Surface Impedance Model Research Articles

Modelling of railway ballast as a poro-elastic medium and its effects on sleeper sound radiation

Conventional railway track is laid in a layer of coarse stones known as ballast. Due to the gaps between the stones, the railway ballast behaves as a porous acoustic material, with absorptive properties that are important for the noise produced by the railway system. Sound radiated by the bottom of the sleepers may also be transmitted through the ballast. Moreover, during a train pass-by the ballast can vibrate, which may contribute to the radiated noise. To consider all three effects simultaneously, the ballast is treated here as a poro-elastic medium. To obtain the properties of the ballast as a porous medium, transfer function measurements are performed in a vertical impedance tube to determine the surface impedance and absorption coefficient of different depths of reduced scale ballast. The complex wavenumber is also determined through transfer function measurements within the ballast in the vertical tube. Porosity and flow resistivity are determined by non-acoustic measurements, and the Johnson-Champoux-Allard model for porous materials is then fitted to the measured wavenumbers, allowing the remaining parameters to be determined. Comparison is made with the measured impedance and normal incidence absorption coefficient. The model is then used to predict the diffuse field absorption coefficients of both the reduced scale ballast and full-size ballast, which are compared with measurements, showing acceptable agreement. Finally, the effects on the sleeper radiation of introducing the poro-elastic ballast model are estimated and the sensitivity of the results to a practical range of ballast properties is assessed. The ballast vibration increases the sleeper radiation at low frequency, and especially between 120 and 280 Hz. This is caused by the structural vibration of the ballast driven by the sleepers, which has a resonance around 250 Hz. The acoustic velocity within the ballast is 180° out of phase with the structural velocity, and this leads to a small reduction in the sound radiation around 100 Hz. These effects could not be predicted using a surface impedance model for the ballast. Compared with the effect of the ballast vibration and sound transmission, the absorption of the ballast has a much smaller influence on the sleeper radiation.

Path Loss and Surface Impedance Models for Surface Wave-Assisted Wireless Communication System

Path Loss and Surface Impedance Models for Surface Wave-Assisted Wireless Communication System

Insert Misalignment Studies of a Coaxial-Cavity Gyrotron—Full-Wave Approach

Insert misalignment studies are carried out for a coaxial-cavity gyrotron with triangular corrugations on the insert wall using the full-wave approach, space harmonics method (SHM). By applying electromagnetic boundary conditions, dispersion relation is derived for a coaxial-cavity with misaligned insert. Misalignment of the insert caused by axial displacement as well as tilting of the insert axis from the outer resonator axis are taken into consideration in the study. As the electromagnetic fields in the interaction space vary with the insert misalignment, due to this the mathematical formulations of the beam-coupling coefficient, wall losses, RF interaction efficiency, and output power are modified. For a 2-MW, 220-GHz gyrotron, the insert misalignment studies are carried out using the proposed full-wave model with the help of our in-house code Gyrotron Design Suite. For validation, the results obtained using the SHM approach are compared with that of the surface impedance model (SIM) approach. In addition, comparison studies between SIM and SHM approaches are performed for the practically developed 170-GHz, 2-MW coaxial-cavity gyrotron with both triangular and rectangular corrugations in the insert.

Loosely coupled reflective impedance metasurfaces: Precise manipulation of waterborne sound by topology optimization

Waterborne acoustic metasurfaces (WAMs), unlike airborne acoustic metasurfaces, generally suffer from nonlocal interaction induced by the strong fluid–solid coupling. Unpredictable parasitic scattering is usually caused by nonlocal vibration coupling between solid units, thereby interfering with the prescribed sound control. In this work, we propose a loosely coupled reflective impedance WAM to realize precise manipulation of waterborne sound. A function–structure integrated topology optimization framework involving surface impedance model and vibration coupling restriction is systematically established to inversely design WAMs. Successful individual design of lossy units with multiple inclusions is realized by weakening vibration coupling of solids through local resonance. Various customized waterborne sound fields, including extraordinary beam steering with steep deflection, propagating-to-evanescent mode conversion and super-resolution near-field focusing, have been successfully implemented and demonstrated. Good agreements between the theoretical and simulated results are observed, thereby validating the feasibility and effectiveness of the design strategy. In addition, inverse-design WAMs show very good robustness to the operating frequency, incident angle and geometrical shape. Deep-subwavelength precise manipulation of waterborne sound is further achieved by the WAM with the thickness of λ/40. The excellent performances of WAMs result from the precisely customized surface impedance distribution. The proposed strategy opens the door to practical applications of metasurfaces in the delicate and complex waterborne sound control.

On the surface impedance modeling of metasurfaces composed of graphene-coated spherical nanoparticles

In this paper, we discuss the electromagnetic homogenization of graphene-based nanoparticle arrays using the surface impedance approach. For this purpose, we first investigate the contribution of the different harmonics to the equivalent surface impedance of the array. We conclude that the size of the nanoparticles is small compared to the operating wavelength, and the higher-order modes have a negligible impact on the overall response of the array. Then, the accuracy of the homogenization method to describe the macroscopic response of graphene-coated spherical particle arrays is discussed. In particular, it is demonstrated that the surface-impedance modeling provides reliable results when the level of coupling between the nanoparticles is moderate and the model accuracy can be slightly improved by considering the Floquet expansion-based interaction coefficient. Finally, approximate formulas for the array surface impedance, as well as an equivalent circuit model of the metasurface, are extracted.

Temperature and power characteristics of quarter-wavelength superconducting coplanar waveguide resonator

A quarter wavelength superconducting aluminum film coplanar waveguide resonator with a high-quality factor was designed and fabricated. Furthermore, its resonant frequency and quality as a function of temperatures and exciting powers were investigated. The experimental results showed that the resonance frequency decreases about 1% with the increase of temperature from 50 mk to 1 K, and the load quality factor of the resonator also decreases. The resonant frequency decreases with power from − 120 to − 70 dBm. The quality factor increases with increased excitation power due to the loss decreases and nonlinearity. The results are consistent with the theoretical analysis of the surface impedance model.

Characterization of Additively Produced RF-Structures on Low-Cost PCB Materials Based on Inkjet Technology for Industrial Applications up to 80 GHz

Usually, the printed circuit board industry has to use special subtractive manufacturing methods, if small line and space dimensions down to 50 μm are desired. This drastically raises production effort and costs. In this paper a method is shown, how the inkjet technology can be used to produce passive RF structures with minimum line and space dimensions of 25 μm. For the first time, this is possible over complete panels of low-cost PCB substrates, which have a relatively high surface roughness compared to ceramic or glass carriers. To ensure process reliability, printed lines must also be plated with an additional electroless copper layer to overcome the surface roughness with conductive layers and to lower insertion loss in the two-digit GHz range. Additionally, a surface impedance model is developed, which allows broadband first time right simulations. Finally, additively produced, passive RF filters are compared to their subtractive counterparts to show their benefits regarding production costs and electrical performance up to 80 GHz.

Reflective elastic metasurface for flexural wave based on surface impedance model

Inspired by the recent advance of acoustic metasurface in achieving wave manipulation, a surface impedance matched method rather than Generalized Snell's Law for designing a reflective elastic metasurface is presented to redirect the flexural waves without much loss in thin plates. The designed elastic metasurface that is simply fabricated by regularly arranged structural beams allows nearly arbitrary control of reflected waves, including extraordinary reflection, normal incidence and negative reflection. Obtained results show that the designed metasurface has a high accuracy of redirecting reflected waves into desired way and simultaneously the scattering waves in other directions are efficiently suppressed. We also demonstrate the elastic metasurfaces with free and fixed boundary conditions which all show electromagnetic and acoustic analogies of anomalous reflection response. Based on the surface impedance matched method, the theoretical prediction of redirecting reflection waves has an agreement with numerical simulation and experiments, and we think that the minimum characteristic scale of a non-resonant reflective elastic metasurface is confined to the first period of input impedance. This work provides an effective strategy for designing an elastic metasurface, and it is potentially useful for the functionalities of flexural wave manipulation.

Macroscopic Modeling of Anomalously Reflecting Metasurfaces: Angular Response and Far-Field Scattering

In view of extremely challenging requirements on the design and optimization of future mobile communication systems, researchers are considering the possibilities of creating intelligent radio environments by using reconfigurable and smart metasurfaces integrated into walls, ceilings, or facades. In this novel communication paradigm, tunable metasurfaces redirect incident waves into the desired directions. To design and characterize such smart radio environments in any realistic scenario, it is necessary to know how these metasurfaces behave when illuminated from other directions and how scattering from finite-sized anomalous reflectors can be estimated. In this work, we analyze the far-field scattering of reflective metasurfaces and study the angular response of anomalous reflectors for arbitrary illumination angles. Using the surface-impedance model, we explain the dependence of the reflection coefficients of phase-gradient metasurfaces on the illumination angle and present numerical examples for typical structures. We also consider scattering from finite-sized metasurfaces and define a route toward including the full-angle response of anomalous reflections into the ray-tracing models of the propagation channel. The developed models apply to other diffraction gratings of finite size.

Effect of net direct current on the properties of radio frequency sheaths: simulation and cross-code comparison

In order to understand, predict and control ion cyclotron range of frequency interactions with tokamak scrape-off layer plasmas, computational tools which can model radio frequency (RF) sheaths are needed. In particular, models for the effective surface impedance and DC rectified sheath potentials may be coupled with full wave RF simulation codes to predict self-consistent wave fields near surfaces and the resulting power dissipation and plasma–material interactions from ion sputtering. In this study, previous work assuming zero net DC current flow through the sheath is generalized to allow the surface to collect net positive or negative current, as is often observed in experiments. The waveforms, DC potential and RF admittance are investigated by means of analytical theory, nonlinear fluid and particle-in-cell codes. Cross-code comparisons provide detailed model verification and elucidate the roles of ion and electron kinetics. When the sheath draws negative (positive) DC current, the voltage rectification is reduced (increased) compared with the zero-current case, and the magnitude of both the real and imaginary parts of the admittance are increased (reduced). A previous four-input parametrization of the sheath rectification and admittance properties is generalized to include a fifth parameter describing the DC sheath current.

Single-source formulation for the analysis of electromagnetic penetrable objects

Modified global surface impedance (MGSI) formulation, a fast and efficient single-source integral equation for analyzing penetrable objects including plasmonic circuits and dielectric periodic structures, is proposed. Using the equivalence principle, a single-source formulation for the exterior region of the desired problem is constructed. Then the assumed equivalent source (surface electric current) is written as the sum of two surface electric currents, one related to the other based on the global surface impedance (GSI) model. Thus, the conventional surface integral equation (SIE) for the exterior problem will be modified by this new single-source formulation. The interior problem is also formulated using the GSI model resulting in our proposed MGSI formulation. MGSI eliminates the need for equivalent magnetic current in the SIE formulation. It also helps one to formulate the interior and exterior problems independently. Moreover, in our approach material property does not affect the problem convergence behavior, while the convergence behavior of the conventional SIE deteriorates for a plasmonic structure and also for a dielectric object with high contrast to its surrounding medium. The accuracy and efficiency of the proposed formulation are demonstrated by comparing its results with the conventional SIE in solving several two-dimensional examples.

Electromagnetic modelling of multiband frequency reconfigurable antenna for wireless communications

ABSTRACTThe present work aims to propose a new formulation by combining the moment method and generalized equivalent circuit's method (MOM-GEC) to study the performance of a frequency reconfigurable antenna commanded by a PIN diode(s) as switching component(s). This method makes it possible to reduce the 3D problems to an alleviate calculation in the discontinuity plane using the admittance operators. The antenna structure is excited by a localized voltage source and the PIN diode is introduced in the mathematical formulation by a surface impedance model. A parametric study is made to achieve a good approximation of PIN diodes longitudinal dimension ensuring the switch operation. Then we focus on the analysis of reconfigurable antennas controlled by one and two PIN diodes. The simulation results are in good agreement with those obtained by software simulation and they show that it is possible to shift the resonant frequency depending on the PIN diode state.

Revisiting the Surface Impedance and Effective Medium Models Applied to Near‐Field Radiative Heat Transfer

The role of the optics of surface and interfaces in the near‐field radiative heat transfer for finite‐layered media and superlattices is reviewed. The definition of surface impedance is compared with effective medium approximations for the dielectric functions. It is shown that the presence of polar materials makes the use of effective medium models ineffective, in particular, when the topmost layer supports surface modes. Furthermore, the effect on the near‐field heat transfer is quantified when approximate methods are used.

Near shore atmospheric acoustic transmission loss: Numerical predictions

This work presents advances in the development of a numerical model of atmospheric acoustic propagation designed for a littoral or riverine environment with a near-shore acoustic source and on-shore receivers. A parallel experimental effort uses a measurement system that records concurrent atmospheric and acoustic transmission loss data. The numerical model uses a generalized terrain parabolic equation method to account for sea surface roughness and ground topography along the propagation path. The model accounts for vertical temperature and wind speed profiles as well as surface impedance at the shore. For the comparison with experimental data, wind speed is used to predict the sea state. The propagation range consists of three segments: over water, over swash and sandy shore, and over complex dune with highly varied vegetation of up to 2 m height. Surface impedance estimates for the sandy shore are made based on grain size distribution and impedance tube measurements of excised samples. Existing models for surface impedance of vegetation were used for the dune portion of the propagation range.This work presents advances in the development of a numerical model of atmospheric acoustic propagation designed for a littoral or riverine environment with a near-shore acoustic source and on-shore receivers. A parallel experimental effort uses a measurement system that records concurrent atmospheric and acoustic transmission loss data. The numerical model uses a generalized terrain parabolic equation method to account for sea surface roughness and ground topography along the propagation path. The model accounts for vertical temperature and wind speed profiles as well as surface impedance at the shore. For the comparison with experimental data, wind speed is used to predict the sea state. The propagation range consists of three segments: over water, over swash and sandy shore, and over complex dune with highly varied vegetation of up to 2 m height. Surface impedance estimates for the sandy shore are made based on grain size distribution and impedance tube measurements of excised samples. Existing models ...

Design Method for Modulated Metasurface Antennas Composed of Anisotropic Elements Based on Generalized Boundary Conditions

A novel and efficient design method for modulated metasurface antennas composed of anisotropic elements is proposed in this letter, based on generalized boundary conditions. An analytical model of surface impedance is derived with the effective surface susceptibilities of the patch layer, an equivalent circuit model of the element, and the transverse resonance technique. The analysis method of elements is then utilized to design modulated metasurface antennas with desired radiation patterns. A linearly polarized antenna prototype with a circular aperture of 180 mm in diameter is designed and measured to demonstrate the effectiveness of this approach. The prototype shows good radiation characteristics at 9.75 GHz with the measured gain of 21.77 dB and the aperture efficiency of 44.5%.

Compact High-Efficiency Broadband Metamaterial Polarizing Reflector at Microwave Frequencies

A compact highly efficient broadband microwave polarizing reflector, employing a quasi-2-D metamaterial composed of a single layer of square split-ring resonators, is presented and its performance is reported. Numerical and experimental results show a cross-polarization average polarization conversion ratio of greater than 90% for normal incident linearly polarized waves over a frequency range of 8.2–23 GHz. Due to multiple resonances occurring over this frequency range, the polarizing reflector presents both broadband performance and high polarization conversion efficiency. Transfer matrix and equivalent surface impedance theory and modeling are discussed to explain the physical underpinnings of the reflector’s multiresonance behavior. These physical mechanisms are further analyzed by examination of simulated surface current distributions. The reflector is expected to be employed in applications where the control of the signal polarization is of central importance.

Deriving a Lumped Element Surface Impedance Model for Periodic Arrays of Graphene Micro-Rings

In this paper, a lumped element circuit model for a periodic array of Graphene rings is derived using analytical procedures. The computations are in the subwavelength regime and under normal incidence. It is shown that the model is also valuable for a single Graphene ring. The methodology includes solving the surface current integral equation for the rings by designing an eigenvalue problem. The absorption spectrum of proposed model is compared with full-wave simulations to verify the model accuracy. Furthermore, inspection of the simulation results for different Fermi energies and unit cell dimensions, helped us examine the validity of analytical formulas. This model opens up the way to control the structure performance and refine it in favor of our requirements for different applications.

Analysis of coupling between magnetic dipoles enhanced by metasurfaces for wireless power transfer efficiency improvement

In this paper, we investigate the possibility of improving efficiency in non-radiative wireless power transfer (WPT) using metasurfaces embedded between two current varying coils and present a complete theoretical analysis of this system. We use a point-dipole approximation to calculate the fields of the coils. Based on this method, we obtain closed-form and analytical expressions which would provide basic insights into the possibility of efficiency improvement with metasurface. In our analysis, we use the equivalent two sided surface impedance model to analyze the metasurface and to show for which equivalent surface impedance the WPT efficiency will be maximized at the design frequency. Then, to validate our theory, we perform a full-wave simulation for analyzing a practical WPT system, including two circular loop antennas at 13.56 MHz. We then design a metasurface composed of single-sided CLSRRs to achieve a magnetic lensing based on the calculated equivalent surface impedance. The analytical results and full-wave simulations indicated non-radiative WPT efficiency improvement due to amplifying the near evanescent field which can be achieved through inserting the proposed metasurface.

Efficient prediction of acoustic pulses accounting for fractional travel time.

Predicting a full waveform of an acoustic broadband signal propagating over different impedance surfaces is a stringent test of both the method used in the modeling of propagation and the surface impedance models. It has been shown that predicted waveforms might be sensitive to the fractional travel time, when the propagation time of the pulse does not equal an integer number of computational time steps. A method overcoming this issue is developed and demonstrated for different propagation conditions: a pulse propagating over a snow layer, frozen ground, and their combinations along the propagating path with homogeneous and vertically stratified atmosphere for a range of 60 m. For the numerical simulations, a conventional one-way parabolic equation with the Crank-Nicholson numerical algorithm is modified to improve computational efficiency and insure that the experimental time of arrival and spatial location of the receiver are matched exactly to the digital grids used in the simulations. The results are in a good agreement with experimental measurements and prior knowledge, and confirm that physical properties of a snow layer, sublayer ground, atmospheric conditions, and the order of range dependent ground properties affect the pulse waveforms.

Face-Centered Anisotropic Surface Impedance Boundary Conditions in FDTD

Thin-sheet models are essential to allow shielding effectiveness of composite enclosures and vehicles to be modeled. Thin dispersive sheets are often modeled using surface-impedance models in finite-difference time-domain (FDTD) codes in order to deal efficiently with the multiscale nature of the overall structure. Such boundary conditions must be applied to collocated tangential electric and magnetic fields on either side of the surface; this is usually done on the edges of the FDTD mesh cells at the electric field sampling points. However, these edge-based schemes are difficult to implement accurately on stair-cased surfaces. Here, we present a novel face-centered approach to the collocation of the fields for the application of the boundary condition. This approach naturally deals with the ambiguities in the surface normal that arise at the edges on stair-cased surfaces, allowing a simpler implementation. The accuracy of the new scheme is compared to edge-based and conformal approaches using both planar sheet and spherical shell canonical test cases. Staircasing effects are quantified and the new face-centered scheme is shown have up to 3-dB lower error than the edge-based approach in the cases considered, without the complexity and computational cost of conformal techniques.