Spurious Resonances Research Articles

An overview of the method of fundamental solutions—Solvability, uniqueness, convergence, and stability

In this paper we give an overview of the Method of Fundamental Solutions (MFS) as a heuristic numerical method. It is truly meshless. Its concept and numerical implementation are simple. It has the flexibility of using various forms of fundamental solutions, singular, hypersingular, or nonsingular, and mixing with general solutions and particular solutions, for different purposes. The collocation matrix, however, is not guaranteed to be invertible. There are other issues. For example, in using the logarithmic fundamental solution, a degenerate scale can exist, causing the nonuniqueness of solution. For metaharmonic operators, such as the Helmholtz equation, the zeros of the fundamental solutions can create spurious resonance frequencies. These and other issues are discussed, and remedies are offered.The traditional error analysis for the MFS shows that when the boundary condition is prescribed by a harmonic function, the convergence is exponential either by increasing the number of terms in the approximation, or by increasing the radius of the fictitious boundary. In practical problems, however, a harmonic boundary condition hardly exists. Numerical experiments show that the sources need to stay close to the boundary, and there is an optimal distance. Based on the maximum principle, a posteriori error can be monitored on the boundary to seek the optimal fictitious boundary location. Other topics discussed include the origin of the MFS, the equivalence between the MFS and the Trefftz collocation method, effective condition number, nonsingular MFS, and solving ill-posed and inverse problems.

Virtual sensor fusion for high precision control

High performance control requires high loop gain and large control bandwidth. However, the spurious resonances at the higher frequencies can limit the performance of such type of systems. This drawback can be overcome by using sensor fusion technique. In sensor fusion, two or more sensors are combined in synergy such that good performance is achieved at lower frequencies while ensuring robustness of the system at higher frequencies. This paper presents a new technique, termed as “virtual sensor fusion”, in which only one of the sensors is physically installed on the system while the other sensor is simulated virtually. The virtual sensor is selected based on desired high frequency response. The effectiveness of the proposed technique is demonstrated numerically for a case of active seismic isolation. A robustness analysis of virtual sensor fusion is also carried out in order to study its stability in the presence of spurious resonances. Finally, the technique is experimentally verified on active isolation of pendulum system from ground motion. The results obtained demonstrate good isolation performance at lower frequencies and robustness to plant uncertainties (spurious resonances) at higher frequencies. This technique can be effectively used for high precision control of sensitive instruments.

Design of wideband CPW bandpass filters using phase comparison method and oblique air bridges

ABSTRACT This work presents two wideband coplanar-waveguide bandpass filters using open-circuited stubs (Design 1) and short-circuited stubs (Design 2), respectively. The electrical lengths of stubs were accurately determined by a phase comparison method. In Design 1, a spurious resonance was found at the high band edge of the passband. The problem was solved by introducing oblique air bridges to ruin the undesired resonance path for the suppression of the spurious resonance. Design 1 achieves bandwidth of 38.1% and low insertion loss of 0.7 dB. Another CPW filter, Design 2, was constructed with short-circuited stubs for compact size, which can achieve a very wide bandwidth of 70.8% and insertion loss of 0.9 dB.

Enhanced sensitivity of nanoscale subsurface imaging by photothermal excitation in atomic force microscopy.

Photothermal excitation of the cantilever for use in subsurface imaging with atomic force microscopy was compared against traditional piezoelectric excitation. Photothermal excitation alleviates issues commonly found in traditional piezoelectrics such as spurious resonances by producing clean resonance peaks through direct cantilever excitation. A calibration specimen consisting of a 3 × 3 array of holes ranging from 200 to 30 nm etched into silicon and covered by graphite was used to compare these two drive mechanisms. Photothermal excitation exhibited a signal-to-noise ratio as high as four times when compared to piezoelectric excitation, utilizing higher eigenmodes for subsurface imaging. The cleaner and sharper resonance peaks obtained using photothermal excitation revealed all subsurface holes down to 30 nm through 135 nm of graphite. In addition, we demonstrated the ability of using photothermal excitation to detect the contact quality variation and evolution at graphite-polymer interfaces, which is critical in graphene-based nanocomposites, flexible electronics, and functional coatings.

Magnetic and Combined Field Integral Equations Based on the Quasi-Helmholtz Projectors

Boundary integral equation methods for analyzing electromagnetic scattering phenomena typically suffer from several of the following problems: (i) ill-conditioning when the frequency is low; (ii) ill-conditioning when the discretization density is high; (iii) ill-conditioning when the structure contains global loops (which are computationally expensive to detect); (iv) incorrect solution at low frequencies due to current cancellations; (v) presence of spurious resonances. In this paper, quasi-Helmholtz projectors are leveraged to obtain a magnetic field integral equation (MFIE) formulation that is immune to drawbacks (i)-(iv). Moreover, when this new MFIE is combined with a regularized electric field integral equation, a new quasi-Helmholtz projector combined field integral equation is obtained that also is immune to (v). Numerical results corroborate the theory and show the practical impact of the newly proposed formulations.

Wide-Stopband SIW Filters Using Modified Multi-Spurious Modes Suppression Technique

A modified multi-spurious modes suppression technique is proposed to realize wide-stopband substrate-integrated waveguide (SIW) bandpass filters (BPFs), which is to set the external ports and internal coupling windows to the positions of weakest electric fields of specific spurious modes. To extend the stopband as wide as possible with the limited design degrees of freedom, different feeding and coupling positions are fully exploited to reject unwanted modes in specific cavities. By suppressing the out-of-band spurious peaks as much as possible and removing the first unsuppressed spurious resonance to the farthest position, the widest stopband can be achieved intrinsically. A second- and a third-order SIW BPFs are synthesized, designed, fabricated, and tested as demonstrations, realizing the stopbands of $2.51{f} _{0}$ and $3.85{f} _{0}$ with the rejection level better than 25 dB and 20 dB, respectively.

Estimating Rotational FRFs of a Complex Structure Using FE Model Updating, Mode Expansion and FRF Synthesis Method

Estimating rotational frequency response functions (FRFs) from experimental data is very challenging, and the estimation often leads to poor FRFs due to the presence of spurious resonance peaks. In practice, special equipment is essentially required in the measurement process, unless the rotational FRFs are synthesised using measured modal data. This paper presents an alternative approach for estimating the rotational FRFs of a geometrically complex structure by using finite element modal updating, mode expansion and the FRF synthesis method. The applicability and accuracy of the proposed approach are demonstrated on a car front-end module A simplified finite element (SFE) model of the test structure is introduced and the SFE model is then updated based on the measured modal model obtained from experimental modal analysis. The mode shapes of the updated SFE model are expanded to the test model to obtain the entire translational and rotational modal vector. The rotational FRFs of the expended experimental model is derived via the FRF synthesis method. The derived translational FRF is compared with the measured counterparts for validation purposes. It was found that the derived translational and measured FRF are in a perfect match, and the derived rotational FRF has successfully estimated all the resonance peaks within the frequency of interest. The findings from this work may be useful in improving the accuracy of the experimental rotational FRFs, which are crucial for particular structural dynamics analysis.

A Wide Stopband Wideband HTS Filter Using Stepped-Impedance Resonators With an Interdigital Capacitor Structure

A stepped-impedance resonator with an interdigital capacitor (IDC) structure has been proposed to design a wideband filter with a wide and deep stopband. With the increase of the IDC part, there is always a maximum ratio of a spurious resonance frequency to a fundamental resonance frequency whether we change the length or number of interdigital fingers. We increase the width of a microstrip line loaded with the IDC structure to reduce the fundamental resonance frequency and increase the spurious resonance frequency. The harmonic ratio of the proposed resonator is raised to 5.6. Moreover, we bend the narrow microstrip line into a meander line to realize the strong coupling for a wideband filter. A ten-pole high-temperature superconducting filter centered at 2.128 GHz with a 22.7% bandwidth is fabricated for demonstration. The filter is fabricated on a 0.5-mm-thick MgO substrate with a circuit size of 26 × 10 mm. The measured maximum insertion loss in passband is 0.11 dB and the return loss is better than 17.3 dB. The measured out-of-band rejection is better than 80 dB up to 8.728 GHz, which is about 4.1 times of the center frequency.

Antenna sensitivity variation depending on the installation of a shield can

AbstractThis letter investigates antenna sensitivity with various installations of a shield can. A commonly used shield can, which is widely used to mitigate electromagnetic interference (EMI) in electronic devices, will produce a spurious resonance by the gap between the shield can and the ground when the shield can is mounted on a printed circuit board (PCB) with only a few soldering points. A noise source is simulated as a loop‐type circuit on the ground to model the digital noise produced in an actual device. The installation methods of the shield can is discussed to verify the performance of the antenna sensitivity. In the analysis, the spurious resonance from the shield can is an important factor to the coupling between the antenna and the noise source. A high sensitivity antenna can be achieved by modifying the installation of the shield can. The measurement of a commercial WiFi module is also conducted to demonstrate experimental antenna sensitivity.

Optical excitation of atomic force microscopy cantilever for accurate spectroscopic measurements

Reliable operation of frequency modulation mode atomic force microscopy (FM-AFM) depends on a clean resonance of an AFM cantilever. It is recognized that the spurious mechanical resonances which originate from various mechanical components in the microscope body are excited by a piezoelectric elemen that is intended for exciting the AFM cantilever oscillation and these spurious resonance modes cause the serious undesirable signal artifacts in both frequency shift and dissipation signals. We present an experimental setup to excite only the oscillation of the AFM cantilever in a fiber-optic interferometer system using optical excitation force. While the optical excitation force is provided by a separate laser light source with a different wavelength (excitation laser : λ=1310 nm), the excitation laser light is still guided through the same single-mode optical fiber that guides the laser light (detection laser : λ=1550 nm) used for the interferometric detection of the cantilever deflection. We present the details of the instrumentation and its performance. This setup allows us to eliminate the problems associated with the spurious mechanical resonances such as the apparent dissipation signal and the inaccuracy in the resonance frequency measurement.

Multi-Degree of Freedom Isolation System With High Frequency Roll-Off for Drone Camera Stabilization

The technological developments in the field of image based sensing have led to a vast growth in the use of drones in various domains. The drone is usually equipped with an image sensor (camera) which collect images over the target area. These images are then post-processed to extract the important information. Efficiency and accuracy of the image based sensing are largely dependent on the captured image quality. Therefore, it is important to prevent the transmission of the drone vibrations to the camera. Most of the current camera mounting systems use passive rubber mounts for isolation. However, these mounts are effective only in vertical direction and essentially adds damping to the system which degrades the performance of the isolation at high frequency. In this paper, a multi-degree of freedom isolation system, based on a Stewart platform configuration, is proposed for drone camera stabilization. The important features of the proposed isolation system are — (i) high frequency roll-off, (ii) no use of flexible joints, (iii) uses non-contact voice coil actuator thus avoiding spurious resonances of the legs, (iv) adjustable stiffness, (v) 3D printed lightweight parts and (vi) centralized control using a single sensor (inertial measurement unit). A prototype of the proposed system has been manufactured and validated experimentally. The proposed isolation system is found to reduce the response of the isolation system near resonance without compromising performance at high frequency. The application of the isolation system can be easily extended to other fields which require high quality image acquisition.

Differential impedance spectra analysis reveals optimal actuation frequency in bulk mode acoustophoresis

This work reports a method to select the optimal working frequency in transversal bulk resonator acoustophoretic devices by electrical impedance measurements. The impedance spectra of acoustophoretic devices are rich in spurious resonance peaks originating from different resonance modes in the system not directly related to the channel resonance, why direct measurement of the piezoelectric transducer impedance spectra is not a viable strategy. This work presents, for the first time, that the resonance modes of microchip integrated acoustophoresis channels can be identified by sequentially measuring the impedance spectra of the acoustophoretic device when the channel is filled with two different fluids and subsequently calculate the Normalized Differential Spectrum (NDS). Seven transversal bulk resonator acoustophoretic devices of different materials and designs were tested with successful results. The developed method enables a rapid, reproducible and precise determination of the optimal working frequency.

Observations of geophone spurious resonance

A detailed understanding of the frequency response of geophones is critical for the design and quality control of broadband seismic surveys. We illustrate a pragmatic methodology for accurate ident...

Quintuple-Mode W-Band Packaged Filter Based on a Modified Quarter-Mode Substrate-Integrated Waveguide Cavity

A novel quintuple-mode filter in one cavity is proposed by modifying a quarter-mode substrate-integrated waveguide (SIW) cavity. Modes can be independently controlled by dimension parameters of the resonator. The quintuple-mode resonator is packaged to prevent electromagnetic leakage, and pillars are added to remove spurious cavity resonances introduced by the packaging. A W-band filter is designed and fabricated by using benzocyclobutene (BCB) polymer as dielectrics. The microelectromechanical systems (MEMS) fabrication process is demonstrated in detail. This filter offers the advantages of easy integration with other active devices. It is suitable for 3-D integration of millimeter-wave and sub-terahertz transceiver systems. Four transmission zeros (TZs) are obtained to improve the stopband, and insertion loss is 1.97 dB at 89 GHz with a fractional bandwidth (FBW) of 22.5%. Simulated results agree with measured results.

Phenomenon-model-based AM-FM vibration mechanism of faulty spur gear

Vibration responses of faulty gear contain modulation components that are commonly used as the indicators to detect the fault. The modulation mechanism has not been revealed clearly, especially the sideband distribution of amplitude modulation and frequency modulation. Aiming at the vibration modulation mechanism of fault gear, the gear meshing stiffness with frequency modulation components is deduced considering the actual speed fluctuation, as well as its influence on vibration responses. A series of phenomenon models of gear pair are built to research the sideband distribution features of vibration responses related to different types of gear faults. Both the steady-type and impact-type gear faults are proved to generate asymmetric amplitude-frequency modulation sidebands around harmonics of the meshing frequency. The marked difference lies in that the steady-type fault features distribute within a finite band while the impact-type fault features cover the entire frequency range and induce spurious resonance peaks. Sidebands with both amplitude and frequency modulations are wider than those with only amplitude modulation, and the product of two groups of frequency modulation components is proved to bring in amplitude modulation components. The phenomenon models of gear vibration responses contribute a deeper understanding of modulation mechanism of faulty spur gear, and the obtained sideband distribution features of amplitude-frequency modulation are an effective aid for gear fault diagnose.

Modified FSIW Filter With $N$ Transmission Zeros Using BCB-Based MEMS Technology

In this letter, a compact self-packaged folded substrate-integrated waveguide filter with loaded stubs is presented. Transmission zeros (TZs) at the same number of filter order are designed to improve out-of-band performance. The position of each TZ is controlled independently. The first spurious resonance increases by up to 3.8 times the fundamental frequency by suppressing the original first parasitic resonance. A Ka -band filter with a benzocyclobutene (BCB) polymer as a dielectric is fabricated and measured to verify the design concept.

Lights Out! Nano-Scale Topography Imaging of Sample Surface in Opaque Liquid Environments with Coated Active Cantilever Probes.

Atomic force microscopy is a powerful topography imaging method used widely in nanoscale metrology and manipulation. A conventional Atomic Force Microscope (AFM) utilizes an optical lever system typically composed of a laser source, lenses and a four quadrant photodetector to amplify and measure the deflection of the cantilever probe. This optical method for deflection sensing limits the capability of AFM to obtaining images in transparent environments only. In addition, tapping mode imaging in liquid environments with transparent sample chamber can be difficult for laser-probe alignment due to multiple different refraction indices of materials. Spurious structure resonance can be excited from piezo actuator excitation. Photothermal actuation resolves the resonance confusion but makes optical setup more complicated. In this paper, we present the design and fabrication method of coated active scanning probes with piezoresistive deflection sensing, thermomechanical actuation and thin photoresist polymer surface coating. The newly developed probes are capable of conducting topography imaging in opaque liquids without the need of an optical system. The selected coating can withstand harsh chemical environments with high acidity (e.g., 35% sulfuric acid). The probes are operated in various opaque liquid environments with a custom designed AFM system to demonstrate the imaging performance. The development of coated active probes opens up possibilities for observing samples in their native environments.

Boosting the Maxwell double layer potential using a right spin factor

We construct new spin singular integral equations for solving scattering problems for Maxwell’s equations, both against perfect conductors and in media with piecewise constant permittivity, permeability and conductivity, improving and extending earlier formulations by the author. These differ in a fundamental way from classical integral equations, which use double layer potential operators, and have the advantage of having a better condition number, in particular in Fredholm sense and on Lipschitz regular interfaces, and do not suffer from spurious resonances. The construction of the integral equations builds on the observation that the double layer potential factorises into a boundary value problem and an ansatz. We modify the ansatz, inspired by a non-selfadjoint local elliptic boundary condition for Dirac equations.

An Augmented Regularized Combined Source Integral Equation for Nonconforming Meshes

We present a new version of the regularized combined source integral equation (CSIE-AR) for the solution of electromagnetic scattering problems in the presence of perfectly conducting bodies. The integral equation is of the second kind and has no spurious resonances. It is well conditioned at all frequencies for simply connected geometries. Reconstruction of the magnetic field, however, is subject to catastrophic cancelation due to the need for computing a scalar potential from magnetic currents. Here, we show that by solving an auxiliary (scalar) integral equation, we can avoid this form of low-frequency breakdown. The auxiliary scalar equation is used to solve a Neumann-type boundary value problem using data corresponding to the normal component of the magnetic field. This scalar equation is also of the second kind, nonresonant, and well conditioned at all frequencies. A principal advantage of our approach, by contrast with the hypersingular electric field integral equation, the combined field integral equation, or CSIE formulations, is that the standard loop-star and related basis function constructions are not needed, and preconditioners are not required. This permits an easy coupling to fast algorithms such as the fast multipole method. Furthermore, the formalism is compatible with nonconformal mesh discretization and works well with singular (sharp) boundaries.

A Novel Quasi-elliptic Bandpass Filter Using Half-mode Substrate Integrated Waveguide Cavities

A fourth-order cross-coupled bandpass filter (BPF) using three half-mode substrate integrated waveguide (HMSIW) cavities and a spurious resonance is proposed. The HMSIW cavity is derived from diamond-shaped SIW; a new spurious resonance mode is built by adding post-wall irises between the two coupled HMSIW cavities and the resonance of spurious mode is analyzed. From the demonstration, an X-band cross-coupled quasi-elliptic filter is designed, simulated, and fabricated. The measured results are in good agreement with simulated results.