Showing papers on "Equivalent circuit published in 2022"
TL;DR: The improved model (IPSO-CNN-BiLSTM) proposes a convolution neural network (CNN) to process EIS data which can not only extract the key points but also simplifies the complexity of manual feature extraction.
Abstract: The state of health (SOH) is critical to the efficient and reliable use of lithium-ion batteries (LIBs). Recently, the SOH estimation method based on electrochemical impedance spectroscopy (EIS) has been proven effective. In response to different practical applications, two models for SOH estimation are proposed in this paper. Aiming at based on the equivalent circuit model (ECM) method, a variety of ECMs are proposed. Used EIS to predict the ECM, the results show that the improved method ensures the correctness of the ECM and improves the estimation results of SOH. Aiming at a data-driven algorithm, proposes a convolution neural network (CNN) to process EIS data which can not only extract the key points but also simplifies the complexity of manual feature extraction. The bidirectional long short-term memory (BiLSTM) model was used for serial regression prediction. Moreover, the improved Particle Swarm Optimization (IPSO) algorithm is proposed to optimize the model. Comparing the improved model (IPSO-CNN-BiLSTM) with the traditional PSO-CNN-BiLSTM, CNN-BiLSTM and LSTM models, the prediction results are improved by 13.6%, 93.75% and 94.8%, respectively. Besides that, the two proposed methods are 27% and 35% better than the existing gaussion process regression (GPR) model, which indicates that the proposed improved methods are more flexible for SOH estimation with higher precision.
71 citations
TL;DR: A design methodology to employ antiparallel windings to smooth the coupling coefficients variation over different positions by reducing the coupling coefficient at central positions and enhancing it at boundary positions is proposed.
Abstract: Free positioning wireless charging for consumer electronics allows the devices to be charged at arbitrary positions and angles to improve user experience. However, a user-initiated sudden movement of the device during charging can cause hazards due to the abrupt variation of the coupling coefficient. To solve this issue, the coupling coefficient variation at different positions should be mitigated, which is also good for the design and high-efficiency operation of power electronics converters. This article proposes a design methodology to employ antiparallel windings to smooth the coupling coefficient variation over different positions by reducing the coupling coefficient at central positions and enhancing it at boundary positions. Two optimization methods are proposed: turn-by-turn optimization and winding-by-winding optimization. A design flow is offered. The hexagonal coil is compared with the square coil and proved to achieve better performance than the latter. An experimental prototype is implemented to validate the effectiveness of the proposed design methodology.
46 citations
TL;DR: In this article , the important basics of electrochemical impedance for electrochemical sensors and biosensors are presented, focussing on the necessary electrical circuit elements and their physical meaning.
Abstract: Electrochemical impedance spectroscopy is finding increasing use in electrochemical sensors and biosensors, both in their characterisation, including during successive phases of sensor construction, and in application as a quantitative determination technique. Much of the published work continues to make little use of all the information that can be furnished by full physical modelling and analysis of the impedance spectra, and thus does not throw more than a superficial light on the processes occurring. Analysis is often restricted to estimating values of charge transfer resistances without interpretation and ignoring other electrical equivalent circuit components. In this article, the important basics of electrochemical impedance for electrochemical sensors and biosensors are presented, focussing on the necessary electrical circuit elements. This is followed by examples of its use in characterisation and in electroanalytical applications, at the same time demonstrating how fuller use can be made of the information obtained from complete modelling and analysis of the data in the spectra, the values of the circuit components and their physical meaning. The future outlook for electrochemical impedance in the sensing field is discussed.
36 citations
TL;DR: In this paper , a novel early internal short circuit (ISC) diagnosis method based on the incremental capacity (IC) curves is proposed, where the leakage current of the battery can be obtained by the area difference between the normal cell and the ISC cell, and it can be converted into the IC resistance.
34 citations
TL;DR: In this article , a fast impedance calculation-based battery SOH estimation method for lithium-ion battery is proposed from the perspective of electrochemical impedance spectroscopy (EIS), where the relationship between EIS and state of charge and degraded capacity is first studied by experimental tests.
Abstract: State-of-health (SOH) is crucial to the maintenance of various kinds of energy storage systems, including power batteries. Relevant research articles are mostly based on battery external information, such as current, voltage, and temperature, which are susceptible to fluctuation and ultimately affects the SOH estimation accuracy. In this article, to solve these problems, a fast impedance calculation-based battery SOH estimation method for lithium-ion battery is proposed from the perspective of electrochemical impedance spectroscopy (EIS). The relationship between EIS and state of charge and that between EIS and degraded capacity is first studied by experimental tests. Some impedance features called health factors effectively indicating battery aging states are selected. Second, an improved fast Fourier transform (FFT) utilizing the conversion relationship between the real and complex signals is proposed to realize online fast EIS acquisition. Compared with ordinary FFT, such treatments reduce computational complexity. Then, the SOH evaluation model is built by the extreme learning machine with regularization mechanism, further reducing the computational burden. The relationship between the health factors and aging capacity of batteries is established. Finally, an experimental bench is established. The results indicate that the estimated SOH can be obtained within 35 s for a four-cell series-connected battery pack and the estimation errors are less than 2%.
32 citations
01 Dec 2022
TL;DR: In this article , a novel EIS-based method is proposed for battery SOH estimation considering variations of temperature and battery state of charge (SOC), and the estimation error can reach 1.29% under certain conditions (e.g. 80% SOC at 30 °C).
Abstract: State of health (SOH) is critical to the efficient and reliable use of lithium-ion batteries (LIBs), especially in electric vehicle (EV) applications. Recently, electrochemical impedance spectroscopy (EIS) based technique has been proved to be effective for SOH estimation of LIB. However, existing EIS-based methods failed to consider the impact of ambient temperature and battery state of charge (SOC), leading to the limited flexibility of these methods under dynamic environments. In this work, a novel EIS-based method is proposed for battery SOH estimation considering variations of temperature and SOC. An equivalent circuit model (ECM) is first introduced, in which the solid electrolyte interface (SEI) resistance and charge transfer resistance are employed to map their relationship with SOH under variant temperature and SOC. Subsequently, a probabilistic model, taking charge transfer resistance, temperature and SOC as input variables, is developed for LIB SOH estimation. Experimental study indicates that the estimation error of the proposed method is around 4% when simultaneously considering the temperature and SOC effects. Moreover, the estimation error can reach 1.29% under certain conditions (e.g. 80% SOC at 30 °C). Both results of estimation error are better than the existing EIS-based methods, which indicates that the proposed method is more flexible for SOH estimation with higher precision.
28 citations
27 citations
TL;DR: In this article , drift-diffusion numerical simulations of typical thin-film, planar perovskites are used to generate impedance spectra avoiding intrinsic experimental difficulties such as instability and low reproducibility.
Abstract: Perovskite solar cells (PSCs) have reached impressively high efficiencies in a short period of time; however, the optoelectronic properties of halide perovskites are surprisingly complex owing to the coupled ionic-electronic charge carrier dynamics. Electrical impedance spectroscopy (EIS) is a widely used characterization tool to elucidate the mechanisms and kinetics governing the performance of PSCs, as well as of many other semiconductor devices. In general, equivalent circuits are used to evaluate EIS results. Oftentimes these are justified via empirical constructions and the real physical meaning of the elements remains disputed. In this perspective, we use drift-diffusion numerical simulations of typical thin-film, planar PSCs to generate impedance spectra avoiding intrinsic experimental difficulties such as instability and low reproducibility. The ionic and electronic properties of the device, such as ion vacancy density, diffusion coefficients, recombination mechanism, etc., can be changed individually in the simulations, so their effects can be directly observed. We evaluate the resulting EIS spectra by comparing two commonly used equivalent circuits with series and parallel connections respectively, which result in two signals with significantly different time constants. Both circuits can fit the EIS spectra and by extracting the values of the elements of one of the circuits, the values of the elements of the other circuit can be unequivocally obtained. Consequently, both can be used to analyse the EIS of a PSC. However, the physical meaning of each element in each circuit could differ. EIS can produce a broad range of physical information. We analyse the physical interpretation of the elements of each circuit and how to correlate the elements of one circuit with the elements of the other in order to have a direct picture of the physical processes occurring in the device.
23 citations
TL;DR: In this article , correlation analysis between equivalent circuit elements and impedance spectra of multiple commercial Li-ion polymer batteries at varying SoC, SoH and internal temperature (IT) levels was performed to identify and quantify the degree of dependence.
Abstract: Electrochemical impedance spectroscopy (EIS) is an effective characterization tool for a multitude of battery states including state of charge (SoC), state of health (SoH) and internal temperature (IT). The intrinsic relationship between equivalent circuit elements and components of an impedance spectra (frequency, real, imaginary and phase) could be exploited to estimate the battery state at a given point of time without the need of continuous historical tracking information. Identification and analysis of battery state sensitive impedance variables is paramount for the development of any impedance-based battery management system (BMS). In this paper, correlation analysis between equivalent circuit elements and impedance spectra of multiple commercial Li-ion polymer batteries at varying SoC, SoH and IT levels was performed to identify and quantify the degree of dependence. Curve fitting techniques were used to fit the measured Impedance spectra on to an equivalent circuit model (ECM) to extract the circuit elements. Pearson's r correlation matrix was employed for quantifying the degree of correlation between each impedance variable and state parameter. Optimal impedance variables that demonstrated high dependence with SoC, SoH and IT are then proposed in this paper. Knowledge of this information is of high value to develop a direct impedance-based state estimation models for real time battery management systems.
22 citations
TL;DR: In this paper , a model-based method is implemented to assess the state of charge (SOC) and state of health (SOH) simultaneously, with recursive least squares online identifying model parameters and unscented Kalman filter estimating battery state.
21 citations
TL;DR: In this article , an improved fractional-order extended Kalman filter (IFO-EKF) was proposed to overcome the shortcomings of the electrical equivalent circuit model (EECM) in a regular LiB integer-order model.
Abstract: Accurate estimation of Lithium-ion battery’s (LiB) state of charge (SOC) in the battery management system (BMS) is very critical to the performance of battery electric vehicles (BEV) because it indicate how much charge is remaining in the battery. However, due to the nonlinear properties of the LiB and the uncertainty of battery models, estimating the SOC of battery online during vehicle operation is often a major challenge. This paper proposes a model-based estimation method named an improved fractional-order extended Kalman filter (IFO-EKF) to overcome the shortcomings of the electrical equivalent circuit model (EECM) in a regular LiB integer-order model. Firstly, a simplified first-order fractional-order model (FOM) which combines the advantages of both the EECM and the electrochemical impedance spectroscopy (EIS) was developed to accurately interpret battery electrochemical processes using electrical circuit made up of resistors and constant phase element (CPE) having fractional-order characteristics. Secondly, the unknown parameters of the FOM model are identified off-line using quantum particle swarm optimization (QPSO) algorithm. In addition, due to the non-linear dynamic characteristics of LiB, Kalman filter family algorithms used in battery state estimation faces some shortcomings which results in filter divergence caused by the implementation of inappropriate co-variance matrix in the algorithm which leads to inaccuracies and estimation error in the model. The convergence rate of the proposed IFO-EKF algorithm in this study was improved by introducing a Grünwald–Letnikov (G–L) fractional derivative and a time-varying measurement error covariance (R) into the proposed estimation algorithm. Finally, to verify the validity of the proposed model, the HWFET, UDDS and NEDC vehicle dynamics condition tests were used to compare the estimation results of the IFO-EKF against the integer-order extended Kalman filter (IO-EKF) algorithm. The simulation results of the IFO-EKF algorithm proved that it is a better estimation algorithm than the IO-EKF in terms of accuracy. • A simplified first-order FOM was designed to interpret battery electrochemistry. • Estimated battery SOC using an improved fractional-order extended Kalman filter. • A time-varying measurement error covariance was used to counter algorithm divergence. • Carried-out comparative study between IFO-EKF, FO-EKF and IO-EKF estimation result. • The proposed method greatly improved the algorithm convergence and SOC estimation accuracy.
TL;DR: The advanced partial element equivalent circuit (A-PEEC) model is proposed in this article to simulate the screening current of a simple coil model and the LBC3 magnet, and the simulated screening current induced fields were compared with the measurements.
Abstract: Since the screening current (SC) in rare earth-barium-copper-oxide (REBCO) coated conductor (CC) generates an undesired magnetic field, it must be accurately estimated, especially for magnetic resonance imaging (MRI) and nuclear magnetic resonance (NMR). Moreover, in recent years, it was pointed out that the screening current enhanced the stress/strain in REBCO CC, when an REBCO magnet was operated as an insert under an ultrahigh magnetic field. The previously reported SC simulation methods may be roughly categorized into finite element method (FEM) and equivalent circuit method. The FEM-based method often adopted an axisymmetric model or a thin film approximation model, while the circuit-based are the simple equivalent circuit model and the network equivalent circuit model, so-called the partial element equivalent circuit (PEEC) model. The latter is newly developed in this paper. Features of those SC simulation models are briefly compared to each other in this paper. Each SC simulation models have pros & cons. We have to adequately chose an SC simulation model depending on a purpose. We extended the original PEEC model to simulate SC. The extended model is named the advanced partial element equivalent circuit (A-PEEC) model. It is also extendable to an SC simulation of no-insulation REBCO pancake coils. To simulate the SC of a simple coil model and the LBC3 magnet, we investigated the screening current distribution maps, and the simulated screening current-induced fields were compared with the measurements. We have confirmed the validity of the newly developed A-PEEC model.
TL;DR: In this paper, the authors proposed a unified analysis framework for galloping-based energy harvesters (GPEH) connected with various interface circuits, which provides an integrated view of the physics of linear GPEHs in multiple domains at the system level.
TL;DR: In this article , the authors present a review of existing OCV-SOC models and propose a systematic approach to select a suitable model for implementation based on various constraints faced by a BMS designer in practical application.
Abstract: A battery management system (BMS) plays a crucial role to ensure the safety, efficiency, and reliability of a rechargeable Li-ion battery pack. State of charge (SOC) estimation is an important operation within a BMS. Estimated SOC is required in several BMS operations, such as remaining power and mileage estimation, battery capacity estimation, charge termination, and cell balancing. The open-circuit voltage (OCV) look-up-based SOC estimation approach is widely used in battery management systems. For OCV lookup, the OCV–SOC characteristic is empirically measured and parameterized a priori. The literature shows numerous OCV–SOC models and approaches to characterize them and use them in SOC estimation. However, the selection of an OCV–SOC model must consider several factors: (i) Modeling errors due to approximations, age/temperature effects, and cell-to-cell variations; (ii) Likelihood and severity of errors when the OCV–SOC parameters are rounded; (iii) Computing system requirements to store and process OCV parameters; and (iv) The required computational complexity of real-time OCV lookup algorithms. This paper presents a review of existing OCV–SOC models and proposes a systematic approach to select a suitable OCV–SOC for implementation based on various constraints faced by a BMS designer in practical application.
TL;DR: In this article, the authors proposed a new methodology based on a recent political optimizer to solve the problem of identifying the unknown parameters of fuel cell equivalent circuit, six parameters are considered as design variables which are E, A, Jo, RΩ, B, and Jmax, the sum of mean squared error between the measured and estimated stack voltages is considered as the fitness function to be minimized.
TL;DR: In this article, a novel space vector pulsewidth modulation (SVPWM) method was proposed to reduce the operating frequency and loss of the auxiliary commutation circuit (ACC) and current stress of auxiliary switches of a parallel resonant dc-link inverter.
Abstract: In order to reduce the operating frequency and loss of the auxiliary commutation circuit (ACC) and current stress of auxiliary switches of a parallel resonant dc-link inverter (PRDCLI), this article proposes a novel space vector pulsewidth modulation (SVPWM) method. The novel SVPWM method can reduce the number of operations of the ACC to once in every PWM cycle on the premise of realizing soft switching of all switches, thereby reducing the operating frequency and loss of the ACC. At the same time, by adding the shunt dead time, the novel SVPWM method can avoid the superposition of the resonant current and load current, thereby minimizing the current stress of auxiliary switches. In addition, the novel SVPWM method can apply to any PRDCLI with the ability of variable zero voltage durations. Under the novel SVPWM method, according to the equivalent circuits of different operation modes, the operation principle, soft switching realization conditions and parameter design methods of the inverter are analyzed. Finally, a 10-kW/16-kHz prototype is built using insulated gate bipolar transistors to verify the validity of the novel SVPWM method.
TL;DR: In this article , the authors summarize procedures for conducting reliable impedance measurements on a battery system, including cell configurations, readiness of a system for impedance testing, validation of the data in an impedance spectrum, deconvolution of electrochemical processes based on the distribution of relaxation time and equivalent circuit fitting of the impedance spectrum.
Abstract: Abstract Electrochemical impedance spectroscopy provides information on the steady state of an electrochemical redox reaction and its kinetics. For instance, impedance is a very useful technique to investigate kinetics in batteries, such as diffusion processes or charge-transfer reaction dynamics during battery operation. Here, we summarize procedures for conducting reliable impedance measurements on a battery system, including cell configurations, readiness of a system for impedance testing, validation of the data in an impedance spectrum, deconvolution of electrochemical processes based on the distribution of relaxation time and equivalent circuit fitting of the impedance spectrum. The aim of this paper is to discuss key parameters for accurate and repeatable impedance measurements of batteries.
TL;DR: In this article , the effect of surface roughness on TENG capacitance is analyzed by the Greenwood-Williamson model to determine a more accurate TENG equivalent capacitance, which can better predict the outputs such as short-circuit current and transferred charge.
TL;DR: In this article , the impact of the inherent characteristics on the initial-stage short-circuit current of modular multilevel converter based multi-terminal direct current (MMC-based MTDC) transmission system is investigated.
Abstract: This paper studies the impact of the inherent characteristics on the initial-stage short-circuit current of modular multilevel converter based multi-terminal direct current (MMC-based MTDC) transmission system. A short-circuit current calculation method based on input-output characteristics is proposed. The MMC’s input-output characteristics are factorized into a series combination of a linear and a nonlinear part through the operator approach. The inherent characteristics of the system represent the inherent properties of the MMC-based MTDC system, which are unrelated to the short-circuit fault. Therefore, short-circuit currents are decoupled and quantitative indices are proposed to measure the impact of the system inherent characteristics on the initial-stage short-circuit current. The proposed decoupled short-circuit current calculation method and the quantitative indices are verified in a typical MMC-based MTDC transmission system under different system parameters and structures. The proposed quantitative indices can effectively evaluate the short-circuit current of the MMC-based MTDC system without calculating the short-circuit current, which indicates that they can provide guidance for the planning of DC system structure, determination of operational modes, and selection of system parameters from the perspective of short-circuit current.
TL;DR: Among seven multiclassification machine learning (ML) models taking optimized hyperparameters found by grid search, AdaBoost achieved the known highest equivalent circuit model prediction accuracy, 0.571, and had a prediction basis that was consistent with a common chemical knowledge as discussed by the authors .
TL;DR: In this article , a method of updating model parameters based on the Dynamic Matrix Control (DMC) algorithm is proposed, and the DMC-EKF algorithm is used to estimate Open Circuit Voltage (OCV) and state of charge (SOC) estimation of LiBs.
Abstract: State of Charge (SOC) estimation is one of the most important functions of the battery management system for new energy vehicles. Extended Kalman Filter (EKF) algorithm has been widely used in SOC estimation of lithium-ion batteries (LiBs). However, the model parameters in the SOC estimation algorithm change with the aging of the battery, which makes EKF unable to obtain accurate estimation results. Because of these defects, a battery model is built based on the second-order RC equivalent circuit model. The parameters of the LiB model are identified by an off-line test and the battery simulation model is calibrated. Then, based on the simulation model, the influence of Open Circuit Voltage (OCV) deviation on SOC estimation accuracy of the EKF algorithm is quantitatively analyzed. The results show that the deviation of OCV will affect the accuracy of SOC estimation by the EKF algorithm. When the OCV deviation reaches 15 mV, the SOC estimation error will reach 5%. Subsequently, a method of updating model parameters based on the Dynamic Matrix Control (DMC) algorithm is proposed. And the DMC-EKF algorithm is used to estimate OCV and SOC. The results show that after the DMC algorithm is used to linearize the RC network, the identified OCV parameter deviation is <10 mV, and the SOC deviation estimated by the DMC- EKF algorithm is <5%, which can meet the application requirements. The EKF algorithm can estimate the SOC more accurately after updating the OCV by the DMC algorithm. Compared with EKF algorithm and UKF algorithm without online OCV updating, DMC-EKF algorithm reduces the maximum deviation of SOC estimation by at least 2%. The proposed DMC-EKF algorithm has good accuracy and robustness.
TL;DR: In this article , a 2-RC model was proposed to estimate the state of health (SOH) of Li-ion batteries over time, which is not only time-dependent but also captures the effect of temperature on battery degradation.
Abstract: Lithium-ion (Li-ion) batteries have increasingly been used in diverse applications. Accurate estimation of the state of health (SOH) of the Li-ion batteries is vital for all stakeholders and critical in various applications such as electric vehicles (EVs). The electrical equivalent circuit (EEC) 2-RC model is often used to model the battery operation but has not been used to capture the degradation of battery cells over time. This paper uses the 2-RC model to capture the degradation of the Li-ion battery. The proposed model is not only time-dependent but also captures the effect of temperature on battery degradation. The proposed approach estimates the SOH accurately and is also considerably flexible for diverse cells of different chemistry. We further generalize an N-RC model approach to evaluate the SOH of the battery. We compare the proposed model (2-RC) with the 1-RC model, and through numerical results, we show that the 2-RC model outperforms 1-RC and reduces the computational cost significantly. Similarly, the 2-RC model outperforms 3-RC and higher-order circuits. We also show that the proposed approach can capture the battery dynamics better for specific smaller orders of the polynomial (associated with Arrhenius equation) when compared with the 1-RC approach with considerably reduced (up to 60%) root mean square error (RMSE). Lastly, the average testing RMSE for 2-RC is 52.4%.
TL;DR: In this paper , a solid-phase diffusion equation based surface-SOC model was proposed to characterize battery open circuit voltage (OCV) behavior and establish the new structure of the enhanced ECM to describe low-sate-of-charge (SOC) behavior more precisely.
TL;DR: In this article , the authors proposed a unified analysis framework for galloping-based energy harvesters (GPEH) connected with various interface circuits, which provides an integrated view of the physics of linear GPEHs in multiple domains at the system level.
TL;DR: In this paper , an equivalent circuit model of a grid-forming (GFM) converter with a circular current limiter was developed and the transient stability of the converter with the limter was analyzed.
Abstract: This letter develops an equivalent circuit model of a grid-forming (GFM) converter with a circular current limiter and analyzes its transient stability. It is revealed that the inner control loop can be simplified as a voltage source behind an equivalent resistor. Based on the developed model, theoretical analysis and experimental tests demonstrate that the transient stability of a $P-f$
TL;DR: In this article , a multi-time scale variable-order equivalent circuit model is proposed for the virtual battery, and the model order changes in order of fractional order value, third-order and second-order.
TL;DR: In this paper , a frequency-selective rasorber (FSR) built on multilayer resistive sheets, which achieves a broad absorption band, was proposed.
Abstract: In this article, the frequency-selective rasorber (FSR) built on multilayer resistive sheets, which achieves a broad absorption band, was proposed. First, the detailed analysis of the absorption and transmission performance for FSR with the single-layer/multilayer resistive sheets based on the equivalent circuit model (ECM) was demonstrated, which proved that the FSR with the multilayer resistive sheets can obtain a broader absorption band. Second, the multilayer resonator (MR) of a smaller size and higher design freedom compared with single-layer resonator was proposed. Then, the FSR on the basis of multilayer resistive sheets using MR was designed. It consists of the three-layered metallic structures and separated by an air spacer. For the top and middle layers, the lumped-resistor-loaded metallic dipole with the MR inserted into the center was applied to generate a wide absorption band and transparent window, respectively. For the bottom layer, the square-slot frequency-selective surface was optimized to match the transmission band of the resistive sheet. Simulated and measured results show that the broad absorption band and transmission band with low insertion loss have been realized, and the proposed FSR yields the widest relative bandwidth $\vert S_{11}\vert \le -10$ dB of 145.2%.
TL;DR: In this article, the feasibility and effectiveness of two different oscillation suppression approaches via respectively increasing the hydraulic losses on the branch tailrace channels or the main tailrace channel were discussed in detail via numerical simulation.
TL;DR: In this paper , a square root UKF algorithm was constructed Systematically on the lithium cobalt oxide battery model to estimate the state of charge (SOC) under complex conditions and environment, the data indicated that SR-UKF algorithm can increase the robust of the filter and the estimation error can be reduced to less than 1.5%.
TL;DR: In this article , a microstrip line loaded with a dumbbell-shaped defect ground structure (DB-DGS) is used for complex permittivity measurements, defined as the variation in the resonance frequency and depth caused by the material under test (MUT), when it is put in contact with the sensitive region of the device.
Abstract: It is shown in this paper that a microstrip line loaded with a dumbbell-shaped defect ground structure (DB-DGS) is useful for complex permittivity measurements. The working principle of the sensor is the variation in the notch (resonance) frequency and depth caused by the material under test (MUT), when it is put in contact with the sensitive region of the device, i.e., the capacitive slot. It is demonstrated that the relative sensitivity of the sensor, defined as the variation of the resonance frequency of the DB-DGS with the dielectric constant of the MUT relative to the resonance frequency of the bare structure, does not depend on the geometry of the DB-DGS, provided the substrate is thick enough. The relative sensitivity, the key figure of merit, is dictated by the equivalent dielectric constant of the substrate, and it increases as the substrate permittivity decreases. Using the circuit model of the sensing structure, simple analytical expressions providing the dielectric constant and the loss tangent of the MUT are derived. Such analytical formulas depend on the notch frequency and depth of the sensor with and without MUT in contact with it, i.e., easily measurable quantities. The analysis carried out is corroborated through full-wave electromagnetic simulation and experiments.