This study, in the ﬁeld of **dielectric** **permittivity**, presents the results from a comparison among three diﬀerent measurement cells. First of all, the combination of two **dielectric** measurement techniques has enabled us to evaluate them against each other at the same frequencies. Furthermore, it allows for measurements of a wider frequency band due to improved accuracy. The latter is owing to the good agreement between the results of diﬀerent systems, obtained under identical experimental conditions, and the inclusion of three diﬀerent materials. As these two cells have been validated, they will be used with conﬁdence in further studies of moist materials.

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Type 1 causing it to dissolve with a high rate and main- taining an ion-rich system. In addition, the rate of the decrease of **dielectric** **permittivity** of Type 3 paste is higher than that of Type 1. In the acceleratory period, the Type 3 paste reacts faster than the Type I paste. This coincides with temperature rise and shorter dormant pe- riod. For setting time, the **dielectric** constant is main- tained until the final setting time because of the high dissolution rate, however the **dielectric** constant drops dramatically with the high hydration rate. At the later stage after formation of the C-S-H structure, the dielec- tric **permittivity** tends to remain constant because of strong constraints imposed by its structure.

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From the graphs in Figs. 5 and 6 for two-layered and multilayered dielectrics, one can see that increase of the number of layers gives rise to that the properties of these **dielectric** become closer to the properties of a homogeneous layer with eﬀective value of **dielectric** **permittivity**. For multilayered structures with number of layers more than 20, the model of such a homogeneous layer produces quite satisfactory results. However, it is typical only for the eﬀective **permittivity**, determined by transmission coeﬃcient and only for TE polarization, but for TM polarization, at the values of angle of incidence more than 20 ◦ , one observes noticeable discrepancies from the Braggeman’s values. The matter is that formula (9) is applicable to the cases, when the electric ﬁeld is parallel to the boundaries of layers of a multilayered structure, as it occurs for TE polarization, but in the cases of ﬁeld orthogonal to the layers, the mixing formula (9) must be written with the index of a power − 1 for all **dielectric** permittivities [2, 3]. That is why for TM polarization, whose electric vector lies in the plane of incidence, its normal component increases with increase of the angle of incidence, and formula (9) becomes inapplicable. Besides, noticeable disagreements from Braggeman’s values arise for eﬀective permittivities, determined by reﬂection coeﬃcients, for both polarizations. Calculations show that the presence of great number of periodical layers by itself is not an essential feature. The relation between the wavelength of transmitting radiation and total thickness of a homogeneous layer is of importance to a far greater extent. The greater the wavelength is in comparison with the given thickness, the more accurate description one obtains using the Braggeman’s formula as for transmission, as for reﬂection from a layer. This formula provides suﬃciently complete description of **dielectric** properties of a plane layered heterogeneous medium only in the limiting case of negligibly small thickness of a medium in comparison with the wavelength of transmitting radiation. It is clear, because the Braggeman’s formula (9) was established for electrostatic ﬁelds.

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The cited publications on the time-harmonic Maxwell equations address homogenization only at low frequencies when the period of the microstructure is small compared to the wave length. Besides, the authors of previous publications do not take into account the skin layer eﬀect while making homogenization. Paper [32] does not involve numerical calculations, and its main result is a mathematical theorem which justiﬁes the macroscopic harmonic Maxwell equations at a ﬁxed low frequency with penetrable boundary conditions. Both the variation of frequency and frequency dispersion of the eﬀective **dielectric** **permittivity** are not addressed in [32]. Moreover, the formulas for the eﬀective **permittivity** and conductivity are restricted to non conductive mixture components; this is why the dispersion eﬀect could not be ﬁxed in this study since the formulas for the eﬀective parameters do not involve the frequency at all.

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continuous variables before averaging. Limited gradients are calculated from averaged values at ver- tices, values at vertices showing **dielectric** **permittivity** discontinuity need to be transformed back from continuous variables. To perform independent limitation, two limit values are computed at the nodes characterized by **dielectric** **permittivity** discontinuity at the two sides. Values in cells are extrapolated on the adjacent vertices using computed derivatives to calculate limit values. Extrapolated values are partitioned into groups according to the value of the **dielectric** **permittivity** in the cell from which ex- trapolation took place. Each group is averaged independently. Limited gradients are calculated from averaged values at vertices. If the vertex is located on the **dielectric** **permittivity** discontinuity and has two average values, the value that corresponds to the **dielectric** **permittivity** in the cell is used to calculate limited gradients.

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One of the most promising methods without the mentioned drawbacks is the use of the open quasi-optic Fabry-Perot resonator (hereinafter OR). OR are used on MW up to hundreds GHz [5] for deﬁnition of electrodynamical parameters of solid substances, gases and plasma. In accordance with [3] the Q-factor for empty OR operating at millimeter wave frequencies is typically in the range (1–2) × 10 5 and can be increased by a factor of ∼ 5 employing so-called Bragg reﬂectors [6]. There are a set of works devoted to measurements of the complex **dielectric** **permittivity** on the base of OR. In [7] the measurements of one-layer materials with low values of ε (quartz and Teﬂon disks) are presented at 20– 40 GHz. The aim of the work is to determine the measurement error as a function of disk diameter. In [8] the possibility of very precise measurements at Ka band is demonstrated for a set of one layer **dielectric** materials with ε < 10. Note that many of recent works are devoted to increasing the measurement’s accuracy of electrodynamic parameters of one layer solid materials with low **dielectric** constant [9–11].

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+ (23) Equations (21) and (23) give the relation between the electromagnetic parameters of the unknown medium and the resonant frequency. The cut off wave number can be determined if the **dielectric** **permittivity** constant is known or viceversa. This system is solved numerically using the Matlab function fsolve. The solution given in Equation (21) reduces to the simple form given in [15] and [6] when n = 0 . The possible sources of uncertainty present in this configuration are the exact dimensions of the cavity, losses in the wall’s finite conductivity and resolution of the measurement equipment [16]-[20]. Equations (21) and (23) reduce to the limit case of a simple cavity resonator filled with a single material when a = b or when the electromagnetic parameters of both mediums are equal. Because the frequency variable was canceled in Equations (21) and (23), some solutions could be added or eliminated. The solution obtained should be checked by using ω 1 = ω 2 .

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Table II lists the real and imaginary parts of the **dielectric** **permittivity** at 3GHz and the refractive index values at 589nm for the tested nematic liquid crystals. The studied materials exhibit a **dielectric** anisotropy varying between 0.25 and 0.83 with low associated losses (typically tan δ ⊥ ~0.05 and tan δ || ~ tan δ ⊥ /2). Figure 4 shows **dielectric** anisotropy ∆ε (in microwave regime) vs birefringence ∆n (589nm) for two sets of data. One set of data was measured by us at 3GHz for the 9 nematic LCs, as listed in Table II. The other set of data was obtained from the work done by Lim K.C. et al at 30GHz [14].

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Fig. 4 (a) & (b) shows 2D & 3D model for FCPW respectively obtained through SONNET software simulation [17]. Simulation is done on Alumina and Roggers substrate with εr =9.8, loss tangent tanδ = 0.0002 and εr =6.0, loss tangent tanδ = 0.0023 respectively. The simulated parametric study results and conformal mapping analysis for FCPW are obtained. Graph shown below represents the effect of aspect ratio and gap between strip and ground plane on capacitance, Effective **dielectric** **permittivity**, transmission coefficient and reflection coefficient for varying height of substrates.

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in terms of the formation of H-bonded linear chains, which increases its dipolar orientational correlation factor. How- ever, the mechanism of its **dielectric** relaxation has been a subject of debate recently. 7–13 The debate has resulted from recent studies 7,8 showing that the slowest **dielectric** relax- ation process, which is responsible for ⬃ 95% of its polariza- tion is associated with an unspecified mechanism that does not contribute to the viscosity and the density fluctuations in the light scattering measurements. Our study showed that 1-propanol can also dissolve a significant amount of ionic salts and, as its ⑀ s is relatively high, the ionic dissociation of the salts is significant. Also, since ionic diffusion in a liquid is determined by its viscosity, , one expects that the dc conductivity, 0 , of 1-propanol would change with tempera-

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the physical parameters reach saturated values gradually. The model for **dielectric** response during the helical unwinding process suggested in this letter is not complete, because it does not consider the helical fractures in the calculations. The helical fracture may enhance the appear- ance of the U part and expand its length, and hence, at the ﬁeld at which the helical fracture occurs, the physical properties may also change sharply. However, the mecha- nism for the occurrence of the helical fracture is not clear, and it is diﬃcult to estimate the electric ﬁeld required to generate helical fractures at this state. As reported in our previous paper [9], we observed that the electric ﬁeld, at which the helical fracture occurs, varies according to the enantiomeric excess ratio in the racemized mixtures. This implies that the material parameters such as the sponta- neous polarization, pitch and the interlayer interactions might aﬀect the emergence of the helical fracture. The complexity in the unwinding process of helix in ferroelec- tric materials, in particular those having large spontaneous polarization, has been reported. Haase et al. [21] suggested a modulated helical structure caused by the tendency of the spontaneous polarization to compensate itself, and Pikin et al. [22] reported dislocation walls induced by moderate electric ﬁelds in ferroelectric liquid crystals having large spontaneous polarization. Their interpreta- tions for their observations are diﬀerent from the heli- cal fracture; the modulated helical structure by Haase et al. [21] uses the continuum approximation, and the dislocation walls by Pikin et al. [22] are apparently diﬀer- ent from the π walls occurring in smectic layers without signiﬁcant deformation of the smectic layers themselves. However, their observations imply that the large sponta- neous polarization might also play a role in generating the helical fractures. For complete understanding the helical unwinding, the emergence and the propagation of the soli- tary wave propagation should be investigated to ﬁnd the mechanism.

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In this paper, we have presented a broad-band electromagnetic characterization technique for measuring isotropic nonmagnetic ﬁlm- shaped materials at low microwave frequencies. It is based on a reﬂection method, which uses an open-end CPW line as sample- cell. The open-end CPW cell is etched onto the sample to be characterized. The extraction method of the substrate **permittivity** ( r ) is obtained from S 11 parameter measurement and a processing

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The present work was mainly motivated by the need for a material exhibiting high **dielectric** properties suitable for 3DP of devices for high-frequency applications, targeting the GHz–THz range. While, as shown in the example above, material extrusion can provide feedstock with **dielectric** **permittivity**, ε , as high as 11, and feature resolution is typically within the 100–200 µ m range. In the present study, the Digital Light Processing (DLP, variation of SLA) was chosen due to its ability to provide smooth surface finishes [4] and high spatial resolution of 20 µm or better [16,17], therefore providing satisfying conditions for 3DP of complex structures with a sub-wavelength (< λ /5) element size. This technology comprises photopolymerization through cross-linking by a light source (VIS, or UV laser or LED) of a liquid mixture of photo-reactive monomer and photo-initiator [18].

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Abstract—In this paper, we present a novel general methodology which ensure a minimum uncertainty in the measurement of the real part of the **permittivity** of a material measured using cylindrical shielded **dielectric** resonators. The method is based on the fact that for any given value of the **dielectric** **permittivity** there is an optimal radius of the cylindrical **dielectric** rod sample. When the **dielectric** rod sample has the optimum radius, the width of the coverage interval associated to the real part of the **dielectric** **permittivity** measurement result — for a given confidence level — is reduced due to a lower sensitivity of the **dielectric** **permittivity** to be measured versus the variations in the resonant frequency. The appropriated radius of a given sample under test is calculated using Monte Carlo simulations for a specific mode and a specific resonant frequency. The results show that the confidence interval could be reduced by one order of magnitude with respect to its maximum width predicted by the uncertainty estimation performed using the Monte Carlo method (MCM) as established by the supplement 1 of the Guide to the Expression of Uncertainty in Measurement (GUM). The optimum radius of the sample under examination is fundamentally determined by the electromagnetic equations that describe the measurement and does not depend specifically of the sources of uncertainty considered.

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Next, we try to add a cover layer (also the FR4 **dielectric** layer) on the MA in front of the metallic resonator with diﬀerent thicknesses to continuously reduce the absorbing frequency. Our previous researches [20, 21] show that the added cover layer would contribute to decreasing the operating frequency. As shown in Fig. 3(b), a moderate reduction of the absorbing frequency is clearly indicated. This is because the added cover makes a higher background **dielectric** **permittivity** around the metallic resonator. However, it cannot decrease the absorbing frequency unlimitedly by increasing the thickness of the cover layer. As can be seen, when the thickness of cover layer increases to 0.5 mm, the absorbing frequency shift is quite small compared with the initial conditions of 0.1 mm or 0.2 mm.

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prove that it is better than its counterpart in industrial applications. It is more complicated and needs many sizes of waveguide to measure values of ε′ over a range of frequencies e.g. 2 - 20 GHz. The **dielectric** probe was found to be easy to use; sample preparation was also easier and the re-calibration facility made re-calibration at each temperature of measurement affordable. If the accuracy required for the values of ε′ and tan δ is not too significant, like in the case of microwave processing, then the **dielectric** probe can be chosen. The HP probe kit was designed for measuring the ε′ and tan δ values at elevated temperatures up to 200 o

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computed from scattering parameter measurements of microstrip lines with substrate as the material under test. This method requires the complicated procedure of sample fabrication and works well only when the transition effect of coax-to-microstrip is small, means the approximate substrate **permittivity** should be known before the measurement so that the cell can be designed to have a characteristic impedance of 50Ω. Lee et. al. [5] proposed two-microstrip line method for the measurement of the **dielectric** constants of substrates. According to them, **dielectric** property of material can be estimated if it is the substrate of a microstrip line, which is not easy, as it is difficult to deposit the metal tracks on polymer, as in our case.

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like the effective plasma frequency for periodic arrays of very thin metal wires [7]. Although the differences between models (4) and (5) have been analyzed in-depth [6, 8], up to now there are no simple analytic expressions for the **permittivity** components, which can predict both results as well as the crossover between them. In principle, the two regimes could be described within the effective medium approach proposed by Rytov [4]. However, the calculation of the effective **permittivity** would require the numerical solution of the exact dispersion equation, especially in the case of electromagnetic modes propagating along the z axis [4] and having a low-frequency gap in their photonic band structure.

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the measurement of the **permittivity**. The parallel plate capacitor method involves sandwiching of a **dielectric** material (agricultural sample) between two plates to form a capacitor. In the present work, a parallel plate capacitor (cell) with plate area 100 X 10 -4 m 2 and separation distance 10 -2 m has been constructed for the measurement of **permittivity**. Since capacitor is a physical device, it has constant plate surface area (A) and distance between the plates (d). Changes in its capacitance are then dependent only on **dielectric** properties of the material placed between the plates. Converting a capacitor into a **permittivity** sensor is practically quite simple, the material to be tested is placed between the capacitor plates as the **dielectric**, as shown in Figure 1.

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