Equivalent Permittivity Research Articles

Theoretical analysis of wide-angle metamaterial absorbers based on equivalent medium theory

In the past decade, most of researchers have been devoted to broadening the bandwidth of absorber. There are few researches on how to achieve wide-angle absorbing materials by detailed theoretical analysis and design guidance. It is still difficult to design wide-angle absorbers. In this paper, based on the equivalent medium theory, the reflectivity of the metamaterial absorber with a single-layered medium backed with metal reflector is analyzed in detail. Starting from the basic electromagnetic theory, the reflection coefficient of the absorber under transverse electric(TE) plane wave and transverse magnetic (TM) plan wave irradiation are derived. And the equivalent electromagnetic parameters of realizing the wide-angle absorbing effect are analyzed, which provide a theoretical basis for designing the wide-angle metamaterial absorber. The theoretical analysis results show that the equivalent electromagnetic parameters required for the medium to achieve low-profile and wide-angle absorbing effect are mainly related to the equivalent permeability and have little relationship with the equivalent permittivity. Moreover, the equivalent electromagnetic parameter value for achieving ultra-wide-angle absorber under TE wave and that under TM wave irradiation are different from each other. In other words, the anisotropic metamaterial with appropriate equivalent permeability has the potential to be used to design the ultra-wide-angle absorbers which are not sensitive to TE waves nor TM waves. In addition, in order to find the theoretically achievable widest absorbing angle value under TE wave and TM wave irradiation, the reflection coefficients at all angles must be less than or equal to –10 dB to obtain the relationship among the equivalent electromagnetic parameters, thickness and angle. The results show that the theoretically achievable widest absorbing angle value is 86.56° under TE wave and TM wave irradiation. The designer can choose the corresponding thickness and permeability from the data obtained from the analysis according to the design requirements. The narrow-band absorbers have limited applications. Therefore, in this paper we also theoretically analyze the values of the equivalent electromagnetic parameters for ahcieving wide-band and wide-angle absorbing materials, and make theoretical verification. The results show that the wide-band and wide-angle absorber can be achieved theoretically, while the equivalent electromagnetic parameters of the medium vary with frequency as some special curves indicate. Although this method is based on the equivalent medium theory and has no direct relationship with the actual structure, it does provide theoretical guidance for designing the wide-angle absorbers.

Equivalent Planar Lens Ray-Tracing Model to Design Modulated Geodesic Lenses Using Non-Euclidean Transformation Optics

This article describes a design procedure that enables a time-efficient evaluation of the focusing properties of modulated geodesic lenses using ray tracing on the equivalent gradient-index planar lens. The method uses transformation optics to define the equivalent planar relative permittivity distribution of axially symmetric surfaces and a ray-tracing model to evaluate the phase distribution in the aperture of the lens. This approach is of interest to optimize modulated geodesic lenses having polynomial profiles, reducing their height while preserving their wideband behavior and wide angular focusing properties. The approach is validated with a specific lens design. The profile is optimized at 30 GHz, while the focusing properties are monitored over the complete Ka up-link frequency band allocated to satellite communications (i.e., 27.5–31 GHz). The manufactured prototype produces 21 beams equally spaced every 7.5° over the extended angular range of ±75°. The ray-tracing model results are compared in detail with the corresponding full-wave model results and experimental data. The manufactured design has return loss better than 15 dB over a fractional frequency bandwidth larger than 30%, in line with the predictions. Excellent scanning properties are demonstrated over an angular range of ±60° with scan losses below 1 dB and good pattern stability, including on sidelobe levels. A height reduction by a factor of 4, when compared to a conventional geodesic lens, is demonstrated with this specific design.

Research Status and Design Method of Slow Wave Transmission Lines

Abstract In this paper, the research status and implementation methods of slow wave transmission lines are analyzed. Slow wave transmission lines are distinguished from other planar artificial transmission lines by the positive and negative values of equivalent permittivity and permeability. On this basis, the realization method is summarized through the analysis of equivalent dielectric constant and permeability. The methods of multi-layer dielectrics, periodically loaded capacitors (inductors or branches), cascaded cells and defective ground structures are summarized to increase the value of e and μ, so as to reduce the phase velocity of electromagnetic wave and realize slow wave transmission line. It provides a reference for the design and application of slow wave transmission lines.

Microwave Resonator for Eye Tracking

This article presents a novel microwave resonator for eye tracking. The system is implemented using coplanar waveguide technology and consists of two identical configurations with a pair of mirror-symmetrical open complementary split-ring resonators. These two sensors are combined with a wearable device placed on the eye and glass frame corners. The proposed evaluation uses two uncoupled and separate reflection magnitudes for differential cross modes. Each sensor has two resonance frequencies, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{L}$ </tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$f_{H}$ </tex-math></inline-formula> , to detect horizontal and vertical eye sweeping, respectively. As the user’s focus sweeps left to right or up and down with the wearable device, the asymmetrical conditions of the eyelid and cornea enhance the variation in differential reflection magnitude. The paired sensors provide information for tracking eye action. By applying the resonator perturbation theory, the eyelid and eye cornea locations above the planar resonator location were analyzed using the equivalent permittivity and conductance loss relationship, respectively. The experimental results indicate that the resonator tracker can detect relative changes in eye gaze from 50° to 130° horizontally (average 8.81-dB variation) and from 40° to 140° vertically (average 9.43-dB variation). These eye sweeping directions, thus, connect at 90°. Initial calculations reveal that the optimal eye tracking function is achieved and that the tracking method is suitable for individual users.

Equivalent permeability and permittivity of Sm substituted Mg–Cd ferrites for high-frequency applications

The effects of Sm3+ ion substitution on the magnetic and dielectric properties of Mg ferrites (Mg0.8Cd0.2Fe2-xSmxO4) with 2.5 wt% Bi2O3 were investigated for use as high-frequency antenna substrates. Various concentrations of Sm3+ ions (x = 0.00, 0.02, 0.04, 0.06, 0.08 and 0.10) were employed to modify the permeability (μ′) and permittivity (ε′) of the ferrites. Experimentally, the composites synthesized using the conventional solid-state reaction method exhibited equal μ′ and ε′ (x = 0.10, μ′ ≈ 23H/m, ε′ ≈ 25 F/m) over a long frequency band covering 1 MHz–100 MHz. Low loss tangents (dielectric loss tanδε≈ 0.004 and magnetic loss tanδμ≈ 0.038) were also obtained over the same frequency range. Furthermore, a saturation magnetization of up to 24.45 emu/g and coercivity of up to 36 Oe were achieved when x increased to 0.10, indicating that the magnetization of the samples was enhanced. The excellent properties obtained in the Sm3+ substituted Mg ferrites suggest that they could be promising candidates for modern high-frequency antenna substrates.

Remarkable performance improvement of copper phthalocyanine organic field-effect transistors with polymeric bilayer gate insulator

CuPc organic field-effect transistors (OFETs) were fabricated based on bilayer gate insulator consisting of polyvinyl alcohol (PVA) and methyl methacrylate co glycidyl methacrylate (P(MMA-GMA)). The complementary property of two polymer materials overcomes the drawbacks of each other, and then improves the dielectric properties of the composite insulator: a higher equivalent permittivity(k ~ 6.0), hydrophobicity, ultra-smooth (1.47 Å) and good compatibility with CuPc. The crystal quality of CuPc film have been improved effectively. As a result, a carrier mobility of 6.55 × 10−2 cm2/Vs and a threshold voltage of −3 V have been obtained. The Ids has increased double with the same insulator thickness.

Transient response predication of nickel coated carbon fiber composite subjected to high altitude electromagnetic pulse

Metal materials are gradually replaced by fiber reinforced composite and the electromagnetic shielding capacity needs to be quantitatively evaluated, especially for intense electromagnetic pulse. Equivalent permittivity and permeability of fiber composite are calculated by multi-scale model based on finite element method, which results are close to theoretical values. Transverse electrical conductivity is obtained by contact network model and numerical results are in agreement with experimental data. The propagation characteristics of high altitude electromagnetic pulse penetration through fiber reinforced composite is investigated by numerical method based on electromagnetic wave theory in time domain. It is found that fiber orientation and stacking sequence can affect the shielding capacity of fiber composite. Composite laminates stacked alternately at 45 degrees satisfy the shielding requirement when high altitude electromagnetic pulse incidence at any angle. Nickel-coated carbon fiber composite laminate show better shielding than that of carbon fiber composite laminate.

Microwave Three-Dimensional Capacitive Stubs

Introduction. Microstrip filters are widely used in a variety of radio-electronic systems, including telecommunications. Low frequency filters (LPFs) are constructed on the basis of quasi-lumped inductances and capacitances. Quasi-lumped capacitances are performed as microstrip sections with a wide signal conductor or open stubs. Traditional quasi-lumped elements are two-dimensional (2D). Three-dimensional (3D) quasi-lumped elements have 1.5 to 4 times greater reactivity values. The purpose of the paper is to analyze 3D-stubs charateristics. Capacitive 3D-stub transfer characteristic. The 3D-stub is a deaf metalized hole. In the presented paper hole is a square with rounded corners. Dependencies of 1D-model parameters of 3D-stub are shown. From a comparison of 3D- and 1D-transfer characteristics of the 3D-stub it is shown that the 3D-stub in the first approximation can be simulated by a 1D-model in the form of a long line stub. Influence of parasitic inductance on stub notch frequency. For a 1D-model, the stub notch frequency is determined by a quarter-wave condition of it’s length. Stub’s T-junction brings in parasitic reactivities. The parasitic inductance and stub form a series oscillatory circuit. The resonance frequency of this circuit is equal to stub notch frequency. Since traditionally this inductance is negative, the notch frequency increases and stub and LPF transfer characteristics slope decreases. In order to reduce the inductance influence for stub and line contact it is suggested to use a small contact pad. 3D-stub notch frequency and parasitic inductance dependences. The dependences of the notch frequency and parasitic inductance on the 3D-stub heterogeneity depth and contact pad length are analyzed. According to simulation results for a variant with a contact pad inductance values can be not only negative, but also positive. If inductance is positive, notch frequency is less than according to quarter-wave condition. In this case, stub and LPF transfer characteristics slope is higher compared to quarter-wave condition. Discussion of the results. With an increase of the 3D-stub heterogeneity depth from 0.5 to 1 mm, its wave impedance is less in 1.4 ... 3.5 times compared to 2D-stub, and the capacity is greater in 1.6 ... 4.1 times. Contact pad between the stub and line allows to optimize the stub parameters from the condition of the required transfer characteristics slope. Conclusion. 3D-stub has significantly better parameters than 2D-stub. Since the LPF requires the specified capacitance values, depending on the 3D-stub inhomogeneity depth, the area of the 3D-stub is less than 1.6 ... 4.1 times. The 1D-model of the 3D-stub allows to characterize the stub by equivalent wave impedance and relative dielectric permittivity and can be used as the first approximation model for the design and simulating of microstrip LPFs based on capacitive 3D-stubs.

Plasmonic Core-Shell Silicon Carbide-Graphene Nanoparticles.

We demonstrate the synthesis of silicon carbide nanoparticles exhibiting monolayer to few-layer graphene coatings and characterize their optical response to confirm their plasmonic behavior. A multistep, low-temperature plasma process is used to nucleate silicon particles, carbonize them in-flight to give small silicon carbide nanocrystals, and coat them in-flight with a graphene shell. These particles show surface plasmon resonance in the infrared region. Tuning of the plasma parameters allows control over the nanoparticle size and consequently over the absorption peak position. A simplified equivalent dielectric permittivity model shows excellent agreement with the experimental data. In addition, optical characterization at high temperatures confirms the stability of their optical properties, making this material attractive for a broad range of applications.

Co-substituted LiZnTiBi ferrite with equivalent permeability and permittivity for high-frequency miniaturized antenna application

Abstract In the present work, a Co-substituted LiZnTiBi (Li0.43Zn0.27CoxTi0.13Fe2.167-xBi0.003O4) ferrite with equivalent permeability and permittivity was prepared by a low-temperature sintering method. In detail, the LiZnTiBi ferrite with high permeability was obtained by a solid phase method. Next, different mass of Co2O3 (x = 0.100, 0.125, 0.150, 0.175 and 0.200) were added to reduce permeability (μr’) and enhance cut-off frequency (fr) of the ferrite. Results indicated that the Co-substituted LiZnTiBi ferrite with equivalent permeability and permittivity (μr’ = er’ = ∼12.3) was obtained when additive amount of Co2O3 (x) is around 0.150. Meanwhile, the cut-off frequency (fr) of the ferrite is more than 500 MHz. Also, the influences of Co2O3 additive on the microstructure and phase structure of the LiZnTiBi ferrite have been investigated and discussed. SEM images indicated that the Co-substituted LiZnTiBi ferrites possess uniform and compact grains (average grain size is ∼1 μm). XRD patterns demonstrated that the LiZnTiBi ferrite material has a pure spinel structure. Rietveld refinement of XRD proved that Fe3+ is substituted by Co3+. And energy dispersive spectrometer (EDS) result indicated that the Co element is existed in ferrite grains. Such a low-temperature sintering ferrite substrate material with equivalent permeability and permittivity at high frequency (@500 MHz) should also be an alternative material for microwave devices, especially for miniature antenna.

Metamaterial inspired THz antenna for breast cancer detection

Metamaterial inspired Terahertz (THz) antenna for breast cancer detection proposed in this paper. The proposed antenna consists of a simple rectangular patch configuration integrated with Complementary Split Ring Resonator (CSRR). The design equations along with the equivalent circuit and permittivity calculations also presented in this paper. The experimental technique for detection of tumor in human breast model by the simulation technique also presented. The proposed metamaterial inspired antenna operates at 1 THz frequency with 20 dBi of gain. Its design evolution process, parametric study, and results such as farfield radiations also presented in this paper.

TiO2 tailored low loss NiCuZn ferrite ceramics having equivalent permeability and permittivity for miniaturized antenna

Abstract Matching permeability and permittivity, low magnetic and dielectric loss tangent and high refractive index play a critical role in designing a miniaturized antenna with high performance. Here, TiO2 was introduced into Ni0.368Cu0.2Zn0.432Fe1.96O3.94 ferrite ceramic to adjust equivalent permeability and permittivity via suppressing grain growth. The effects of concentration of TiO2 and sintering temperature on microstructure, complex permeability and permittivity, DC resistivity, and saturation magnetization of NiCuZn ferrite ceramics were investigated. SEM results indicated that TiO2 obviously retarded grain growth to achieve uniform and dense NiCuZn ferrite ceramics with small grains (∼0.60 μm). Also, it was found that the addition of TiO2 can enhance the DC resistivity and reduce loss factors via increasing in fraction of grain boundaries. Furthermore, different sintering temperatures were chosen to control the matching permeability and permittivity and to promote densification. At last, a NiCuZn ferrite with the equivalent permeability to permittivity (μ′ = 12.90, e′ = 12.76, @ 40 MHz), very low loss factors (tanδμ = 0.050, tanδe = 0.00022, @ 40 MHz), and high DC resistivity was obtained sintered at 1000 °C when 16 wt% TiO2 was added. Thus, NiCuZn ferrite ceramics doping TiO2 show a lot of potential to be used as a substrate material in miniaturizing antenna for futuristic electronic devices.

Optimizing design on the wide-band absorbing plasma using fluorescent lamps

The plasma was generated using the fluorescent lamp array and the generating principle was the glow discharge mode. The electron density and angular frequency of the plasma could be adjusted with the electronic ballast by changing the lamp input power. The microwave measurement system was built to get the transmission parameter as a function of the lamp input power and the frequency. The transmission parameter expression as functions of the plasma electron density and the electron collision frequency was deduced, and the optimized function could be established. Then the electron density and the electron collision frequency could be fit using a nonlinear least square interpolation method in the MATLAB software kit. The effective permittivity and permeability of the equivalent plasma absorber could be calculated, the real permittivity decreased and the imaginary permittivity increased as the lamp power increased. As the lamps filled with plasma were aligned with different duty ratio, the reflection and transmission parameter could be simulated in the Computer Simulation Technology (CST) software, and the equivalent permittivity was calculated. Finally, the genetic algorithm was used to optimize the structure of the plasma in two cases (lamps aligned adjacently or dispersed with space) as the reflection loss (RL) was set less than −10 dB in 1–8 GHz. The results showed that as the lamps were distributed adjacently, the lamp powers were of two kinds and the total layer number was 28, the minimum RL was −47.1 dB at 5.1 GHz. While as the lamp power was the same 25 W and the lamp layer alignment was different, the minimum RL was −38.2 dB at 5.7 GHz, the total layer number was only 9 and much smaller than that in the first case.

Equivalent electromagnetic parameters for microwave metamaterial absorber using a new symmetry model**Project supported by the National Natural Science Foundation of China (Grant Nos. 11574122 and 51731001), the Fundamental Research Funds for the Central Universities, China (Grant No. kzujbky-2017-k20), and the Innovation Special Zone Project of National Defence Science and Technology, China.

Transmission line theory uses the complex nature of permeability and permittivity of a conventional magnetic absorber to evaluate its absorption properties and mechanism. However, because there is no method to obtain the electromagnetic parameters of a metamaterial-absorber integrated layer (composed of a medium layer and a periodic metal array), this theory is seldom used to study the absorption properties of the metamaterial absorber. We propose a symmetry model to achieve an equivalent complex permittivity and permeability model for the integrated layer, which can be combined with the transmission line theory to calculate metamaterial absorption properties. The calculation results derived from both the transmission line theory and the high-frequency structure simulator are in good agreement. This method will be beneficial in practical investigations of the absorption mechanism of a metamaterial absorber.

Influence of microstructure on magnetic and dielectric performance of Bi2O3-doped Mg Cd ferrites for high frequency antennas

Abstract The effects of microstructure on the magnetic and dielectric properties of Mg0.6Cd0.4Co0.05Fe1.95O4 spinel ferrites with the addition of 2.5 wt% Bi2O3 are investigated mainly for high frequency applications. The measurement results reveal that composites processed via low temperature co-fired ceramic (LTCC) technology at different sintering temperatures (900 °C, 920 °C, 930 °C, and 940 °C) possess excellent equivalent permeability (μ′) and permittivity (e′) (at 940 °C, μ′≈e′≈25), over a long frequency range from 1 to 100 MHz. The results also indicate that densification sintering results in ultra low dielectric loss tanδe and magnetic loss tanδμ (tanδe≈0.003, tanδμ≈0.035). In addition, the samples present enhanced magnetic properties, such as high saturation magnetization (approximately 37.94 emu/g) and appropriate coercivity (approximately 60.5 Oe) at 940 °C. This research presents the prospect of wide application of Mg Cd ferrites in high frequency applications.

Bi2O3 adjusting equivalent permeability and permittivity of M-type barium ferrite for antenna substrate application

In this paper, Co-Ti doped M-type barium ferrite [Ba(CoTi)1.22Fe9.56O19] was prepared at low temperature (925 °C) in O2 atmosphere with different amounts of Bi2O3 sintering additive (x = 5–14 wt%). XRD showed superfluous Bi2O3 additive led to BiFeO3 phase formation, which is the important factor to adjust properties of material. SEM revealed that the grain size diminished gradually. For magnetic and dielectric properties, with different amounts of Bi2O3, saturation magnetization (Ms) decreased and coercivity (Hc) gradually increased. Complex magnetic permeability and dielectric permittivity presented excellent regularity, and the equivalent permeability and permittivity were obtained when x = 5 wt%. At x = 5 wt%, the real part of permeability (μ′) and permittivity (ε′) were about 18.3 at a range of 10 MHz–1.0 GHz, the magnetic loss (tan δμ) was about 3.4 × 10−2, and the dielectric loss (tan δε) was about 2.8 × 10−3. It showed that Bi2O3 not only lowered the sintering temperature of ferrite, but also adjusted the magnetic and dielectric properties, and the material has potential to apply for miniaturizing efficient antennas at high frequency.

Dielectric properties of wet steam based on a double relaxation time model.

The last stages of most steam turbines operate in wet steam, resulting in water erosion of the rotor blades and the reduction of turbine efficiency. Accurate measurement of steam wetness is the key to ensure an efficient and stable operation of steam turbines. The equivalent complex permittivity model of wet steam was established by Maxwell-Wagner non-homogeneous dielectric theory, and the complex permittivity distribution of frequency and temperature changes of saturated water, dry saturated steam, and wet steam was derived. The measurement experiments verified the above properties of dry saturated steam and wet steam. The complex permittivity of the wet steam is similar to that for the dry saturated steam. The real part increases with increasing frequency and temperature. When the frequency is large or the temperature is low, the real part approaches 1. The imaginary part increases first and then decreases with the increase of frequency. In addition, with the increase of temperature, the imaginary part becomes larger. When the temperature is low, the imaginary part is close to 0, which is independent of the frequency.

Virtual cathode induced in Rb2Ti2O5 solid electrolyte

Rb2Ti2O5 (RTO) has recently been demonstrated to be a solid electrolyte, producing colossal capacitance when interfaced with metals. In order to understand the mechanisms leading to such colossal equivalent permittivity (up to four orders of magnitude above state-of-the-art values), the charge distribution in RTO is a key feature to be investigated. In the present article, this charge distribution is probed using the pressure-wave-propagation method, in devices made of RTO single crystals or polycrystals sandwiched between two metallic electrodes. Remarkably enough, in both types of samples, negative charges are found to accumulate inside RTO, near the anode, while the electric field near the cathode remains zero. This proves that the ionic carriers are majoritarily negatively charged and provides an explanation for the colossal capacitance. The latter takes place only at the anode while the cathode is virtually shifted into the solid electrolyte.

Compact Equal-Width Equal-Length Phase Shifter With Slow-Wave Half-Mode Substrate Integrated Waveguide for 5G Applications

The emerging fifth-generation (5G) wireless and mobile communications demand high-performance phase shifters to enable the multi-channel transmit/receive systems with phase control ability. In this work, a size-miniaturized wideband phase shifter based on slow-wave half-mode substrate integrated waveguide (SW-HMSIW) is presented. The proposed SW-HMSIW is consisting of conventional HMSIW section and periodically-patterned non-uniform microtrip polyline unit cells. Patterning polyline unit cells in HMSIW can effectively enhance the product of the equivalent permittivity and permeability of SW-HMSIW, so that the slow-wave effect can be exhibited and its associated size reduction will be further achieved. Moreover, lengths and widths of segments of the proposed polyline unit cell can influence the equivalent permittivity and permeability of the SW-HMSIW, and consequently change its phase constant and cutoff frequency. Hence, for a SW-HMSIW with a fixed physical length, an electrical length variation, i.e, phase shift, can be achieved as segments of the polyline employ various lengths or widths. Based on this principle, a wideband equal-width equal-length SW-HMSIW phase shifter is implemented. Measured results are in good agreement with simulated ones, with a phase shift of 90.5 ± 3 degree and a fractional bandwidth of 43.0% achieved. Compared with some similar reported works, the proposed one shows a size reduction more than 80% as well as good magnitude and phase deviations performance. Moreover, its miniaturized size and equal-width equal-length structure make it suitable for the complex multi-channel modules and networks of the 5G applications.

PARAMETERS OF EIGENWAVES AND EQUIVALENT PARAMETERS OF PERIODICAL BRAGG STRUCTURES

The problem of representing a periodic Bragg structure by an equivalent homogeneous layer is under consideration. The relationship of the parameters of such layer and eigen parameters of the periodic structure is examined. For such relationship, the dependence upon frequency for some specific parameters of a layered dielectric structure is analyzed. An approach that makes it possible to obtain physically consistent values of the equivalent permittivity and permeability of the periodic Bragg structure is presented.