The schematic of OR with the sample located on the ﬂat mirror is presented in Fig. 1. The sample is a two-**layer** structure — substrate/**high** K-ﬁlm. The microwave properties of substrate are known from handbooks or on the base of preliminary measurement of the substrate without ﬁlm in open resonator. Installation of the sample changes the resonance frequency and to restore the mode of measurements the frequency shift is compensated by the movement of the plane mirror at a distance p . Theoretical approach of measurements is based on results of theory developed by [13] for E- and H-ﬁeld distribution in open resonator with one **layer** **dielectric**. Relationship between the resonance frequency

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Alumina is the ceramic form of sapphire. It has balanced properties of insulation, thermal conductivity and breaking strength. It is usually available in white color having **dielectric** constant varying from 9.5 to 10 with loss tangent tanδ = 0.0002. Its unique property is surface roughness and excellent adhesion with a thin film and thick film metallization due to fine particles. Various advantages of Alumina are: Physical and chemical properties are stable even at very **high** temperatures, **High** Mechanical strength, Good in insulation properties, Less porous with good smoothness. Gold metallization is frequently used with alumina. Usually a very thin adhesion **layer** is used between alumina and gold.

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The data about graphene influence on the microwave properties of the elastomeric composites are very scarce. Y. Chen et al. used functionalized graphene-epoxy com- posites as lightweight shielding materials for electro- magnetic radiation [12]. I. M. De Rosa and coworkers have a wide expertise in the design of micro/nanocom- posites based on carbon fibers and carbon nanotubes, for the realization of **high** performing radar absorbing screens, with tailored properties [13-15]. In a recent paper [16], the authors have accomplished a Salisbury screen, that consists of three layers. The second **layer** (the spacer) is a low-loss-tangent nanocomposite based on a Bisphenol-A based epoxy resin filled with GNPs at 0, 5 and 1 wt% [16]. The real and imaginary parts of the complex effec- tive **permittivity** within the 8 - 18 GHz range of the nano- composite filled with GNPs have been shown. It has been observed that the real part of the effective permit- tivity is nearly constant.

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The geometric configuration of the proposed ground plane slot resonator is shown in Fig. 1. The structure consists of a 50 Ω microstrip line on the top **layer** and a rectangular slot is etched in the ground plane of substrate. Two metallic plates forming a parallel plate capacitor is soldered with the ground plane across the ground slot. The low loss **dielectric** material could be placed between two metallic plates to increase the loading capacitance. The maximum electric field in the slot is at the centre of the slot; where parallel plates are soldered.

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Through equations available in the literature8, we can see that the combination of the magnetic permeability and the **permittivity** of the absorbing composite satisfying the impedance matching condition is the key to producing a **high**-performance microwave absorber. Specifically, for a single **layer** of absorber backed by a PEC [perfect electric conductor] the reflection loss and the attenuation constant are dependent on complex magnetic permeability, **permittivity**, and frequency. If we consider diamagnetic carbonaceous materials, microwave absorbers are due to **dielectric** losses. In the case of a **dielectric** absorbent, assuming that µ=1 - j0, the maximum reflection loss and the attenuation coefficient depend on real and imaginary part of **permittivity**, **dielectric** loss angle tangents at a given frequency8. This is why to explain the effect observed we investigated the **dielectric** properties of the composites studied.

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We consider the electrostatic ﬁeld computations with ﬂoating potentials in a multi-**dielectric** setting. A ﬂoating potential is an unknown equipotential value associated with an isolated perfect electric conductor, where the ﬂux through the surface is zero. The ﬂoating potentials can be integrated into the formulations directly or can be approximated by a **dielectric** medium with **high** **permittivity**. We apply boundary integral equations for the solution of the electrostatic ﬁeld problem. In particular, an indirect single **layer** potential ansatz and a direct formulation based on the Steklov-Poincaré interface equation are considered. All these approaches are discussed in detail and compared for several examples including some industrial applications. In particular, we will demonstrate that the formulations involving constraints are vastly superior to the penalized formulations with **high** **permittivity**, which are widely used in practice.

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As expected from Mie theory, the **dielectric** sphere is equivalent to a magnetic dipole near the magnetic resonance mode and the magnetic field is mainly localized in the sphere as shown in Figure 4(a). However, when the CTO rods are placed beside the **dielectric** sphere, the magnetic field distribution is changed. The magnetic field in the gap enhances greatly while that in the sphere decreases as the rod approaches the **dielectric** sphere. When the distance between the rod and the sphere is reduced to zero, the intensity of the magnetic resonance even decreases by about 15% from about 5.7×10 4 A/m to

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In this work, barium iron niobate, Ba (Fe1/2Nb1/2) O3 powder has been successfully perovskite structure of BFN was followed ray diffraction (XRD), and has shown a crystallite size at a nanometric scale. The pure perovskite phase was obtained at relatively low temperature (900°C /8 h) compared to the state reaction. Moreover, **dielectric** measurements showed strong relaxation and diffuse phenomena, and a maximum of the **dielectric** **permittivity** at a temperature lower than those reported in the literature, together with resonance phenomenon at **high** frequency values. Impedance parameters were extracted from the **permittivity** analysis and enabled us in particular, to determine the

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There have been numerous approaches to model electromagnetic (EM) backscatter from rough surfaces and from horizontally stratiﬁed media, but these typically involve assumptions that limit the overall solutions to the point that the phenomena being modeled are not physically realizable. Lord Rayleigh [1] developed the perturbation method to study the reﬂection of acoustic waves from a sinusoidal surface and this was ﬁrst extended to electromagnetic waves by Rice [2]. Rice considered static 2D rough surfaces that could be expressed as a Fourier Series with the series coeﬃcients as random variables. The analysis was completed to second order for scatter from a perfectly conducting surface and a horizontally- polarized wave on a rough **dielectric** surface. Wait [3] considered reﬂection of a vertically-polarized EM wave from a 2D periodic surface using the Leontovich boundary conditions and derived results to second order. Barrick [4, 5] was interested in radar propagation across the ocean and considered the wave as being guided by a rough, conductive surface. The scattered ﬁeld was limited to the component traveling away from the surface and multiple scattering was not included in the analysis. These results were extended to all spectral orders of scattering by Rosich and Wait [6]. Rodriguez and Kim [7] developed a uniﬁed perturbation expansion that reduced to Rice’s results when the same assumptions are made, but the second order cross sections deteriorate as incidence angle or surface height increases. Perturbation methods are one of the most common approaches for modeling backscatter from rough surfaces. However they are only valid when the amplitude of surface roughness is much smaller than the radar wavelength and some implementations of the technique assume plane wave incidence.

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The **dielectric** parameters and have been meas- ured for a nematic liquid crystal BKS/B07 in the fre- quency range of 1 kHz to 10MHz for the temperature range of 70˚C to 135˚C. Figure 3 and Figure 4 represent typical frequency dependence spectra of the real and imaginary part of the **dielectric** **permittivity** measured for nematic sample BKS/B07 and dye doped mixtures 1 and 2. The **dielectric** **permittivity** is found to be either con- stant or to decrease as the frequency increases [17-22] for pure sample. Lower values of at higher frequency suggest that the molecules rotate about their long mo- lecular axis [23]. The behaviour of for the dye based mixtures 1 and 2 is similar to that of pure sample but the values of **dielectric** constants are higher in comparison to the corresponding values of pure sample.

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effect of Nd 3+ doping on the dielectric permittivity and magnetization in the wide frequency range.. 21.[r]

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Effect of variation of dielectric permittivity of the medium on the reaction rate It was found that as the dielectric constant of the medium increased, this including r* < r [Where r* an[r]

Hertzian potentials have been used to solve different electromagnetic problems: in the study of the properties of aperture array systems [1], non-linear waveguides [2], Green’s functions for multilayered media [3] and electromagnetic wave interaction with nanodevices [4]. They have also been applied for the determination of TE and TM modes of circular cylindrical cavities using magnetic-type and electric-type Hertzian potentials res- pectively [5]. Figure 1 shows the case of a cylindrical **dielectric** resonator enclosed by a metal shield, where b is the radius of the outer cylinder, a is the inner resonator radius and d is the height (length of the structure). The configuration can be regarded as a cylindrical waveguide enclosing a central sample of radius a, and terminated by perfectly conducting planes. The general solution for the axial E field in TM modes was discussed in [6], proposing a general solution for the axial E field for TM modes.

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Abstract—In this paper, a new measurement method is proposed to estimate the complex **permittivity** for each **layer** in a bi-**layer** **dielectric** material using a Ku-band rectangular waveguide WR62. The S ij - parameters at the reference planes in the rectangular waveguide loaded by a bi-**layer** material sample are measured as a function of frequency using the E8634A Network Analyzer. Also, by applying the transmission lines theory, the expressions for these parameters as a function of complex **permittivity** of each **layer** are calculated. The Nelder-Mead algorithm is then used to estimate the complex **permittivity** of each **layer** by matching the measured and calculated the S ij -parameters. This method has been

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Among the most important parts of a wireless system is the antenna, since it strongly influences the overall receiver sensitivity and the link budget. In the near future, wireless transmission for consumer products will also happen at much higher frequencies than nowadays, i.e. in the millimeter wave (mm-wave) frequency range. This is required to achieve very fast data exchange and HD video streaming between all kinds of consumer products [1-3]. **High** radiation efficiency is particularly important due to significant free-space loss, very limited battery capacity in portable devices and consequential low transmit power levels, which

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size variance. The variance provides a measure of local struc- ture and so it is clear that local structure plays a significant role in the **dielectric** response. Such information is not avail- able via conventional Rietveld analysis of di ﬀ raction data and probes of local structure are required. Nevertheless, it appears that variance may be a useful metric to guide the tuning of properties in TTBs and could be extended to other structure types which contain perovskite units such as Ruddlesen- Popper and Dion-Jacobsen phases.

Recently, several methods have been used to optimize patch antennas with varying success, such as using a **dielectric** substrate of **high** **permittivity** [1], Defected Microstrip Structure (DMS) [2], Defected Ground Structure (DGS) at the ground plane [3] or a combination of them, and various existing optimization algorithms such as particle swarm optimization (PSO) [4] and genetic algorithm [5–7]. The latter is one of the global optimization algorithms that have been used widely in the past by antenna designers for the optimization of the patch shape and size in order to achieve better overall performance of the antenna.

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Continuing with our previous work [1] in this paper, we present an effective method that minimizes the uncertainty in the measurement of the real **dielectric** **permittivity** of a material. As we indicated previously, the method is valid only for low loss materials in view of the nature of the exact relations between **permittivity**, sample and cavity dimensions, measured resonant frequency and the unloaded Q- factor for the resonant structures. Resonant methods are the preferred technique in **dielectric** **permittivity** measurements over non-resonant measurements [2], in view to their higher accuracy and sensitivity. Although, recent papers have discussed the problems associated to the estimation of uncertainty in the measurement of **dielectric** **permittivity** of materials, but only a few have proposed a systematic methodology for the reduction of the uncertainty associated to the measurement of the **dielectric** **permittivity** using resonant cavities [3].

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visually due to the use of metal electrodes in our system. The tuning voltage in our measurement system is limited to 40 Vp-p and the cell thickness is about 28µm. The resulting field strength of 1.43 V/µm may not be **high** enough to achieve maximum tunability. The other reason could be the possibility of affecting accuracies at the edge of measurement frequency ranges. The data at 1GHz by Weil el. al. was measured at the edge of their measurement frequency range (0.1-1 GHz), whereas it was in the middle in our case (frequency range: 0.01-6 GHz).

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determined by contacts between Al nano-particles. At the boundaries of clusters in the alternating electric field an accumulation and redistribution of free charges occurs, which changes the initial internal electric field. It is known that at low frequencies, internal electric fields are distributed accordingly conductivity and **high** frequen- cies—respectively the **dielectric** **permittivity**. Therefore, the decrease ε '' and tg δ with increasing content of alu- minum nano-particles can be explained by the appearance of a relatively strong internal field in semiconductors and nano-clusters.

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