Mutual Inductance Research Articles

Self- and Mutual Inductance of NbN and Bilayer NbN/Nb Inductors in a Planarized Fabrication Process With Nb Ground Planes

We present measurements of the self- and mutual inductance of NbN and NbN/Nb bilayer inductors (microstrips, striplines, serpentines, etc.) with Nb ground plane(s) fabricated in an advanced process for superconductor electronics developed at MIT Lincoln Laboratory. In this process, the signal traces of logic cell inductors are made either of a 200-nm NbN layer with <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">T_c</i> ≈ 15.5 K or an in-situ deposited NbN/Nb bilayer, replacing a 200-nm Nb layer M6 in the standard SFQ5ee process with nine superconducting layers on 200-mm wafers. Nb ground planes are preserved to maintain a high level of interlayer shielding and low intralayer mutual coupling. A two-step patterning of the top Nb and the bottom NbN layers of the NbN/Nb bilayer allows the creation of inductors with a very wide range of inductances, from low values ∼ 0.4 pH/µm typical for Nb geometrical inductors to ∼ 35 pH/µm typical for thin-film kinetic inductors. The mutual inductance of various combinations of NbN, Nb, and NbN/Nb inductors does not depend on superconducting properties of the signal traces in the studied range of linewidths, <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</i> ; it equals the mutual inductance of the Nb inductors with the equivalent geometry and placement between the ground planes. The measured magnetic field penetration depth in NbN films deposited by reactive sputtering at 200 °C is <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">λ_NbN</i> = 491±5 nm. The measured kinetic inductance of the films with thicknesses <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> = 200 nm and 150 nm, respectively 1.51 pH/sq and 2.06 pH/sq, is larger than that expected for conventional superconductors with short mean free path, corresponding to about 25% lower superfluid density. We also measured kinetic inductance of the right-angle bends of NbN striplines and found it to be negligible at <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">w</i> < λ <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">_NbN</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> / <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">t</i> , indicating an insignificant effect of current crowding in the presence of superconducting ground plane(s). Implementing NbN and NbN/Nb kinetic inductors enables a significant increase in the integration scale of superconductor digital electronics.

New Control Method for Receiver-Side DC–DC Converter With Large Stability Margin and Fluctuation Suppression Toward DWPT System

Dynamic wireless power transfer (DWPT) system is applied to electric vehicles, medical treatment, communication and many other fields. Usually, a DC-DC converter is cascaded at the receiver side to suppress output fluctuation caused by mutual inductance change in the moving process. However, there occurs instability in some conditions in the system under conventional topology and control method. This work proposes a new control method based on dual buck-boost converter to handle the above two problems at the same time. It can, in theory, reduce the peak-peak and average values of DC inductor current, meanwhile, increase the converter efficiency. Also, it can improve the stability margin of the whole system. In this paper, we use a simulator to replace the actual DWPT system. Through the simulator, the WPT system can produce the same fluctuating output voltage as that under dynamic conditions to support experiment. The stability of the system is explored by constructing the small signal model of the system. Then, the effectiveness of the method is proved by simulation and experiment results.

Wireless coupling for LVDT sensor for reactor applications

Wireless coupling can offer significant advantages for in-reactor applications. For instance, wireless signal couplings can avoid electrical feedthroughs penetrating fuel cladding or other high-temperature pressure barriers in fuel performance testing. This paper presents a feasibility study of a wireless coupling technology for the linear variable differential transducer (LVDT), as LVDTs have been successfully demonstrated in reactor applications and can be used to measure a variety of physical parameters. The coupling technology utilizes mutual inductance at a low frequency to transfer power into and signal out of a stainless steel pressure barrier. Using Kirchhoff’s law and magnetic circuit analysis, a theoretical model is developed, including the LVDT, wireless power coupling parts, and wireless signal coupling parts. The LVDT is assumed to have a constant inductance of the primary coil and the sum of two secondary coils. An experimental system is built to test and verify the performance of the technology with a commercial LVDT. The experimental setup has an input voltage limitation to prevent the excessive heating. The non-linearity of the commercial LVDT is ±0.77% as measured in the lab. After coupling the LVDT with the wireless system, the measurement non-linearity is increased to ±1.26%, which shows the wireless power and signal transfer can be applied with LVDTs with limited additional measurement uncertainty. The theoretical model prediction agrees with the experiment results, with the maximum discrepancy of 1.5% between prediction and experiment. The model and experimental results of this study can be directly used to guide the design and optimization of wireless LVDT measurement systems for future in-reactor experiments.

An Accurate Power Model and High Power Density Design Method of Free-Standing Magnetic Field Energy Harvesters With H-Shaped Core

To achieve more output power of the free-standing magnetic field energy harvester (FSMFEH) with a smaller core volume, designing the core and coil parameters of FSMFEH is critical. However, the lack of an FSMFEH power model leads to the absence of a detailed design method. To address this issue, building an accurate FSMFEH output power model is required. In this work, by quantifying coil mutual inductance and internal resistance as core and coil parameters, an accurate power model of FSMFEH with all parameters is established based on the H-type core. As a result, based on the proposed model, the optimal values of the core column size, the core lamination size, the coil turns, and the wire diameter are designed. Experiment results show that the proposed model can maintain high accuracy, and the power density deviation is within 5% compared with the theoretical value. Besides, the optimized parameters designed according to the model analysis are effective for improving the power density. When the current of the busbar is 100A, the maximum power density can reach 4.182mW/cm <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup> , and the corresponding maximum output power is 13.25mW with the optimized parameters.

Stripline Topology for Flux Mitigation

The increasing complexity of modern single flux quantum (SFQ) circuits has increased the importance of flux trapping and trapped magnetic fields within SFQ systems. This trapped flux reduces margins while damaging the operability of superconductive circuits. In this paper, an area efficient stripline topology is introduced to prevent flux from being trapped within striplines. The topology is composed of coupled narrow lines rather than wide striplines. The proposed topology uses a fingered narrow line configuration. The fingered narrow line topology enhances the scalability of SFQ systems while not requiring additional area. The proposed topology decreases the length of the striplines by exploiting the mutual inductance between narrow parallel lines. The topology requires less area while preventing flux from being trapped within wide superconductive striplines. Due to the configuration of the proposed stripline, residual current is eliminated in VLSI complexity SFQ circuits. The fingered narrow line topology also reduces coupling capacitance between striplines. The proposed topology is compatible with automated routing of large scale SFQ integrated circuits.

Geometric decoupling using clip-path conductors for whole-brain transceiver array at 7 T

In magnetic resonance imaging (MRI), a radiofrequency (RF) coil array with a large number of elements is commonly employed for transmission and reception to improve the uniformity of the RF transmitting magnetic field and increase the signal-to-noise ratio. Additionally, multi-element RF arrays can reduce the acquisition time using the parallel imaging technique. However, mutual inductance coupling is unavoidable in multi-element RF coil arrays. Therefore, many researchers have studied geometric and artificial decoupling techniques to minimize mutual inductance coupling. This study proposes a decoupling method using clip-path conductors (CPCs). The CPC geometry locates the top-right and bottom-left positions in the loop coil to reduce the mutual inductance coupling between adjacent elements. The decoupling performance of the CPC coil was verified via electromagnetic simulations and bench measurements. An eight-element transceiver CPC array was manufactured, and phantom and healthy volunteer images were acquired using a 7-T MRI system.

WIRELESS POWER TRANSFER FOR UNDERWATER VEHICLES

Wireless power transfer (WPT) through magnetic resonance coupling (MRC) offers a safe and simple solution for underwater (UV) vehicles without being affected by water conductivity. Due to its ease of control in WPT systems, the most suitable topology is Serial-Serial (SS). In this study, square transmitting and receiving coils with dimensions of 40 cm - 40 cm were designed for 3.3 kW power transmission at 85 kHz. The design was studied in the air, pure water, and seawater environments. Three different cases were analyzed with ANSYS Maxwell 3D. The WPT system responded similarly in air and pure water environments. However, it was determined that the eddy current loss increased, the mutual inductance decreased, the coupling factor weakened, and the critical air gap decreased by about 0.2 cm in the seawater environment. The results showed that the WPT system's efficiency was similar for air and pure water but tolerably lower in the marine environment. Further, the health effects of the WPT design were examined through the ANSYS HFSS, in line with the IEEE standard and ICNIRP guidelines.

A Quadrupole Receiving Coil With Series-Connected Diode Rectifiers for Interoperability of Nonpolarized and Polarized Transmitting Coils

Non-polarized and polarized coils are utilized in an electric vehicles (EV) wireless charging system. These coils are decoupled from each other at the central position, leading to interoperability issues. This letter proposes a new decoupling method and a quadrupole receiving coil with series connected diode rectifiers for interoperability purposes. Decoupling windings are added to achieve decoupling of the four receiving poles. The total mutual inductance between the transmitting coil and the quadrupole receiving coil is the summation of the absolute values of the mutual inductances between the transmitting coil and the four receiving poles. In this way, the proposed quadrupole coil can be tolerant with not only the non-polarized transmitting coil, but also with the polarized transmitting coils along two perpendicular directions. The experimental results confirm that a large coupling and efficient power transfer can be achieved with the non-polarized coil and the polarized coil placed at two perpendicular directions with good misalignment tolerance.

Micromachined Two-Dimensional Weak Magnetic Field Sensors of Soft Magnetic Film/Planar Coil Laminated

Two-dimensional magnetic sensors of soft magnetic film/planar coil laminated have outstanding advantages in miniaturization and integration. However, due to the cumbersome process and complicated structure of the sensor, its yield rate is extremely low, and the gap between magnetic films is large, resulting in increased leakage flux and low sensitivity. Therefore, a high-performance soft magnetic film with through-holes/ planar coil laminated micro-magnetic sensor with mutual inductance is designed and the sensor is fabricated by Micro-Electro-Mechanical System technology. The micro-magnetic sensor can be processed in 15 steps, with a yield rate of more than 95%, and the gap between magnetic films can be effectively reduced, resulting in reduced leakage flux and improved sensitivity. Moreover, the effect of coil resistance is eliminated, the noise level of the proposed mutual inductance micro-magnetic sensor is reduced and the detectivity can be significantly enhanced. The experiment result shows that the sensitivity of the proposed mutual inductance micro-magnetic sensor is 46.5 mV/Oe in the range of 0 Oe~0.3 Oe, the voltage noise is as low as 0.8 μV/√Hz, and the noise level reaches 17.2 μOe/√Hz. Therefore, the detectivity of the proposed mutual inductance micro-magnetic sensor can reach 17.2 μOe (1.72 nT), which has significant potential in several areas, such as biosensing and geomagnetic navigation.

Contactless-Sensor-Based Output Feedback Control With Maximum Efficiency Tracking Technique in Inductive Power Transfer Systems

To maximize the overall efficiency of a series-series inductive power transfer (SSIPT) system, the maximum efficiency tracking (MET) control should be employed. Based on a contactless current sensor which is designed for the mutual inductance estimation and the output voltage feedback, this paper proposes a novel MET control method for the SSIPT system with front-side and load-side converters. In this method, the output voltage of the rectifier on the load side is estimated and used as a control reference on the front side. Moreover, this paper analyzes the small-signal model of the SSIPT system and presents an impedance-based stability criterion. The factors which influence output feedback control are investigated, and a comprehensive control strategy based on the impedance stability criterion is developed. Finally, a 600 W prototype is built to validate the proposed method. MET control is implemented in a wide range of load variations, with a maximum efficiency drop of approximately 2.3% over a 100 mm misalignment. The results show that the proposed scheme significantly improves the robustness and response performance of the SSIPT system.

An adaptive energy acquisition power supply for power transmission line

Reliable power supply is of great significance to the stable operation of the online monitoring device. This paper studies a kind of electric energy collection power supply based on the principle of current mutual inductance. The iron core is made of nanocrystalline alloy with high permeability, and the relationship between the number of turns and the energy consumption power is analyzed by equivalent circuit. A discharge circuit is formed by connecting multiple diodes in series to avoid oversaturation of the iron core, and the residual voltage on the diode supplies the load electric energy. Combined with simulation and experiment, the number of turns and the number of diodes in series are optimized, so that the power supply has high efficiency and is not easy to be deeply saturated. The rectifier bridge and DC-DC voltage regulator module are used to stabilize the output voltage. The test shows that the power supply can support reliable energy extraction within the range of wire current of 17A at least and 1000A at most, and can be applied to lines of various voltage levels.

A numerical method to calculate screening current-dependent self and mutual inductances of REBCO coils

The screening current and its relaxation cause the variation of the self- and mutual inductances of REBCO coils—REBCO is one of the high-temperature superconductors. However, most studies of coil voltage analysis on a REBCO magnet, a stack of coils, have reported simulation results assuming invariant self- and mutual inductances so far. Although the conventional assumption of invariant inductances is still acceptable for fundamental coil voltage analyses, it can cause misleading conclusions due to inductive voltage errors when a precise coil voltage analysis is demanded. Hence, here we report a numerical method to calculate screening-current-dependent self- and mutual inductances of REBCO coils for advanced studies based on a lumped-circuit analysis model. In this work, we aim to investigate the inductance variation due to the screening current with a case study and discuss its effects on the coil voltage. We assume that there is a stack of 12 REBCO single-pancake coils. No transverse current in each coil is considered for simplicity. A numerical simulation of the current density in the magnet is performed, and then the inductances are calculated by considering the spatially non-uniform current density due to the screening current. From this case study, we confirm that the self- and mutual inductances are changed by up to 110% and 30% each. It is also confirmed that the discrepancy is notable at the beginning of the charge while marginal at the end. Finally, we discuss the effect of inductance variation on the quench voltage analysis.

Simulation and Theoretical Study on the Mutual Inductance of the B-Dot Used for High-Power Transmission Lines

For the B-dot used for high-power transmission lines, due to its special structure, the current method to obtain its mutual inductance is calibration experiments and there lacks an effective method to estimate its mutual inductance at the design stage. In this paper, the mutual inductance of this kind of B-dot is studied by simulation and theoretical analysis. Through simulation, the frequency response of the mutual inductance is obtained and it is found that the mutual inductance at high frequency which is the main working frequency range of the B-dot is lowest and stable. Through theoretical analysis, the approximate calculation formula of mutual inductance at any frequency is derived. Using the experimental results in previous reference, the theoretical results and the simulation results are verified. The influencing factors of the B-dot’s mutual inductance at high frequency are analyzed. The results show that the number of wire loops, the inner radius of wire loops and the radius of hole are positively related to the mutual inductance, and the height of the center of the wire loops is negatively related to the mutual inductance. Among these four factors, increasing the inner radius of wire loops can improve the mutual inductance more significantly. The work in this paper reveals the physical meaning of the mutual inductance change and provides guidance for the design of the B-dot.

Highly tunable and ultrasensitive hybrid plasmonic platform for multi-spectral sensing: Non-invasive diabetes surveillance and global warming directives

The development of tunable and extremely sensitive devices, as well as the emergence of metamaterials, has tremendously aided the evolution of plasmonic sensing technologies. However, the natural property of metamaterials severely restricts the scalability and application potential of mono-functional sensor systems. To address this shortcoming, we have investigated an ultranarrow five-band plasmonic sensor with structural tunability and high sensing behaviors in compatibility with multi-purpose application scenarios, using the finite-difference time-domain approach rigorously. Meanwhile, we theoretically formulated a hybridization model for the mutual induction of Fabry–Pérot resonances and localized surface plasmon polariton resonance, providing a theoretical basis for the utilization and conception of the highly-sensitive tunable plasmonic sensor. Most notably, we discovered and interpreted far-field phase extinction inducing separation of polarization resonance peaks in physical mechanisms. The tunability of its mutual inductance effect at the intersection distances from two-intersecting silver nanogroove was adequately exploited to further validate and effectively attain five ultra-narrow absorptivities of 96.70%, 93.93%, 99.73%, 100.00%, and 89.72% by top-level optimization. In addition, the redundant proximity between nearby peaks is compensated, extending the operating band and enhancing the practicability in multi-purpose scenarios. As a reliable source for future optical sensing, it performs well in the visible to near-infrared region, enabling detection response to non-invasive diabetes mellitus, global climate warming, and unrestricted temperature and pressure measurement. Meanwhile, minimum FWHM = 4.806 nm and maximum FOM = 115.13 RIU−1 are obtained at 293.15 K, with an associated highest sensitivity of 557.93 nm/RIU. Moreover, the fabrication technologies development of electron beam lithography and focused ion beam etching technologies enables large-scale mass production at low cost and long-term stability.

Underground Displacement Measurement Method Based on Double Mutual Inductance Voltage Contour Model of Optimized Dual Kriging

Landslide is a common geological hazard. Existing displacement monitoring sensors for landslides are classified into surface displacement and underground displacement. However, current underground displacement sensors cannot effectively monitor the vertical displacement caused by soil accumulation of landslides, which cannot meet the needs of landslide monitoring. Therefore, this study has designed a three-dimensional underground displacement measurement sensor based on the double mutual inductance voltage contour method. Since the double mutual inductance voltage measurement model has low measurement accuracy due to low interpolation accuracy and complex location calculation method when solving the spatial position, the improved Dual-Kriging interpolation method based on quantum pigeon inspired algorithm is adopted to improve the original interpolation accuracy. The experimental results show that this method avoids the complex problem of Kriging interpolation calculation and improves the calculation speed. At the same time, the overall accuracy is significantly improved, reducing its fitting error and actual value to a maximum of three ADC12 resolutions. The landslide experiment on the landslide simulation experiment platform shows that the sensor can effectively reflect the displacement of underground soil, and has important application value for slope displacement monitoring.

Design of a Highly Compatible Underwater Wireless Power Transfer Station for Seafloor Observation Equipment

Conventional cabled seafloor observatories (CSOs) power in-situ instruments via wet-mated or dry-mated direct electrical contact (DEC) connectors to achieve long-term and real-time observation. However, the DEC connectors have high risks of water leakage and short circuits in power feeding, especially under high water pressure. This paper proposes a highly compatible underwater station based on inductive wireless power transfer (IPT) technology to address the above reliability issue. A novel energy transmitter with runway-structure coils is applied to the proposed underwater station to cover a sufficient power feeding area so that various in-situ equipment can be powered with desirable misalignment tolerance. The magnetic field distribution is analyzed by both derivation and finite element analysis (FEA) methods, and the principal parameters of the transmitter are further optimized and compared with both the mixed-integer sequential quadratic programming (MISQP) algorithm and the evolutionary algorithm (EA) for better performance. The same results show a reliable optimization process. The WPT circuit characteristics are also investigated to power different loads and improve the power transmission efficiency. The output power decreases, and the transmission efficiency rises and then decreases as the load increases. In addition, receivers with higher mutual inductance have better transmission performance. A prototype of the underwater station has been tested both in air and in water, and the experimental results have proven it can power multiple seafloor observation instruments stably and achieve compatibility requirements. The maximum output power of the station prototype for testing is 100 W, and the maximum overall transmission efficiency is 61%.

Electromagnetic Displacement Sensor and Docking Method Based on Elliptic Integral Series Expansion

Automatic charging can improve the endurance of unmanned work platforms, but the docking accuracy limits its success rate and charging efficiency. In order to solve this problem, an accurate docking method based on elliptic integral series expansion is proposed. The relationship between load voltage and coil transverse offset distance is constructed by establishing a coil mutual inductance circuit, a coil center points transverse offset mutual inductance coefficient calculation model, and a triangular positioning geometry structure Numerical integration and elliptic integration series expansion are used to solve the exact correspondence between the coil mutual inductance coefficient and the coil transverse offset distance. Finally, the relationship between the load voltage and the lateral offset distance from the center of the coil is obtained. The method does not require the arrangement of additional sensors and coils, nor does it require extensive prior data collection for unique coil configurations. The system can be used for energy transmission and as a displacement sensor. It has been verified by COMSOL simulations that the maximum relative error in the coefficient of mutual inductance is 6.507% for the numerical integration method and 9.022% for the elliptic integration series expansion approach. After experimental verification, the maximum average relative error of the load voltage is 4.048% for the numerical integration method and 11.89% for the elliptic integration series expansion approach. This method achieved high accuracy positioning measurement with the error range at the centimeter level. The method contributes to the long-term application of unmanned operating platforms.

A Family of IPT Battery Chargers With Small Clamp Coil for Configurable and Self-Sustained Battery Charging Profile

To self-sustain the constant current (CC) output to constant voltage (CV) output transition for inductive power transfer (IPT) chargers, the clamp coil assisted IPT battery chargers are better than the existing solutions due to the merits of no additional switching components, sensors, and control circuits. However, the clamp coil of these IPT chargers is bulky and hard to design, as the mutual inductances between the clamp coil and the main coupler coils are significant to the output performances. To facilitate the small clamp coil in the transmitter, this paper proposes a family of IPT battery chargers with a proper secondorder compensation network on the secondary side. The output thresholds of the IPT charger with the proper compensation can be readily configured to cope with the desired charging profile, and the clamp coil can be designed very small to decrease the corresponding cost and size. In addition, the proposed threecoil IPT charger still features automatic and smooth CC-to-CV transition to eliminate wireless communication, near unity power factor to minimize voltage-ampere (VA) ratings, soft switching to improve transfer efficiency, and open-circuit protection during CC charging. An experimental prototype of a 48 V/2.5 A battery charger is built to verify the analysis.

Optimal Design of Transmission Characteristics for Hexagonal Coil Wireless Power Transfer System Based on Genetic Algorithm

Effective optimization methods are used to guide the optimal design of coil parameters, which is significant for improving the transmission performance of the wireless power transfer (WPT) system. Traditional methods mostly rely on the exhaustive attack method and finite element analysis (FEA) to achieve the coil parameter design, which have the disadvantages of complex modeling and time-consumption. To overcome these limitations, this study proposes an optimization strategy based on the genetic algorithm (GA), which considers the actual requirements of the efficiency and power of the WPT system. First, a direct integration method is proposed to simplify the analytical solution process of the mutual inductance between the hexagonal coils. Based on the mutual inductance model, the transmission characteristics of the hexagonal coil WPT system are deeply analyzed by the control variable method. Most importantly, with the proposed optimization objective function and its constraints, the GA is used to automatically achieve multi-parameter optimization of the hexagonal coil. Finally, a 500 W WPT system experimental platform is established, and the experimental results verify the feasibility of the proposed optimization method.

Calculations of Self- and Mutual Inductances for Racetrack Coils Using Equivalent Models

This paper presents the calculations of self and mutual inductances for thin racetrack coils using a novel approach. Approximate rectangular and diamond shape models for racetrack coils are used for the analysis with the same cross-sectional area and circumference as the racetrack coils. A 3D analytical method using separation of variables method and Fourier series is developed for the magnetic fields analysis and calculation of self and mutual inductances for thin racetrack coils. The analytical method utilizes magnetic vector potential with two components to solve Maxwell differential equations. Different racetrack coils with different dimensions are considered for the validation of analytical modeling for the inductance calculations. The inductance calculations of circular coils are also presented as special cases for racetrack coils. The approaches for the mutual inductance calculation of racetrack and circular coils could be utilized for wireless power transfer and charging applications.