A new method for simulation of saturation behavior in magnetic materials of inductive components

Transcription

1 A new method for simulation of saturation behavior in magnetic materials of inductive components Dr. Jörn Schliewe, Stefan Schefler EPCOS AG, eidenheim, Germany Summary A common characterization method of the saturation behavior of inductive components is the inductance versus dc-current curve. The established methods of calculating the apparent or incremental inductance with only a single B--curve is an oversimplification of the underlying physics of the real system. In this paper we present a new method, which uses a B--curve for calculating the point of operation and a second µ-b-curve for calculating the inductance. These curves characterize the material properties and are typically measured on toroidal cores. To prove the new method, an example composed of ferrite and iron powder cores was simulated and measured. Keywords Simulation, magnetic material, inductors, transformers, inductive components, ferrite, iron powder, PermeabilityLink, Ansys, Maxwell, EPCOS, hysteresis 1. Introduction Power electronic systems play a major role in todays and future megatrend applications like green energy, energy management in general, drive systems and electrical vehicles. Inductive components like inductors or transformers are crucial parts in different kinds of power electronic systems. They store energy, reduce EMC problems as filters and ensure galvanic isolation in different applications. To develop and optimize the inductive components is usually a crucial point for a successful system design. In order to speed up the design process of inductive components and to save development costs, simulation becomes increasingly important. Determining of the saturation behavior is one of the most important steps to find an optimal solution. The established methods estimate the saturation behavior by aid of a single B--curve. This approach is an oversimplification of the real physical behavior. A commonly accepted technique for characterization of saturation behavior of inductive components is the inductance versus dc bias measurement. For different dc currents the inductance is measured with a small oscillating signal. This paper describes a new method of simulating the inductance versus dc bias measurement. By use of two different material curves the physical behavior can be reproduced more realistically. Section 2 gives an overview of the theoretical background of magnetic materials. Section 3 describes the established methods and the new method. Section 4 provides a proof of concept by comparing the simulation results with a measurement of an inductor composed of ferrite and iron powder cores.

2 2. Theory of Magnetic Materials It is well known, that magnetic materials exhibit a nonlinear behavior. For high magnetic field strengths the materials saturate, since all magnetic domains are aligned along the magnetic field and the maximal magnetic polarization is achieved. Furthermore, the behavior depends not only on the point within the hysteresis but also on the history, i.e. on how this point is reached. For small changes in the field strength reversible rotation of magnetization and shifting of domain walls dominates, while for large changes irreversible jumps of the domain walls, so called Barkhausen jumps, occur [1, p. 157]. The irreversible jumps result in a strong increase of magnetization which corresponds to a higher permeability than the permeability of reversible magnetization or the initial permeability. The inductance in terms of stored energy uses the full magnetization no matter reversibly or irreversibly magnetized. The stored energy corresponds to the grey marked area above the B-curve, illustrated on the left side of figure 1. For materials with a small coercive field and remanence, the reversible processes dominate [1, p. 181]. The inductance in terms of a voltage drop induced by a small change in current is defined by reversible magnetization processes. The reversible permeability decreases with increasing dc-field because the Bloch walls, whose movability defines the permeability at small excitations, disappear [1, p. 215]. In contrast the incremental permeability, defined by the derivative of the B--curve, uses reversible and irreversible processes. On the right hand side of figure 1 it is shown that the reversible small signal permeability, illustrated as the slope of the small loops, is smaller than the incremental permeability. B B O B B O B O BO B µ app = µ inc = O O Fig. 1: Illustration of the apperant (left) and incremental (right) inductances O 3. Simulation Methods 3.1 Established Methods For the simulation of the saturation behavior of magnetic components two approaches are commonly used. Both are based on a single B--curve and differ by the way the permeability is defined. The apparent inductance is calculated by the permeability which is defined by the operation point (, ): = (1) The apparent inductance is related to the stored energy in the inductor, where the inductance can be defined by the capability to store magnetic energy in the inductor: = As shown on the left hand side in figure 1, the apparent inductance is a simplification of the real stored energy (gray marked) inductance. The energy of the apparent inductance is marked as blue hatching. Only in the linear range this simplification is a good approximation of the reality. For description of the saturation behavior this method is not appropriate, because the calculated inductance is much higher than the observed one.

3 The second approach, the incremental inductance is calculated by the permeability defined by the derivative at the operation point:, which is = (2) The incremental inductance is related to the electromotive force against a change in magnetic flux, where the inductance can be defined by the impedance of an inductor: = Because in the inductance versus dc-current characterization the inductance is measured by an impedance measurement, the incremental inductance should describe the characterization best. owever, as illustrated on the right hand side of figure 1, the small signal excitation does not equal the derivative of the B--curve. The slope of the minor loops, due to the small signal excitation, is not always the same as the slope of the derivative of the B--curve. Due to this, the incremental inductance cannot exactly simulate the real inductance for all materials. It turned out by experience, that as higher the losses of the material are as higher is the deviation between simulated incremental inductance and measured inductance. 3.2 PermeablilityLink Method To gain a more realistic simulation of the inductance versus dc-current characteristic of an inductor, a new method is proposed. In this method two characteristic curves of the magnetic materials are used. The first material curve is the classical B--curve. The initial curve is usually given by the material suppliers as µ ac -B- or µ ac --curves, which can be easily transformed into a B--curve by use of µ ac =B/. These curves are derived by a large signal measurement on a toroidal core, where the applied current (primary winding) gives the -field and the induced voltage (secondary winding) allows calculating the magnetic flux density B. The second material curve needed is the µ s -B-curve or small signal permeability versus B-field curve. Some suppliers provide the µ s --curve, which is measured with a small signal inductance measurement under dc-current. The current gives the -field which can be converted to B-field by use of the B--curve. If this data is not provided by the supplier, they have to be calculated from an inductance versus dc-current measurement on a toroidal core. The simulation procedure of the PermeabilityLink method reproduces the real measurement. In the first step the magnetic flux density B at dc-current is simulated. The magnetic material is defined by the nonlinear B--curve as in the established methods. For every point in the magnetic material the reversible permeability depends on the actual magnetic flux density. To account for that a second simulation is prepared in such a way, that the permeability in every mesh cell of the discretized magnetic material is defined by the derived B of the first simulation via the µ s -B-curve. With this second simulation the inductance at dc-bias can be simulated. Fig. 2: Advanced permeability option in ANSYS Maxwell 15

4 On our suggestion a possibility for such a simulation was newly included in ANSYS Maxwell 15. The second simulation is linked to the first simulation by use of the advanced permeability option. Figure 2 shows this option. In the upper line an executable file is linked. This executable reads a file exported by Maxwell with all flux densities of each mesh cell. Then it calculates the corresponding permeability by use of the µ s -B-curve and writes a file with the permeability which is used by Maxwell for the linked simulation. The arguments in the lower line of the advanced permeability option are set to 3D <control file>. In the control file the link between the solid and the material is defined. For this the command MuBFile=<µ s -B-curve> follows in the next line the command ParentPartID=<nb> which defines the solid in the simulation model. The ParantPartID can be determined manually from the *.mxwl file. Figure 3 shows the process flow chart of the PermeabilityLink method. On the left hand side the operation of the executable can be seen. On the right hand side the central part of Maxwell is illustrated. The two linked simulations export the flux densities for all mesh cells and import after the external generation the new defined permeability for all mesh cells. An outer loop realized by a visual basic scripting controls the variation of the currents for simulating the inductance versus dc-current curve. The results are written into a simple text file. Fig. 3: Process flow chart of the PermeabilityLink method 4. Example 4.1 Configuration As an example an inductor composed of ferrite and iron powder cores was investigated. The inductor consists of two 120x60x25 N87 ferrite blocks, two 50x30x20 FS26 Iron powder blocks and two windings with 17 turns each. The two windings are connected in serial to achieve the maximum inductance. Figure 4 shows a sketch and a photograph of the realized inductor. The inductance of this inductor is approximately 210 µ.

5 Fig. 4: A sketch (left) and a photograph (right) of the measured example 4.2 Characteristic Material Curves For both needed curves of the powder core material FS26 Arnold-Micrometal published dependencies in the data sheet [2] which gives the percentage values from the initial permeability. To check the initial permeability of the material of our specific cores we measured the inductance of the setup shown in figure 5. For a low permeability material like this powder core material it is essential to subtract the inductance of the winding without core. With = ( ) eff eff the initial permeability has been calculated to 23. Fig. 5: Photograph of the measurement setup for determining the permeability From equation 3 given in the data sheet [2] the large signal permeability has been derived. is flux density given in Gauss, which can be transferd into Tesla by = /1000. =.... By use of =B/µ ac the B--curve has been derived. The result is shown on the left hand side of figure 6. The material goes approximately at A/m slowly into saturation. The saturation flux denisity is slightly above 1.5 T. To derive the µ s -B-curve equation 4 from data sheet [2] and the B--curve have been used. The equation 4 from the data sheet uses a -field in Oersted which can be transfromed into A/m by = =... ; (4) (3)

6 On the right hand side of figure 6 the two permeabilities µac and µs versus the flux density are shown. While the large signal permeability µac decreases at approximately 0.6 T below the initial value, the small signal permeability µs decreases beginning at small flux densities m s m B m@m0d B Fig. 6: B--curve (left) and µ-b-curves (right) of the iron powder material FS The B--curve for the EPCOS ferrite material N87 has been derived by transforming the µ ac -B-curve given in the Magnetic Design Tool [3] by use of =B/µ ac into the B--curve. The resulting curve is shown on the left hand side in figure 7. The N87 material starts to saturate at a magnetic field approximately 100 A/m. The saturation flux density is below 0.5 T. To derive the µ s -B-curve an inductance from dc-current measurement has been performed. For this, a toroidal core R4012 with outer diameter =40mm, inner diameter =27mm, height h =12mm and =12 turns has been used. The effective length eff = ( + ) 2 of this core is 108.4mm and the effective area eff = h ( ) 2 is 90mm 2. With equations 5 and 6 and by use the B--curve the µ s -B-curve has been calculated. The two permeabilities µ ac and µ s are shown on the right side in figure 7. While the small signal permeability µ s decreases steadily with increasing flux density, has the large signal permeability µ ac much higher values nearly over the whole flux density range. = = eff eff eff (5) B m@m0 D m s m B Fig. 7: B--curve (left) and µ-b-curves (right) of the ferrite material N Results To use an automatically generated mesh, the simulations have been performed with the magneto static solver of ANSYS Maxwell 15. On the left hand side of figure 8 the flux density inside the inductor is shown. At a current of 60 A the flux density inside the iron powder cores is approximately 700 mt. This is below saturation flux density. Inside the ferrite cores the flux densities varies strongly with

7 position. While the edges are nearly free of fields, is the flux density next to the powder cores close to saturation Fig. 8: Flux density inside the inductor at 60 A (left) and comparison of the simulated and measured L vs. I curves (right) Measurement B- incremental B- appearend PermeabilityLink DC- On the right hand side of figure 8 a comparison of the simulated and measured L vs. I curves is presented. The measurement has been performed on special equipment for measuring the L vs. I curves. The measured curve is decreasing form small currents on. The simulated apparent inductance is much larger than the measured one. Even the incremental inductance is up to 60 A much larger than the measured inductance. The curve of the new PermeabilityLink method follows the measured curve quite closely. 5. Conclusion A new method for simulation of saturation behavior in magnetic materials of inductive components has been presented. This method gives more realistic simulation results than the established methods in comparison to inductance versus dc-current measurements. The method resembles the real physical behavior during the measurement. The dc-current leads to a B-field inside the magnetic material. The permeability as a reaction of a small signal excitation in this operation point depends on the actual B- field and lead to the inductance in this measurement. By use of two material curves, the B--curve and the µ s -B-curve this can be accurately simulated. An example consisting of ferrite and iron powder cores illustrates the beneficial results of this approach. Current and future development is dedicated to the use of this method in designing innovative inductive components. 6. Acknowledgment We thank Dr. Leon Voss and the ANSYS team for supporting us with implementing this method and discussions regarding programming the executable. 7. References [1] Kampczyk W. and Röß E., Ferritkerne Grundlagen, Dimensionierung, Anwendungen in der Nachrichtentechnik, Verlag Siemens Aktiengesellschaft, 1978, ISBN [2] Micromatels Arnold Powder Cores, [3] EPCOS AG, Magnetic Design Tool,