Complex Permittivity Extraction Research Articles

Measurement Errors and Uncertainties in the Complex Permittivity Extraction With a Fabry–Perot Open Resonator

A Fabry–Perot open resonator (FPOR) has recently become one of the most popular fixtures dedicated to the characterization of dielectric materials in the microwave and millimeter-wave range, mainly due to its quasi-broadband operation combined with large accuracy typical for resonant methods. However, to become a widely recognized measurement standard, an error budget of this approach has to be evaluated, accounting for systematic and random errors in the extraction of the dielectric constant (Dk) and loss tangent. It will be shown in this article that the main sources of the systematic and random Dk errors are the choice of the electromagnetic (EM) model and variation of the thickness of the dielectric sheet, respectively. The first one can be controlled to some extent by the developer of the measurement system, however, thickness variation cannot be easily controlled. Therefore, it has to be accounted for in the form of uncertainty bars. In the case of the loss tangent, systematic and random errors are mainly due to the electric energy filling factor error and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -factor variation, respectively. Moreover, it is shown in this article that the loss tangent uncertainty (LTU) is the lowest when the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -factor with the sample is 40%–50% of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -factor of the empty cavity. In addition to that, it is shown that the noise floor of the measurement is much less important when the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -factor is estimated with the aid of curve-fitting algorithms instead of the 3-dB-point method. However, complete knowledge on the LTU cannot be acquired from just one measurement as it does not account for the finite repeatability of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Q$</tex-math> </inline-formula> -factor measurement. It is, therefore, proposed in this article how to practically evaluate and suppress this error. Although the main attention has been focused on the FPOR, many conclusions presented in this study are not limited to a particular type of resonant technique.

Liquid Permittivity Sensing Using Teeth Gear-Circular Substrate Integrated Waveguide

A new design of teeth gear-circular substrate integrated waveguide (TG-CSIW) sensor to extract complex permittivity of liquids is suggested in this study. The proposed sensor size is decreased up to 20% after the Angle Between Input and Output Ports (ABIOP) was introduced. As the outcome, there was a very excellent quality factor of 700 unloaded. The sensor operated at 2.45GHz resonant frequency, and it is progressively designed by the ANSYS program HFSS. The sensor’s simulated response was evaluated by different permittivity of liquid under test (LUT) with an amount of 0.11mL aqueous. A strong correlation is obtained between the simulated and experimental findings of complex permittivity of LUTs with a minimal error of less than 0.4%. In addition, the modelled sensor was employed to estimate the complex permittivity of unknown specimens. It has contributed to a miniaturized, low-cost, secure, non-contact, fast-detection system utilizing limited liquid volumes filled into Polypropylene tubes. The proposed sensor is practically useful for food or beverage products, fluids/tissues of organic and natural herbs industry applications.

Investigation of Systematic Errors of an Indirect Resonant Planar Material Characterization Method

Indirect measurement principles have always been presented as a solution to save simulation and modeling efforts for complex permittivity extraction methods. However, detailed investigations on remaining systematic errors as well as recommendation guidelines for reference material selection are missing in the literature. In this article, typical systematic error sources of a planar coplanar waveguide over ground material sensor are investigated. An indirect error compensation algorithm is presented, and its ability to compensate the main error sources is simulatively analyzed. A measurement setup is created by considering the specified requirements. The measurement principle is validated by measuring three different plastics. Overall, the results are plausible and have uncertainties of the same or lower order of magnitude compared with the state of the art. However, the findings show that indirect planar methods suffer from fundamental problems, which limit the achievable measurement uncertainty. The findings of this work can be used as a basis for decision-making when considering an indirect planar measurement principle.

Microwave Characterization of Dielectric Sheets in a Plano-Concave Fabry-Perot Open Resonator

Despite its long history, a double-concave (DC) Fabry-Perot open resonator (FPOR) has recently gained popularity in the characterization of dielectrics in the 20–110 GHz range, mainly due to such novel accomplishments as full automation of the measurement process and the development of even more accurate and computationally efficient electromagnetic model. However, it has been discovered that such a DC resonator suffers from unwanted mode coupling present for electrically thick samples. Such limitations are missing in a plano-concave (PC) FPOR. For those reasons, the aim in this article is to apply the newly proposed scattering matrix method in the study of major properties of that kind of a resonator and, subsequently, to propose a new tool dedicated to the measurement of dielectrics without the aforementioned limits. For the first time in the literature, major properties of the PC FPOR with and without the sample, such as resonance frequencies, geometric factors, energy filling factors, and the resulting quality factor, are rigorously computed. Moreover, their impact on the accuracy of the loss tangent extraction is investigated. Such a study, which opens the way for accurate microwave characterization of electrically thick dielectric sheets above 20 GHz, has never been performed before. The whole complex permittivity extraction algorithm presented in this article is validated experimentally by measuring well-known materials, namely, C-plane sapphire, silicon, and Z-cut monocrystalline quartz.

Invasive and Noninvasive Measurement of Complex Permittivity Using ACS-Fed Stepped Impedance Sensor

Compact asymmetric coplanar strip (ACS) fed stepped impedance sensors for complex permittivity measurement of liquids are presented in this article. The step impedance discontinuities in the feed line improve the sensitivity and compactness of the sensor. Two sensors operating at 5.6 GHz with different impedance discontinuities are designed on a low-cost substrate with an overall size of 11 × 10 × 1.6 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> . Invasive and non-invasive sensing techniques are simulated using 3D electromagnetic simulation software and experimentally validated using the fabricated prototype. The change in reflection characteristics of the sensor with varying dielectric constant and loss tangent are analyzed for the extraction of complex permittivity. The proposed sensors’ extracted permittivity values strongly agree with the Keysight dielectric probe measurement. Invasive sensing is carried out by submerging the sensor in liquid samples, whereas non-invasive sensing is carried out by holding the sensor at a varying distance from the samples. The sensor’s single port and compact topology necessitate a minimal volume of liquid samples for measurements. According to the results of the experiments, the ACS-fed stepped impedance resonator (SIR) sensor has a maximum sensitivity of 6.6 % for invasive sensing and 4.6 % for non-invasive sensing. In contrast, the ACS fed extended stub SIR sensor shows a maximum sensitivity of 10.3 % and 6.2 % for invasive and non-invasive sensing approaches, respectively. The sensor measures permittivity values ranging from 2 to 78.

Mm-Wave Complex Permittivity Extraction of LTCC Substrate Under the Influence of Surface Roughness

As many emerging technologies require the use of high-speed signals, the understanding of dielectric properties of materials used in manufacturing printed circuit boards (PCBs) is an essential aspect for accurate high-speed circuit designs, especially at millimeter-wave (mm-wave) frequencies. This work demonstrates a methodology for extracting complex relative permittivity of dielectric substrates covering mm-wave frequencies. For this purpose, low-temperature cofired ceramic (LTCC) substrate was measured up to 85 GHz and its complex relative permittivity was extracted. The approach used in this work is based on multiline thru–reflect–line (TRL) calibration for measuring the propagation constant and electromagnetic (EM) simulations to estimate the losses contributed by the conductor while accounting for surface roughness. An estimate of complex relative effective permittivity is obtained, from which the actual relative dielectric constant and the loss tangent of LTCC substrate are extracted. The estimated values for the relative dielectric constant and the loss tangent show an excellent agreement compared with the results obtained via split cavity resonator measurements.

High temperature W-band complex permittivity measurements of thermally cycled ceramic-metal composites: AlN:Mo with 0.25 to 4.0 vol% Mo from 25 °C to 1000 °C in air

An apparatus for measuring the W-band (75–110 GHz) complex permittivity of dielectrics at 1000 °C was developed. This apparatus allows for measurements at approximately twice the temperature of previously published high temperature free-space measurement systems while maintaining similar precision. Challenges were addressed related to high temperature measurements, including temperature uniformity, the accuracy of temperature measurements, and preventing temperature related changes to mm-wave measurement systems. The details of complex permittivity extraction from the measured S-parameters are discussed. Sources of error related to permittivity measurement and mathematical models were identified and are discussed in detail herein. Thermally-cycled, mm-wave absorbing, aluminum nitride ceramic composites containing varying levels of molybdenum additives were measured over the range of 25 °C–1000 °C. These measurements were compared to the same composites before thermal cycling. It was found that ceramic composites are largely stable after thermal cycling in terms of dielectric properties despite the presence of visible surface modifications.

Estimation methods to extract complex permittivity from transmission coefficient in the terahertz band

In this paper, the characteristics of the transmission coefficient (S_{21}) measured in free-space at terahertz frequencies are analyzed. The analysis results are used to estimate the permittivity of the material under test, and the estimated permittivity is adopted as an initial-value for the iterative algorithm to extract the complex permittivity of the material from the S_{21}. The iterative extraction technique based on the estimation is efficient, while the iterative extraction technique without the estimation is inefficient. Various known materials in the literature are used to validate the technique in the terahertz band.

Complex Permittivity and Permeability Extraction of Ferromagnetic Materials For Magnetically Tuned Microwave Circuits

Ferromagnetic materials, such as ferrites, are employed for magnetically tuned radio frequency (RF) circuits. Ferrites exhibit both electric permittivity and magnetic permeability and independent RF characterization of these two properties is crucial for accurate design and modeling of RF circuits. A method that independently extracts each property over Wi-Fi frequencies is presented here, where complex permittivity and permeability of ferrite nano-particles are extracted using resonance frequency sensitivity of a 3D printed metallic cavity to various samples under test and their placement in the cavity. Air-filled 3D printed rectangular cavity using acrylonitrile butadiene styrene (ABS) are shielded using copper sheets; the structure of air-filled cavity is designed to excite TE <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">101z</sub> as the dominant resonance mode that resonates at 2.4 GHz. A cylindrical shape material under test (MUT) was added to the cavity at different positions for high electric and magnetic fields, while the resonant frequency change and degradation in quality factor of the resonant cavity are employed for accurate independent extraction of electric permittivity and magnetic permeability of MUT. The sample was prepared with volumetric distribution of 60:40 nanoparticles to glue ratio. In particular, a 3D printed composite sample of ABS with NiFe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> magnetic nanoparticles is placed in positions of high electric or high magnetic energy densities of the metallic cavity, while any changes in resonant frequency and its frequency selectivity are observed from the cavity insertion loss characteristics. Both perturbation theory (as analytical) and finite element method (as numerical) techniques are employed for extraction of complex permittivity and permeability of NiFe <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sub> O <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> . The perturbation theory provides accurate extraction, which is also numerically confirmed using curve fitting of the full wave simulated scattering parameters to the measured results.

Review of Recent Microwave Planar Resonator-Based Sensors: Techniques of Complex Permittivity Extraction, Applications, Open Challenges and Future Research Directions.

Recent developments in the field of microwave planar sensors have led to a renewed interest in industrial, chemical, biological and medical applications that are capable of performing real-time and non-invasive measurement of material properties. Among the plausible advantages of microwave planar sensors is that they have a compact size, a low cost and the ease of fabrication and integration compared to prevailing sensors. However, some of their main drawbacks can be considered that restrict their usage and limit the range of applications such as their sensitivity and selectivity. The development of high-sensitivity microwave planar sensors is required for highly accurate complex permittivity measurements to monitor the small variations among different material samples. Therefore, the purpose of this paper is to review recent research on the development of microwave planar sensors and further challenges of their sensitivity and selectivity. Furthermore, the techniques of the complex permittivity extraction (real and imaginary parts) are discussed based on the different approaches of mathematical models. The outcomes of this review may facilitate improvements of and an alternative solution for the enhancement of microwave planar sensors’ normalized sensitivity for material characterization, especially in biochemical and beverage industry applications.

Extraction of Stable Complex Permittivity and Permeability of Low-Loss Materials From Transmission/Reflection Measurements

In this article, a technique based on artificial neural networks (ANNs) is proposed to extract stable complex permittivity and permeability of low-loss materials from transmission/reflection (T/R) measurements. The equations of attenuation constant $\alpha $ and phase constant $\beta $ of $a$ sample-filled transmission line are derived. The calculated $\alpha $ and $\beta $ are put into an ANN model. The outputs of the ANN model are stable complex permittivity and permeability over the whole measurement frequency range, while the values extracted by other techniques are resonant at the frequencies corresponding to integer multiples of one-half wavelength in the sample materials. Two low-loss materials with substantial thickness are measured in X-band to validate the proposed technique. Compared with the Nicolson–Ross–Weir (NRW) technique, the short-circuited technique, and an ANN technique without the derived equations, the proposed technique provides stable results for the two samples. In addition, the extracted values are compared with the “true values” measured from the thinner samples to further present the advantages of the proposed technique.

Erratum to “Extraction of Stable Complex Permittivity and Permeability of Low-Loss Materials From Transmission/Reflection Measurements” [2021 Art. no. 6003608

Erratum to “Extraction of Stable Complex Permittivity and Permeability of Low-Loss Materials From Transmission/Reflection Measurements” [2021 Art. no. 6003608

Complex Permittivity Extraction of Planar Dielectrics Using a Noninvasive Microwave Transmission Line Resonant Technique

This article presents a novel planar resonant method for complex permittivity measurement of planar dielectric substrates. Conventional planar dielectric sensors are composed of resonant structures, such as metamaterials, annular rings, and patch coupled to transmission lines to generate resonance. Here, we demonstrate a simple microstrip line resonator for complex permittivity measurement, and the generated resonant modes in the microstrip line are much like in 3-D conventional microwave cavities. The proposed prototype is distinguished from regular planar resonators due to the presence of a number of distinct electric and magnetic perturbable resonant modes and the absence of additional resonating structures in the design. The use of test samples in the commercially available thickness eliminates extensive sample preparation and possible air gaps or errors introduced due to the stacking of multiple dielectric layers. The microstrip line resonator fabricated on the FR4 substrate shows good agreement in measured permittivity and loss tangent values compared with the manufacturer’s datasheets. The proposed technique is a simple, fast, compact, and cost-effective measurement method for dielectric characterization, and it could be extended for other microwave transmission lines also.

3D printed re-entrant cavity resonator for complex permittivity measurement of crude oils

This paper presented a microwave resonator-based dielectric metrology technique using a new unified analytical model to extract complex permittivity of low-loss liquid materials. The main design drive of the modified re-entrant cavity is to confine the electric field and therefore enhance the interaction with the material under test while maintaining high quality factor of the cavity. This enables high sensitivity when measuring complex permittivity of low loss materials. The fabrication of the resonator was made easy by using stereo-lithography (SLA) 3D printing. The measured resonance frequency of the fabricated cavity is 2.09 GHz and the quality factor is 5250. The device was first validated using several common solvents. A unified analytical perturbation model based on simulations is developed for the extraction of the complex permittivity. The influence of the dielectric constant on the loss-tangent model has been fully taken into account. Results obtained agree very well with literature values. The device has subsequently been used in the measurement of crude oil samples and the correlation between permittivity measurement and crude oil category has been established.

Broadband RF Characterization and Extraction of Material Properties in 3-D Printed Composite Substrates for Magnetically Tuned Circuits

3-D additive printing technology has been employed recently for the manufacturing of a wide variety of tunable radio frequency (RF) components. In particular, this article is focused on the extraction of magnetically tuned 3-D printed materials suitable for RF circuits. The design and modeling of tunable RF circuits require an accurate electromagnetic (EM) characterization of the 3-D printed dielectric [polylactide (PLA)] as a primary substrate, magnetic particles (CoFeO) as the tunable component in the composite substrate, and copper traces at RF frequencies. The extraction of complex permittivity, permeability, and conductivity parameters is reported over broadband (50–7000 MHz) and narrowband Wi-Fi bands (2.4 and 5.4 GHz) using the best fitting of EM simulated to measured scattering ( $S$ ) parameters. Broadband characterization is performed using best-fit modeling of three different physical lengths of microstrip transmission lines that are fabricated on unknown 3-D printed PLA substrates. Error analysis of this approach was evaluated on commercially available RT/Duroid substrate as a baseline. An accurate narrowband extraction procedure around the resonance frequency of 3-D printed annular ring resonators (ARRs) at 2.4 and 5.4 GHz is performed by the best fitting of simulated material RF properties to measured results. Further modeling improvements are presented through completely 3-D printed circuits that include the bottom and top copper traces with extracted conductivity of one tenth of bulk copper. Moreover, a 50-MHz tuning of ARR operating at Wi-Fi bands is observed and complex permeabilities are extracted at zero and 2-kG external magnetic field for the 3-D printed composite substrate.

A simple calibration-free method of complex permittivity extraction

Here we present a new calibration-free method for relative complex permittivity extraction, which allows using accessible and cheap materials and simplifies the measurement process. The method combines the advantages of resonant and non-resonant techniques and provides results for liquids and solids in 0.5-5GHz frequency band in dependence on the material type. The essence of the proposed method is based on measuring of the magnetic dipole resonance of a spherical sample. The size of such a sphere can be dynamically changed making it possible to evaluate its permittivity at different frequencies. Mie theory serves as the basis for connecting the resonant frequency of the sample with the real part of the permittivity, while imaginary part can be found from Q-factor. In this work we demonstrate the efficiency of the method for water. In addition, we evaluate the applicability of the method for lossy materials.

Experimental and Modelling the Combined Measurements Technique for Microwave Absorbing Coatings Testing with Finite Difference Time Domain Method

Because of the structure property of radar absorbing coatings, using of the existing methods for testing these materials is quite difficult. In this paper, a combined-measurement technique was proposed for broadband characterization of microwave absorbing coatings using flanged rectangular waveguide sensor. The technique combines both frequency sweep reflections measurement and two-layer method to provide two different test conditions of the needed reflection coefficients necessary to extract both complex permittivity and complex permeability over a given frequency range. The first set of reflection coefficients is obtained by directly placing the sensor alongside the coating material and performing broadband measurement using frequency sweep over the selected frequency points of frequency range. The same procedure is applied on a combination of known material followed by the test material to measure the second set of the respective reflection coefficients. Finite Difference Time Domain (FDTD) method was employed to numerically calculate the sensor reflection coefficient and analyse the influence of the sensor geometry and coating material thickness on measurement accuracy. The measurement results of both complex permittivity and permeability for various samples of microwave absorbing coatings were agreed well with reference data. Simple interpolation approximation was introduced in their extraction process from multiple reflection coefficient data since they are frequency dependent parameters . The proposed technique speeds up and simplifies coating materials testing, while it decreases the error due to repeatability of measurement.

Permittivity and permeability of epoxy–magnetite powder composites at microwave frequencies

Radio, millimeter, and sub-millimeter astronomy experiments as well as remote sensing applications often require castable absorbers with well known electromagnetic properties to design and realize calibration targets. In this context, we fabricated and characterized two samples using different ratios of two easily commercially available materials: epoxy (Stycast 2850FT) and magnetite (Fe3O4) powder. We performed transmission and reflection measurements from 7 GHz up to 170 GHz with a vector network analyzer equipped with a series of standard horn antennas. Using an empirical model, we analyzed the data to extract complex permittivity and permeability from transmission data; then, we used reflection data to validate the results. In this paper, we present the sample fabrication procedure, analysis method, parameter extraction pipeline, and results for two samples with different epoxy-powder mass ratios.

Liquid Permittivity Sensing Using Planar Open Stub Resonator

A method to extract complex permittivity of liquids using a coplanar waveguide fed open stub resonator is proposed in this paper. A quarter-wave long open stub printed on a substrate is used as the sensor for the computation of complex permittivity. The free-standing unloaded sensor is designed to operate at 1.8 GHz and resonates at a lower frequency when immersed in a test liquid. The resonant frequency and the reflection phase from the sensor are recorded for the computation of real and imaginary parts of the permittivity of the test sample. The simulated response of the sensor, when immersed in liquid samples of different permittivities, is validated by measurements. Equations␣for the extraction of real and imaginary values of permittivity are also presented in this paper. The experiments demonstrate that the sensor is capable of characterizing complex permittivity of liquids with minimal error.

Complex Permittivity Extraction From Synthetic Aperture Radar Images

Microwave and millimeter wave synthetic aperture radar (SAR) imaging techniques are commonly used to generate high-resolution qualitative images showing the reflectivity (or complex permittivity) contrast in a sample-under-test (SUT). These techniques have been successfully applied for many diverse applications. However, these images lack quantitative information about the SUT, namely; its complex permittivity distribution. In this article, a novel method to extract the spatial distribution of complex permittivity from SAR images is proposed. The principle of the proposed method is outlined, then verified by a series of electromagnetic simulations, demonstrating that the proposed method can accurately extract the complex permittivity. Additionally, it is shown that the results are robust with respect to most critical parameters of the SAR imaging technique. Subsequently, measurements were performed to verify the efficacy of the proposed method on two SUTs with different complex permittivities, corroborating the utility of the proposed method. Moreover, the measurement results of one of the SUTs showed that the proposed method is capable of detecting local inhomogeneities with a relatively high spatial resolution. Then, an SUT with artificial defect was prepared to investigate this capability. Compared to quantitative methods based on inverse scattering techniques, this proposed method requires much less computational resources and has the potential for becoming an effective material characterization technique in the nondestructive evaluation (NDE) field.