Conventional Equivalent Circuit Model Research Articles

(Invited) Evaluation of Long-Term Corrosion Behavior of Metallic Biomaterials in Simulated Body Fluid By Electrochemical Impedance Spectroscopy

One of the major problems associated with the use of metallic biomaterials is their corrosion. Corrosion reactions, which are unavoidable in metals, cause not only deterioration or fracture of the products but also serious harm to living tissue. Nevertheless, metallic biomaterials are commonly used in the fields of medicine and dentistry because of their superior mechanical properties: an excellent combination of strength and ductility, resulting in high fracture toughness can not be substituted by other materials. Therefore, highly corrosion-resistant metals and alloys such as Ti, Ti alloys, Co-Cr alloys, and stainless steels are used for implant devices. All of them show superior corrosion resistance results from the formation of a passive film on the surface of the metal. However, very small quantities of the metallic ions actually dissolve through the passive film on these metallic biomaterials. There are already many literatures about the corrosion resistance of metallic biomaterials about the breakdown of the passive film. However, only limited information is available concerning the corrosion with extremely small rate accompanying metal ion release via stable passive film. Therefore, in this study, long-term measurement of in-situ electrochemical impedance spectroscopy, dissolution test, and surface analysis were performed to clear the difference in the corrosion behaviors of various metallic biomaterials.Disk shaped specimens of pure Ti (Ti), Ti-33.5Nb-5.7Ta beta-type Ti alloy (Ti-Nb-Ta), Ti-Ti-50.8mol%Ni super elastic alloy (Ti-Ni), Co-20Cr-15W-10Ni alloy (L605, ASTM F90) (Co-Cr), type 316L stainless steel (316 SS), and pure Zr (Zr) were prepared. The specimens for corrosion tests were mechanically ground to #800 grit SiC abrasive paper. The specimens for XPS were additionally polished and mirror-finished with 9 μm diamond paste and 0.04 μm colloidal silica. The specimens were then ultrasonically cleaned in acetone and ethanol. In this study, the simulated body fluid, 5.85 gL-1 NaCl and 10.0 gL-1 lactic acid, as a corrosion test solution was prepared. The pH of the solution was checked in advance and was confirmed to be within the range of 2.30 ± 0.05 just after preparation. This solution was intended to be an accelerated body fluid for rapid testing of corrosion measurements of dental metallic materials prescribed by ISO 10271. EIS measurement was performed with an electrochemical measurement system. A couple of the specimen disks were prepared and embedded in cold-mounting epoxy resin. After grinding the surface, the electrodes were immediately immersed in the test solution and placed face-to-face at a constant distance. EIS measurement was started with an alternative potential of 10 mV in amplitude just 10 min after immersion. The measurement was continued for at least 48 h. For Ti-Nb-Ta, the measurement was further extended and continued for up to 28 d. The dissolution test was performed to evaluate the corrosion rate and amounts of the released metal ions during the immersion in the test solution. Twenty mL of the test solution was then put into the glass bottle, followed by the specimen. The bottle was completely sealed and kept for 7 d. The concentrations of the metal ions were measured with ICP-AES.After the measurement of EIS, curve fittings could be performed using conventional equivalent circuit models. The corrosion rates of all specimens decreased during the immersion period. However, the declines in the corrosion rates of Co-Cr and Zr were much larger than those of Ti, Ti-Nb-Ta, Ti-Ni, and 316 SS. It means that the growth rate of the passive film of each alloy showed much different tendency in initial period. From the result of the dissolution test, it was found that the amounts of the released ions from 316L were much higher than those of another specimens. Ti-Ni released certain amount of Ni ions which are very hazardous for metal allergy. On the other hand, the amounts of the ions from Co-Cr and Zr were almost same level as detection limit of ICP-AES. It indicates that the protective performances against mass transfer via the passive films of Co-Cr and Zr are superior to those of other biomaterials. From the long-term EIS measurement of Ti-Nb-Ta, the maturation of the passive film originated from both film growth and compositional change was observed. The corrosion inhibition effects of Nb and Ta in Ti alloy was confirmed by long-term EIS measurement. Therefore, this technique provides a useful diagnostic of the long-term biosafety of metallic biomaterials, which are required to have an extremely higher level of corrosion resistance.

Electrochemical impedance spectroscopy measurements on time-variant systems: the case of the Volmer-Heyrovský corrosion reaction. Part I: theoretical description

One of the theoretical requirements of electrochemical impedance spectroscopy measure­ments is that the studied system should not be varying with time. Unfortunately, this is rarely the case of physical systems. In the literature, quite a few methods exist to check and correct a posteriori the effect of time-variance, allowing to use conventional equivalent circuit models to fit and interpret the data. We suggest a different approach where, for a given electro­chemical mechanism and specific experimental conditions, assuming stationarity during each measurement, a time- and frequency-dependent expression of the Faradaic impe­dance is derived from the kinetic equations. The case of a potential relaxation at zero current following an anodic steady-state polarization is considered for a system where a Volmer-Heyrovský corrosion mechanism is supposed to take place.

Study of Solid-State Diffusion Impedance in Li-Ion Batteries Using Parallel-Diffusion Warburg Model

Anomalous diffusion impedance due to the solid-state Li+ diffusion in Li-ion batteries is often troublesome for the analysis. In this work, we propose a novel analytical Parallel-diffusion Warburg (PDW) model and couple it with the conventional equivalent electrical circuit model (EECM) analysis to tackle this long-standing challenge. The analytical expression of the PDW is derived from the classical Fickian diffusion framework, introducing non-unified diffusion coefficients that originate from the diverse crystalline conditions of Li+ diffusion paths, as theoretically demonstrated in the atomistic modeling results. The proposed approach (EECM + PDW) is successfully employed to study the diffusion impedance of thin-film LiNi0.5Mn1.5O4 (LNMO) electrodes and porous LiNi0.80Co0.15Al0.05O2 (NCA) electrodes, demonstrating the applicability and robustness of this method.

The lithium battery state of charge estimation based on the fractional order unscented kalman filter algorithm

Abstract In the assessment of the state of charge (SOC) of lithium batteries, it has been observed that the conventional integer-order second-order resistance-capacitance (RC) network falls short in accurately replicating the non-linear attributes and the precision of SOC estimation influenced by the internal polarization reaction within the battery. Thus, we present the incorporation of constant-phase element (CPE) and Warburg components to achieve a model with superior recognition accuracy compared to the conventional second-order equivalent circuit model(ECM). The parameterization is carried out using the particle swarm optimization algorithm, resulting in enhanced robustness of parameter identification. Later on, when we mixed the regular Unscented Kalman Filter (UKF) algorithm with the fractional-order model (FOM), we obtained an algorithm to estimate the SOC of lithium battery in real time, named FOUKF, and compared FOUKF with the integer-order Extended Kalman Filter (EKF) and UKF algorithms. This confirms that the model is reliable and the algorithm’s estimation is accurate.

Efficiency Improvement of Permanent Magnet Synchronous Motors Using Model Predictive Control Considering Core Loss

The highway cycle is an important consideration in the EV’s new European driving cycles (NEDCs) range, as the steady-state efficiency improvement in such conditions can be greatly beneficial. In the model predictive control (MPC) of the permanent magnet synchronous motors (PMSMs), the predicted next-step feedback reference generated by the equivalent circuit model (ECM) will contribute directly to the voltage vector selection, therefore influencing the performance of the motor control. In the current MPC scheme, when the conventional ECM is applied, it only considers copper loss, and the core loss is usually disregarded. In some circumstances, such as the highway cycle of EVs, the motors are at high speed, the torque is low, and the core loss can be significant in the losses, thus affecting the accuracy of control and the efficiency of the system; hence, the introduction of core loss ECM into the MPC would be beneficial. This paper aims to investigate the steady-state efficiency improvement of a novel ECM of PMSM considering core loss ECM, and the comparison will be based on model predictive direct torque control (MPDTC) using the core loss ECM, which will be compared to MPDTC with the conventional ECM of the PMSM. The results demonstrate the proposed ECM’s efficiency improvement in various conditions, the limitations of the model and the simulation are discussed, and future work is proposed.

Study on the difference of high frequency dielectric properties of biological tissues measured by air and packed coaxial probe

In this paper, the differences between air probe and filled probe for measuring high-frequency dielectric properties of biological tissues are investigated based on the equivalent circuit model to provide a reference for the methodology of high-frequency measurement of biological tissue dielectric properties. Two types of probes were used to measure different concentrations of NaCl solution in the frequency band of 100 MHz-2 GHz. The results showed that the accuracy and reliability of the calculated results of the air probe were lower than that of the filled probe, especially the dielectric coefficient of the measured material, and the higher the concentration of NaCl solution, the higher the error. By laminating the probe terminal, liquid intrusion could be prevented, to a certain extent, to improve the accuracy of measurement. However, as the frequency decreased, the influence of the film on the measurement increased and the measurement accuracy decreased. The results of the study show that the air probe, despite its simple dimensional design and easy calibration, differs from the conventional equivalent circuit model in actual measurements, and the model needs to be re-corrected for actual use. The filled probe matches the equivalent circuit model better, and therefore has better measurement accuracy and reliability.

Identification of fractional-order equivalent circuit model of lithium-ion battery for improving estimation of state of charge

Accurate estimation of State of Charge (SOC) based on equivalent circuit model (ECM) of Lithium-ion batteries (LIBs) is an important research topic. Recent research has found that fractional-order model (FOM), as one kind of equivalent circuit model, can provide a better description of LIBs dynamics than the conventional integer-order ECMs. However, it is difficult to directly identify an FOM online. In this paper, a synergy of Beetle Antennae Search and Recursive Least Squares (BAS-RLS) is proposed to identify the parameters of an FOM for LIBs. Specifically, the BAS is adopted to determine the fractional order, while the remaining parameters of FOM are estimated via the well-established RLS algorithm. A comparison study will demonstrate that this method offers a similar modeling accuracy as the Particle Swarm Optimization (PSO), and the online estimated model is more accurate than offline estimated models. Based on the identified FOM, this article then explores the battery SOC estimation from two aspects: initial value effect of the SOC and the comparison of multiple estimation algorithms, thus verifying the advantage of the proposed method for LIBs modeling and SOC estimation.

Impulse Response-Based Induction Machine Model for Starting Simulation Considering Deep-Bar Effect

This paper proposes a novel model for the starting simulation of induction machines (IMs) where its dynamics are computed directly from the impulse response produced by finite element analysis (FEA). This model realizes an accurate starting simulation owing to considering the skin effect of the cage rotor winding, which cannot be entirely represented by the conventional equivalent circuit model even if several auxiliary branches are added on its rotor side to reduce the modeling error in the high-frequency region. Furthermore, the dynamics can be computed by simply executing the convolution integral for the impulse response and input voltage. In other words, the model requires no fitting or approximation to determine the equivalent circuit parameters, which has been studied extensively in many kinds of literature. For the starting characteristics as an example, the accuracy of simulations using the model was investigated thorough comparing its result with that of measurement and FEA. These researches demonstrated that the proposed model provided a remarkable improvement for the starting simulation.

Two-Dimensional Equivalent Circuit Model of Ultrasonic Wireless Power Transmission

In this article, piezoelectric ceramic is a core device of an ultrasonic wireless power transmission (UWPT) system. The most commonly used piezoelectric ceramic in research and applications of UWPT has a ring-like shape. The piezoelectric ceramic rings usually work in the presence of significant radial and axial vibrations as long as they are not extremely thin. However, in most studies related to the UWPT, only the axial vibration mode is considered. The Mason equivalent circuit model of axial vibration is widely used and the effect of radial vibration on the whole system is ignored. In this article, first, a method to analyze the piezoelectric ceramic ring considering the radial-axial coupled vibration is proposed. Second, the analytical expressions of the constitutive equations of the piezoelectric ceramic ring are derived. Third, a new form of analytical equations is constructed, and a novel two-dimensional equivalent circuit of the UWPT system considering the radial-axial coupled vibration of the piezoelectric ceramic ring is proposed. Fourth, the input and output characteristics of the proposed model and the conventional Mason equivalent circuit model are simulated using MATLAB. Last, the simulation results are compared and verified by experiments. The results demonstrate that the proposed model can describe the system resonance more accurately and comprehensively than the conventional Mason model. As a whole, this study increases the accuracy of the equivalent circuit model of the UWPT system and has important theoretical significance for UWPT research.

3D Impedance Modeling of Metal Anodes in Solid-State Batteries-Incompatibility of Pore Formation and Constriction Effect in Physical-Based 1D Circuit Models.

A non-ideal contact at the electrode/solid electrolyte interface of a solid-state battery arising due to pores (voids) or inclusions results in a geometric constriction effect that severely deteriorates the electric transport properties of the battery cell. The lack of understanding of this phenomenon hinders the optimization process of novel components, such as reversible and high-rate metal anodes. Deeper insight into the constriction phenomenon is necessary to correctly monitor interface degradation and to accelerate the successful use of metal anodes in solid-state batteries. Here, we use a 3D electric network model to study the fundamentals of the constriction effect. Our findings suggest that dynamic constriction as a non-local effect cannot be captured by conventional 1D equivalent circuit models and that its electric behavior is not ad hoc predictable. It strongly depends on the interplay of the geometry of the interface causing the constriction and the microscopic transport processes in the adjacent phases. In the presence of constriction, the contribution from the non-ideal electrode/solid electrolyte interface to the impedance spectrum may exhibit two signals that cannot be explained when the porous interface is described by a physical-based (effective medium theory) 1D equivalent circuit model. In consequence, the widespread assumption of a single interface contribution to the experimental impedance spectrum may be entirely misleading and can cause serious misinterpretation.

An improvement of equivalent circuit model for state of health estimation of lithium-ion batteries based on mid-frequency and low-frequency electrochemical impedance spectroscopy

Electrochemical impedance spectroscopy (EIS) is a non-invasive, information-rich measurement method. The biggest advantage is that it is possible to identify and analyze the battery state using a suitable equivalent circuit model (ECM) without the need for complete knowledge of the battery's past operation. Conventional equivalent circuit models (CECMs) achieve a high degree of accuracy by identifying model parameters with relatively fixed circuit components. However, CECM method fitting process may suffer from fitting failure and fitting error, resulting in poor estimation accuracy. To solve this problem, it is crucial to establish a suitable ECM with good fitting effect and high accuracy. Accordingly, this study proposes a method of mid-frequency and low-frequency domain ECM (MLECM) based on fusion SEI film resistance and charge transfer resistance. Firstly, two model building methods are presented. Then, by fitting and analyzing the model parameters of two different types of batteries, we conclude that MLECM has the advantages of fewer parameters and better parameter fitting. Finally, a method of power battery state of health (SOH) estimation based on the improved model is proposed by MLECM and the mathematical model of SOH. Validated by two datasets of experiments with different types of batteries, the results show that the maximum RMSE of the proposed estimation method is only 1.38% in the two datasets. And the average root mean squared error (RMSE) of MLECM is reduced by 0.708% compared to CECM, while the computational load of the former is reduced by 69.57% compared to the latter. Compared with the CECM method, the MLECM has high estimation accuracy, high applicability and low computational load.

A decomposed electrode model for real-time anode potential observation of lithium-ion batteries

The anode potential inside the lithium-ion battery is crucial for battery internal state observation in electric vehicles since it indicates the states of lithium deposition at the anode surface. Conventional equivalent circuit models (ECMs) used in the battery management system (BMS) can only predict limited battery external characteristics. Electrochemical models which can simulate the battery internal behaviors are too complex for onboard applications. In this paper, a novel decomposed electrode model (DEM) is proposed for real-time anode potential observation in real BMSs. The cathode and anode parameters can be calibrated by inserting a reference electrode inside the battery. The decomposed electrode model shows high accuracy in predicting the cell terminal voltage and the anode potential under various current conditions. This model also has predominance considering both model simplicity and computational efficiency. An online anode potential observation algorithm is developed based on the DEM and the extended Kalman filter. A lithium plating-free fast charging algorithm is formulated further by integrating the closed-loop potential observer and the closed-loop current controller. The result indicates that the proposed decomposed electrode model is suitable for online applications in the BMS. • A novel decomposed electrode model (DEM) of lithium-ion batteries is proposed. • The DEM shows advantages in model accuracy, simplicity, and computing efficiency. • A high precision anode potential observation method is proposed based on the DEM. • A lithium plating-free fast charging algorithm is formulated with a PID controller.

A Comprehensive Physics-Based Equivalent-Circuit Model and State of Charge Estimation for Lithium-Ion Batteries

An accurate battery model plays a vital role in assessing the performance of a lithium-ion battery cell. Although a conventional equivalent circuit model (ECM) such as second-order RC model has been widely employed in developing battery management system, it is difficult to capture the electrochemical behaviors of lithium-ion batteries. To address this issue, we propose a comprehensive physics-based equivalent-circuit model (PECM) and state-of-charge (SOC) estimation method for lithium-ion batteries (LIBs). First, a simplified pseudo two-dimensional model is reformulated in the frequency domain to establish the relationship between the battery electrochemical and electrical properties. Different from the previous methods, the improved boundary conditions of electrolyte are introduced to obtain a group of dynamic electrolyte concentration regarding the variations of electrode thickness. Next, by incorporating the extended Kalman filter, a SOC estimation procedure is presented based on the developed PECM. Finally, the effectiveness of proposed PECM is validated in predicting battery terminal output voltage and SOC in case of two different test profiles. The simulation and experimental results show that, in contrast to the conventional ECM, our developed PECM is more suitable for characterizing the LIBs with high accuracy no matter under the US06 or HPPC current working conditions.

Parameterization of physical properties of layered body structure into equivalent circuit model

BackgroundThis study presents a novel technique to develop an equivalent circuit model (ECM) for analyzing the responses of the layered body structure to transcutaneous electrical nerve stimulation (TENS) by parameterizing electrical and geometrical properties.Many classical ECMs are non-parametric because of the difficulty in projecting intrapersonal variability in the physical properties into ECM. However, not considering the intrapersonal variability hampers patient-specifically analyzing the body response to TENS and personal optimization of TENS parameter design. To overcome this limitation, we propose a tissue property-based (TPB) approach for the direct parameterization of the physical properties in the layered body structure and thus enable to quantify the effects of intrapersonal variability.ResultsThe proposed method was first validated through in vitro phantom studies and then was applied in-vivo to analyze the TENS on the forearm. The TPB-ECM calculated the impedance network in the forearm and corresponding responses to TENS. In addition, the modelled impedance was in good agreement with well-known impedance properties that have been achieved empirically.ConclusionsThe TPB approach uses the parameterized circuit components compared to non-parametric conventional ECMs, thus overcoming the intrapersonal variability problem of the conventional ECMs. Therefore, the TPB-ECM has a potential for widely-applicable TENS analysis and could provide impactful guidance in the TENS parameter design.

A novel equivalent circuit-based model for photovoltaic sources

This paper presents a novel circuit-based model of photovoltaic (PV) source (cell, module or array) that can be easily integrated into any circuit-oriented simulators such as PSpice, PSCAD/EMTDC, PSIM, PowerSys of MATLAB/Simulink, etc. This proposed model is able to simulate accurately any commercial PV module behavior either exposed to uniform or non-uniform irradiance distributions. Moreover, it can also simulate perfectly PV arrays behavior in large scale PV systems. It is mainly derived from the conventional one-diode equivalent circuit model, which consists of a current source, a diode and two resistors. By modifying the linear part of this latter and including implicitly the effect of weather parameters (irradiance and cell temperature) on the circuit elements, our proposed model will encompass two types of dependent sources (voltage and current sources) and two resistances.To validate the truthfulness of the proposed novel model, comparisons between simulated and outdoor measured I-V characteristics on commercial PV module are done. Preliminary results have shown promising outputs and accuracy of this model.

Real‐time identification of partnership for a new generation of vehicles battery model parameters based on the model reference adaptive system

Partnership for a new generation of vehicles (PNGV) model is a conventional battery equivalent circuit model (ECM). However, identifying the best parameters for this model is a challenge. In this study, the PNGV model is transformed into a directly identifiable difference equation to identify its parameters. Subsequently, the model reference adaptive system (MRAS) is used to realize the real-time identification of the model parameters. The identification accuracy of the MRAS is found to be superior to that of the recursive extended least square algorithm. For a single hybrid pulse power characterization (HPPC), the PNGV model identified by the MRAS can achieve a high-precision terminal voltage estimation. For lithium iron phosphate, lithium titanate, and nickel-metal hydride batteries, the root mean square errors are 0.024, 0.048, and 0.020 V, respectively. Besides, the real-time state of charge (SOC) estimation can be realized by the identified open-circuit voltage (OCV). The average errors of the three batteries are only −0.02, −0.01, and −0.01, respectively. Since the PNGV model has a capacity of describing the change of OCV with the current accumulation effect, the model is only suitable for simulating single HPPC or positive-negative pulses with equal amplitude and not for other current pulses. This is a major drawback of the PNGV model. The real-time PNGV model parameters identification method proposed in this study can provide a solid foundation for various state estimation of a battery. Novelty Statement Transformation of the PNGV model into a difference equation that can be directly identified. Real-time identification of the PNGV model parameters via the MRAS. The identified OCV realized the real-time SOC estimation and discussed the deficiencies of the PNGV model.

Anticorrosive polypyrrole/zirconium-oxide composite film prepared in oxalic acid and dodecylbenzene sulfonic acid mix electrolyte

In this study, the surface of aluminum (Al) was coated by Polypyrrole (PPy) and Polypyrrole/Zirconium-oxide (PPy/ZrO2) films by using galvanostatic method in oxalic acid (OXA) and dodecylbenzene sulfonic acid (DBSA) mixture electrolyte. Structural and thermal characterization of the coatings were performed by Fourier transform infrared (FT-IR), X-ray diffraction (XRD) and Thermogravimetric (TG) analyses, while surface morphologies were examined by Scanning Electron Microscopy (SEM) and Atomic Force Microscopy (AFM). The anticorrosive effect of these coatings in a corrosive medium was investigated by Tafel Polarization and Electrochemical Impedance Spectroscopy (EIS) techniques. While the experimental data were evaluated with conventional equivalent circuit model, polarization resistance (Rp) values were estimated by using the Cole-Cole plotting. The PPy film increased the polarization resistance of the Al electrode 13 times, while the PPy/ZrO2 film increased it enormously by about 330 times. Furthermore, PPy/ZrO2 film provided almost 100 % protection efficiency against corrosion. The anti-corrosive performance of the coatings was associated with the anodic protection, barrier effect and prevention of charge transport by nanometal-oxide particles. It is thought that the Cole-Cole plotting approach could be a simpler and more useful method than the equivalent circuit fit method in calculating the Rp value for EIS curves containing inductive loop.

Simplified equivalent circuit approach for designing time-domain responses of waveform-selective metasurfaces

In this study, we demonstrate simplified equivalent circuit models to effectively approximate responses of recently reported waveform-selective metasurfaces that distinguish different electromagnetic waves even at the same frequency depending on their waveforms or pulse widths. Compared to conventional equivalent circuit models that represent behaviors of ordinary metasurfaces in the “frequency” domain, the proposed models enable us to explain how waveform-selective metasurfaces respond in the “time” domain. Our approach well estimates not only time constants of waveform-selective metasurfaces but also their entire time-domain responses. Particularly, this study reports the importance of resistive components of diodes as well as the limitation of our models with respect to the power dependence although still the models effectively work when waveform-selective mechanisms are clearly exhibited with a sufficiently large input power. Thus, the idea of the proposed equivalent circuit models contributes not only to a greater understanding of waveform-selective mechanisms but also to facilitating the design process of such unique structures.

On-Board State Estimation in Electrical Vehicles: Achieving Accuracy and Computational Efficiency Through an Electrochemical Model

Success of electric mobility and connected future depends on advanced high capacity Lithium-ion batteries and a tailored battery management system that keeps track of battery health and safety to optimize the performance. The drive for advanced batteries is being pursued on one front via the development of novel chemistry, for example, blended composite cathodes to achieve enhanced performance and life. On the other front, the need for optimal battery performance via operational control viz. a robust Battery Management System (BMS) that accurately predicts state-of-charge (SOC), state-of-power (SOP) and state-of-health (SOH) in a computationally efficient way, has been lacking in many ways due to the reliance on simple and fast-to-compute models such as equivalent circuit models (ECM) that lack the accuracy needed for large battery packs. This paper reports an on-board reduced-order electrochemical thermal model (ROTM) based SOC and voltage estimation for a 12S1P configuration composite-cathode battery pack and demonstrates its practicality by implementing it on four different micro-controller units (MCU) (ATmega:2560&328, Infineon:TC275&TC297). We show that on-board ROTM based SOC and voltage prediction have better accuracy compared to the conventional ECM based methods under both static and dynamic load conditions.

Electromechanical Equivalent Circuit Model of a Piezoelectric Disk Considering Three Internal Losses

Heat generation by internal loss factors of piezoelectrics is one of the critical issues for high power density piezoelectric applications, such as ultrasonic motors, piezoelectric actuators and transducers. There are three types of internal losses in piezoelectric materials, namely dielectric, elastic and piezoelectric losses. In this paper, a decoupled equivalent circuit is proposed to emulate a piezoelectric disk in radial vibration mode considering all three types of internal losses. First, the decoupled equivalent circuit is derived according to the conventional electromechanical equivalent circuit model. Then, a piezoelectric disk configuration in radial vibration mode is explored and simulated. The resonance and antiresonance frequencies and their corresponding mechanical quality factors are achieved by the proposed circuit. In order to verify the accuracy of the simulation results, the piezoelectric disk is fabricated and tested. Simulation results with the new circuit exhibit a good agreement with experimental results. Finally, the equivalent circuit with only dielectric and elastic losses are simulated and compared which further validates the accuracy improvement of the new equivalent circuit considering all three losses.