Ultra-thin Coating Materials Sensor Based on Constitutive Parameters Near-zero Media

This article presents an optimized microwave sensor for the non-contact measurement of complex permittivity and material thickness. The layout of the proposed sensor comprises the parallel combination of an interdigital capacitor (IDC) loaded at the center of the symmetrical differential bridge-type inductor fabricated on an RF-35 substrate (εr = 3.5 and tanδ = 0.0018). The bridge-type differential inductor is introduced to obtain a maximum inductance value with high quality (Q) factor and low tunable resonant frequency. The central IDC structure is configured as a spur-line structure to create a high-intensity coupled electric field (e-field) zone, which significantly interacts with the materials under test (MUTs), resulting in an increased sensitivity. The proposed sensor prototype with optimized parameters generates a resonant frequency at 1.38 GHz for measuring the complex permittivity and material thickness. The experimental results indicated that the resonant frequency of the designed sensor revealed high sensitivities of 41 MHz/mm for thickness with a linear response (r2 = 0.91567), and 53 MHz/Δεr for permittivity with a linear response (r2 = 0.98903). The maximum error ratio for measuring MUTs with a high gap of 0.3 mm between the testing sample and resonator is 6.52%. The presented performance of the proposed sensor authenticates its application in the non-contact measurement of samples based on complex permittivity and thickness.

A novel time domain measurement technique is proposed to facilitate the simultaneous measurement of electrical properties (complex relative permittivity) and geometrical parameters (thickness) of the material under test (MUT). The overall process is noninvasive and noncontacting, which uses the measured scattering data of the MUT in the equivalent time domain or spatial domain. The effective time domain scattering data are employed to detect the primary and secondary peaks of the overall reflection and transmission coefficients. To this end, a novel algorithm is proposed to obtain the complex permittivity and thickness of the MUT in terms of extracted reflection and transmission power peaks. From the practical point of view, the main advantage of the proposed scheme is that one avoids the complicated calibration procedure normally required to define the reference plane. For increasing the accuracy of the overall reconstruction process, an automated optimization procedure based on parameter sensitivity analysis is proposed, which uses standard time gating procedure to implement the corresponding direct problem. The proposed technique is validated by extracting the relative permittivity, the dielectric loss (effective conductivity), and the thickness of various standard materials, such as polyethylene, Plexiglas, PVC, mortar, nylon, and so on, and comparing the extracted data with their values available in the literature.

A modified level-set method (MLSM) is proposed to simultaneously reconstruct the shape and electrical properties of 2-D objects. As a numerical technique, the formal level-set method (LSM) can retrieve the shape and position of objects, using synthetic/measurement data. In general, the constitutive parameters of an object (e.g., its relative complex permittivity) are among the a priori information needed for the LSM. For MLSM, an evolution strategy is proposed to simultaneously calculate both the shape and complex permittivity of a 2-D object. The initial guesses in respect of the complex permittivity and shape of the target object converge on their real values as the cost function is minimized. The cost function is regularized with two penalty terms. To prevent sudden change in the shape of the object, a curvature-based regularization is used. Also, Laplacian regularizer is used to reduce fluctuations in the object’s constitutive parameters during the process. Using different synthetic data sets, the capabilities of MLSM in microwave imaging and parameter estimation are evaluated. It is found that, using MLSM, it is possible to completely separate two adjacent objects, separated by a distance of one-fifteenth of a wavelength. The proposed method can retrieve targets of different relative permittivities, with less than 10% error. One interesting feature of this method is its high fidelity in retrieving the immersed one-tenth-wavelength targets in highly contrasting (up to as high as 8:1) domains. In the case of targets with little contrast (10%), the proposed method, with more iterations, can converge on a value, which is 57% more than the actual value. These features are valuable in distinguishing malignant tissue from normal tissue.

The imaginary part of the complex permittivity of a lossy dielectric material is large and couples with its real part. The resonant frequency of a cavity with the sample depends not only on the real part of the complex permittivity of the sample but also the imaginary part, resulting in serious ambiguity in determining the sample's complex permittivity. This work proposes a contour mapping method to determine the complex permittivity. The full-wave simulation gives us the contours of the resonant frequency and the quality factor, which are functions of the relative dielectric constant and the loss tangent. By mapping the measured resonant frequency and the measured quality factor, one can uniquely determine the complex permittivity of the sample. Five liquids were examined, including three low-loss materials for benchmarking and two lossy materials. The measured complex permittivities of the three low-loss materials agree very well with the other methods. As for the lossy materials, the measured relative dielectric constant and the loss tangent of alcohol are 6.786 and 0.895, respectively. Besides, the measured dielectric constant of glycerin is 6.811, and its loss tangent is 0.562. The proposed contour mapping technique can be employed to measure the complex permittivity of liquids and solids from lossless to lossy materials.

Substrate-integrated waveguides (SIWs) are widely used in microwave systems owing to their low cost and ease of integration. In this study, an SIW-based resonator that reacts to the complex permittivity variation of solutions with dimensions of 79.2 mm × 59.8 mm is introduced. This octagon-shaped sensor can be installed on a preliminary monitoring system to test water quality by observing the parameter variations caused by external factors. The resonant structure was used to test different concentrations of ethanol–water and acetone–water mixtures for verification. The resonant frequency and quality factor (Q-factor) were found to vary with the relative complex permittivity of the liquid in the S-band, and the electric field distribution varied when liquid droplets were placed in the center of the substrate. The designed sensor operates at 2.45 GHz in the air, and the observed minimum resonant frequency shift with liquid was 15 MHz. The measurement error was approximately 3.1%, and the results reveal a relationship between the resonant frequency and temperature as well. Considering the observed sources of error, the measured relative permittivity is consistent with the actual values. The proposed sensor is economically convenient and suitable for various test environments.

Complex permittivity is one of the most important parameters to characterize the interaction between microwave and medium, especially for microwave-excited plasma. It is convenient to study plasma’s dielectric properties and microwave propagation characteristics by measuring its complex permittivity. A dynamic measurement method of equivalent relative complex permittivity of microwave-excited plasma at atmospheric pressure is proposed in this paper. Firstly, a cavity based on WR-430 at a frequency of 2.45 GHz was specially designed in COMSOL. Then, the samples with different real parts of complex permittivity and loss tangent were simulated in the designed cavity to obtain their corresponding S parameters, and they were used to train the BP neural network until the error was lower than 0.001. A two-port network was built to excite the plasma. The input power, reflected power, and transmitted power could be measured by the transmission reflection method. Finally, the measured power values were converted into S parameters and used as inputs in the BP neural network. The plasma’s real parts of complex permittivity and loss tangent were obtained by inversion. The variation of plasma complex permittivity conforms to the interaction principles between microwave and plasma, which verifies the accuracy of the method.

This study focuses on the measurement and analysis of the complex permittivities of polymer blends using the field enhancement method (FEM). The blends, consisting of air-powder or solvent-solute mixtures, are placed in a Teflon holder and inserted into the FEM cavity to determine the complex permittivity. The resonant frequency and quality factor of the FEM cavity coupled with the samples provide information on the blends' dielectric constant and loss tangents. To extract the complex permittivities of three specific samples of DC-840, MCL-805, and MCL-Siloxane, we employ effective medium theories and the high-frequency structure simulator (HFSS) together with the measured data. The results reveal that when the volume fraction of the DC-840 solute in the xylene solvent surpasses a specific threshold, the dielectric constants and the loss tangents experience a notable increase. This phenomenon, known as percolation, strongly correlates with the viscosity of polymer blends. The observed percolation effect on the dielectric behavior is further elucidated using the generalized dielectric constant and the Debye model. By employing these models, the percolation effect and its impact on the dielectric properties of the blends can be explained.

Complex permittivity of tomato and tobacco leaves have been measured over the 20 Hz − 2 MHz frequency range using a precision LCR-Meter, and over frequency range from 500 MHz to 15 GHz using a Vector Network Analyzer. Complex permittivity of leaves is found to increase as the moisture content in the leaves increases, at a fixed frequency. At lower frequencies, the dielectric constant ε’ of leaves decreases with increase in frequency up to 2 MHz. At 2 MHz, the complex permittivity ε* = ε′ – jε″ for Tobacco leaves varies from 3855 – j 2863 to 6.12 – j 0.29 with decrease in moisture content, whereas for Tomato leaves ε* varies from 5900 – j 3116 to 3.06 – j 0.29 with decrease in moisture contents in the leaves. Over the microwave frequency range, the dielectric constant and dielectric loss of low moist leaves decreases with increase in frequency. For the leaves having higher moisture content, the dielectric loss decreases rapidly with increase in frequency from 500 MHz to about 5 GHz, after which it starts to increase with increase in the frequency, approaching a relaxation peak. At 14 GHz, the complex permittivity ε* for Tobacco leaves varies from 26.86 – j 26.45 to 2.31 – j 0.034 with decrease in moisture content, whereas for Tomato leaves ε* varies from 23.37 – j 17.50 to 1.67 – j 0.004 with decrease in moisture contents in the leaves. A good agreement is observed between measured values of complex permittivity, with the values calculated using Debye-Cole dual-dispersion dielectric model. Brewster’s angle corresponding to vertical polarization in emissivity calculation is found to increase with increase in moisture content in the leaves.

This paper presents an interdigital capacitor (IDC)-based high sensitivity microwave sensor for the multidimensional (complex permittivity and thickness) characterization of solid materials. The proposed sensor was implemented by etching a slot resonator with an IDC on the ground layer of 0.76 mm-thick RF-35 substrate with relative permittivity of 3.5 and loss tangent of 0.0018. The IDC fingers were configured as a spur-line structure to create an intense electric field zone that interacted significantly with the material under test (MUT), resulting in high sensitivity. A sensor prototype with optimized dimensions generated dual resonant frequencies of 2.35 GHz and 5.79 GHz and was used to measure the MUT’s complex permittivity and thickness, respectively. Experimental results revealed that the resonant frequencies of the developed sensor exhibited high sensitivities (276 MHz/ <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\varepsilon _{r}$ </tex-math></inline-formula> for permittivity and 143 MHz/mm for thickness) and resolutions (0.27678 for permittivity and 0.1439 for thickness) of solid materials. Moreover, the sensing accuracies were 99.9% for real permittivity and 97.7% for imaginary permittivity. The demonstrated high performance of the developed sensor validates its applications in the multidimensional characterization of various solid materials.

The advances in information communication have increased the usage of microwaves in the 0.5–5 GHz range because of the demand for the transmission of large amounts of data. Accordingly, the problem of electromagnetic interference has become increasingly serious, and therefore much attention has been paid to microwave absorbers to solve the problem. Thin microwave absorbers are required with high values of relative complex permeability (μr = μr′ + jμr″) and permittivity (εr = εr′ + jεr″). In this study various permalloy alloys with high permeability were designed, melted in a high-frequency induction furnace in air, melt-dragged into flakes, crushed into powders by a vibration mill, and deformed into ultrathin flakes by an attrition mill. The flake powders were then mixed with silicone rubber and formed into a sheet. When the flakes were mixed with the silicone rubber and formed into a 1 mm thick sheet the complex permeability and complex permittivity were substantially increased and the reflection loss at 0.8 GHz was –2.13 dB. It is possible to make thin and high-performance microwave-absorbing sheets with a flake powder of 79Ni–Fe alloy. (© 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

The essential technologies of the complex permittivity of microwave dielectric materials are systematically designed, and the complex permittivity of materials is tested nondestructively by the free-space resonance method. A testing system was built by using a mobile surveying platform, and the complex dielectric constant of the material in the X band was nondestructively tested by using the algorithm of variable physical cavity length and constant physical cavity length. Focusing on the impact of variable physical cavity length on the test results, the cavity calibration technology is proposed to reduce the influence on the complex dielectric constant test of materials. The free-space resonance method was used to test the complex permittivity of polytetrafluoroethylene, glass steel plate (fiber reinforced plastics), and corundum plate. The results show that the test results of complex permittivity obtained by the two algorithms are consistent, and the error of complex permittivity is less than 5%.

As a standard measurement instrument, a vector network analyzer (VNA) provides high measurement accuracy of signal reflection and transmission for various applications. For some applications, however, there are limitations of using a VNA in terms of cost and bulkiness. This work presents an alternative low-cost mobile instrument for complex permittivity measurement of liquid samples using resonant cavity method. With the proposed instrument, resonant frequencies and quality factors have been measured in cases of an empty cavity and cavity loaded with materials under test including distilled water (high dielectric loss), ethanol (moderate dielectric loss) and diesel fuel (low dielectric loss). From the measured resonant parameters, complex permittivity values have been derived. Good agreement of measurement results when using the proposed system and when using a VNA can be achieved. By using cavity perturbation method described in the literature, relative complex permittivity can be determined from the measured resonant parameters. The values agree well with theoretical ones from the table of material properties.

Characterization of complex permittivity has been performed using TM0mn modes in an overmoded cylindrical cavity. The Rayleigh-Ritz technique is employed to find a rigorous relationship between the relative permittivity, resonant frequency, and the dimensions of the resonant structure. A functional relationship between the structure's S -parameters and the system's unloaded Q factor is established. Complex permittivities of several materials, including polytetrafluoroethylene, high-density polyethylene, cross-linked polyethylene, and sodium naphthalene treated PTFE, are measured at room temperature. Their accuracy is assessed by comparing the results with those obtained from other well-known techniques. An error analysis is also presented to estimate the errors incurred due to the uncertainties in cavity dimensions, resonant frequency, scattering parameters, and the conductivity of the coating layer. In this measurement, an accuracy of better than ±0.5% is attained in measurement of the relative permittivity, while the uncertainty in the measured loss tangent is within a range of ±6%. For properly chosen sample dimensions, this presented method is examined to be very useful for measurement of the complex permittivity over the widely used microwave frequency range, such as the L-, S-, C-, and X-bands.

Microwave Materials such as Rogers RO3003 are subject to process-related fluctuations in terms of the relative permittivity and dielectric loss. The behavior of high frequency circuits like patch-antenna arrays and their distribution networks is dependent on the effective wavelength. Therefore, fluctuations of the complex permittivity will influence the resonance frequency and beam direction of the antennas. This paper presents a grounded coplanar waveguide based sensor, which can measure the complex permittivity at 77 GHz, as well as at other resonance frequencies, by applying it on top of the manufactured depaneling. The relative permittivity of the material under test (MUT) is a function of the resonance frequency shift and the dielectric loss of the MUT can be determined by transmission amplitude variations at the resonances. In addition, the sensor is robust against floating ground metallizations on inner printed circuit board layers, which are typically distributed over the entire surface below antennas. Furthermore, the impact from conductor surface roughness on the measured permittivity values is determined using the Gradient Model.

Complex conductivity and permittivity of single wall carbon nanotubes/polymer composite at microwave frequencies: A theoretical estimation