Effective Coupling Coefficient Research Articles

Band Pass Filters Based on GaN/Si Lumped-Element SAW Resonators Operating at Frequencies Above 5 GHz

This paper reports on a GaN/Si surface acoustic wave (SAW) impedance element filter operating in the few gigahertz region. The PI-type filter consists of three SAW resonators with the same digit/interdigit widths, integrated with series/parallel planar inductors. The design procedure is based on modeling the SAW resonators using four parameters, independent of the equivalent circuit model representation (series resonance frequency, static capacitance, quality factor, and effective coupling coefficient). The series frequency is tuned by a planar inductor placed in series, while the parallel resonant frequency is tuned by a planar inductor placed in parallel with the SAW resonator. Closed-form equations are derived for the analysis of lumped-element SAW resonators. The design procedure is further based on the area of the SAW resonator and the lengths of the planar inductors as independent variables. Full-wave electromagnetic and circuital co-simulations and parametric optimizations are employed for the final filter design, which is implemented in the coplanar waveguide topology. The lumped-element SAW bandpass filter is fabricated using e-beam lithography for the definition of the 200-nm-wide interdigital transducers. Measurement results show the insertion losses of 12.9 dB at 5.49 GHz, the return losses of 16 dB, 3-dB bandwidth of 8.3 MHz, and the out-of-band rejection of 24 dB. The filter is compatible with monolithic integration with GaN active electronics.

Buckling solutions of clamped-pinned anisotropic laminated composite columns under axial compression using bifurcation approach and finite elements

Following the bifurcation approach, a generalized closed form buckling solution for clamped-pinned anisotropic laminated composite columns under axial compression is developed using the energy method. The effective axial, coupling, and flexural rigidity coefficients of the anisotropic layups are determined following the generalized constitutive relationship using dimensional reduction by static condensation of 6×6 rigidity matrix. The presented analytical explicit formula reproduces Euler buckling expression in the case of isotropic or specially-orthotropic materials once the effective coupling term vanishes. On the other hand, the analytical formula furnishes two extra terms which are functions of the effective coupling, flexural and axial rigidity. The analytical buckling formula is confirmed against finite element Eigen value solutions for different anisotropic laminated layups yielding high accuracy for a wide range of stacking sequences. A parametric study is then conducted to examine the effect of ply orientations, material properties including hybrid carbon/glass fiber composites, FE element type, and column size. Relevance of the numerical and analytical results is discussed in comparison to previous results in literature for cross ply laminates.

Analytical and Finite Element Buckling Solutions of Fixed–Fixed Anisotropic Laminated Composite Columns Under Axial Compression

A generalized analytical formula is developed to predict buckling of anisotropic laminated composite fixed–fixed thin columns by using the Rayleigh–Ritz displacement field approximation. Based on the generalized constitutive relationship, the effective extensional, coupling and flexural stiffness coefficients of the anisotropic layup are determined using dimensional reduction by static condensation of the 6[Formula: see text][Formula: see text][Formula: see text]6 composite stiffness matrix. The resulting explicit formula is expressed in terms of the flexural stiffness since the coupling and extensional stiffness coefficients drop out of the formulation for this boundary condition when following the standard Rayleigh–Ritz formulation steps. This formula is similar to the Euler buckling formula in which the flexural rigidity is expressed in terms of the flexural stiffness coefficient of laminated composites. Motivated by reducing some of the discrepancy with the finite element results, the pre-buckling solution was substituted into the bifurcation expression to yield an updated formula that includes the coupling and extensional stiffness coefficients. The analytical results are verified against finite element Eigen value solutions for a wide range of anisotropic laminated layups yielding high accuracy. A parametric study is then conducted to examine the effect of ply orientation and material properties including hybrid carbon/glass fiber composites. Relevance of the numerical and analytical results is discussed for all these cases. In addition, comparisons with an earlier buckling solution for cross-ply laminated columns are made.

Closed form stability solution of simply supported anisotropic laminated composite plates under axial compression compared with experiments

Closed form expression for the buckling load of generally anisotropic laminated composite simply supported thin plates is derived. The Rayleigh-Ritz displacement field approximation based on the energy approach introduced an upper bound solution compared to the FE results. Therefore, the critical stability matrix is used to obtain an accurate buckling formula. The effective axial, coupling and flexural stiffness coefficients of the anisotropic layup is determined from the generalized constitutive relationship using dimensional reduction by static condensation of the 6×6 composite stiffness matrix. The resulting explicit formula has an additional term, which is a function of the effective coupling and axial stiffness. This formula reduces down to Euler buckling formula once the effective coupling stiffness term vanishes for isotropic and certain classes of laminated composites. The closed form results are verified against finite element Eigenvalue solutions for a wide range of anisotropic laminated layups yielding high accuracy. Comparisons with a limited number of experiments are also performed showing good correspondence. A brief parametric study is then conducted to examine the effect of ply orientations and material properties including hybrid carbon/glass fiber composites. Relevance of the numerical and closed form results is discussed for all these cases.

A flexible, gigahertz, and free-standing thin film piezoelectric MEMS resonator with high figure of merit

In this paper, a 2.6 GHz air-gap type thin film piezoelectric MEMS resonator was fabricated on a flexible polyethylene terephthalate film. A fabrication process combining transfer printing and hot-embossing was adopted to form a free-standing structure. The flexible radio frequency MEMS resonator possesses a quality factor of 946 and an effective coupling coefficient of 5.10%, and retains its high performance at a substrate bending radius of 1 cm. The achieved performance is comparable to that of conventional resonators on rigid silicon wafers. Our demonstration provides a viable approach to realizing universal MEMS devices on flexible polymer substrates, which is of great significance for building future fully integrated and multi-functional wireless flexible electronic systems.

Resonant spectrum method for characterizing Ba0.5Sr0.5TiO3 based high overtone bulk acoustic wave resonators

This letter reports the use of the resonant spectrum method to characterize a high overtone bulk acoustic wave resonator (HBAR) which has a thin film ferroelectric BaSrTiO3 (BSTO) active layer on a YAG substrate. The HBAR works on the principle of electric field induced piezoelectricity of the thin film ferroelectric BSTO and exhibits switching functionality. From the parallel and series resonant frequencies of each of the multiple peaks in the frequency spectrum of the HBAR, the distribution of spacing of parallel resonance frequency and the distribution of effective coupling coefficient are studied and parameters like acoustic wave velocity, electromechanical coupling coefficient, elastic constant, and density for the thin film are determined. The influence of dc bias voltages on the distribution of the effective coupling coefficient and the electromechanical coupling coefficient is also reported. This letter also establishes the relationship between the relative tunability of the device capacitance and the electromechanical coupling coefficient.

Steady method to retrieve effective electromagnetic parameters of bianisotropic metamaterials at one incident direction in the terahertz region

We propose a steady method to extract the effective constitutive parameters of a slab of bianisotropic split-ring resonator metamaterial from reflection and transmission coefficients. The effective permittivity, permeability and magnetoelectric coupling coefficient of bianisotropic metamaterial can be simply retrieved by our derived analytical inversion equations. In our retrieval method, the transmission and reflection coefficients in only one direction of wave propagation were applied. The method was verified by the retrieval constitutive parameters for different metamaterials, among which one is isotropic structure and the other one is bianisotropic metamaterial. The intrinsic difference between the normal isotropic metamaterial and the bianisotropic metamaterial was evidently revealed. The resonant characteristic of the split ring resonator metamaterial including electric coupling to magnetic resonance was verified by the extracted effective constitutive parameters. The proposed method can be effectively applied in investigation of bianisotropic performance of metamaterials.

Multigap Superconductivity at Extremely High Temperature: A Model for the Case of Pressurized H2S

It is known that in pressurized H2S the complex electronic structure in the energy range of 200 meV near the chemical potential can be separated into two electronic components, the first characterized by steep bands with a high Fermi velocity and the second by flat bands with a vanishing Fermi velocity. Also the phonon modes interacting with electrons at the Fermi energy can be separated into two components: hard modes with high energy around 150 meV and soft modes with energies around 60 meV. Therefore we discuss here a multiband scenario in the standard BCS approximation where the effective BCS coupling coefficient is in the range 0.1- 0.32. We consider a first (second) BCS condensate in the strong (weak) coupling regime 0.32 (0.15). We discuss different scenario segregated in different portions of the material. The results show the phenomenology of unconventional superconducting phases in this two-gap superconductivity scenario where there are two electronic components in two Fermi surface spots, the pairing is mediated by either by a soft or a hard phonon branch where the inter-band exchange term, also if small, plays a key role for the emergence of high temperature superconductivity in pressurized sulfur hydride.

Piezoelectric cylindrical discs and solid rods: Dependence of the resonance frequencies and effective coupling coefficients on aspect ratio.

Dependencies of the resonance frequencies and effective coupling coefficients for solid circular cylindrical piezoelements (discs) of finite size are considered as a function of their height-to-diameter aspect ratios, h/2a. At aspect ratios in the range of approximately 0.5 < h/2a < 1.5 the piezoelements are treated analytically, as a two degree-of-freedom coupled system by applying the coupled mode theory approach [Aronov, Bachand, and Brown, J. Acoust. Soc. Am. 126(6), 2983-2990 (2009)]. Results are presented as plots of resonance frequencies and effective coupling coefficients vs aspect ratios. Experimental verification showed good agreement with the analytical predictions and allowed sufficiently reliable characterization of the trends of parameters in the range of aspect ratios, for which the analytical treatment could not be applied. The equivalent parameters that characterize energy relations in the course of coupled vibration are determined, and the equivalent electromechanical circuit is introduced for calculating frequency response of the transducers.

Detection of non-aqueous phase liquid contamination by SH-TE seismoelectrics: A computational feasibility study

In this work we propose a one dimensional numerical study of the seismoelectric signals produced in a fresh water aquifer contaminated by either light or dense non-aqueous phase liquids ((L/D)NAPLs), considering a pure SH-wave seismic source. We investigate the nature of the electromagnetic response generated at media interfaces, the so called Interface Response (IR), by comparing it with the electromagnetic field generated by a current sheet; wherefrom we are able to interpret that the source of the IR behaves as an electric current flowing along the interface, differently to what happens when the IR is originated by the action of a P-wave, where electric charge accumulation generates an electric dipole. We perform a parametric study to analyze how the presence of contaminants affects the IR, resorting to an effective media approach to compute mechanical and electromagnetic properties, and considering three different effective fluid-saturation dependent electrokinetic coupling coefficient models. We observe, as expected, that porosity plays an important role in the amplitude of the IRs. When considering different NAPL saturations, significant effects on the IRs are only seen when the thickness of the contaminated layer is above a threshold value, which depends on the present contaminant and the considered effective electrokinetic coupling coefficient model.

A coupling numerical methodology for weakly transient conjugate heat transfer problems

This study deals with the development of a partitioned coupling strategy at the fluid–solid interface for weakly transient heat transfer problems. The thermal coupling is carried out by an iterative procedure (strong coupling) between a transient solid and a sequence of steady states in the fluid. Continuity of temperature and heat flux is ensured at each coupling time step.Emphasis is put on the choice of interface conditions at the fluid–solid interface. Two fluid–solid transmission procedures are considered in this paper: Dirichlet–Robin and Neumann–Robin conditions. These conditions are theoretically examined and it is shown that the Biot number is a key parameter for determining relevant interface conditions. Stability diagrams are provided in each case and the most effective coupling coefficients are highlighted and expressed. Numerical thermal computations are then performed for two different Biot numbers. They confirm the efficiency of the interface conditions in terms of accuracy, stability and convergence. At the end of this paper a comparison between a partitioned and a monolithic approach is presented.

Mechanical and electrical strain response of a piezoelectric auxetic PZT lattice structure

A two-dimensional auxetic lattice structure was fabricated from a PZT piezoceramic. Tape casted and sintered sheets with a thickness of 530 μm were laser cut into inverted honeycomb lattice structure with re-entrant cell geometry (θ = −25°) and poling direction oriented perpendicular to the lattice plane. The in-plane strain response upon applying an uniaxial compression load as well as an electric field perpendicular to the lattice plane were analyzed by a 2D image data detection analysis. The auxetic lattice structure exhibits orthotropic deformation behavior with a negative in-plane Poisson’s ratio of −2.05. Compared to PZT bulk material the piezoelectric auxetic lattice revealed a strain amplification by a factor of 30–70. Effective transversal coupling coefficients of the PZT lattice exceeding 4 × 103 pm V−1 were determined which result in an effective hydrostatic coefficient 66 times larger than that of bulk PZT.

Sezawa Propagation Mode in GaN on Si Surface Acoustic Wave Type Temperature Sensor Structures Operating at GHz Frequencies

This letter investigates the applicability of Sezawa propagation mode for various GaN/Si surface acoustic wave (SAW) temperature sensor structures. First, different acoustic propagation modes in GaN on Si single SAW resonators, operating at GHz frequencies, were evaluated. The variation of the phase velocity versus the normalized thickness of the GaN layer is analyzed experimentally for different propagation modes, on the SAW structures manufactured using e-beam lithography. The different acoustic modes were also identified using finite-element method calculations. The effective coupling coefficients for the Sezawa mode are determined and show larger values than those obtained for the Rayleigh mode. The sensitivities obtained for the temperature sensor structures are 1.8 times higher for Sezawa than for the fundamental Rayleigh mode.

Trichromatic π-Pulse for Ultrafast Total Inversion of a Four-Level Ladder System

We present a numerical solution for complete population inversion in a four-level ladder system obtained by using a full π-pulse illumination scheme with resonant ultrashort phase-locked Gaussian laser pulses. We find that a set of pulse areas such as √3π , √2π , and √3π completely inverts the four-level system considering identical effective dipole coupling coefficients. The solution is consistent provided the involved electric fields are not too strong and it is amply accurate also in the case of diverse transition dipole moments. We study the effect of detuning and chirp of the laser pulses on the complete population inversion using the level structure of atomic sodium interacting with ps and fs pulses as an example. Our result opens the door for multiple applications such as efficient ultrashort pulse lasing in the UV or the engineering of quantum states for quantum computing.

A top-crossover-to-bottom addressed segmented annular array using piezoelectric micromachined ultrasonic transducers

We design and fabricate segmented annular arrays (SAAs) using piezoelectric micromachined ultrasonic transducers (pMUTs) to demonstrate the feasibility of acoustic focusing of ultrasound. The fabricated SAAs have 25 concentric top-electrode signal lines and eight bottom-electrodes for grounding to enable electronic steering of selectively grouped ultrasonic transducers from 2393 pMUT elements. Each element in the array is connected by top-crossover-to-bottom metal bridges, which reduce the parasitic capacitance. Circular-shaped pMUT elements, 120 μm in diameter, are fabricated using 1 μm-thick sol–gel lead zirconate titanate on a silicon wafer. To utilize the high-density pMUT array, a deep reactive ion etching process is used for anisotropic silicon etching to realize the transducer membranes. The resonant frequency and effective coupling coefficient of the elements, measured with an impedance analyzer, yields 1.517 MHz and 1.29%, respectively, in air. The SAAs using pMUTs are packaged on a printed circuit board and coated with parylene C for acoustic intensity measurements in water. The ultrasound generated by each segmented array is focused on a selected point in space. When a 5 Vpp, 1.5 MHz square wave is applied, the maximum spatial peak temporal average intensity () is found to be 79 mW cm−2 5 mm from the SAAs’ surface without beamforming. The beam widths (−3 dB) of ultrasonic radiation patterns in the elevation and azimuth directions are recorded as 3 and 3.4 mm, respectively. The results successfully show the feasibility of focusing ultrasound on a small area with SAAs using pMUTs.

Multi-sensitive temperature sensor platforms using aluminum nitride MEMS resonators

This paper presents three MEMS platforms that exhibit multiple thermal sensitivities and multi-frequency capabilities. Multiple sensors with a variety of operating frequencies and thermal sensitivities can co-exist in the same device wafer. Aluminum nitride is the active layer of the three platforms. The impact of stack and substrate modifications on the performance of test devices is discussed as well. To test the platforms’ performance, temperature sensors are realized using Lamb-acoustic-wave micro-electro-mechanical (MEMS) resonators, each one featuring a different thermal coefficient of frequency that scales with frequency. Resonators designed for frequencies between 200 MHz to 1.5 GHz operate at their first symmetric mode (S0) and feature first-order TCFs in the range from −12 up to −30 ppm °C−1 depending on the frequency and design. Furthermore, TCFs of devices can be tailored to get smaller values through process variations. The platforms exhibit high electromechanical performance, with quality factors in excess of 1500 and maximum effective coupling coefficient of 6.43% for radio frequency (RF) applications above 1 GHz.

Carbon nanotube forests as top electrode in electroacoustic resonators

We grow carbon nanotube forests on piezoelectric AlN films and fabricate and characterize nanotube-based solidly mounted bulk acoustic wave resonators employing the forests as the top electrode material. The devices show values for quality factor at anti-resonance of ∼430, and at resonance of ∼100. The effective coupling coefficient is of ∼6%, and the resonant frequencies are up to ∼800 MHz above those observed with metallic top electrodes. AlN promotes a strong catalyst-support interaction, which reduces Fe catalyst mobility, and thus enforces the growth of forests by the base growth mechanism.

Nonuniform piezoelectric circular plate flexural transducers with underwater applications.

An analytical treatment is presented for circular flexural plate transducers that have nonuniform electromechanically active-passive mechanical systems with particular interest in underwater applications. The analysis is made using the energy method that was previously applied to calculating parameters of uniform fully active (bimorph) circular plate transducers [B. S. Aronov, J. Acoust. Soc. Am. 118(2), 627-637 (2005)]. It is shown that the vibration mode shapes remain sufficiently similar to those for uniform plates for a large range of relative dimensions of active and passive laminates of radially nonuniform mechanical systems, and they may be used for calculating transducer parameters. Therefore the transducers can be considered as having a single degree of freedom, and their operational characteristics can be determined using the same technique as previously used for uniform plates. Dependences of the resonance frequencies, effective coupling coefficients, and parameters of the equivalent electromechanical circuit on relative dimensions of active and passive laminates for several combinations of the active and passive materials are presented and compared with those parameters of uniform plates having the same overall dimensions. The results of experimental verification are in good agreement with theoretical predictions.

Dependency of resonance frequencies and effective coupling coefficients of piezoceramic rectangular bars and plates on aspect ratio.

The resonance frequencies and effective coupling coefficients of piezoceramic rectangular plates polarized through their width and transversely polarized bars are presented as functions of their lateral aspect ratios. The results are obtained by employing the coupled vibration analysis technique that was previously illustrated for rectangular plates polarized through the thickness [J. Acoust. Soc. Am. 126(6), 2983-2990 (2009)]. The results of calculations show good agreement with experimental data. Conclusions are made on preferable values of the aspect ratios in terms of the effective coupling coefficients.

Magnetic Field Measurement with Heisenberg Limit Based on Solid Spin NOON State**Supported by the National Basic Research Program of China (No 2011CB921200), the Strategic Priority Research Program(B) of the Chinese Academy of Sciences under Grant No XDB01030200), the National Natural Science Foundation of China (No 11374290), the Fundamental Research Funds for the Central Universities and the Foundation for Authors of

The maximum entangled number state (NOON state) can improve the sensitivity of physical quantity measurement to the Heisenberg limit 1/N. In this work, the magnetic field measurement based on the individual solid spin NOON state is investigated. Based on the tunable effective coupling coefficient, we propose a generation scheme of the three-spin NOON state, i.e, the Greenberger—Horne—Zeilinger (GHZ) state, and discussed the measurement resolution reduction due to decoherence. It is unnecessary to entangle spins as many as possible when decoherence exists. In practice, defect spins in diamond and 31P donors with long coherence time can be applied with current techniques in the nano-scaled high resolution magnetic measurement.