Normalized Surface Impedance Research Articles

Improvement of sound absorption of porous materials through periodic holes of sinusoidal decreasing profile

Porous materials used in several engineering applications for noise attenuation present poor acoustic performance at low frequencies. In this paper, a design of porous materials with various periodic decreasing hole profiles is presented and studied using the finite element method. The sound absorption coefficient and the normalized surface impedance are compared for different periodic decreasing hole profiles. A small drop in sound absorption is observed after the first peak with a decreasing linear profile. Using a sinusoidal decreasing hole profile, it is shown that the drop is attenuated. The impacts of the amplitude and the period of the sinusoidal profile on the sound absorption coefficient and the surface impedance are demonstrated. The proposed porous material design with periodic holes having a sinusoidal decreasing profile shows a significant improvement in sound absorption over a large frequency band compared to conventional porous materials.

Improvement of micro-perforated panel absorbers sound performance using resistive screens and sensitivity analysis of the composite absorber models

The sound attenuation performance of a composite absorber constituted by a micro- perforated panel, a resistive screen that is inserted into the air cavity and a rigid back plate, is studied. Using a nonlinear acoustic impedance model, the surface impedance of the absorber is determined by transfer matrix method, and the models are validated by comparison with experimental measurements performed at different sound pressure levels up to 150 dB. The contribution of the resistive screens in improving the acoustic performances of micro-perforated panel absorbers is presented. It is shown that the resistive screen increases the resistance of the absorber resulting in broadening of the absorption frequency band and improvement of the absorption coefficient when an appropriate perforation ratio of the panel is used. Sensitivity analysis is performed at higher pressure excitations, and the dimensionless input parameters are the perforation ratio of the panel, the ratio of the perforation diameter by the thickness of the panel, the ratio of the cavity depth by the thickness, the orifice Mach number and the resistance per unit area of the screen. The analysis shows the impact of the input parameters on the normalized surface impedance and the sound absorption coefficient of the absorber. It is demonstrated that the resistance per unit area of the screen influences strongly the acoustic properties of the absorber in the linear regime, while the perforation ratio of the panel and the orifice Mach number are the dominant parameters which control the acoustic behavior of the absorber in the nonlinear regime.

Surface Field Analytical Solution of the Impedance Boundary Condition Circular Cylinder Canonical Problem

A surface field analytical solution of the impedance boundary condition circular cylinder canonical problem is contributed in the work at hand. The accurate representation of the primary ray contribution of the tangential surface magnetic field, of a tangential magnetic current excited relative electromagnetic structure, is given via series expansion in powers of the normalized surface impedance. Furthermore, each term in the series is represented as series of the inverse of the cylinder radius. This is achieved by approximating the Hankel functions by a uniform asymptotic expansion within the spectral integral representation of the relevant Green’s function. All the resulted integrals are evaluated analytically in an exact fashion. and, thus, the final process entails only summations and differentiations. The attained formulas are valid both within and outside the paraxial region. Validity of the contributed analytical solution is provided by successful comparison with published results.

Hybrid composite meta-porous structure for improving and broadening sound absorption

In order to improve and broaden the sound absorption performance of porous materials with low flow resistance, this study proposes the composite meta-porous structure embedded multiple lateral plates of different lengths, and investigates the corresponding sound absorption coefficients with the fixed and periodic boundary. Characteristics of spatial fluctuation and slow wave effect are embodied in acoustic pressure distributions. Further, the hybrid composite meta-porous structure with periodic boundary could achieve high sound absorption in range of 0–6.4 kHz. The Theoretical model using transfer matrix method suitable for these models is proposed, and verify the FEM results. Normalized surface impedance, phase and trajectory of the complex reflective coefficient illustrates the loss of acoustic energy inside the structure and leakage to the outside. By detailed discussion on the relationship between the geometric parameters and the corresponding sound absorption coefficients, the three boundaries would have different effects on sound absorption performance. Sound absorption test results by acoustic impedance tube confirm the rationality of the composite meta-porous structure with fixed boundary in range of 0.2–5.716 kHz and its practical application in the noise reduction.

Tunable terahertz absorber with multi-defect combination embedded VO<sub>2</sub> thin film structure

The metamaterial absorber has the advantages of thin thickness, small size, simple structure and high absorption. As is different from the traditional metamaterial absorber, the adjustable material is used for designing the structure, which can realize the dynamic modulation of the device by changing the external factors without changing the device structure. In this paper, an adjustable terahertz absorber with multi-defect combination embedded VO<sub>2</sub> thin film is proposed. It is composed of three layers: the upper metal pattern layer, the substrate and the bottom metal plate. Vanadium dioxide medium is sandwiched between the upper surface and the substrate. The absorption performance of the absorber composed of different defect combinations is studied, and the electric field distribution of each combination is analyzed. At the same time, the influences of defects on the absorption performance of the absorber are compared with each other and analyzed. After comprehensive analysis, the defects are combined into the final proposed structure, and the electric field distribution and surface current distribution are analyzed. The relevant parameters affecting the performance of the absorber are scanned and analyzed, and the final optimized structural parameters are obtained. The results show that the absorption rate at <i>f</i> = 4.08 THz and <i>f</i> = 4.33 THz are 99.8% and 99.9%, respectively. The phase transition of vanadium dioxide can be controlled by changing ambient temperature, so that the absorption rates of two frequency points can be changed from 99.8% to 1.0%. In addition, the surface normalized impedance of the proposed absorber is analyzed, which shows that the normalized surface impedance of the designed absorber matches the impedance of the free space well. By changing the incident angle and polarization of terahertz wave, the results show that the absorption rate of the absorber under TE and TM polarization wave both can be more than 98% with the incident angle ranging from 0° to 40°. The proposed terahertz wave absorber has the characteristics of high absorption, dynamic tuning and insensitive polarization. It has good application prospects in terahertz wave related fields such as detectors and stealth technology.

Sensitivity analysis of micro-perforated panel absorber models at high sound pressure levels

Sensitivity analysis is performed using a nonlinear acoustic impedance model of micro-perforated panel absorbers constituted by a micro-perforated panel bonded on a honeycomb structure in order to assess the impacts of the input parameters on the outputs of interest namely the normalized surface impedance and the sound absorption coefficient. The theoretical results predicted by the nonlinear impedance model show good agreement with experimental measurements performed at high sound pressure level using an impedance tube. The inputs of the model are the plate thickness, the orifice diameter, the perforation ratio, the cavity depth and the sound pressure level. For higher pressure levels excitations, it is demonstrated that the perforation ratio is the key parameter which affects significantly the resistance and the sound absorption of the absorber at the resonance while the impacts of the thickness and orifice diameter of the panel are negligible. In addition, the study confirms that the acoustic reactance is dominated by the cavity depth especially at low frequencies and the sound pressure level influences strongly the acoustic behaviour of micro-perforated panel absorbers. Therefore, the design of a micro-perforated panel absorber requires the knowledge of the sound pressure level and the perforation ratio control quality must be done carefully in order to get the target performances of the absorber.

Improving Power Integrity by Using Magnetodielectric Absorbers Along the Perimeters of Printed Circuit Boards

Maintaining low and smooth impedance over a wide range of frequency is one of the main issues in designing high-speed digital systems or mixed signal integrated circuits. Cavity resonances of a printed circuit board coupled with discontinuous return current paths, series inductance of the power distribution network, and parasitic inductance make potentials at power/ground planes unstable. One possible solution to improve power integrity and electromagnetic interference is to utilize a magnetodielectric absorber on the perimeter of the board. A mode-matching method and an impedance boundary condition are employed to obtain a computationally inexpensive model of the system. A contour plot of transfer impedance versus normalized surface impedance is introduced to provide useful information for determining the most suitable absorber. Numerical and measurement results are discussed. The results from the proposed modeling agree with those from the measurement and the simulation. The selected absorber effectively reduces selfimpedance and transfer impedance at resonant frequencies, but resonances are not completely eliminated at low frequencies due to the low loss of the absorber.

Experimental measurements of acoustical properties of snow and inverse characterization of its geometrical parameters

Snow is a sound absorbing porous sintered material composed of solid matrix of ice skeleton with air (+water vapour) saturated pores. Investigation of snow acoustic properties is useful to understand the interaction between snow structure and sound waves, which can be further used to devise non-destructive way for exploring physical (non-acoustic) properties of snow. The present paper discusses the experimental measurements of various acoustical properties of snow such as acoustic absorption coefficient, surface impedance and transmission losses across different snow samples, followed by inverse characterization of different geometrical parameters of snow. The snow samples were extracted from a natural snowpack and transported to a nearby controlled environmental facility at Patsio, located in the Great Himalayan range of India. An impedance tube system (ITS), working in the frequency range 63–6300Hz, was used for acoustic measurements of these snow samples. The acoustic behaviour of snow was observed strongly dependent upon the incident acoustic frequency; for frequencies smaller than 1kHz, the average acoustic absorption coefficient was found below than 0.4, however, for the frequencies more than 1kHz it was found to be 0.85. The average acoustic transmission loss was observed from 1.45dBcm−1 to 3.77dBcm−1 for the entire frequency range. The real and imaginary components of normalized surface impedance of snow samples varied from 0.02 to 7.77 and −6.05 to 5.69, respectively. Further, the measured acoustic properties of snow were used for inverse characterization of non-acoustic geometrical parameters such as porosity, flow resistivity, tortuosity, viscous and thermal characteristic lengths using the equivalent fluid model proposed by Johnson, Champoux and Allard (JCA). Acoustically derived porosity and flow resistivity were also compared with experimentally measured values and good agreement was observed between them.

On the accuracy of approximate techniques for the evaluation of lightning electromagnetic fields along a mixed propagation path

In this paper we review simplified analytical expressions derived by Wait using the concept of attenuation function for the analysis of the propagation of lightning‐radiated electromagnetic fields over a mixed propagation path (vertically stratified ground). Two different formulations proposed by Wait that depend on the relative values of ground surface impedances are discussed. It is shown that both formulations give nearly the same results for the time domain electric field. However, depending on the values of the normalized surface impedance for each ground section, the use of one of the two formulations is computationally more efficient. The accuracy of the Wait formulations was examined taking as reference full‐wave simulations obtained using the finite difference time domain technique. It is shown that Wait's simplified formulas are able to reproduce the distant field peak and waveshape with a good accuracy.

Propagation of HF radio waves over sloping coastal land

The field of a TM wave at a reception point over sloping coastal land, farther than a wavelength from the sea, has been calculated for a transmitting element located infinitely far away over a flat sea. The field obtained is normalized to that of a wave approaching the water/land boundary from infinity. A transmitting element placed both at some elevation angle and on the surface of the sea has been considered. In both instances, simple formulas providing fast computation of the field have been obtained by employing the integral equation approach formulated in terms of the normalized surface impedance. It has been found that the sloping land to some extent compensates for power losses in the ground and may even enhance the power density of high-frequency waves coming from low elevation angles. The expressions obtained remain valid for flat ground in place of sea. In this instance, the permittivity and conductivity of the sea should simply be substituted by those of the ground.

Application of radio ground-wave propagation theory to the tomographic imaging of ground surfaces

Radiowave propagation over ground has been historically studied for predicting the radiated fields when the ground properties are known and the field has been well covered over the past hundred years. The theory of ground-wave propagation is applied to the inverse problem of the tomographic imaging of ground surfaces. After the inverse problem is formulated, an iterative technique for solving it is illustrated. This is based on the minimization of the cost function of the measured and estimated scattered fields produced by the surface under investigation in isolation. Numerical simulation results are presented for the reconstruction of four different ground features surrounded by sea water namely: (1) dry ground; (2) wet ground; (3) dry-wet mixed ground; and (4) dry ground with a central water pool. It has been demonstrated that the technique is able to reconstruct the distributions of normalized surface impedance of the isolated surfaces and, hence, their images. The iterative process can converge with a small number of iterations using the normalized surface impedance of sea water as the initial guessed values. However, better images can be produced using a priori information. This study thus illustrates a new application of ground wave propagation theory with possible applications in ground surface mapping, remote sensing, target positioning and monitoring, and navigation.

Estimation of temperature gradient effects on the normalized surface impedance of soils

Ground impedance measurements are used for sound propagation predictions and to determine soil properties. Solar heating of the ground leads to significant temperature swings and gradients in the near surface soil. The equations of thermoacoustics are applied to estimate the magnitude of the temperature effects on the impedance and develop an approximate equation for the adjustment of measured impedance. Ambient temperature effects are shown to be significant; temperature gradient effects in soils are negligible. The theory is applicable to noise control applications where larger gradients may occur in sound absorbing materials.

First-order symmetric modes for a slightly lossy coaxial transmission line

A complete set of solutions for Maxwell's equations to first order in the normalized surface impedance z/sub s/ of the coaxial conductors is found. The derivation of the fields outlined assumes a vacuum dielectric and an infinitely thick outer conductor. It starts from J.P. Stratton's work (1941) with a derivation of the determinantal equation for finding the eigenvalues for both the principal and waveguide modes in a lossy line. The first-order determinantal equation is found, preceded by an equation for calculating the proportionality constant for the fields intermediate between the center and outer conductor. The equations for lossy waveguide modes are new, and the principal mode fields include a term missing from the expressions that are found elsewhere in the literature. The resulting characteristic admittance and distributed line parameters are calculated; the distributed line resistance is significantly different from other calculations found in the literature. >

Optical properties of Al, Fe, Ti, Ta, W, and Mo at submillimeter wavelengths

Measurements of the optical constants of metals at submillimeter wavelengths are sparse. We have used a nonresonant cavity to measure, at room temperature, the angle averaged absorptance spectra P(omega) of aluminum, molybdenum, tantalum, titanium, tungsten, and iron in the 30-300-cm(-1) wavenumber region. The real part of the normalized surface impedance spectrum, z(omega) = r(omega) + ix(omega), was determined from P(omega). Measurements were also made on iron from 400 to 4000 cm(-1) using standard reflectance techniques. The r(omega) spectrum was combined with previous measurements by others at higher frequencies and Kramers-Kronig analyses of the resultant combined r(omega) spectra provided epsilon(omega) = epsilon(1)(omega) + iepsilon(2)(omega) and N(omega) = n(omega) + ik(omega).

Propagation over an inhomogenous irregular surface

A new integral equation has been obtained for the attenuation factor of a radio wave launched by an elevated element, as the wave propagates over a radially inhomogeneous surface of varying height, with an elevated current element as a receiver. In the analysis use is made of the vector form of compensation theorem, using the concept of a real surface impedance on the irregular surface together with that of an equivalent normalized surface impedance in air, at points which follows the contour of the irregular surface. The new integral equation generalises previous work to treat arbitrary terrain, so that both gradual and sharp changes of terrain height, such as a cliff and a knife edge are considered. The validity of the integral equation has been tested theoretically by comparison with alternative solutions for particular cases, and also by experiment.

Optical properties of Au, Ni, and Pb at submillimeter wavelengths

Measurements of the optical properties, and thus the optical constants, of metals at submillimeter wavelengths are almost nonexistent. We used a nonresonant cavity to measure at ambient temperature the angle averaged absorptance spectra P(omega) of gold, nickel, and lead in the 30-300-cm(-1) wave-number region. The real part of the normalized surface impedance spectrum z(omega) = r(omega) + ix(omega) was determined from P(omega). The r(omega) spectrum was combined with previous measurements by others at higher frequencies, and Kramers- Kronig analyses of the resultant r(omega) spectra provided (omega) =, (1) (omega) + i(2)(omega) and N(omega) = n(omega) + ik(omega) for gold and nickel in the 35-15,000-cm(-1) region and for lead in the 15-15,000-cm(-1) region. We also derived an exact analytical expression for P(omega) of a metal.

Design theory of dielectric-coated circular metallic waveguides for infrared transmission

A circular metallic hollow waveguide with inner dielectric multilayers is designed with the emphasis on low-loss transmission of the HE 11 mode for the infrared. The effects of absorptions and variations of thickness of coated dielectric materials are discussed and are shown to be small on the minimum attainable transmission losses. Mode structure and transmission properties are also clarified for the general class of hollow waveguides by using a normalized surface impedance and admittance.