Magnetic property measurement and analysis of high-frequency soft magnetic materials under non-sinusoidal excitation considering temperature effect

High frequency and miniaturization of transformers is an essential way to increase the power density of electrical equipment.¹ solid state transformer (SST) is gradually replacing traditional power frequency transformers in electrical grid, while high frequency transformer (HFT) is the main part of SST.² Meanwhile, HFT often operates under high temperature and non-sinusoidal excitation,³ which makes the magnetic properties and loss of soft magnetic materials more complicated.⁴ As a key part of HFT, the magnetic properties of soft magnetic materials under complex working conditions have attracted extensive attention.

The mainstream high-frequency soft magnetic materials include ferrite, amorphous and nanocrystalline alloy. Ferrite has significant advantages in the high frequency application, such as its low conductivity, which can effectively reduce eddy current effects.^5,6 However, the saturation magnetic density B_s of ferrite is relatively low and significantly affected by temperature, which limits its application.⁷ Amorphous and nanocrystalline alloys have high permeability μ and high saturation magnetic density B_s. However, their high conductivity leads to large eddy current loss under high-frequency excitation,⁸ which increases the working temperature of the core and can lead to the change of magnetic properties.⁹ It should be noted that the HFT is usually used in DC–DC converters which generate square and rectangular excitation.¹⁰ At present, most of the relevant researches separate the temperature dependence of magnetic properties from non-sinusoidal excitation, which not sufficient to characterize the magnetic properties of soft magnetic materials.¹¹ Hence it is necessary to study the temperature dependence of the magnetic properties under non-sinusoidal excitation.

The whole experimental system includes three parts: heating and temperature control system, non-sinusoidal excitation generation system, and magnetic property measurement system. The schematic diagram of the overall experimental system is shown in Fig. 1. A thermotank is used to heat the ring sample in the temperature system. The internal temperature of the thermotank is controlled in real-time by using the PID algorithm, which ensures that the sample can be measured stably at a specific temperature. In the non-sinusoidal excitation generation platform, the DC source is used as the power supply, and different typical non-sinusoidal excitation waveforms can be generated through the inverter controller composed of SiC MOSFET. The PWM control signal is generated by DSP, which controls the switch tube through the self-made drive.

The magnetic field intensity, H, and flux density, B, can be calculated by Ampère's circuital law and Faraday's law of electromagnetic induction, respectively, as in (1) and (2). The primary side current i₁(t) and secondary side voltage u₂(t) can be measured respectively through voltage and current probes, and transmitted to LabVIEW, which is communicated with the oscilloscope. Various from the traditional post-processing step, this paper uses the real-time program of LabVIEW to process the data during the measurement and displays the magnetic characteristic curve on the screen at the same time. This method can improve measurement accuracy and efficiency. The core loss P_loss is calculated by the Poynting equation as in (3). N₁ and N₂ are the turns number of the primary and second windings, respectively. A_e is the cross-section area, l_e is the effective magnetic path length, p(t) is the loss of the core during one period T, V is the volume of the core, and f is the excitation frequency.

In this paper, magnetic properties and loss characteristics of the ferrite (N87) and nanocrystalline (3KL) are measured and analyzed in the range of 25 °C to 125 °C from 5 kHz to 20 kHz under both square and rectangular excitation with different duty cycles (0.1–0.9). The nanocrystalline ring sample (3kl) are provided by Hitachi Metals, Ltd. The ferrite ring sample (N87) is provided by TDK, Ltd. The parameters of the ring samples are shown in Table I. OD is the outer diameter of ring; ID is the inner diameter; d is the thickness; µ_r25 is the relative permeability at 25 °C.

Figures 2(a) and 2(b) show the change of the hysteresis loop of nanocrystalline 3KL and N87 under rectangular excitation. When the amplitude of the flux density B_m is constant, as the duty ratio decreases, the hysteresis loop of 3KL becomes wider laterally, which means the magnetic field strength H and coercive force H_c increase accordingly. With the increasing temperature, the hysteresis loop of N87 narrows laterally, and the H required for excitation becomes larger, while the coercive force H_c decreases. It can be seen that different excitation conditions and temperature have significant effects on the magnetization process of the material.

The permeability μ of ferrite N87 under square excitation changes with temperature as shown in Fig. 2(e). Since the permeability of ferrite is proportional to the saturation magnetization M_s and inversely proportional to the magnetocrystalline anisotropy coefficient K₁. When the temperature increases, the magnetocrystalline anisotropy coefficient decreases faster than the saturation magnetic density, which dominates the contribution of permeability. So the permeability increases with temperature in the low magnetic flux density region as shown in Fig. 2(e); Due to the disturbance of the thermal field, the exchange energy in the ferrite is reduced, and the saturation magnetization M_s decreases with the increase of temperature. Therefore, as the temperature increases, the ferrite at higher temperatures first reaches saturation, resulting in a rapid decrease in permeability in the near-saturation region as shown in Fig. 2(e). These behaviors indicate that ferrite is suitable for working at low magnetic flux density in a high-temperature environment.

The permeability μ of nanocrystalline 3KL varies with temperature under square excitation, as shown in Fig. 2(f). Compared with N87, the permeability of nanocrystalline is stable in the unsaturated region and decreases with temperature increase, which indicates that the nanocrystalline is suitable for operation at room temperature and has stable magnetic properties in the linear region.

Figure 2(g) is the magnetic permeability curve of ferrite N87 under rectangular wave excitation. It is found that the excitation conditions of different duty ratios have a significant influence on the magnetic properties of magnetic materials. As the duty ratios decrease, the excitation waveform gradually tends to pulse excitation. At this time, the overall permeability of the material in the working area decreases significantly.

The magnetization curve of ferrite N87 with frequency and temperature is shown in Fig. 2(c). It can be seen that the saturation magnetic density Bs of N87 has an obvious dependence on temperature and frequency. The saturation magnetic density Bs decreases from 0.4424 T to 0.3116 T when the temperature increases from 25 °C to 125 °C at 5 kHz, which changes by 29.6%. When the temperature is 25 °C, the value of Bs at 5 kHz is 0.4424 T, which is higher than the 0.4269 T at 20 kHz and changes by 3.48%. Obviously, N87 is more sensitive to temperature than frequency. It should be noted that N87 is in the linear region before 0.25 T, and in this region both the frequency and temperature stability are strong.

Figure 2(d) shows the relationship between saturation magnetic density Bs of nanocrystalline 3KL with temperature and frequency. It can be seen that the saturation magnetic density of 3KL also decreases with temperature increasing. In the linear region, 3KL has better temperature stability than 20 kHz under the excitation of 5 kHz. The saturation magnetic density Bs of 5 kHz is 1.102 T, which is 2.8% higher than that of 20k HZ at 25 °C. The Bs of 3KL changes by 7.5% from 25 °C to 125 °C at 20 kHz, which indicates that the temperature stability of saturation magnetic density of nanocrystalline is higher than ferrite.

Figure 3(a) shows the relationship between the loss of nanocrystalline 3KL and the frequency as well as temperature. The loss of the 3KL increases with the frequency and temperature rising. At 25 °C, the loss of 5 kHz is 5.73, and the loss of 20k HZ is 51.2. At 20 k HZ, the loss at 125 °C is 63.9, a change of 24.8%. It is not difficult to find that the contribution of frequency to loss is much higher than temperature. Therefore, the loss of nanocrystalline alloy has better temperature stability than ferrite alloy.

Figure 3(b) shows the temperature dependence of the loss of nanocrystalline 3KL under different duty ratios of the square excitation. It can be seen that the loss appears to be a minimum when the duty ratio is 0.5 and exhibits a symmetrical distribution. At each duty ratio, the loss increases with temperature. It should be noted that as the duty ratio becomes more extreme, the temperature dependence of the loss is more obvious than the traditional sinusoidal and symmetrical square wave excitation.

Figure 3(c) shows the loss of nanocrystalline 3KL under rectangular wave excitation with different duty ratios. The loss decreases with the increase of the duty ratio, which is different from the square wave excitation. It is not difficult to find that the loss of each duty ratio is quite different under the rectangular wave excitation, which indicates the excitation conditions have a great influence on the loss of the nanocrystalline material.

Figure 3(d) shows the temperature dependence of loss of nanocrystalline 3KL under rectangular wave excitation with different duty ratios. Obviously, the loss of nanocrystalline is less affected by temperature and more susceptible to excitation conditions.

Figure 3(e) shows the relationship between the loss and frequency as well as temperature of ferrite N87. The loss of N87 is less affected by frequency than 3KL. It should be noted that the loss of ferrite decreases first and then increases with temperature increasing.

Figure 3(f) shows the temperature dependence of the loss of ferrite N87 under different duty ratios. It can be seen that the overall trend is similar to 3KL, reaching a minimum at a duty ratio of 0.5, but with less difference in loss between different duty ratios. This indicates that the waveform sensitivity of ferrite is lower than nanocrystalline.

Figure 3(g) shows the loss of ferrite N87 under rectangular wave excitation with different duty ratios. The loss of N87 has similar trend with 3KL, however, the loss of ferrite is closer at different duty ratios except for extreme duty ratios.

Figure 3(h) shows the temperature dependence of loss of ferrite N87 under rectangular wave excitation with different duty ratios. It can be seen that N87 is greatly affected by temperature. Under the same excitation conditions, the loss at 100 °C is reduced by more than 30% compared with 25 °C and reaches a minimum value.

In this paper, a non-sinusoidal magnetic measurement system considering the influence of temperature is proposed to measure the magnetic properties of soft magnetic materials more efficiently. The influence of non-sinusoidal excitation and temperature on the magnetic properties of high-frequency transformer core materials is comprehensively analyzed, which is closer to the working conditions of high-frequency transformers than previous studies. Based on the comparative analysis, the sensitivity of the two materials to temperature and waveform excitation is summarized. In addition, the application scope of the two materials is indicated.

The magnetic properties and loss of nanocrystalline have the finest temperature stability. Compared with temperature conditions, nanocrystalline alloy is more sensitive to excitation conditions. The magnetic properties and loss of ferrite alloy have obvious temperature dependence. Meanwhile, ferrite alloy is less affected by excitation conditions relative to temperature conditions. However, its loss increases significantly under the excitation of the extreme duty ratio. Overall, nanocrystalline alloy materials are suitable for working in intermediate frequency and high power conditions with stable waveform quality excitation. Ferrite alloy is suitable for working in high frequency and low magnetic density area. This work provides a theoretical basis for high-frequency transformer core material selection and application. It also provides data support for core material loss modeling under high-frequency transformer working conditions.

This work was supported in part by the National Natural Science Foundation of China, (No. 52130710), the Funds for Creative Research Groups of Hebei Province, (No. E2020202142), the Cultivate Foundation of Innovation Ability of Hebei Education Department for Ph.D. student under Grant CXZZBS2021026.

The authors have no conflicts to disclose.

Yongjian Li: Formal analysis (equal); Investigation (equal); Methodology (equal); Project administration (equal); Resources (equal); Supervision (equal); Writing – review & editing (lead). Chuhao Jin: Conceptualization (equal); Data curation (equal); Formal analysis (equal); Investigation (equal); Writing – original draft (equal). Ming Yang: Writing – review & editing (equal). Shenghui Mu: Software (lead); Validation (equal); Writing – review & editing (equal). Changgeng Zhang: Writing – review & editing (equal).

The data that support the findings of this study are available from the corresponding author upon reasonable request.