Complex Permittivity Of Materials Research Articles

Measuring and Extracting the Complex Permittivity of Porous Ceramic Materials in the Y-Band

ABSTRACT Porous ceramics find extensive applications in aerospace and other fields, and the measurement of their electromagnetic parameters is helpful in optimization of material properties and device designs. In this paper, a free-space 8f quasi-optical measurement system consisting of a vector network analyzer, a 325–500 GHz frequency expansion module, and four off-axis parabolic mirrors have been established to measure the transmission parameter S21 of porous ceramics. The complex permittivity was extracted according to the Newton-Raphson iterative method utilizing its measured S21 parameters based on flat mode. The porous ceramics with different porosity and density were measured and the relationships between their permittivity and porosity and density was established, respectively. These results are beneficial to the quality evaluation and application design of porous ceramic materials in the aerospace field.

High-Sensitivity Differential Sensor for Characterizing Complex Permittivity of Liquids Based on LC Resonators.

This paper proposes a high-sensitivity microstrip differential sensor for measuring the complex permittivity of liquids. The prototype of the differential sensor was formed by cascading two LC resonators on a microstrip transmission line based on stepped impedance. A strong electric field was found to be distributed in the circular patch of the LC resonator; therefore, a cylindrical micropore was set in the center of the circular LC resonator to measure the dielectric sample, which maximized the disturbance of the dielectric sample on the sensor. By optimizing the size of the circular LC resonator, a high-sensitivity sensor circuit was designed and manufactured. The complex permittivity of the test sample was calculated by measuring the transmission coefficient of different molar concentrations of ethanol-water solutions. The experimental results show that the designed differential sensor can accurately measure the complex permittivity of liquid materials with an average sensitivity of 0.76%.

Anisotropic complex permittivity measurement using a microstrip air line

Abstract A microstrip air line system for measuring the complex permittivity of anisotropic materials in the band from 0.3 to 1 GHz is proposed. The multireflect-thru method is used to calibrate the measurement system in the whole band with a single microstrip air line without suffering from the limited space resolution of time-gating technique. During the measurement, the material under test (MUT) is placed both above and below the strip. With this deployment, the TEM mode propagates along the microstrip in the MUT. Therefore, it is possible to measure the anisotropic permittivity. Since a small portion of the electric field is parallel to the ground plane around two edges of the strip, the extracted property is not purely along one direction. To obtain higher accuracy, with the help of linear combination, the properties along two directions are disentangled by two measurements. For validation of the method, an isotropic material and an anisotropic material in the microstrip air line were simulated and their permittivities were extracted from simulation results. An anisotropic material polytetrafluoroethylene (PTFE) and two anisotropic materials, FR4 and honeycomb absorber, were measured. The results of PTFE show that there is a maximum relative error of 1.4% and 2.5% for the permittivity extracted from simulation and measurement, respectively. The validity and the accuracy of the system for measuring anisotropic materials are verified by the simulation and measurement results.

Innovative and Cost-Effective Fabrication Technique for Dielectric Composite Material

In this paper, the fabrication process of epoxy resin and nanocomposite barium titanate using a cost-effective apparatus is presented along with measurements of complex permittivity. The material is prepared by mixing epoxy resin and barium titanate powder which has high permittivity. Measurement of complex permittivity of materials is performed using a waveguide technique in the G-band with a frequency between 4 and 6 GHz. The results are then compared with the previous works that use advanced and precision instrumentation. The results indicate that the material’s permittivity, determined using our proposed technique, performs admirably. Specifically, at a frequency of 5 GHz, the permittivity is 7.32 with a loss tangent of 0.025 for a filler concentration of 20%. These values not only meet but also closely match those obtained with high-end equipment. Therefore, the proposed technique could be a good potential as an alternative technique for dielectric material preparation which is suitable to be used as a substrate antenna.

Resonant cavity method based on RF measurement and simulation for measuring complex permittivity or permeability of RF absorbing materials

Accurate measurement of complex permittivity and/or permeability of radio-frequency (RF) absorbing materials is essential to predict the performances of higher-order-mode damping in damped accelerating cavities or in vacuum chambers. We propose an improved resonant cavity method that can be used as a complement to the widely used Nicolson–Ross–Weir method for measuring the RF characteristics of materials. The conventional resonant cavity method is based on the cavity perturbation theory. However, the measurements are inaccurate when losses in the materials are large. The improved method we propose determines the complex permittivity or permeability of materials from the measured resonant frequencies and Q factors based on eigenmode simulations. Because the reliability on the eigenmode calculation for RF cavities with lossy materials has become sufficiently reliable, determination of complex permittivity and permeability can be achieved using such a simulation software. We demonstrate this method using ferrite HF70 (TDK Corp.), which is useful for RF absorbers in damped accelerating cavities or in vacuum chambers.

Characterizing Complex Permittivity of Thin Materials by Free Space Transmission and Reflection Coefficients

Characterizing Complex Permittivity of Thin Materials by Free Space Transmission and Reflection Coefficients

Surface modification of carbon fibers for enhanced electromagnetic absorption

The exceptional chemical and physical properties of carbon fiber make it highly promising for utilization in the field of wave-absorbing materials. However, the low magnetic loss and high complex permittivity of conventional carbon fiber materials limit their use in wave-absorbing materials. Hence, this study presents the synthesis of a FeCoNi/N-doped carbon coating/SCF composite with a distinctive microstructure by an in-situ reduction process. The successful formation of this unique architecture was confirmed through various characterization techniques. The composite material displayed both magnetic and dielectric characteristics. It showed an effective bandwidth spanning 14.77 GHz with a reflection loss (RL) of − 10 dB or less. In addition, it attained the minimum RL value of − 50.5 dB at a distance of 3.5 mm. The composite material is hypothesized to show great potential in electromagnetic wave absorption.

High-Temperature Measurement Technology for Microwave Surface Resistance of Metal Materials

The resonant cavity method is a commonly used method for high-temperature testing of the complex permittivity of dielectric materials. When a resonant cavity is used for high-temperature testing, the microwave surface resistance of the cavity metal material will deteriorate due to factors such as oxidation reaction and thermal fatigue, resulting in a decrease in testing accuracy and repeatability. Therefore, when designing a high-temperature resonant cavity, the temperature response characteristics of the microwave surface resistance of the cavity metal material should be obtained in advance. In this paper, a high-temperature measurement method of microwave surface resistance of metal materials based on a separate cylindrical resonator is proposed, a mathematical model of microwave surface resistance inversion based on the resonator quality factor is established, and a high-temperature measurement system of microwave surface resistance is integrated. The reliability of the proposed method and system is verified through simulation and experiment. The measurement frequency covers 7-18 GHz, and the maximum test temperature reaches 500°C. Systematic error of microwave surface resistance measurement at room temperature is less than 3%.

Study on effect of barium titanate concentration in epoxy-based composite towards dielectric material properties

The properties of dielectric material can be controlled either by combining new composite materials or by altering the composition between the filler and matrix materials. This paper focuses on the development of epoxy-barium titanates composites at different filler concentrations and their relationship with dielectric properties. Epoxy resins are frequently utilized for their affordability, ability to withstand high humidity and resistance to chemicals. Meanwhile, barium titanate is recognized for its high permittivity. When these two materials are combined, they can create a high permittivity value that is advantageous for the design of small and compact antennas. In this work, five samples of different epoxy resin-barium titanate composites are made, at five different volume ratios of filler (5 vol%, 10 vol%, 15 vol%, 20 vol%, and 25 vol%). A low volume of filler results in a lower permittivity value due to the quantity of filler being less than the volume of the matrix base. Adding nano powder barium titanate to the matrix base can increase the permittivity of the composite material. However, when the volume of filler is too high, it may agglomerate, which can adversely affect the electrical performance. In this work, the complex permittivity of composite materials of epoxy resin and filler barium titanate is measured between 4 and 6 GHz using the waveguide technique. The results showed that the permittivity of epoxy-barium titanate grows continuously as the filler volume increases.

Estimating complex dielectric permittivity of materials by the frequency dependences of reflection and transmission coefficient magnitudes in the microwave range

Electromagnetic waves of the microwave range are an effective tool for solving problems of non-destructive testing and diagnostics as applied to dielectric, semiconductor, and composite materials, ferrite products. An algorithm is suggested for estimating the complex permittivity of non-magnetic materials by the frequency dependences of reflection and transmission coefficient magnitudes during the interaction of electromagnetic waves in the microwave range with a sample in the form of a plate located in the cross section of a closed rectangular waveguide. Statistical analysis methods are applied to evaluating the errors arising during the application of this algorithm due to imperfect matching of the waveguide measurement path with the receivers and generator of the scalar circuit analyzer. It is shown that the proposed algorithm using the results of measuring reflection and transmission coefficients in a wide frequency range can significantly reduce the influence of frequency-dependent measurement errors on the accuracy of complex permittivity estimation. An additional advantage of the algorithm is that its implementation does not require vector network analyzers, which are very expensive.

A Novel Parallel-Plate Dielectric Resonator Method for Broadband Complex Permittivity Measurement in the Millimeter-Wave Bands

This article proposes a novel measurement method based on parallel-plate dielectric resonator (PPDR) for determining complex permittivity of low-loss dielectric materials over a wide frequency range. Two 1.0-mm coaxial probes are placed symmetrically as a coupling structure in the center of top and bottom of the PPDR, and only the TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\mathrm{0np}}$</tex-math> </inline-formula> resonant modes will be selectively excited. For each value of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$p$</tex-math> </inline-formula> , the resonator will operate over a specific frequency range, within which there are usually multiple frequency points available for testing. Based on this unique feature, dielectric constants of cylindrical or disk-shaped samples can be measured from less than 20 up to 110 GHz by utilizing TM <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$_{\mathrm{0np}}$</tex-math> </inline-formula> high-order modes. Rigorous analysis of the PPDR based on the electromagnetic field matching method is carried out and verified numerically. Moreover, the PPDR method is further validated experimentally by measuring several specimens processed from well-known materials, the main sources of measurement uncertainty are also analyzed in detail, and some recommendations are made accordingly. The results show that the PPDR method can perform high-accuracy measurement of complex permittivity in the millimeter-wave bands, even when the sample thickness exceeds the maximum value limited by the current state of the art.

Test technique for arbitrary length high dielectric sheet materials based on perturbation method

In this article, a very effective method is proposed to measure the permittivity of sheet materials with a high dielectric constant and loss. To meet the constraints of the perturbation method, controlling the magnitude of the perturbation by reducing the sample size is necessary. However, this will cause significant changes in the polarization field within the sample and, consequently, affects the accuracy of the calculations. To solve the problem, the effects of the polarized electric field and the non-uniformity of the electric field in the resonant cavity have been considered and an empirical model is developed based on this using curve fitting techniques. Taking the optimized depolarization factor into the resonant perturbation equation, the dielectric properties of arbitrary length of the sample can be accurately calculated when the frequency shift and the quality factor variation are known. Then, the method is validated and analyzed by numerical simulations. Finally, practical tests are carried out on a variety of materials at different sizes, and the results are stable and in excellent agreement with the simulated ones. Therefore, we can conclude that the method can accurately measure the complex permittivity of high dielectric sheet materials.

A method of measuring complex ermittivity of nonmagnetic materials and selecting its initial value based on iterative inversion

Complex permittivity is an important parameter to reflect the macroscopic electromagnetic properties of material. The selection, design, and application of related materials and devices in the electromagnetic field must be based on the electromagnetic parameters of materials in the working frequency band. The numerical iterative method is an important method to inverse and calculate the complex permittivity of material. But there always exists a difficult problem that the initial value of iteration is difficult to give accurately. Based on the relationship between the complex permittivity and the reflectivity of absorbing material, an initial value selecting method for iteration to invert permittivity of absorbing material is proposed in this work. For absorbing materials with arbitrary thickness at a certain frequency, the complex permittivity must be near the complex permittivity of perfect matching layer. Therefore, the permittivity of perfect matching layer can be used as the initial value of the iterative algorithm. On this basis, a method of calculating the complex permittivity of monolayer absorbing material by using the reflection parameter is constructed. The experimental results show that the complex permittivity of lossy material can be calculated more accurately at the frequency with absorbing performance. However a great error can be caused at the frequency where the reflectivity is close to zero. Based on the iterative solution of the complex permittivity of single-layer absorbing material, a new method of measuring the complex permittivity of material is constructed by combining multi-layer absorbing materials to enhance full-band reflectivity. Given the electromagnetic parameters of other layer materials , the permittivity of absorbing materials and low-loss materials can be obtained accurately.

A modified AMC-based antenna sensor for contactless measurement of complex permittivity

The paper proposes a modified artificial magnetic conductor (M-AMC)-based antenna sensor for retrieving the complex permittivity of material under test (MUT). The antenna sensor measurement system is composed of a coplanar waveguide (CPW) antenna and a M-AMC structure. The M-AMC structure consists of a 3×3 array, and each unit cell is fabricated by two-layer dielectric substrates. The M-AMC unit cell is evolved from the traditional square unit one, and in each cell, four bent microstrip lines are embedded in the middle plane of M-AMC structure to connect the top square metallic patch through metallic holes. Compared with traditional AMC structure, the added bent microstrip line can increase the current path. Besides, four complementary split-ring resonators (CSRRs) are etched on the top plane of each unit to improve the density of electrical field. A large metallic patch covers the bottom plane of M-AMC. The resonant frequency of M-AMC structure is reduced a lot than the traditional one, which is beneficial to realize miniaturization. In measurement, the antenna is placed on the upper surface of M-AMC structure with an appropriate distance, and the MUT is placed on top plane of M-AMC. The MUTs with different thicknesses and complex permittivity will alter the resonant frequency and quality factor of the antenna sensor. Experiment is carried out to demonstrate the performances of proposed antenna sensor. An average sensitivity of 1.89 % is achieved and the maximum error is less than 3.516 % in extracting the real permittivity. All in all, the proposed antenna sensor has a potential superiority in the scope of material characterization.

Investigating Imbert–Fedorov shift at a planner interface of dispersive–dissipative dielectric–magnetic metamaterial

The main objective of this paper is to analyze the spatial Imbert-Fedorov shift (IFS) on a planar interface of dispersive-dissipative dielectric-magnetic metamaterial. Spatial IFS is calculated by utilizing the energy flux method. The Lorentz–Drude Model is used to calculate the complex permittivity and permeability of frequency-dependent material. The behavior of spatial IFS is examined in both lossy and lossless mediums of transmission. Furthermore, spatial IFS is analyzed by varying the losses of dispersive–dissipative dielectric–magnetic metamaterial. The impact of the resonance frequency is also observed in this manuscript. DPS metamaterial behaves like an ordinary material and highest positive IFS with value of 33λ is observed for lossless case. ENG and MNG metamaterials behave like the metal and negative shifts are observed with the order of −0.014λ and −2λ respectively for lossy case. Because of the backward travelling wave, the DNG metamaterial has a negative shift. IFS observed for Lossless DNG metamaterial is −15λ, which is larger than the ENG and MNG metamaterials.

Measurement of complex permittivity of liquids in the frequency range 100-1000MHz by using a re-entrant cavity.

For many liquid materials and biological media, their complex permittivity varies with frequency in the P-band (100-1000MHz). In this paper, a re-entrant coaxial cavity resonance test system with intensive multi-frequency points testing capability is designed for the P-band to realize the test of the complex permittivity of P-band materials. For this system, a test algorithm has been written, and on the basis of this system, a perturbation block has been designed, using stepper motors to control the up and down movement of the perturbation block to achieve frequency tunability of the cavity, enabling more P-band frequency test data to be obtained. The experimental results show that the system is suitable for testing the electrical parameters of P-band biological media and liquid materials and for testing solid materials in aerospace, electromagnetic shielding, and other fields where there is a great demand for P-band testing.

Complex permittivity measurement technique using metamaterial broadside coupled split ring resonator

A simple and effective method for the determination of complex permittivity of dielectric materials at microwave frequencies using a Broadside Coupled Split Ring Resonator (BCSRR) metamaterial structure is presented. A single BCSRR unit cell placed between the transmitting and receiving probes of a Vector Network Analyzer (VNA) is used as the test probe. Resonance frequencies and bandwidths of transmission curves, measured with and without the sample placed over the BCSRR test probe, are used to determine the real and imaginary parts of the complex permittivity by treating the BCSRR as an LC resonant circuit. Relevant equations connecting equivalent capacitance and resonance frequencies are derived from the basic equivalent circuit parameters of the BCSRR through a quasi-static analysis by considering the fringing fields in its vicinity, especially on the top and bottom. Accuracy of the theoretical formula derived for determining the complex permittivity using the BCSRR is verified through experiments and simulations.

Методы и средства для измерения комплексных диэлектрической и магнитной проницаемостей материалов на СВЧ

This paper describes methods and tools for measuring the complex permittivity and permeability of various materials in the range of 0.9 – 40 GHz. A list of equipment necessary for the practical implementation of methods for experimental evaluation of the complex permittivity and permeability (ε, μ) of various materials, as well as the coefficients R of reflection and T of the transmission of electromagnetic radiation through samples of materials, is proposed. In the measuring circuits, the vector network analyzer PNA-X N5244 is used. Six schemes are given for connecting standard horn antennas to a network analyzer. Three methods for measuring the complex permittivity and permeability by the values of the reflection coefficient and one method for the values of the reflection coefficient and the transmission coefficient are considered: waveguide method for measuring ε and μ by the values of the reflection coefficient; methodology for measuring ε and μ by the values of the reflection coefficient in free space; resonator technique for measuring ε and μ; a technique for measuring ε and μ by the values of the reflection and transmission coefficient in free space. A comparative analysis of the measurement results of images obtained at the installation equipped with a vector analyzer of circuits of Agilent PNA-X N5244A and a complex based on panoramic VSWR meters in the range of 8 – 38 GHz is carried out. The measurements carried out made it possible to test the proposed methods.

Determination of the Complex Permittivity of Materials by a Modified Resonator Method Based on the Theory of Small Perturbations Using a Resonator of the Reflective Type

Determination of the Complex Permittivity of Materials by a Modified Resonator Method Based on the Theory of Small Perturbations Using a Resonator of the Reflective Type

A Compact CSRR-Based Sensor for Characterization of the Complex Permittivity of Dielectric Materials

A sensor is proposed to characterize the complex permittivity of dielectric materials in a non-destructive and non-invasive way. The proposed sensor is based on a rectangular patch microstrip two-port circuit with a complementary split-ring resonator (CSRR) element. The slotted CSRR element of the sensor plays a key role in determining the electrical properties of the materials under test (MUT). The sensitivity analysis is determined by varying the permittivity of the MUT. The proposed sensor is simulated and analyzed using Ansoft HFSS software. A prototype was fabricated and measurements were made on two different samples of dielectric materials with complex permittivity values available in the literature. The simulated and measured results showed good agreement.