Permittivity Error Research Articles

Effects of electrical conductivity on uncoated- and coated-rods of eight electromagnetic soil water content sensors

Soil water content stands as a pivotal parameter across numerous research disciplines and engineering applications. Electromagnetic (EM) sensors have gained widespread usage in monitoring soil water content. While commonly employed sensors are suitable for typical agronomic- or landscape-soil environments, they may exhibit significant deviations under conditions of high-salinity or -electrical conductivity (EC). We investigated sensing limits under the influence of increasing EC and the resulting accuracy of dielectric permittivity (ε) determinations using commercial soil water content sensors. Tests were conducted using eight commercially available EM sensors (CS655, HydraProbe II, TDR-305N, TDR-310N, TDR-315N, TEROS 12, TEROS ONE, and WET150). For these uncoated rod sensors, most were accurate within ±3 % relative permittivity errors in saline solutions within the range of 0‒4 dS m−1 while TDR-305N, TEROS ONE and WET150 maintained an accuracy of 5 % for EC values up to 9.24 dS m−1. We explored extending the working range of some sensors to high-saline environments by adding an insulating coating on sensor rods. Since the coated probe not only perceives the characteristics of the immersed medium but also interacts with the coating material itself, a calibration model was evaluated for determining the actual ε of the evaluated medium. The strong correlation between a four-point calibration and the model demonstrates the effectiveness of calibrating coated EM sensors for ε determination using only a limited number of calibration materials. The findings presented here could serve as a valuable resource when selecting EM sensors for use in high-saline environments. Results also shed light on the potential to extend the sensing range through the integration of insulating coatings.

A high sensitivity planar electric–magnetic isolated sensor for full characterization of magneto-dielectric materials

Magneto-dielectric (MD) materials have received much attention due to their applications in design of high-performance antenna and microwave components. Usually, their permittivity and permeability are key parameters in design of these components. Unfortunately, full characterization of these parameters faces challenge of measurement coupling between permittivity and permeability. To address this issue, an electric and magnetic isolated sensor based on a planar resonance structure is proposed and verified. Several shorting pins are used to separate the electric and magnetic regions, which effectively reduces the measurement coupling between permittivity and permeability. These shorting pins form a magnetic cavity pins (MCP) structure. The resonance structure is used for permittivity measurement, and the MCP structure is designed for measuring permeability with enhanced sensitivity. Moreover, to further improve the quality factor, a metal patch and two 50 Ω chip resistors are integrated on the microstrip line. To extract the imaginary part, the quality factor calculated from S21 will be used. By integrating these techniques, the sensor developed in this paper provides possibility of full characterization of MD materials with high sensitivity. Moreover, the magnetic cavity provides more space than the original design, allowing measurement in the Ultra-Wideband (UWB) range possible. Two sensors are designed and fabricated for validating the sensitivity and accuracy. Several materials with different permittivity and permeability are measured. The extracted measurement values show high agreement with the reference values. The permeability errors for real and imaginary parts are smaller than 3% and 4.5%, respectively. And the permittivity errors are smaller than 2.6% and 6.4%.

Monotonicity-Based Interval Analysis Methods of Half-Wave Wall Radomes With Thickness and Permittivity Errors

The complex relation between permittivity and transmission coefficients has been a great obstacle to the interval-based tolerance analysis of radomes. This work presents two monotonicity-based methods (global/local) to facilitate precise interval analysis (IA) of half-wave-wall radomes with thickness and permittivity errors. The global monotonicity method reveals that the key parameters of radome transmission coefficients decrease monotonously with permittivity under a loose constraint in the form of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert $ </tex-math></inline-formula> tan(x) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\vert \le \text {x}$ </tex-math></inline-formula> , which makes the IA of permittivity errors as simple/accurate as thickness errors. The local monotonicity method, with no premises and less accuracy, treats the two correlative parts of the key parameters independently and can be a potential supplement to the global one. Results of spherical radomes and tangent ogival radomes indicate that the monotonicity-based methods can well improve the IA precision, and the global monotonicity method applies to general cases.

Current-Mode Dielectric Spectroscopy for Liquid Permittivity Measurement.

In this work, we propose a current-mode dielectric spectroscopy integrated circuit (IC) for the detection of liquids permittivity at microwave frequency range. The current-mode sensing scheme presents wideband operation with enhanced dynamic range compared to conventional voltage-mode sensing approach. A low intermediate frequency (IF) receiver architecture further provides better performances in flicker noise, dc offset, and harmonic mixing that degrade a sensor accuracy in zero-IF receiver architecture. Measured maximum conversion gain is 31.4 dB at 0.4 GHz RF frequency, while the 1dB-compression point ([Formula: see text]) is measured to be -8 dBm at 1 GHz RF frequency. The operation frequency of the proposed spectroscopy IC is from 50 MHz to 4 GHz according to 3 dB bandwidth. The permittivity measurements for propanol across the frequency range of 0.03-10 GHz are performed with root mean square (rms) permittivity error of 0.49. The dielectric spectroscopy IC is fabricated in 28-nm CMOS technology with active area of 0.5 mm × 0.2 mm only, while consuming 13 mW from a 1.2 V supply.

Permittivity Measurement of the Dielectric Material at the Off-Axis Position in a Cylindrical Cavity

In most measurement models of the cylindrical cavity, concentricity between the rod-like sample and cylindrical cavity is a basic premise of an accurate calculation model. Once a sample is randomly placed in the off-axis position in the sample hole of the cavity, the real will not conform to the established calculation model and the off-axis position should be taken into account to the measurement error. In this article, a measurement method to calculate permittivity of the sample placed at the off-axis position in the sample hole is presented. The actual location of the sample in a cylindrical cavity is first obtained in the application of vision measurement. Field distribution in the cavity is calculated by using the mode-matching method. The measured sample in the cavity is divided into finite small elements with arc shapes, and permittivity calculation expression is established by using the perturbation theory. A TM-mode cylindrical cavity that installed two miniature camera probes around the cavity wall is designed and used to measure permittivity of the material. Teflon and fused silica with different off-axis positions are measured and compared with the published results at several resonance frequencies. The maximum permittivity errors of Teflon and fused silica are 1.6% (at around 2 GHz) and 0.68% (at around 10.8 GHz), respectively. The maximum loss tanδ errors are 5.8e <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-5</sup> (at around 12.5 GHz) and 1.44e <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-4</sup> (at around 9.9 GHz), respectively.

The influence of parameters of disk electrode with guard electrode system and sample on permittivity error caused by equivalent electrode area calculation and its correction method

To improve the accuracy in the permittivity measurement using disk electrode with guard electrode, a 3D model of this type of electrode is built in Comsol software and validated. The influence of parameters of sample and disk electrode with guard electrode system on the permittivity error caused by equivalent electrode area calculation is systematically investigated. The results reveal that the permittivity errors by means of the equivalent electrode area presented by the IEC 60250 standard are nearly always negative. From a global perspective, the area of the guarded electrode is closer to the accurate equivalent electrode area than the area provided by the IEC 60250 standard. The error decreases with increasing sample thickness and increases with increasing sample permittivity, gap width, radius of the electrode corner. If the sample is thick and the permittivity is low, the error increases significantly with increasing guarded electrode potential. The sample radius has nothing to do with the accuracy if it is slightly larger than the inside radius of the guard electrode. In the normal range, the size of shielding box, the electrode location, the deviation between the guarded electrode and the whole electrode center, the deviation between the guard electrode and the unguarded electrode, and the potential of the bolt have little effect on the accuracy. Based on the model, a permittivity correction method based on interpolation is proposed. First, the models with different parameters of electrode system and sample, measured and real values of permittivity are built. Second, the relationship among parameters of electrode system and sample is obtained. Finally, the measured permittivity can be corrected by using the relationship and the interpolation method. The accuracy in the permittivity measurement is greatly improved. Because of taking potential of guarded electrode and radius of the electrode corner into account, the error introduced by the proposed method is less than that of the existing correction methods in some situations.

High-Temperature RF Material Characterization Using a Dual-Chambered Rectangular Waveguide Fixture

A rectangular waveguide (RWG) fixture is proposed for the high-temperature RF characterization of materials. Composed of two RWGs in a side-by-side or over-under orientation, the new apparatus permits the calibration and specimen measurements to be collected simultaneously reducing high-temperature measurement time by two full days over the traditional method. In addition, the permittivity and permeability, determined from measured S-parameters, are independent of sample position and can be found in closed form. The design and construction of the dual-chambered RWG fixture are detailed. The closed-form, position-independent, permittivity and permeability extraction method is also discussed. Finally, high-temperature material characterization experiments are performed to validate the fixture. The errors in permittivity and permeability are estimated assuming uncertainties in sample thickness and measured S-parameters.

A Wide-Band Fully-Integrated CMOS Ring-Oscillator PLL-Based Complex Dielectric Spectroscopy System

A fully-integrated sensing system is proposed for wideband complex dielectric detection of materials under test (MUT). The system utilizes a ring oscillator-based phase-locked loop (PLL) for wide tuning range and precise control of the sensor's excitation frequency. Characterization of both real and imaginary MUT permittivity is achieved by measuring the frequency difference between two voltage-controlled oscillators (VCOs): a sensing oscillator, with a frequency that varies with MUT-induced changes in capacitance and conductance of a delay-cells' sensing capacitor loads, and a MUT-insensitive reference oscillator that is controlled by an amplitude-locked loop (ALL). The fully integrated system is fabricated in 0.18 $\mu{\rm m}$ CMOS, and occupies 6.25 ${\rm mm}^{2}$ area. When tested with common organic chemicals $(\epsilon_{r}^{\prime} , the system operates between 0.7–6 GHz and achieves 3.7% maximum permittivity error. Characterization is also performed with higher $\epsilon_{r}^{\prime}$ water-methanol mixtures and phosphate buffered saline (PBS) solutions, with 5.4% maximum permittivity error achieved over a 0.7–4.77 GHz range.

A 0.62–10 GHz Complex Dielectric Spectroscopy System in CMOS

This paper presents an integrated sensing system for complex dielectric spectroscopy in the 0.62-10 GHz frequency range. A capacitive sensor exposed to the material under test (MUT) shows variations in its admittance according to the complex permittivity of MUT. The sensing capacitor along with a fixed capacitor forms a voltage divider circuit and is excited by an RF signal at the sensing frequency. The magnitude and phase of the voltages across the two capacitors which depend on the sensor admittance are measured using a quadrature downconversion architecture to find the real and imaginary parts of the MUT's permittivity. At the lower frequency end, the system is configured as a direct-conversion architecture with third and fifth harmonic-rejection to alleviate the problem of harmonic mixing and improve the sensitivity. On the other hand, at the higher frequency end, the system works as a dual-downconversion topology and employs a sub-harmonic mixing technique to reduce the required input clock frequency span. As a proof of concept, the spectroscopy system is used for complex permittivity detection of pure organic chemicals and shows an rms permittivity error of less than 1% over the frequency range of 0.62-10 GHz. The fabricated chip in 0.18-μm CMOS occupies an active area of 2.3 mm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> and consumes 65-72 mW from a 1.8 V supply.

Three‐dimensional electrical capacitance tomography reconstruction by the Landweber iterative algorithm with fuzzy thresholding

The image reconstruction for electrical capacitance tomography is a non-linear, underdetermined and ill-posed inverse problem. It is difficult to obtain a reconstructed image with high quality, especially in the case of three-dimensional (3D) reconstruction. An iterative image reconstruction algorithm with fuzzy thresholding is proposed in this study. The threshold value in each iteration is generated by minimising the measure of fuzziness of current reconstructed image. The algorithm proposed is tested by the noise-free and the noise-contaminated capacitance data. Extensive computer simulations demonstrate that the fuzzy thresholding can reduce low grey-level artefacts effectively. As a result, the spatial error, volume error, permittivity error and scattered artefacts of the reconstructed image are reduced obviously; not only that, the number of iterations needed to obtain a good reconstruction result is decreased greatly. The result of 3D reconstruction of a H-shape object verifies the effectiveness of the fuzzy thresholding further.

A CMOS Fractional-$N$ PLL-Based Microwave Chemical Sensor With 1.5% Permittivity Accuracy

A highly sensitive CMOS-based sensing system is proposed for permittivity detection and mixture characterization of organic chemicals at microwave frequencies. The system determines permittivity by measuring the frequency difference between two voltage-controlled oscillators (VCOs); a sensor oscillator with an operating frequency that shifts with the change in tank capacitance due to exposure to the material under test (MUT) and a reference oscillator insensitive to the MUT. This relative measurement approach improves sensor accuracy by tracking frequency drifts due to environmental variations. Embedding the sensor and reference VCOs in a fractional- N phase-locked loop (PLL) frequency synthesizer enables material characterization at a precise frequency and provides an efficient material-induced frequency shift read-out mechanism with a low-complexity bang-bang control loop that adjusts a fractional frequency divider. The majority of the PLL-based sensor system, except for an external fractional frequency divider, is implemented with a 90-nm CMOS prototype that consumes 22 mW when characterizing material near 10 GHz. Material-induced frequency shifts are detected at an accuracy level of 15 ppmrms and binary mixture characterization of organic chemicals yield maximum errors in permittivity of 1.5%.

Frequency response and tolerance of reflection-mode magneto-optical multi layer film isolator

Using the transfer matrix method, we investigated the influence of permittivity error on the properties of magneto-optical multi layer isolator with single-defect, and presented a new type of multi layer structure with multi defect. Compared with single-defect structure, the bandwidth of Faraday rotation frequency response of multi defect structure was increased greatly, and the tolerance of permittivity was increased by one order. Furthermore, the multi defect structure has greater tolerance of film thickness and incidence angle.

Permittivity measurement of low and high loss liquids in the frequency range of 8 to 40 GHz using waveguide transmission line technique

AbstractThis paper presents the complex permittivity of a number of liquids measured using waveguide transmission‐line techniques. These liquids are measured over four frequency ranges: 8–12.4 GHz, 12.4–18 GHz, 18–26.5 GHz, and 26.5–40 GHz (or at the X, Ku, K, and Ka bands). The measured results of liquids are discussed and compared with results in the literature and the calculated data using Debye's method. Finally, statistical values such as the means and standard deviations, and the percentages of permittivity errors are computed for the consideration of data spread and error estimation. All of the possible sources of errors are also discussed with regard to improvements and developments of measurements in the near future. © 2005 Wiley Periodicals, Inc. Microwave Opt Technol Lett 48: 275–281, 2006; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/mop.21326