Quarter-wavelength Resonators Research Articles

Design of Equal-Ripple Dual-Wideband Bandpass Filter With Minimum Design Parameters Based on Cross-Shaped Resonator

A novel quarter-wavelength cross-shaped resonator (CSR) is presented in this brief for the design of equal-ripple dual-wideband bandpass filter (DWB BPF) with minimum design parameters. The proposed CSR is composed of a pair of parallel-coupled lines (PCLs) with short- and open-ended stubs. To extract the transmission poles and zeros, rigorous scattering-parameters and ABCD -matrix theories with even-odd-mode analysis method are used. After theoretical analysis, it is found that two passbands with equal-ripple responses can be realized on both sides of the operation frequency. In contrast to the reported DWB BPFs with complex structures, the proposed one is only formed by a quarter-wavelength CSR and featured as minimum design parameters. To verify this, a prototype is designed and fabricated. The measured results are in good agreement with the simulated ones, verifying a simple design approach of equal-ripple DWB BPFs.

Topology optimization design for total sound absorption in porous media

Acoustic porous layers used for noise reduction have the unique functionality of dissipating sound energy. It is very difficult for finite length porous layers to realize total sound absorption if they are filled only with homogeneous materials. Rigid inclusions inserted in a porous medium will certainly alter the acoustic field, realizing total sound absorption at some frequencies, but finding their optimal distributions by trial and error is intractable, especially for multiple target frequencies. The aim of this study is to develop a finite element-based numerical method to distribute rigid inclusions inside a porous layer having a fixed thickness for the total sound absorption. Without any special treatment for initial layout, multiply divided rigid inclusions are distributed systematically in an optimized porous layer by the present density-based topology optimization formulation. Considering single target frequency problems, we initially assess the effectiveness of the developed formulation with regard to achieving total sound absorption. In these problems, various resonance mechanisms, such as the Helmholtz resonance and the quarter-wavelength resonances, are generated inside the porous layer by the distributed rigid inclusions. Subsequently, we solve problems considering multiple target frequencies. The numerical results show that different types of resonances occur appropriately in the optimized porous–rigid layer to achieve total sound absorption simultaneously for all the different target frequencies considered here.

Virtual Herschel-Quincke tube using the multiple small resonators and acoustic metamaterials

This study is on the practical application of the acoustic metamaterials to the design of a silencer with high acoustic and geometric efficiencies, and negligible pressure drop. The object is to achieve broadband and low-frequency attenuation simultaneously by combining the effects of resonance, periodicity, phase difference, and impedance mismatch. An array of multiple small resonators, which is periodically applied to the wall of a duct, invokes the dispersion of sound propagating in the duct. This phenomenon is implemented to construct a virtual Herschel-Quincke (HQ) tube system. The main duct is split into two parallel ducts of the same length: a rigid duct and a duct with a wall covered by the periodic resonators. For a modelling of sound propagation in a dispersive duct, the phase speed of sound is analytically derived in the presence of a mean flow. Also, the attenuation conditions of the virtual HQ tube are proposed to establish a guideline in selecting the proper design parameters for achieving the required transmission loss (TL) in the desired frequency range. The predicted TL spectra are compared with the test results, for a virtual HQ tube system with 9 identical quarter-wavelength tube resonators, and they generally agree well. With increasing flow speed, the amount of attenuation decreases a bit, but the general spectral characteristics are maintained for |M|≤0.1. Based on the same principle, the acoustic metamaterials (AMM) are applied to the practical silencer design to achieve the wide-band sound reduction at low- to mid-frequencies for a given small space. A virtual HQ tube having 26 cells of AMM is tested, of which a cell is composed of 3 types of quarter-wavelength tube resonators. The experiment well validates the predicted TL. The results show that TL is at least 5 dB for a wide frequency range of 230–1000 Hz. The additional volume due to the attachment of the AMM layer is only 40%, while the TL is far larger than that of the simple expansion chamber or the dissipative silencer having the same excess volume.

Automotive wheel and tyre design for suppression of acoustic cavity noise through the incorporation of passive resonators

Tyre cavity noise is a narrow band, high amplitude resonance which occurs when the sound waves in a car tyre oscillate back and forth in one direction with a low loss factor. Manufacturers add damping materials to vehicles, due to the difficulty of reducing the source noise, or mitigating the transmission path from wheel hub to the interior, as part of reducing the overall structure borne noise. When the wheel is rolling, the Doppler effect leads to two characteristic cavity resonance frequencies, which change with speed, loading and temperature. If these couple with a suspension component resonance, a transmission path to the cabin can result. One method to attenuate the sound is by using passive resonators, such as Helmholtz and quarter wavelength resonators. Here, a rapid design method is developed, based around one-dimensional waveguide equations in order to optimise the dimensions and thus the tuned resonant frequency of the wheel based Helmholtz resonators.With three tuned resonators, a reduction in the peak sound amplitude from 103 to 88 dB is possible, over a speed range from 54 km/h to 108 km/h. With five resonators, a reduction from 103 to approximately 87 dB is shown. Thus, the larger number of resonators is better able to attenuate the cavity noise over a larger frequency range.

A Filtering Power Divider with Tunable Center Frequency and Wide Stopband

AbstractIn this paper, a tunable power divider (PD) with a good band-pass filtering response using quarter-wavelength stepped impedance resonators (SIRs) is presented. By appropriately adjusting the impedance and electrical length ratio of SIR, the proposed structure can achieve wide stopband performance. Meanwhile, four varactor diodes are loaded to the external resonators to achieve electrical reconfiguration. In addition, a pair of transmission zeros (TZs) can be generated by applying source and load coupling on each side of the passband, which can effectively improve passband selectivity and out-of-band rejection. In order to verify the feasibility of the proposed design method, a prototype circuit of the proposed filtering power divider (FPD) with tunable center frequency is simulated, fabricated and measured. A good agreement between the simulation and measurement results is observed.

Efficient acoustic energy harvesting by deploying magnetic restoring force

Acoustic piezoelectric energy harvesters in quarter-wavelength resonator tubes undergo linear resonant vibration due to the external force. However, the variation of environmental conditions, such as temperature, directly alters the speed of sound in air, which in turn changes the tube resonance frequencies. This discrepancy between the tube acoustic and harvester resonance frequencies leads to reduced power generation. This paper proposes the addition of a nonlinear restoring force onto an acoustic cantilever beam piezoelectric energy harvester to tune and broaden the resonance bandwidth. The restoring force is applied by the attachment of permanent magnets at the beam tip and two external magnets. First, the nonlinear distributed parameter model of the bimorph is provided. Then, the associated dimensionless lumped-parameter model, including the magnetically coupled equations, is developed. To study the system response, an approximate-analytical solution based on the harmonic balance method is constructed. Initially, the variations of the speed of sound, and subsequently the tube resonance frequency, versus temperature, based on real statistical data, are studied. Furthermore, the effects of two scenarios of hardening and softening magnetic restoring forces are investigated. The results show that, at relatively low sound pressure levels (SPLs), the restoring forces can improve the efficiency by tuning the resonance frequency of the energy harvester. As the SPL increases, the force of the additional magnets tunes the natural frequency and broadens the resonance region. Finally, it is observed that the added magnets can change the optimum time constant ratio.

A Novel Compact Self-Packaged SPDT Switchable BPFs Based on SISL Platform

This paper presents a novel compact low loss switchable bandpass filter (BPF) with self-packaging by using substrate-integrated suspended line (SISL) technology. The proposed self-packaged switchable BPFs are designed by using two kinds of suspended controllable resonators, which are smaller than a quarter-wavelength resonator and the commercial p-i-n diodes are used as the control elements. The designed method of suspended controllable resonator is investigated by using an equivalent circuit model. The center frequency of the proposed low loss SISL switchable BPF is designed at 1 GHz with 56% fractional bandwidth. The measurement results show that insertion loss is 0.9 dB of the turn on state. Furthermore, a high isolation SISL self-packaged switchable BPF with more compact size is proposed for comparison. Measurement results show that the isolation is higher than 40 dB and insertion loss is 1.57 dB at 1 GHz, and its core circuit size is only ${\text{0.09}}\,\lambda _{g}\times {\text{0.04}}\,\lambda _{g}$ .

Design of High Selectivity Filtering Power Divider with High Out-of-Band Rejection

ABSTRACTA novel high-selectivity filtering power divider is presented in this paper. The proposed circuit utilizes two fourth-order filters with a surface mount resistor. The fourth-order filter is realized by quarter-wavelength and half-wavelength resonators. And by controlling the electric and magnetic coupling, two transmission zeros can be realized at the two sides and the passband. Furthermore, the source-load coupling is also adopted. Thus, four transmission zeros are realized, which ensure high selectivity and suppression level for the filtering power divider. To verify the proposed idea, a filtering power divider with operating frequencies of 2.45 GHz is implemented. The design procedures are discussed in detail, and the simulated and measured results are presented.

Experimental validation of deep-subwavelength diffusion by acoustic metadiffusers

An acoustic metadiffuser is a subwavelength locally resonant surface relying on slow sound propagation. Its design consists of rigidly backed slotted panels, with each slit being loaded by an array of Helmholtz resonators. Due to the slow sound properties, the effective thickness of the panel can therefore be dramatically reduced when compared to traditional diffusers made of quarter-wavelength resonators. The aim of this work is to experimentally validate the concept of metadiffusers from the scattering measurements of a specific metadiffuser design, i.e., a quadratic residue metadiffuser. The experimental results reported herein are in close agreement with analytical and numerical predictions, therefore showing the potential of metadiffusers for controlling sound diffusion at very low frequencies.

Realization of Multiple Transmission Zeroes for Bandpass Filters With Simple Inline Topology

The realization method of multiple transmission zeroes (TZs) for second-order bandpass filters (BPFs) is presented in this brief. A modified filter topology with mixed couplings is investigated at first. With the cancelation effect of electric and dominant magnetic couplings, two close-to-passband TZs can be easily realized for a second-order inline filter. Furthermore, the dual-function feature of loaded quarter-wavelength ( $\lambda $ /4) resonators is analyzed. Besides of filtering response, $\lambda $ /4 resonators can be used to realize two more TZs in the stopband. At last, multiple open stubs are loaded asymmetrically at feeding lines, each of which can generate one TZ independently. Due to the asymmetric loading, the extra circuit area of bandstop structures is reduced by half. For demonstration, a wideband BPF using $\lambda $ /4 resonators and four asymmetric open stubs is designed, fabricated, and measured. The stopband suppression can be improved to 10.2 GHz without sacrificing in-band properties or enlarging circuit size. Good agreement can be observed between the measured and simulated results of the proposed BPF.

Novel Ultrawideband and Multimode LTCC Common-Mode Filter Based on the Dual Vertical Coupling Paths

A novel ultrawideband and miniaturized common-mode filter (CMF) is proposed for suppressing the CM noise based on the dual vertical coupling paths. In the proposed CMF, a modified quarter-wavelength transmission line resonator and a modified half-wavelength transmission line resonator are utilized to introduce three CM transmission zeros. Moreover, another CM transmission zero is produced by the dual vertical path coupling. An ultrawide CM stopband is achieved by the four CM transmission zeros. Subsequently, equivalent circuit models have been established to give physical insight into the CMF operating mechanism, and the design procedures are also provided. By using the low-temperature cofired ceramic technology, a surface-mounted device prototype is fabricated and measured. The measured results show that the CM noise can be suppressed over 10 dB from 2.45 to 9.85 GHz with 120.3% fractional bandwidth. Meanwhile, the low insertion loss and the relatively constant group delay for differential mode ensure that the proposed CMF can maintain the signal integrity of differential signals below 10 GHz.

3D-printed sound absorbing metafluid inspired by cereal straws

Used as building biomaterials for centuries, cereal straws are known for their remarkable acoustic performances in sound absorption. Yet, their use as fibrous media disregards their internal structure made of nodes partitioning stems. Here, we show that such nodes can impart negative acoustic bulk modulus to straw balls when straws are cut on either side of a node. Such metafluid inspired by cereal straws combines visco-thermal diffusion with strong wave dispersion arising from quarter-wavelength resonances within straws. Large spectral bandgaps and slow sound regimes are theoretically predicted and experimental data from impedance tube measurements on an idealised 3D-printed sample layer are in good agreement with the theoretical model. Perfect absorption is achieved at wavelengths 13 times larger than the thickness of the metafluid layer, and slow sound entails an increased density of states causing a cascade of high absorption peaks. Such features could lead cereal straws to serve as cheap acoustic bio-metamaterials.

Effect of Stack Spacing on the Performance of Thermoacoustic Refrigerators Using Helium and Air as Working Substances

This paper deals with the design of thermoacoustic refrigerators using linear thermoacoustic theory. The refrigerator components are designed at 3% drive ratio by considering the practical limitations of providing sufficient spacing for attaching the loudspeaker to the resonator tube and accommodating instrumentation. The effects of spiral stack spacing in terms of thermal penetration depth on the theoretical performance of refrigerator using helium and air as working substances are discussed. The quarter-wavelength resonator designs with taper and divergent section terminated with hemispherical end are optimized with helium and air for better performance. Theoretical results are validated with DeltaEC software results and are in agreement with each other. Helium shows better performance compared to air but lacks power density. The DeltaEC predicts COP 0.514 at the cold heat exchanger temperature of [Formula: see text]C with helium compared to air (COP 0.616 at [Formula: see text]C) for the 50[Formula: see text]W cooling power 100[Formula: see text]mm diameter quarter-wavelength resonator designs.

Tidal amplitude decreases in response to estuarine shrinkage: Tokyo Bay during the Holocene

Tidal changes in Tokyo Bay during the last 10,000 years were investigated by combining a numerical model with newly compiled model bathymetries for the present day, the early 20th century, and every 1000 years from 4000 to 10,000 years ago. Over this time period, sea level has changed by more than 30 m, and the coastline has shifted 50–60 km. Tides during the early 20th century and 4000–9000 years ago were larger than those at present; from 9000 to 4000 years ago, the bay setting was mesotidal, in contrast to the modern microtidal setting. The maximum tidal level at the head of the bay was 72% higher 7000 years ago than at present, and M2 tidal currents at the bay mouth from 10,000 to 9000 years ago were three times stronger than those at present. When tides were compared at a fixed location, the greatest tidal enhancement was found to have occurred 9000 years ago. The weakening of tides over the last 9000 years can be explained by introducing the concept of estuarine shrinkage together with quarter-wavelength resonance theory. Tidal weakening occurred in two phases: during the first phase, 9000–7000 years ago, it was due to the rise in sea level (type 2 shrinkage), and during the second phase, a decrease in the length of the bay was responsible (type 1 shrinkage). These findings can be applied to the assessment of both past tidal changes and potential future tidal changes in other elongated estuaries with lengths of several tens of kilometers.

Microstrip Spurious-Coupling Band-Pass Filters with Quarter-Wavelength and Π-Shaped Resonators

Microstrip band-pass filters (BPFs) containing quarter-wavelength resonators and a Π-shaped half-wavelength resonator placed next to each other along the same line have been analyzed. These filters have more various frequency characteristics from the use of a Π-shaped half-wavelength resonator and spurious magnetic cross-talk coupling. The possibility of describing these filters using a coupling matrix is considered. The results of the simulation and measurement of the frequency characteristics of three microstrip BPFs with a central frequency of 2 GHz have been presented.

Novel Absorptive Balanced Bandpass Filters Using Resistive Loaded Transmission Lines

This paper reports on design of novel balanced bandpass filters (BPFs) using quarter-wavelength stub resonators. For the design purposes, differential-mode (DM) and common-mode (CM) half-equivalent circuits are established and analyzed carefully. In this paper, CM noise is introduced into the filter and dissipated on the resistors on periodic bands. First, a balanced BPF topology based on conventional quarter-wavelength stub filter is presented. By symmetrically introducing series matching resistors to the ground at the center of the stub, CM noise can be rejected either reflectively or reflectionlessly without affecting DM performance. The harmonic property of stubs provides periodic CM suppressing response as long as the resistor has no serious parasitic reactance. By doing so, CM noise can be suppressed under a certain level at all frequencies. However, the harmonic property also leads to some spurious passbands. This defect can be avoided by an improved filter topology with two additional capacitors. To reserve the CM feature, the corresponding DM and CM half equivalent circuits are developed as well. The proposed layouts are fabricated on a two-layer printed circuit board. The resulting experimental circuits exhibit the expected electrical performance, forming balanced BPFs with CM noise suppression level over 12 dB at all frequencies, and show an agreement with the simulated results.

Influence of two-level defects on the transmission of a microwave signal in an open coplanar waveguide

Microwave superconducting quantum circuits are strongly affected by various defects that are unavoidable during the production process. This paper presents a new method for measuring losses in an open transmission line. This line interacts through a capacitive coupling with a coplanar quarter-wavelength resonator, which is used to study losses therein. The authors have investigated the dependencies of losses on power and temperature (in the millikelvin range). It has been shown that major losses in a transmission line are due to the interaction of a microwave field with defects which are effectively described by two-level systems.

Tidal resonance in the Gulf of Thailand

Abstract. The Gulf of Thailand is dominated by diurnal tides, which might be taken to indicate that the resonant frequency of the gulf is close to one cycle per day. However, when applied to the gulf, the classic quarter-wavelength resonance theory fails to yield a diurnal resonant frequency. In this study, we first perform a series of numerical experiments showing that the gulf has a strong response near one cycle per day and that the resonance of the South China Sea main area has a critical impact on the resonance of the gulf. In contrast, the Gulf of Thailand has little influence on the resonance of the South China Sea main area. An idealized two-channel model that can reasonably explain the dynamics of the resonance affecting the Gulf of Thailand is then established in this study. We find that the resonant frequency around one cycle per day in the main area of the South China Sea can be explained with the quarter-wavelength resonance theory, and the large-amplitude response at this frequency in the Gulf of Thailand is basically a passive response of the gulf to the increased amplitude of the wave in the southern portion of the main area of the South China Sea.

A 0.97–1.53-GHz Tunable Four-Pole Bandpass Filter With Four Transmission Zeroes

In this letter, a miniature 0.97–1.53-GHz tunable four-pole bandpass filter with constant fractional bandwidth is demonstrated. The filter consists of three quarter-wavelength resonators and one half-wavelength resonator. By introducing cross-coupling, two transmission zeroes are generated and are located at both sides of the passband. Also, source–load coupling is employed to produce two extra transmission zeroes, resulting in a miniature ( $0.09\lambda _{{\text {g}}}\times 0.1\lambda _{{\text {g}}}$ ) four-pole, four-transmission zero filter with high selectivity. The measured results show a tuning range of 0.97–1.53 GHz with an insertion loss of 4.2–2 dB and 1-dB fractional bandwidth of 5.5%. The four transmission zeroes change with the passband synchronously, ensuring high selectivity over a wide tuning range. The application areas are in software-defined radios in high-interference environments.

Tidal wave propagation along The Mekong deltaic coast

A two-dimensional, barotropic numerical model was employed to investigate the dynamics of tidal wave propagation in the South China Sea with a particular interest for its characteristics along the Mekong deltaic coast. The study indicates that tidal waves propagate from the Pacific Ocean into the South China Sea mainly through the Luzon Strait (LS), where the K1 diurnal tide dominates due to a quarter wavelength resonance in this semi-enclosed basin, and that the incoming tidal waves from the Celebes open boundary play a more important role than those from the Andaman and Flores open boundaries. Previous studies have not explained why both adjacent seas including the South China Sea and the Gulf of Thailand are dominated by a diurnal tide, while a semidiurnal tide dominates along the eastern Mekong deltaic coast. By means of Green's law, continental shelf tidal resonance theory and standing wave theory, this study clarifies that the large amplified M2 semidiurnal amplitude leading to a prevailing mixed semidiurnal tide is caused not only by the shoaling effect and the continental shelf oscillation resonance phenomenon but also by the position on the standing wave anti-node line. Moreover, the finding of radial tidal currents occurring along the southern Mekong estuarine coast has not been revealed in earlier studies. Based on a number of numerical, geometrically schematised experiments, we suggest that the interaction between the large amplified amplitude near the shoreline associated with the adjacent low amplitude band system, causing convex hydraulic gradients of tidal amplitude due to basin geometry as well as sloping topography, is the mechanism for developing these radial tidal current systems. The results reveal that wind monsoon climate could cause either damped or amplified tidal amplitudes around the Mekong deltaic coast of which approximately 2–3 cm is due to the changing atmospheric pressure, the tangential stress of wind over the water surface and wind enhanced bottom friction. Also, this study suggests that the tidal generating forces should be considered to achieve accurate model results depending on the geographical region of interest. Findings achieved from this study contribute to a deeper insight of tidal wave propagation from a deep ocean to a shallow flat basin similar to the South China Sea and its Mekong deltaic coast.