Design and Analysis of Inductive Power Transfer System Using Nanocrystalline Flake Ribbon Core

This article proposes the design and analysis of an inductive power transfer (IPT) system that features novel nanocrystalline flake ribbon (NFR) cores. The flake ribbons are produced by compressing the dielectric material with nanocrystalline ribbons, leading to a reduction in the eddy current loss. A complete magnetic core is then fabricated by laminating the ribbons, imparting anisotropic properties. The article outlines the design methodology for NFR cores, considering this lamination characteristic in Double-D IPTs. Accordingly, NFR cores with a lamination factor of 0.375 and a core thickness of 3.2 mm have been designed, produced, and experimentally validated. The tests indicate an over 95% dc–dc efficiency and an over 96.3% ac–ac efficiency at the output power of 8.9 kW. To assess their thermal attributes, one-hour duration tests at continuous 6.6 kW operation were performed on NFR cores and ferrite groups. Results demonstrate that NFR cores maintain a cooler temperature at 76.4 °C, whereas the DMR44 and DMR95 reach 91.7 °C and 84.9 °C respectively. Additionally, the designed NFR cores have achieved 51% core weight reduction, 31% volume reduction, and 20% thickness reduction. The proposed NFR cores based on the design methodology can greatly enhance high power density IPT systems.

To heighten their competitiveness with conventional cable charging, improving the efficiency and power density of IPT systems has become a significant research objective.Typically, magnetic materials are used to provide a low magnetic reluctance path and enhance the coupling between the charging pads.Manganese zinc (MnZn) ferrites have been the most popular magnetic material choice for IPT applications so far, primarily due to their cost-effectiveness and widespread availability.However, these materials present inherent limitations, such as variations in characteristics with temperature changes, lower thermal conductivity, and high core loss [7], [8], [9], [10], [11], [12].The manufacturing process of MnZn ferrites results in challenges for production with high length-width ratios and low thickness [13], [14].This will inevitably bring micro air gaps during the core placement, resulting in highly uneven temperature distribution.The high thermal expansion coefficient of ferrite increases the risk of cracking at high operating temperatures, potentially endangering the system's stability.Many research studies were carried out to optimize the ferrite core placement, aiming to minimize this effect [7], [15], [16], [17], [18], [19].However, using extra core material significantly reduces power density and increases overall weight.This poses a significant issue in automotive wireless charging, where the space for embedding wireless charging pads within the vehicle is particularly constrained.
In recent years, nanocrystalline-based Fe-Cu-Nb-Si-B materials have surfaced, attracting substantial research attention.This material exhibits a high saturation flux density (approximately 1.2 T), superior permeability, and low hysteresis losses [19].Nevertheless, their high conductivity results in exceptionally high eddy current losses.Research has been done to mitigate this issue.In [20], a crushed nanocrystalline material has been proposed and demonstrated in an 11 kW IPT system.Even though the core loss was reduced compared with ferrite, its coupling and overall efficiency did not show an improvement because of the low permeability after crushing, design targets and methodology are lacking.Gaona et al. [21], [22], Zhang et al. [23] proposed the implementation of nanocrystalline ribbon cores (NRC).The material exhibits both high permeability and conductivity.The eddy current losses can be reduced dramatically by laminating the nanocrystalline ribbons perpendicular to the flux pipe direction in IPT.However, the NRC is manufactured with low flexibility, with these developments yielding no improvement in the power density.Furthermore, the complexity involved in manufacturing such cores hinders its practical application, degrading its potential use in real-world scenarios.In [24] and [25], nanocrystalline flake ribbon (NFR) has been proposed and utilized in inductor and transformer designs.The material has demonstrated better performance than ferrite in terms of saturation flux density, thermal performance, and stability under dc bias conditions.However, due to large air gaps in IPT applications, the design methodology is still lacking in the current literature.
Research on the use of NFR in IPT applications is scarce.Design considerations of NFR core in IPT applications should differ from those of inductor and transformer because of the dominant leakage field, pure ac excitations and complexity of flux paths.Considering those, the characteristics of NFR can significantly benefit the magnetic coupler design for Double-D IPTs as below.
1) The flexibility of core dimension makes it possible to produce cores with a high length-width ratio.Such cores can be placed along the flux pipe without any air gap, increasing coupling and eliminating hot spots.2) Both saturation flux density, as well as the thermal conductivity of the NFR, are higher than ferrite, making it possible for high power density design.
3) The stacking factor can be flexibly changed to tune effective permeability considering the anisotropic characteristics; core design can be optimized accordingly to achieve better overall performance than ferrite, particularly considering power density.
This article analyses NFR in the magnetic design for the Double-D IPT system, especially in terms of the coupling coefficients and core losses in different stacking factors and thicknesses.The design methodology for practical high power design is proposed.In Section II, the filling factor and stacking factor are introduced for the composition of NFR.Equivalent permeability is obtained.Core losses between NFR and traditional ferrite are compared to yield the characteristics of the material.Section III introduces the simplified magnetic circuit in the Double-D IPT system.The circuit model can provide insights into the optimization targets for the magnetic couplers.The flux distribution difference between solid ferrite and laminated NFR is pointed out and compared qualitatively.The homogenization method commonly applied for laminated cores exhibits significant inaccuracy due to the non-unified flux distributions inside the cores.Based on this, simulations are carried out in Section IV.Design methodology for NFR stacking factor and thickness is proposed, considering its property anisotropy and core loss characteristics, to achieve high power density.The methodology can be expanded to other laminated cores.A combination of stacking factor and thickness is selected to fulfill the system requirement.Section V, the experiments are carried out for different core thicknesses to verify the design.The coupling coefficient and efficiency are measured up to 9 kW.An extended duration test is also performed at 6.6 kW to demonstrate its practical use.

II. NFR IN IPT APPLICATIONS
A. Permeability of NFR Core Fig. 1 shows the simplified manufacturing process of NFRs.By crushing and compressing original nanocrystalline ribbons with adhesives, the current path inside the material is effectively cut, resulting in reduced eddy current loss.The filling factor, the ratio between nanocrystalline material and dielectric material, determines the effective permeability of the flake ribbons.Lower filling factors indicate more intercept filling, which leads to smaller eddy current loops.Therefore, the permeability and core losses are reduced simultaneously.The typical relative permeability of NFRs ranges between 1000-14 000, excluding the adhesive materials.Table I shows the property comparison of DMR44 and DMR95 from DEMGC and NFR from AT&M.The ferrite group, equivalent to TDK N87 and N95 [26], [27], is widely adopted in IPT applications.The conductivity is measured with the four-probe method by HPS2661.The permeability, core loss, saturation flux density and maximum temperature of the NFR material are superior to ferrite.The thermal conductivity of NFR ranges between 7-10 W/mK [28], [29], higher than MnZn ferrite, which is about 5 W/mK [30].Therefore, the thermal distribution for NFR is also expected to be more uniform than ferrite, enabling higher power density design.
The flake ribbons can be further laminated with a specific stacking factor F, to form a complete core.During this process, anisotropic property is obtained.The permeability in Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.stacking direction µ stack and ribbon direction µ ribbon can be calculated as follows [31]: where µ NFR is the relative permeability of the NFRs, and µ 0 is the permeability of air.
Fig. 2 shows the proposed lamination structure of an NFR core.The cores include NFR layers and adhesive layers as the basis, while the additional forming layer can be added to control the stacking factors.The nominal thickness of the NFR layer is 20 µm, and the adhesive layer on each side of the ribbon layer is around 3-5 µm.Luo et al. [25] proposed a stacking factor calculation method based on weight.However, in IPT applications, the thickness of the non-magnetic layer also plays a role.Considering the flux directions are not uniform, the anisotropic property must be considered.Therefore, traditional thickness-based stacking factor calculation is used where t r and t m are the thickness of the ribbon and the entire core, respectively, the material of the forming layer can use isolation material with high thermal conductivity, such as a thin silicone thermal sheet.The thickness of the forming layer, considering commercial availability, ranges between 100 µm-1 mm.Therefore, a range of 0.15-0.55stacking factor is achievable in the laboratory conditions.Higher stacking factor involves precision tools as well as stacking machines to eliminate the introduced airgap and to well flatten the ribbons.A lower stacking factor will result in smaller effective permeability but also brings reduced core loss due to lower conductivity between the magnetic layers.Therefore, compromises must be made for different applications.The design method is discussed in Sections III and IV.

B. Core Loss Characteristics of NFR
Modified Steinmetz is commonly used to evaluate the core loss characteristic for magnetic materials, and the coefficients can be used to assess the suitability of the applications.The modified Steinmetz equation is shown as follows: where P core is the power loss in kW/m 3 , T is the operating temperature, f is the excitation frequency, and B m is the peak flux density.The rest of the parameters are empirical.
Particularly, α and β are related to the excitation frequency and flux density, respectively.Parameters a-c are the unitless temperature coefficients extracted from the temperature tests.
In [25], the modified Steinmetz parameters for NFR are given.Coefficients are then converted for a single ribbon.The comparison of the coefficients for NFR and DMR44 is shown in Table II.The exponent α for NFR exceeds that of DMR44, suggesting that NFR's loss increases more rapidly as frequency increases.This aligns with the understanding that the primary loss in nanocrystalline materials is eddy current loss, which sharply rises with increasing frequency [32].In contrast, the exponent β for the flux density B m of NFR is 1.96, lower than the 2.57 of ferrite.This suggests that the core loss increase of NFR concerning flux density increase is notably less compared to ferrite.Consequently, NFR holds a potential advantage over ferrite in high power density designs.Additionally, the temperature coefficients b and c of NFR are all smaller than those of ferrite.Therefore, the impact of temperature on core loss variation is weaker for NFR material compared to ferrite.This observation is further supported by the temperature tests conducted in [33].

C. Magnetic Circuit in Double-D IPT System
Unlike toroidal inductors and transformers, leakage flux dominates in the IPT applications.Typical equivalent magnetic circuit models cannot be used for analytical solutions.However, the flux paths in IPT can be divided into non-coupling flux s and coupling flux m [34].The simplified illustration of the flux paths is shown in Fig. 3(a).Based on the two different types of flux, the respective magnetic reluctances can be extracted for both coupling and leakage flux [35].Therefore, a qualitative magnetic circuit can be derived, as shown in Fig. 3(b).The circuit can be used for the interpretation of design targets in IPT [12], [18], [36].The derived circuit assumes a symmetric pad construction, where F denotes the magnetomotive force (MMF) excited by the Double-D windings.R m and R m_s are the magnetic reluctance of the magnetic material in the mutual flux path and side flux path respectively.R air and R air_s are the equivalent magnetic reluctance of air in adjacent to the winding, which contribute to the leakage flux.R gap is the reluctance of the airgap between the primary pad and secondary pad.The mutual flux path can be identified in the circuit model, the flux m can be represented as The coupling coefficient k can also be explained from the perspective of the magnetic circuit as the ratio of mutual flux and total flux total where The existence of R m_s does not contribute much to increase coupling, but rather essential to restrict the leakage field to fulfill the human exposure requirement defined in the standard [37].Therefore, R a and R s are predominantly deter- mined by the air around the windings and are not controllable.Since R gap is the most significant reluctance, it limits the maximum achievable coupling coefficient.

D. Design Target and Variables for the Magnetic Coupler
Many references have pointed out that the magnetics design figure of merit (FOM) for IPT applications is to maximize the product of coupling coefficient and quality factor kQ [38], [39], [40], which leads to the highest overall ac-ac efficiency.The quality factor Q is calculated as where L is the inductance of the winding, R ac is the winding ac resistance, and R mag is the equivalent resistance of the introduced magnetic material.The former one, typically the ac resistance of the litzwire, can be calculated based on the number of strands and cross-sectional area.At the same time, the latter one is directly related to the core loss of the material.
Minimizing the reluctance R m and the equivalent resistance R mag will push kQ toward its maximum, as both the coupling and the inductance increase.The magnetic reluctance can be calculated based on the flux path length l m , cross section area A m , and relative permeability of the core µ m where the area A m is calculated from the thickness of the core t m and the width of the core area w m .Double-D winding IPT typically utilizes core bars to cover the winding area [21], [22], [41], [42].Therefore, l m and w m can be determined by the winding geometry.The two main design parameters of the magnetic core in Double-D IPT applications can then be extracted from the analysis of ( 5) and (7), which is the thickness t m and the relative permeability µ m .Furthermore, since the permeability is controlled by the stacking factor F, the essential design variables for the NFR core are the thickness t m and the stacking factor F.

A. NFR Lamination Direction
The high flexibility of the ribbons makes it possible to laminate the core in different directions.Fig. 4 shows two different lamination directions, which are the vertical laminated cores and lateral laminated cores.
The vertical lamination laminates the ribbon perpendicular to the winding plane, as shown in Fig. 4(a).The width of a single core w m is then also the width of a single ribbon.The lamination process can be simplified by peeling off the polyester films and stacking the ribbons with force.The adhesive layer is nonconductive and can provide insulation between the NFR layers.The conductivity between the layers can be reduced.However, this lamination direction can lead to inconsistent flux density distribution because of the anisotropic properties.
On the contrary, the lamination direction of the lateral laminated core is parallel to the winding plane, as shown in Fig. 4(b).In this case, the ribbons must be cut into narrower strips and then stacked into a larger core.This process brings high manufacturing costs, as the stacking position must be precisely controlled to ensure thickness consistency.Additionally, with the stacking thickness growing, the laminated core becomes more vulnerable to the stacking force applied to the ribbon because of the relatively small force area.Therefore, in this article, vertical lamination is chosen for the laminated NFR core to ensure good mechanical integrity as well as low cost.

B. Influence of Different Stacking Factors on Coupling and Thermal Performance
The stacking factor can describe the proportion of NFR material inside the core.A higher stacking factor results in higher magnetic permeability, according to (1), which further contributes to a higher coupling factor.However, eddy current loss also increases with denser stacking because of higher conductivity.
A lower stacking factor is easier to implement.Nevertheless, the coupling coefficient can drop below the system requirement.Also, with less magnetic material, the loss density can increase dramatically, bringing overheating issues.Therefore, the choice of stacking factor should be verified both from efficiency and thermal perspectives.

C. Influence of Core Thickness on the Coupling Coefficient
The core thickness is a determinant factor of power density as it is directly related to the thickness of the IPT charging pad.It also has an essential influence on the coupling coefficient according to ( 5) and (7).This influence, however, varies for laminated core and solid core.
From the model in Fig. 3, the mutual flux enters the core primarily from the flux window in the vertical direction perpendicular to the winding plane.This brings no significant difference in the flux distribution for a solid core because of the isotropic characteristic.However, the anisotropic property for a vertically laminated core brings flux attenuation along the lamination direction.This causes a difference from the traditional solid material core, where uniform flux distribution is assumed.To show the influence of anisotropy on the flux distribution of NFR materials, the intuitive magnetic model of the laminated core is illustrated in Fig. 5.The model assumes a current source exciting a multilayer NFR core.Since the permeability of the NFR layer is much greater than that of the adhesive layer and forming layer, the magnetic reluctance R r is much smaller than R ad .This results in that most of m will concentrate on the first few dozens of NFR layers located closer to the windings.The relations can be qualitatively expressed as (8) where i denotes the number of layers and i indicates the flux in the ith layer.The value of reluctances R ad and R air cannot be precisely determined, because the flux line can be diverse, and the cross-sectional area A cannot be obtained accurately.Therefore, the equation cannot provide an analytical solution on i .Nevertheless, by combining with ( 5) and ( 7), it can be deduced that as layer number i increases, the contribution of the magnetic material to the improvement of mutual flux m diminishes.Consequently, the increase of coupling coefficient k and the flux density in the outer layer can be ignored at a certain point as its relationship with the thickness conforms to a reciprocal equation.
This effect also applies to solid ferrites.However, the uniform distribution inside the ferrite material results in a different change rate of k with respect to the increase in thickness.Fig. 6 shows the comparative impact of thickness on the coupling coefficient between the solid ferrite core and laminated NFR core.The black dots are the gathered finite element analysis (FEM) simulation results in the Double-D IPT application, while the blue line is the fitting curve.The fitting function is the combination of ( 5) and (7).The variable Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply. is the thickness of the core t m , and all other parameters are fitting coefficients.
Apparently, for solid ferrite, the fitted function can precisely describe the influence of thickness on the coupling coefficient.The fitted curve has a low sum of square for error (SSE), which is only 7.1428e-8.However, for laminated NFR core, the SSE is 0.002037.A significant disparity between FEM simulation results and fitting curves can be observed.The coupling coefficient of NFR cores saturates at a much lower thickness.Further increase of thickness does not lead to the improvement of coupling anymore.
Considering this feature, the following design considerations for vertical laminated NFR core in IPT can be deduced.
1) The thickness of NFR cores should be first chosen to reach the maximum coupling.A larger stacking factor, F, is needed if the maximum possible coefficient is lower than the system requirement.2) Further increasing the thickness of the laminated core does not lead to higher coupling.However, core loss, as well as thermal performance, can be further optimized.

D. Design Flow for High Power Density Laminated NFR Cores
A complete IPT charging pad design involves multiple steps, such as coil design, compensation networks, power electronics design, magnetics design, and mechanical design.The start of the design flow often requires many constraints, such as size, power requirements, power density, and so on.This article focuses on the design of magnetic material NFR.The design flow of laminated NFR core for IPT applications is proposed to maximize power density as well as to achieve an improved overall performance than the traditional ferrite.
The design flow is shown in Fig. 7.It is assumed that the dimension of the coil, as well as the power ratings, is determined.Therefore, the required minimum coupling coefficient k req and required maximum core loss P core are known.To ensure a high power density, initial stacking factors and thickness should be chosen as the minimum values for FEM simulations.Simulations are then performed to find the maximum coupling point by increasing the step thickness of the core t gradually.The maximum coupling coefficient k max is defined when the increase of k is smaller than 1% with a step increase of t, indicating a further increase of the thickness does not contribute to a further increase of coupling.The core thickness at k max is the corresponding thickness t max.If k max is smaller than the required coupling k req , stacking factor F must be increased to achieve higher k max .If F exceeds the achievable value, which is defined as 0.55 in this article, the IPT pad design must be revised by increasing pad dimensions or winding turns.
After the determination of stacking factors, core loss is obtained to verify the efficiency and thermal performance.Thickness shall be increased to reduce loss density.Due to the crushed microstructure inside the ribbon, heat capacity and thermal expansion coefficient are challenging to determine.Thermal simulation for the NFR core can have large errors due to the adhesive inside.Therefore, thermal verification is performed experimentally at this moment.This process can be simplified if detailed thermal parameters are available.
With this design flow, the combination of the core's stacking factor and thickness can fulfill the coupling coefficient requirements and core loss requirements.Thermal verification can deliver a convincible temperature figure for practical applications.High power density is therefore achieved.The design methodology also applies to laminated cores with other materials in IPT applications.

A. Simulation Settings
The simulation model is shown in Fig. 8.The simulation model has symmetric primary and secondary pads to simplify Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.Core loss of NFR.
the magnetic evaluation process.Each consists of the NFR core, Double-D stranded windings, and aluminum shielding.The core area is 440 × 180 mm, containing nine cores with 20 mm width for each core.The core bars stretch to the entire length of the winding, and the core area covers most of the flux window.A small distance is kept between the core and the lateral section of the windings to avoid concentrated magnetic field in the winding corner.The air gap of the primary and secondary pad is 145 mm.B-H curves and core loss are measured with a toroidal core at 85 kHz in 25 • C, shown in Fig. 9.The saturation flux density reached over 1.1 T. Note that this B-H curve is only applicable for a single ribbon excluding the adhesive and forming layers.Some literature simulates the anisotropic material with equivalent isotropic property calculated with (1).However, it produces high inaccuracy because of the dominant leakage flux and nonuniform flux directions in IPT applications.The properties of a single flake ribbon, excluding the adhesive layers and forming layers, should be used for the simulations.Core composite is selected as lamination, with the stacking factor set.The thickness of lamination is selected with a nominal value of 20 µm.
SAEJ2954 suggests the ferrite core thickness to be 5 mm for a 6.6-kW WPT2 level system [37], which brings a coupling coefficient up to 0.25 with a given winding geometry.Therefore, k req is set to be 0.26 for demonstration.Thickness increase step t and stacking factor step F are set as 0.1 mm and 0.1, respectively, while the maximum thickness and stacking factor are 4 mm and 0.55.The values are chosen to ease the production process in the laboratory, as well as maintaining a competitive power density and efficiency.Finer steps are possible with more professional stacking machines.The current excitation is configured at 16.5 A, approximately corresponding to an output of 6.6 kW for a 400-V battery.The actual current can differ in reality due to a different coupling factor.

B. Maximum Coupling k max and Corresponding Thickness t max in Different Stacking Factors
Simulations are first done to find the maximum coupling k max as well as the corresponding thickness.To compare and analyze the influence of the two factors, the parameter sweeping covers the whole range, which is redundant and can be simplified using the proposed design flow.
Fig. 10(a) shows the coupling coefficient respective to core thickness in stacking factor 0.15, 0.25, 0.35, 0.45, and 0.55.Apparently, the maximum coupling increases with a higher stacking factor.This is due to more magnetic material inside the core, which lowers overall magnetic reluctance.Also, with a higher stacking factor, the coupling coefficient increases faster before the saturation coupling.Compared with ferrites, the maximum coupling coefficients of NFR cores are higher than DMR44 but slightly lower than DMR95, except for the lowest stacking factor of 0.15.Fig. 10(b) shows the k max points and their corresponding thickness t max .k max increases while t max decreases with a higher stacking factor.Other than the lowest stacking factor of 0.15, the other four core stacks show both improved coupling as well as lower thickness, implying enhanced performance on efficiency and power density.Since k req is 0.26, stacking factors 0.15 and 0.25 can be abandoned for further design.

C. Determination of Core Thickness Based on Core Loss P cor e
Fig. 11 shows the core losses over thickness for the three candidates of stacking factors.The core losses increase before the saturation thickness and then start to decrease.Additionally, as shown in Fig. 11(a), the stacking factor of 0.35 shows less core loss.The reason for that can be explained as follows.
1) When the thickness of the core lies in Area I in Fig. 11(b), an increase in the core thickness leads to an apparent decrease in magnetic reluctance.The flux, including both mutual and self-flux, increases dramatically according to (4).Therefore, the flux density of B core also increases despite an increase in cross-sectional area.This leads to a rise in total core loss based on Steinmetz equations for soft magnetic materials.2) In Area II, further increase of the core thickness does not contribute to the rise in total flux, since the magnetic circuit now is dominated by the magnetic reluctance of the airgap.However, an increase in the core thickness can increase the equivalent cross-sectional area and, therefore, reduce flux density.Total core loss decreases in this case, even though more core material is added.3) Total core loss becomes almost invariant in Area III.
The flux concentrates in the inner laminations, which can be qualitatively explained in Fig. 5.The reluctances Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.  of air and the NFR layer behave like flux dividers.As the number of laminations increases, the flux density in the outer layers will drop significantly.The newly added layers do not contribute to increasing total flux and mutual coupling.Therefore, the total core loss does not experience a noticeable change.Choosing a thickness higher than saturation thickness would naturally make the core design lie in Areas II and III.This proves the feasibility of increasing thickness to reduce P core in the design flow.It can be observed that the stacking factor 0.35 exhibits the lowest core loss compared with the other two variants, except in the range of 2.3-2.5 mm.Considering the much higher core losses in their corresponding saturation Laminated NFR core with 0.375 stacking factor and 3.2 mm thickness.
thickness for stacking factors 0.45 and 0.55, it is reasonable to select stacking factor 0.35 as the design target.An increase in thickness in this stacking factor brings more core loss reduction, and the potential for thermal improvement is more promising than the other two.

A. Lamination Process of Core
The forming layer with 100-µm silicone thermal sheets is introduced inside the core to achieve the desired stacking factor.The thermal sheet has a high thermal conductivity of 15 W/mK, which is higher than both the NFR material and ferrite, improving the overall heat dissipation of the core.The detailed composition of the core is shown in Fig. 12.The total core thickness is 3.2 mm, with two forming layers added, which are in total 0.2 mm.The NFR layer contains 60 layers of NFR material and adhesive, equivalent to a 1.2-mm nanocrystalline flake material.The lamination process is done manually; therefore, air gaps are introduced.Considering the thickness, a stacking factor of about 0.375 is achieved.This slightly deviates from the design target due to the thickness constraints of the material in the forming layer as well as a nonoptimized manufacturing process.Nevertheless, the combination of this stacking factor and thickness is also expected to fulfill the system requirement as well as the high power density.A more accurate stacking factor can be achieved with machine laminating.The dimension of a single laminated core is 440 × 20 × 3.2 mm.A charging pad consists of nine cores in total.

B. Experimental Setup and Equivalent Circuit
The experimental platform is shown in Fig. 13.Double-D windings are constructed for primary and secondary pads.The pads are supported with Teflon material with high temperature endurance of up to 250 • C. The magnetic couplers under test are placed directly next to the windings.The windings connected with compensation capacitor boards and then to the ac full bridge inverter, which is designed with SiC module CCB021M12FM3; the inverter is controlled by DSP TMS320F28379D, which interfaced to the gate drivers UCC21710 by differential transceivers; Schottky diode C4D40120D is used for the passive rectifier; BSL800-10 supplies dc power up to 800 V, with output power displayed; Tektronix MSO46 with probes THDP0200 and TCP0030A is used to observe current and voltage waveforms, and it is also embedded with power suite SUP4-PS2; Yokogawa WT-5000 is used to measure ac-ac efficiency.FLIR E6-XT is used to capture the thermal distribution.
The setup uses circulating energy analysis, in which the output is directly connected to the input.The output power will feedback to the input.This allows for high current and power flow inside the coils while drawing only a small amount of power from the input.The equivalent circuit diagram is shown in Fig. 14.The compensation topology uses series-series (S-S) to minimize the number of passive components and generate a constant current output [43].The dc-dc efficiency µ dc−dc can be easily calculated based on the measurement of inject power P inject from the dc supply, output current I out , and input voltage U DC .The calculation method is shown as follows: where P inject represents the entire system losses drawn from the dc supply, including power electronics losses, winding losses, and magnetic losses.
A commercially available ferrite material, DMR44, is used for the secondary magnetic coupler in the comparison test to compare the performance.The ferrites cover a similar area as the NFR cores, shown in    cores.The width of each NFR core is determined as 20 mm, considering the difficulty of the lamination process and market availability.

C. Passive Parameters
The passive properties of the experimental IPT system with the ferrites and NFR magnetic couplers are shown in Table III.It is evident that the self-inductance and the coupling coefficient of NFR are higher than DMR44.This can be attributed to the high permeability of the single ribbon.Even though the stacking factor is only 0.375, the equivalent magnetic reluctance is still smaller than DMR44.Additionally, due to the shape and dimension of the ferrite block, small air gaps can be formed during assembly, which leads to a possible reduction of the magnetic reluctance.The nanocrystalline ribbons can eliminate this possibility due to their high flexibility.The initial permeability of DMR95 is 3300, leading to a comparable self-inductance and coupling coefficient with the NFR cores.
The increase in mutual inductance for NFR cores leads to higher input impedance.Therefore, to transfer the same amount of power, the IPT system with the NFR magnetic coupler requires higher voltage and less current than the ferrite coupler.This feature can reduce the winding losses and the power electronics, as the conduction loss can be reduced.The switching loss, related to the input voltage, is minimized in IPT systems, with soft switching achieved.Also, compensation capacitors are used in different values for NFR and DMR44 IPT systems to ensure a similar resonant frequency.The system is designed for 85-kHz nominal frequency.

D. Operation Waveforms and Efficiencies
Fig. 16(a)-(d) shows the voltage and current waveforms of the IPT system with NFR cores in output power of 1.55, 2.45, 6.24, and 7.9 kW, respectively.The corresponding dc voltage input U DC is 200, 250, 400, and 450 V.The output power comparison of the ferrites and NFR is shown in Fig. 17(a).The output power is proportional to U 2 DC .The switching frequency is set as 85.5 kHz, to let the impedance be slightly inductive and achieve soft switching, which can be reflected by the smooth edges on primary voltage waveforms.
The comparison of dc-dc efficiencies between NFR cores and the two ferrites is shown in Fig. 17(b).The efficiency of NFR cores increases with the increase of output power, reaching the peak value of 95.12% at 8.9 kW.This is higher than ferrites, which are 94.29% at 8.21 kW for DMR44 and 94.79% at 4.48 kW for DMR95.Due to higher coupling coefficients, DMR95 has the lowest output power under the same input dc voltage as expected.
The ac-ac efficiencies are shown in Fig. 17(c).The ac efficiency of the NFR coupler increases gradually from low output power until 96.33% peak efficiency at maximum power.In comparison, the ac efficiencies of DMR44 and DMR95 couplers decrease as the output power ramps up.The upward trend in ac efficiency for NFR cores may be counterintuitive as both winding loss and core loss increase with higher currents.This is because the output power P out is proportional to the square of the current.The magnetic field H increases proportionally with the current.Consequently, the flux density B also increases in line with the current.However, the exponent β in the Steinmetz equation (3), which is the exponent for flux density, stands at 1.69 for NFR material listed in Table II.This exponent is less than a square, indicating that if the output current doubles, the power will increase four times accordingly, and then, the core loss P core will grow less than four times its original amount, resulting in a higher efficiency.However, the core loss of ferrite grows proportionally with B 2.57 and B 2.52 for DMR44 and DMR95, respectively, according to Table II, leading to a decrease in efficiency as the power increases.This loss equation demonstrates the significant advantage of NFR compared with ferrite in high power and high power density IPT.Fig. 18(a) and (b) illustrates the primary and secondary currents, respectively.The measurements are consistent with the coupling coefficients of different materials in Table III.Compared with DMR44, the NFR cores bring a higher coupling coefficient, requiring less current to output the same power.For DMR95, the comparable self-inductance and coupling coefficient result in very similar operating points for the NFR and DMR95.Despite requiring slightly higher coil currents, NFR cores outperform DMR95 regarding ac and dc efficiencies when the output power is above 1.5 kW.This suggests that a decrease in core loss plays a significant role in the increase in the efficiencies.

E. Thermal Performance
To verify the thermal performance of the proposed NFR core, long-duration tests were performed, with both NFR and ferrite groups operating at 6.6 kW.Fig. 19 shows the thermal images captured by the thermal camera.In the first test with DMR44, as shown in Fig. 19(a), an extreme hot spot was formed at the intersection of two ferrite blocks, the test to be stopped after only 15-min operation due to the temperature rising close to 150 • C limit for the litzwire underneath.This hot spot can be attributed to a localized concentration of flux density introduced by the small air gaps between two ferrite blocks.A similar problem was described in [7].Even small assembly tolerances can lead to this hot spot.These extreme temperature differences bring different thermal expansions inside a single ferrite block, considering typical IPT end applications need to be potted to ensure internal mechanical integrity.The potting material will limit the expansion space for ferrite blocks and create thermal stress.This thermal stress will grow with the expansion, leading to cracks and fractures in the material blocks [7].Localized fringing flux will be generated and further contribute to higher core loss.The permeability will drop sharply once the hotspot approaches the Curie temperature [44], [45].The cracks can propagate because of the thermal imbalance, eventually leading to system thermal failure.Based on this result, another drawback of using ferrite material in a high-power IPT system can be clearly reflected in this test result.
The assembly was then improved by adding elastic material along the edges to fill the tolerance gaps.This behaves like a buckle, enabling the ferrite to be compressed, effectively minimizing the forming of small air gaps that often occur during the assembly process.As a result, the ferrite blocks can be tightly and closely positioned together.The thermal figure in   thermal image of the proposed NFR material.Compared with DMR44 and DMR95, the maximum temperature has been reduced to 76.4 • C, benefiting from its higher efficiency and thermal conductivity.This brings advantages for the practical applications as the cost of cooling methods can be reduced.
The added forming layers contribute to the heat dissipation of the core.The thermal performance can be accepted, and therefore, no iteration should be made for the given power ratings.
The information is summarized in Table IV.The designed NFR cores outperform DMR44 cores in the listed aspects.Power density is significantly improved.The weight is reduced by 51%, core volume is reduced by 31%, and core thickness is reduced by 20%.The ac-ac and dc-dc efficiencies of NFR cores reach 96.33% and 95.12%, respectively.Higher efficiency and superior thermal conductivity contribute to a decrease in maximum temperature from 91.4 • C for DMR44 and 84.9 • C for DMR95 to 76.4 • C.

F. Cost Analysis in the Current Market
NFR is already available for low-power wireless charging in the industries, such as smartphones and wearables [46].For the material used in this work, the raw material cost of NFR is even lower than that of ferrite, as shown in Table V.However, since customized stacking factors and forming layers are used, the lamination process is done in the laboratory environment.For high-power applications, the stacking process to form a thicker core will increase the manufacturing cost.Nevertheless, this cost can be reduced with mass production.In addition, the high power density and superior thermal performance of NFR cores can potentially reduce additional costs, such as the need for active cooling, assembly, and maintenance costs.

VI. CONCLUSION
This article presents the design and analysis of NFR cores in high-power IPT system.A new lamination structure is proposed to contain forming layers and achieve higher thermal conductivity.The anisotropic characteristic of NFR cores in IPT applications is pointed out, and design methodology is proposed accordingly.This methodology can ensure high power density as well as fulfilling system requirements.
Furthermore, an experimental platform with 85-kHz switching frequency, and up to 9-kW output power is built to demonstrate the design.The magnetic design is evaluated on efficiency, power density, assembly feasibility, and thermal performance.The NFR design achieves over 95% dc-dc efficiency and exhibits lower temperature distribution than traditional ferrite, even with a 51% reduction in weight, 31% reduction in volume, and 20% core thickness reduction.The long-duration test also verifies its practical utilization, with a lower temperature distribution than benchmark ferrites.The flexibility of the NFR cores also brings high consistency for practical applications as no air gaps are formed during the assembly.Local hot spots are therefore avoided.Based on the cost analysis, the NFR material shows increasing potential for enhancing the design of high power density IPT applications.

Fig. 1 .
Fig. 1.NFR cores.(a) Simplified manufacturing process of NFR cores.(b) Configuration of NFRs with the description of filling factors in the ribbons.

Fig. 3 .
Fig. 3. Simplified flux paths in symmetric Double-D IPT systems.(a) Categorization of mutual and self-flux paths.(b) Qualitative magnetic circuit from the cross-sectional view.

Fig. 4 .
Fig. 4. Lamination directions of NFR core.(a) Vertical laminated core with lamination direction perpendicular to winding plane.(b) Lateral laminated core with lamination direction in parallel to winding plane.

Fig. 5 .
Fig. 5. Intuitive magnetic model explaining the uneven distribution of flux density inside the laminated core structure.

Fig. 6 .
Fig. 6.FEM simulation and fitting curve results of the core thickness influence on coupling coefficient.(a) Solid ferrite with fitting SSE of 7.1428e-8.(b) Laminated NFR with fitting SSE of 0.0020.

Fig. 7 .
Fig. 7. Magnetics design flow of NFR laminated core for IPT applications, with predetermined requirement and aiming for high power density target.

Fig. 8 .
Fig. 8. FEM simulation model for a high-power IPT demonstration platform.

Fig. 9 .
Fig. 9. Measurements for a toroidal core at 85 kHz in 25 • C. (a) B-H curve.Core loss of NFR.

Fig. 10 .
Fig. 10.Influence of stacking factor and thickness on the coupling coefficient.(a) Change of coupling in relation to thickness and comparison with ferrites.(b) Saturation couplings and corresponding core thicknesses at different stacking factors.

Fig. 11 .
Fig. 11.Core loss over thickness (a) with different stacking factors F = 0.35, 0.45, and 0.55.(b) Area of core loss variation with F = 0.55 as an example.

Fig. 13 .
Fig. 13.Detail of experimental setup for the evaluation of magnetic design.

Fig. 15 .
Each ferrite block has a dimension of 46 × 25 × 4 mm.The total area is 460 200 × 4 mm, consisting of 40 pcs ferrite block.In comparison, the NFR core area is 440 × 180 ×3.2 mm, consisting of nine NFR

Fig. 15 .
Fig. 15.Core placements for DMR44 and NFR with a stacking factor of 0.375 and thickness of 3.2 mm.

Fig. 19 (
b) showed an improvement in thermal distribution, and the maximum temperature was reduced from 126 • C to 91.9 • C even after 1-h operation.Fig.19(c) illustrates the temperature distribution of the DMR95 coupler, and Fig.19(d)shows the Authorized licensed use limited to the terms of the applicable license agreement with IEEE.Restrictions apply.

TABLE III PASSIVE
PARAMETERS WITH DIFFERENT CORES

TABLE IV PERFORMANCE
COMPARISON OF NFR AND FERRITE IN THE DESIGNED 6.6-kW IPT SYSTEM

TABLE V COST
COMPARISON OF THE NFR AND FERRITE MATERIALS