Nicolson-Ross-Weir Method Research Articles

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.

Determination of dielectric properties of plaster blocks for sealing masonry using non-destructive frequency scanning methods

With the increasing use of traditional and new models of wireless communication systems, the study and determination of the electrical characteristics of materials used in civil construction is an important topic to establish an understanding of how the radio frequency signal behaves inside built environments. This study presents an extensive process of characterization of electrical parameters of plaster blocks used in the construction of walls. Different from the literature where a prior estimation of the data occurs to enable sampling parameters to be obtained, this work proposes an innovative way of obtaining them entirely based on the analysis of the material through frequency measurements, which results in a greater level of precision of the data results. Analyses are made in the frequency range from 0.7 to 5.2 GHz, which has been used for several wireless communication standards. To carry out the electrical characterization of dielectric materials, a non-invasive methodology is proposed based on an innovative combination of the Nicolson–Ross–Weir Method (NRW) and the Ray Tracing Method. Through the proposed methodology and an extensive campaign of measurements using frequency scanning equipment, calculated and experimental data of Shielding Effectiveness (SE), complex relative electrical permittivity, loss tangent, attenuation coefficient and conductivity were obtained for a wide range of frequency, considering different samples of plaster blocks. The obtained results are compared to those available in the related literature, confirming the accuracy of the proposed analysis.

Pattern Similarity and Gain Enhancement of Dual-Band Antenna Using an ENZ Metamaterial

A dual-band antenna with pattern similarity using the energy-squeezing mechanism of an epsilon-near-zero (ENZ) metamaterial is designed, and experimental results are presented with simulated data. To achieve high gain and pattern similarity, a waveguide-based ENZ metamaterial property is adopted in a planar microstrip form at the upper band. The designed dual-band antenna is resonating at 4.3 GHz and 9.8 GHz frequencies with the desired radiation pattern. A metamaterial unit cell with ENZ characteristics at 9.8 GHz is designed to improve the antenna’s performance. The permittivity and permeability of the unit cell are characterized using the Nicolson–Ross–Weir method. By adding a square ring structure, the antenna geometry exhibits ENZ characteristics. Using the ENZ material’s energy-squeezing mechanism, a 12-dB gain improvement is achieved in the upper band without affecting the lower band radiation characteristics without increasing the complexity. It can be used in C- and X-band applications, such as mobile, military, defense, and radar communication. The dual-band antenna with ENZ material is fabricated, and the measured results show a good match with the simulated results. The proposed antenna size at 4.3 GHz is 0.58λ × 0.58λ × 0.02λ.

A Formal Approach to the Extraction of Permittivity and Permeability of Isotropic and Anisotropic Media Using the TM11 Mode in Rectangular Waveguides

Based on our previous work on the propagation of electromagnetic waves in a layered medium placed in a rectangular waveguide, we present the theory of using the TE10 and TM11 modes to determine the complex parameters of isotropic and anisotropic media. The Nicolson–Ross–Weir method was used. The cases of isotropic, uniaxial, and biaxial materials were considered. It has been shown that the TM11 mode can be used to extract parameters of non-magnetic uniaxial anisotropy media by a single measurement, without changing the sample position. This is not possible with the previously used TE10 mode. It is also possible to use the TM11 mode to quickly determine whether a material is isotropic or not. Experimental results are presented for some isotropic materials.

Wide Microstrip Line Type Probe With Slits and Permeability Evaluation of Thick Magnetic Material

We have developed a new microstrip line type probe with a wide conductor having some slits to eliminate the measurement error of the demagnetizing effect in thick samples. The slits enhanced the homogeneity of the high-frequency current in the wide direction of the microstrip conductor, which resulted in the application of a uniform high-frequency magnetic field to the sample. Complex relative permeability of thick NiZn ferrite sheet and carbonyl iron particle (CIP) sheet ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$3\times $ </tex-math></inline-formula> 1 mm, <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$100 ~\mu \text{m}$ </tex-math></inline-formula> in thickness) has been evaluated accurately using the probe. The measurement error of permeability was evaluated within about 15% in 0.1–20 GHz compared with the conventional Nicolson–Ross–Weir method.

Valley-dependent topological edge states in plasma photonic crystals

Plasma photonic crystals designed in this paper are composed of gas discharge tubes to control the flow of electromagnetic waves. The band structures calculated by the finite element method are consistent with the experimental results which have two distinct attenuation peaks in the ranges of 1‒2.5 GHz and 5‒6 GHz. Electromagnetic parameters of the plasma are extracted by the Nicolson–Ross–Weir method and effective medium theory. The measured electron density is between and which verifies the correctness of the parameter used in the simulation, and the collision frequency is near As the band structures are corroborated by the measured scattering parameters, we introduce the concept of photonic topological insulator based on the quantum Valley Hall effect into the plasma photonic crystal. A valley-dependent plasma photonic crystal with hexagonal lattice is constructed, and the phase transition of the valley () occurs by breaking the spatial inversion symmetry. Valley-spin locked topological edge states are generated and excited by chiral sources. The frequency of the non-bulk state can be dynamically regulated by the electron density. This concept paves the way for novel, tunable topological edge states. More interestingly, the Dirac cone is broken when the electron density increases to which distinguishes from the methods of applying a magnetic field and changing the symmetry of the point group.

New Measurement Technique for Complex Permittivity in Millimeter-Wave Band Using Simple Rectangular Waveguide Adapters

This research presents a novel methodology for measuring the complex permittivity of a material under test (MUT) in a millimeter-wave (mmWave) band by using two rectangular waveguide adapters. Contrary to the conventional Nicolson-Ross-Weir (NRW) method, the proposed complex permittivity measurement method does not require a material fabrication process for exact MUT insertion into a waveguide. In our complex permittivity measurement, simple commercial waveguide adapters are employed instead of large flange structures. The proposed complex permittivity measurement of a non-destructive MUT is achieved by combining the NRW method, the Gaussian weighting moving average filtering technique, a full-wave electromagnetic analysis, and an optimization technique. Furthermore, the proposed methodology is validated by fabricating a Teflon-based MUT and by measuring the complex permittivity of the MUT in the Ka band (26.5–40 GHz). The results indicate that the proposed methodology exhibits good agreement with the data sheet.

Extraction of the Electromagnetic Parameters of a Metamaterial Using the Nicolson–Ross–Weir Method: An Analysis Based on Global Analytic Functions and Riemann Surfaces

The characterization of electromagnetic metamaterials (MMs) plays a fundamental role in their engineering processes. To this end, the Nicolson–Ross–Weir (NRW) method is intensively used to recover the effective parameters of MMs, even though this is affected by the branch ambiguity problem. In this paper, we face this issue in the context of global analytic functions and Riemann surfaces. This point of view allows us to rigorously demonstrate the mathematical foundations of an algorithmic approach for avoiding the branch ambiguity problem, in which the phase unwrapping method is merged with K-K relations for recovering the effective parameters of an MM. In addition, exploiting the intimate relationship between the K-K relations and the Hilbert transform, a simple variant of the above algorithm is presented.

Modified Coptic Cross Shaped Split-Ring Resonator Based Negative Permittivity Metamaterial for Quad Band Satellite Applications with High Effective Medium Ratio.

This research article describes a modified Coptic cross shaped split ring resonator (SRR) based metamaterial that exhibits a negative permittivity and refractive index with a permeability of nearly zero. The metamaterial unit cell consists of an SRR and modified Coptic cross shaped resonator providing quadruple resonance frequency at 2.02, 6.985, 9.985 and 14.425 GHz with the magnitude of −29.45, −25.44, −19.05, and −24.45 dB, respectively. The unit cell that was fabricated on a FR-4 substrate with a thickness of 1.6 mm has an electrical dimension of 0.074λ × 0.074λ; the wavelength (λ) is computed at the frequency of 2.02 GHz. The computer simulation technology (CST) microwave studio was employed to determine the scattering parameters and their effective medium properties, i.e., permittivity, permeability and refractive index, also calculated based on NRW (Nicolson–Ross–Weir) method through the implementation of MATLAB code. The frequency range of 2.02–2.995 GHz, 6.985–7.945 GHz, 9.985–10.6 GHz, and 14.425–15.445 GHz has been found for negative permittivity. An effective medium ratio (EMR) of 13.50 at 2.02 GHz shows that the proposed unit cell is compact and effective. The lumped component based equivalent circuit model is used to validate with simulation results. The proposed unit cell and its array were fabricated for experimental verification. The results show that the simulation result using CST and high-frequency structure simulator (HFSS) simulator, equivalent circuit model result using advanced design system (ADS) simulator and measurement results match each other better. Its near zero permeability, negative permittivity, negative refractive index, high EMR and simple unit cell design allow the proposed metamaterial to be used for S-, C-, X- and Ku-band satellite applications.

A new design of stepped antenna loaded metamaterial for RFID applications

Radio frequency identification is being overloaded with data information, making wideband band antennas very appealing. In this paper, we present a new design of dual band antenna for RFID reader applications operating at 2.45Gz and 5.8GHz with an average gain of 1.16dB at the lower frequency band and 3.2dB at the higher frequency band. The antenna is designed on an FR-4 substrate having a relative dielectric constant of 4.4 and loss tangent of 0.025. The proposed antenna is simulated, designed and, optimized using CST Microwave Studio and has a small size of 32 mm x 26 mm x 1.6 mm. The antenna consists of a steeped rectangular patch antenna using a partial ground plane loaded a modified split ring resonator. The metamaterial structure was designed and optimized to operate at 2.45GHz and its effective parameters was verified using the Nicolson-Ross Weir method. The performance of the proposed antenna is confirmed by another 3D electromagnetic solver HFSS.

Errors in Broadband Permittivity Determination Due to Liquid Surface Distortions in Semi-Open Test Cell

We study how surface distortions of liquid samples due to a meniscus and a tilt of a semi-open coaxial test cell affect errors in a broadband permittivity determination. The study is based on the scattering parameters, obtained using the electromagnetic simulations of samples with flat and distorted surfaces in a broad frequency range up to 18 GHz. The parameters are processed with the classic Nicolson–Ross–Weir (NRW) method and our new meniscus removal technique. We analyze the errors for several samples of different properties, such as distilled water and propan-2-ol. The results show that the meniscus removal technique is more robust and provides smaller errors in the permittivity determination compared to the classic NRW method. The effect of the cell tilt, to our best knowledge, has not been considered in the literature yet.

Retrieving the Effective Parameters of an Electromagnetic Metamaterial Using the Nicolson-Ross-Weir Method: An Analytic Continuation Problem Along the Path Determined by Scattering Parameters

Electromagnetic metamaterials (MMs) are composite structures that allow one to potentially develop unique and innovative microwave, millimetre wave, and optical devices due to their unusual physical properties. In this process, their electromagnetic characterization plays a fundamental role. Various procedures have been proposed to accomplish this task, but the Nicolson-Ross-Weir (NRW) method still appears to be the most commonly adopted one even though it is afflicted by the severe issue of branch ambiguity. In this paper, we have demonstrated that rigorously, as the branch ambiguity can be entirely overcome through the analytic continuation of a specific analytic logarithm element along the path determined in the complex plane by the scattering parameters of an MM under analysis. Furthermore, the underlying relationship between analytic continuation, phase unwrapping approach, implemented through a procedure devised by Oppenheim and Schafer for the homomorphic treatment of signals (hereafter named PUNWOS), and the Kronig-Kramers relation has been discussed and enlightened, demonstrating the full equivalence among the methods. To clarify this aspect, a couple of numerical examples is presented. The results discussed in this study open the possibility of employing the vast theoretical equipment developed in the phase unwrapping field to achieve the retrieval of MMs’ effective parameters when the NRW method is applicable.

A Position-Independent Approach to Accurate Measurement of Broadband Electromagnetic Constitutive Parameters of Magnetodielectric Materials

Magnetodielectric materials have been recently attracting great attention owing to their significant advantages for miniaturization and wide bandwidth of antennas. A precise measurement of broadband permeability and permittivity is crucial to develop and evaluate advanced magnetodielectric materials. The Nicolson-Ross-Weir (NRW) method is widely used to extract electromagnetic constitutive parameters from measured scattering parameters. One of the drawbacks of this method is requiring direct measurement of the actual sample position in the measurement fixture, which leads to uncertainties in the measured permeability and permittivity. In this article, we improve the standard NRW method by removing the need for prior knowledge of sample position. For any isotropic material, the sample position in the measurement fixture can be precisely determined by matching the phasor angles of the reflection coefficients at the sample surfaces. Due to eliminating the error from the direct measurement of sample position, the improved NRW method effectively reduces the uncertainties in the calculated permeability and permittivity. Based on the results from two kinds of magnetodielectric materials measured in two sets of test fixtures of different geometries, this straightforward, explicit, and noniterative method is theoretically and experimentally proven to have a high and position-independent accuracy over a wide frequency range.

An electromagnetic parameter retrieval method based on deep learning

The electromagnetic parameter retrieval method based on scattering (S) parameters is widely used because S parameters are easy to obtain. As a classic S parameters retrieval method, the Nicolson–Ross–Weir (NRW) algorithm has problems such as half-wave resonance, phase angle jump, and multivaluedness. In this work, an electromagnetic parameter retrieval method based on deep learning is proposed, which aims to solve the multivaluedness problem in the traditional NRW method. The method we proposed is suitable for retrieval of inhomogeneous medium that satisfies the theory of effective medium. The simulation shows that the electromagnetic parameter retrieval method based on deep learning has high calculation accuracy without the multivaluedness problem.

Measurement of Electric and Magnetic Properties of ZnO Nanoparticles in the X-Band Using Nicolson–Ross–Weir Analysis

The electric and magnetic properties of zinc oxide (ZnO) nanoparticles (NPs) have been investigated through waveguide measurement in the x-band. Because of the advantages of the x-band, the application of the Nicolson–Ross–Weir (NRW) method was able to be used to extract the mentioned characteristics from the scattering parameters. The advantages of the NRW method are that it is fast and applicable to waveguides and coaxial lines, and it can also be used to determine both the permittivity and permeability. Therefore, the results show two main resonant frequencies at 9.279 GHz and 10.46 GHz. The response of the ZnO NPs for an incident electromagnetic wave implies that both capacitance and inductance behaviors can be observed. Finally, the obtained magnetic susceptibility characteristic confirms that the ZnO NPs are ferromagnetic over the frequency range from 8 GHz to 8.265 GHz and paramagnetic up to 12.5 GHz.

A Simplified Nicolson–Ross–Weir Method for Material Characterization Using Single-Port Measurements

We present a simplified Nicolson-Ross-Weir (NRW) material characterization procedure that employs only a single-port network analyzer for data collection. This approach is particularly attractive for mmW and THz applications, as it eliminates the need for costly two-port instrumentation required in the conventional NRW method. Akin to the well-known adapter removal techniques, we use two successive calibrations of the defined measurement ports and deduce the two-port response of the sample under test. Subsequently, the conventional NRW procedure can be employed to simultaneously determine permittivity and permeability of the material under test. We demonstrate our approach for the WR8.0 waveguide band (90-140 GHz) using a multioffset-short calibration method. Similar to the two-port through-reflect-line calibration, the multioffset-short process determines the propagation constant of the waveguide, which provides additional verification of the quality of the collected measurements and the validity of the NRW procedure. We demonstrate that the simplified one-port NRW method is as effective in performance as the conventional two-port procedure. To our knowledge, this is the first-time realization of the single-port NRW method for mmW and THz bands.

A Noniterative and Efficient Technique to Extract Complex Permittivity of Low-Loss Dielectric Materials at Terahertz Frequencies

In this letter, a noniterative technique is proposed to efficiently extract complex permittivity $(\varepsilon)$ of low-loss dielectric materials at terahertz frequencies while mitigating the effects at Fabry–Perot frequencies. For this goal, the formula of $\varepsilon $ with little resonance is first derived by applying boundary conditions for the transmission-reflection-based free-space method. In order to demonstrate the advantages of the proposed technique, we compared the proposed technique with the classical Nicolson–Ross–Weir method and the Newton–Raphson method. The proposed noniterative technique is verified by experiments and simulation at 220–325 GHz.

Complete Meniscus Removal Method for Broadband Liquid Characterization in a Semi-Open Coaxial Test Cell.

We present a new technique for broadband liquid characterization using a semi-open, vertically oriented test cell that is measured with a calibrated vector network analyzer in three states: the empty one and filled with two different volumes of the liquid under test. Using the measurements, we de-embed a transfer matrix representing a volume increment of the liquid sample and determine its column height with a novel closed-form formula. Thanks to the de-embedding, the method enables one, for the first time, to completely remove effects caused by a reproducible meniscus forming the top surface of a liquid tested in the cell and determine not only the propagation constant, but also characteristic impedance of the liquid sample, from which its permittivity and permeability are calculated. The results are highly consistent, because all the measurements are performed without disassembling the cell. We validate experimental results of the meniscus removal method by comparing them with reference data and outcomes of the Nicolson–Ross–Weir method.

Determination of Complex Permittivity of Low-Loss Materials From Reference-Plane Invariant Transmission/Reflection Measurements

In this paper, a novel method is proposed to determine unique and stable relative complex permittivity of low-loss materials from the transmission/reflection (TR) measurements, though the positions of the materials under test are unknown. The proposed method systematically combines artificial neural network (ANN) models with the Nicolson-Ross-Weir (NRW) method. Firstly, an ANN model is established to estimate the position of the sample in the transmission line. Secondly, the NRW method is adapted to estimate the relative complex permittivity, and the unique solutions are selected with the help of dielectric properties. Thirdly, the noniterative technique in the literature is adapted to avoid the instabilities in the relative complex permittivity. Finally, the S-parameters of the amplitude-only or transmission-only measurements are used to accurately determine the relative complex permittivity. The proposed method is experimentally validated by two samples. The simulated data are used to further validate the accuracy of the proposed method. The results of the proposed method based on the transmission-only measurements are the most accurate.

Free space material characterization of carbon nanotube thin films at sub-terahertz frequencies

A free space, non-destructive, vectorial continuous wave terahertz analysis method is employed to study the material properties of single-walled and multi-walled carbon nanotube thin films deposited on substrates of fused quartz and silicon. The electrical and optical properties of the thin films have been investigated using a vector network analyzer, in the frequency range of 220–325 GHz (WR 3.4) and 325–500 GHz (WR 2.2). The Nicolson–Ross–Weir method is used to extract the material parameters. The refractive index, absorption coefficient, and the complex conductivity of the single-walled and multi-walled carbon nanotube thin films are extracted and studied.