, aluminum nitride (AlN) limits the bandwidth of the FBAR filter because of its small electromechanical coupling coefficient (kt 2) of ~6.5%. On contrast, lithium niobate (LiNbO3, LN) crystals with some certain specific orientations have much better acoustic properties, making this type of material the promising candidate for FBAR applications. In this work, the acoustic resonant mode in LN crystal is analyzed by FEM simulations. In order to obtain the optimal orientations with good longitudinal wave property, Euler angle (EA) method is used to simulate the resonant modes and calculate the corresponding kt 2 of different orientations. Besides, the correctness of EA method has been demonstrated in this work by comparing the displacement change under electrostatic field with the traditional matrix transformation operation depending on the piezoelectric effect. The simulations show that the 43°Y-cut LiNbO3 has a high kt 2 and a pure longitudinal wave vibration mode simultaneously, making this orientation the most proper candidate for FBAR filters application with large bandwidth.

Magnetic Field Tunable Ferromagnetic Shape Memory Alloy-Based Piezo-Resonator

In this letter, we have performed a comprehensive analysis of the influence of the magnetic field on BAW resonator consisting of a highly magnetostrictive layer and AlN thin film. The fundamental resonant frequency of the fabricated BAW resonator is about ~4.22 GHz. In the presence of a magnetic field, we studied the effect on the resonator parameters such as resonant frequency, acoustic velocity, and coupling coefficient. For the magnetic field of strength 1200 Oe, the resonant frequency significantly shifts by ~360 MHz. Resonant frequency increases and electromechanical coupling coefficient ( $\text{k}_{t}$ ) decreases with the increase in the DC magnetic field. The maximum acoustic velocity of ~7350 m/sec was observed at the magnetic field of 1500 Oe when applied parallel to the surface. Agilent Advanced Design Software (ADS) was used to extract the equivalent Modified Butterworth-Van Dyke circuit parameters (R m , C m , and L m ) of the resonator. Further, in the presence of the magnetic field, we obtained the variation in values of R m , C m , and L m of the resonator structure. Such tunable resonators can be useful and vital in dealing with varying frequency bands for sustainable growth in wireless communication and magnetic field sensor applications.

Performance improvements of a tunable bandpass microwave photonic filter based on a notch ring resonator using phase modulation with dual optical carriers.

A tunable bandpass microwave photonic filter can be achieved by using a notch ring resonator with optical phase modulation. However, the filter's out of band rejection ratio and shape factor are limited due to the ring resonator's residual phase, which can seriously degrade the filter's performance. By using dual optical carriers and setting their wavelengths oppositely detuned from two resonant frequencies of a notch ring resonator, the residual phase induced by the ring resonator at radio frequencies falling outside the region of the notch stopband is reduced, thus the out-of-band rejection ratio and shape factor of the microwave photonic filter are greatly improved. The proposed microwave photonic filter was both verified theoretically and experimentally. Compared with single optical carrier method, the out-of-band rejection ratio of the filter can be enhanced from 17.7dB to 31.5dB, and the filter's shape factor is improved from 3.05 to 1.78. Besides, the filter's frequency and bandwidth can be tuned by varying the wavelengths of the two optical carriers and the ring resonator's coupling coefficients. Finally, a tunable bandpass microwave photonic filter with frequency tuning range of 2~14GHz, 3dB bandwidth tuning range of 0.673~2.798GHz is demonstrated.

Study the effect of Li+ on the ν2/ν3+ν4 Fermi resonance of acetonitrile by Raman Spectroscopy.

Raman spectra of the solution of LiClO4 in acetonitrile (CH3CN) at different concentrations have been measured. With increasing the concentration of Li+, it was noted that several vibrational modes of CH3CN had significant changes in Raman shifts and some new Raman peaks emerged due to the CH3CN⋯Li+ complex formation. In addition, Fermi resonance phenomenon between the ν2' and (ν3 + ν4)' Raman bands of CH3CN⋯Li+ complex was observed. Based on the Bertran's equations, Fermi resonance parameters of free CH3CN and CH3CN⋯Li+ complex at different concentrations have been calculated, respectively. Compared the Fermi resonance coupling coefficients W of free CH3CN with CH3CN⋯Li+ complex at different concentrations, the free CH3CN had a little smaller value, which indicated that the ν2'/(ν3 + ν4)' Fermi resonance in CH3CN⋯Li+ complex was much stronger than the ν2/ν3 + ν4 Fermi resonance in CH3CN. From the detailed analysis of the effect of Li+ on the spectral features of CH3CN, the effect mechanism of Li+ coordination to CH3CN at the nitrogen of the CN group on the ν2/ν3 + ν4 Fermi resonance of CH3CN has been elucidated.

The Effect of Fractional Orders on the Transmission Power and Efficiency of Fractional-Order Wireless Power Transmission System

To avoid the problems of integer-order magnetic resonant wireless power transmission (WPT) systems, such as low output power and transmission efficiency, high resonant frequency, frequency splitting, and parameter coupling, a novel WPT system based on the fractional-order calculus theory is proposed; the resonant frequency and coupling coefficient can be regulated by the fractional order, so that this system has completely different transmission characteristics from the integer-order WPT system. Therefore, in this paper, the circuit model based on the phasor method of fractional-order WPT system is established, and the output power and transmission efficiency of the system are analyzed. In addition, the comparative analysis of output power and transmission efficiency under different fractional orders are performed to estimate the optimal combination of fractional orders, which is beneficial to produce better characteristics of output power and transmission efficiency and provides a theoretical basis for the design and implementation of an experimental system.

Influence of Geometric Parameters and Permittivity of Stripline Filters on Resonator Coupling Coefficients

It has been proved that electromagnetic coupling coefficients K of resonators in stripline filters with homogeneous dielectric depend only on geometric parameters of the filter designs and are independent of relative permittivity er (if the dielectric is two-layer, coefficients K depend only on geometric parameters of the filter designs and ratio er2/er1). It has been shown that the revealed earlier influence of permittivity er and the operating frequency on K is only a consequence of the influence of the length of stripline resonators on K: the lesser is the length, the larger is coefficient K. It has been found that these propositions enable consideration of frequency characteristics of the same design of the bandpass filter in different frequency bands by changing er and performing slight changes in outermost resonators. The results of computer simulation of the transfer of frequency characteristics of a stripline bandpass filter from 3 GHz to 6 and 12 GHz with retaining the fractional bandwidth and selectivity are presented.