# Understanding the Development Process of Inductor Design

## This article will analyze the challenge of measuring the saturation roll off and introduce the BsT-pulse which attempts to solve this problem.

Within the development process like inductor design, numerous questions can arise. “How large is the linear area of a certain magnetization curve?”, “How hard is soft saturation?” or “How lossy is a magnetic component?” Without answers, these questions can needlessly slow down the development process.

Without answers, these questions can needlessly slow down the development process. However, to get answers one needs to go to a socalled “expert” with “experience”. Bs&T is here to deliver the answers, the data, the exact numbers in an open and transparent way.

High power density and high efficiency are two major technical requirements for magnetic component. Each soft magnetic material has saturation, and the ideal magnetic material is supposed to have linear area to perform virtual inductive design within circuit simulation. There are two commercial available solid materials with relatively high saturation flux density, and high Curie temperature on the market, they are “metal alloyed powder core” and “stress annealed metal-metalloid tape wound core”.

Metal alloyed powder cores consist of highly permeable metal grains, isolated with inclusion. These cores are macroscopically homogenous and magnetically isotropic [1]. The metal-metalloid tape wound core on the other hand is rapid solidified and annealed in combination of uniaxial anisotropy with controlled tensile stress along the ribbon direction. These cores are highly versatile and provide desired levels of linear permeability. An additional transversal magnetic annealing can be applied as post treatment which reduces coercivity within the so called Rayleigh area. Not having discrete air gaps guarantees homogenous thermal loading especially during long term excitation. This makes these cores extremely reliable.

This article will analyze the challenge of measuring the saturation roll off and introduce the BsT-pulse which attempts to solve this problem. We will present a case study of two common examples and end on a technical discussion of the proposed solution.

**Challenge and solution of quantify the softness of saturation **

The (re)magnetization curve has saturation and it limits the linear working area, for each inductor cored regardless with metal alloyed powdered or rapid solidified and stress annealed one. The roll off of differential permeability and its approaching to saturation can be characterized by the width of anisotropy distribution, determined by the Baradiaran method [3]

p(HK)=-H d^2J/dH^2

The second deviation of B and H is, by definition, the differential permeability for each particular current amplitude along the demagnetization curve.

Current validation method for such low permeable material is performed by small signal ac excitation at given frequency and small enough ac magnetization, with increasing dc biased with DC sources, the particular measurement delivers incremental permeability [4], it is very sensitive, especially at "sharp" roll up area, approaching to saturation. Because the infinitesimal ac interval is systematically enhanced the drop off with increasing dc bias. A principle description of incremental permeability is given by IEC 62024 edition 2, as well as the operation difficulty of such measurement; however description of measuring condition in quantity is dismissed.

Complementarily, BsT-Pulse delivers differential inductance on demagnetization curve quickly [1], directly and not sensitive by operational condition. And so does the differential permeability.

The BsT-pulse micro is based on thyristor technology, the working principle is described as following: Pulse energy, storage in capacitor, is discharged at desired voltage, and the device under test and capacitor formulate a LC resonance circuit, the full reversal current enables characterization of damping behavior and the transient large current amplitude drives device under test into saturation. [4] With given effective length and cross section, and number of turns, the impulse amplitude permeability and demagnetization curve can be found in the material analysis page of the data processing.

Further depiction of the HK vs. H/Hm can be described accordingly, Gaussian distribution at HA quantifies the stiffness or so called “softness” of the roll off to saturation. Sharp Gaussian distribution with curvature R, defined as ratio of the field strength, at which the linear working area ends, and the local maximum of differential permeability takes place. The high number of R differentiates the hardness of saturation behavior. [5]

**Demonstration with two examples:**

Now we have selected two typical commercial available examples, the one inductor under test (with courtesy of company: Fuss EMV) is constructed with metal alloyed powder core, shaped as 2 pieces E6527 in stack, the material in use is XFlux FeSi6.5 040 (company Mag-Inc), and wound with solid wire with number of turns as 139. And the other one is stress annealed finemet type nanocrystalline Fe73.5Si13B9Nb3Cu1 tape wound core (with courtesy of company AmorNano in Beijing).

*1. Metal alloyed powder core XFlux R ~0,26*

Metal alloyed particles are compacted and annealed, wound with solid wire [1]

The characteristic point is located at HA~ 13000A/m, the differential permeability (starting with ~ 54) ends to 13000 A/m, and saturation flux density of 1,6 T is seen at 50000 A/m, the curvature is calculated as 0,26. The initial magnetic permeability is 54 by data processing, the Rayleigh constant is 0,125, the Ms is calculated as 1,2 MA/m, Néel constant is -5859 Joule.

*Figure 1: Powder core XFlux, wound with solid wire with number of turns 139, pulsed at discharge voltage of 300 V*

- voltage current decay DUT
- BH curve of bipolar excitation
- rebuild of BH curve (zoom part) with Rivas coefficients [6]
- μ π,a vs. H IEEE389
- Q factor ωLs/Rs is calculated as 0,08, and the insertion loss among6,5 ms and 17 ms is 3,285 dB
- distribution of anisotropy as differential permeability (green) [3]

As shown in the Figure 1 the B-H curve can be re-built according to Rivas [6]

And the coefficients can be calculated by

where the factors: Ms, χ, λ, and α can be found by parameters of the where the factors: Ms, χ, λ, and α can be found by parameters of the

First, the χ is actually relative permeability of the material and read directly from the material relative permeability of the material and read directly from the datasheet, alternatively ontained from initial differential permeability of DUT permeability of DUT; the *Ms *is the *M *value when the *H-> inf.*, thus is defined as the maximal magnetic flux density during damping process, which can be as Bs/Uo , the factor λ is considered as considered as Rayleigh constant:

*Figure 2: Stress annealed finemet type nanocrystalline, pulsed with discharge voltage of 70 V*

- voltage current decay DUT
- BH curve of bipolar excitation
- distribution of anisotropy as differential permeability (green) [3]

therefore by Hc is read between the neighboring cross zero points of flux density, right from pulse testing, at last, the is considered considered as Néel constant, it is the intercept of the linear function *M H* of *H*, defined as

And the curve must cover the point when the M = Ms and point (Ht, Mt) Mt). In this exercise of fitting, the α is selected as 8000 A/m and then the can also be calculated based on the pulse testing data.

*2. Stress annealed tape wound nanocrystalline core R 0,67*

Finemet type nanocomposite is made as ingot, rapid solidified as plan amorphous ribbon, despoolt through continuous kiln under strain loading, and respoolt to tape wound core, the whole process is automatically performed, afterward boxed in plastic cover, labor cable (0,5 m) is wound over the core, the number of turns is 8. The inductor is right connected on the two terminals of BsT-pulse micro, and formulated with the storage capacitor as LC resonance circuit.

The curvature R (~ 0,67) is independent on permeability performed by stress annealing [5], the characteristic point is located at HA~ 1200A/m, ending with linear area. The local maximum of differential permeability is illustrated with pronounced peak at field strength of 1800 A/m. The discharge voltage is 70 V, the Hc and Br are read as 115 A/m and 70 mT.

## Discussion and Conclusion

BsT-pulse enables the differentiation of softness of saturation behavior, and the full reversal current enables the articulation of loss (insertion loss) behavior with limit values for serious specification. It can be embedded into monitor system to ensure reliable operation. The rebuilt magnetization curves and loops are quick and intuitive. Those fitting coefficients with physical interpretation can be then used for simulation routine in numerical way.

#### Literature:

[1] JC Sun, Yi Dou 2020 damp oscillation solution for validation ofmetal alloyed powder core

[2] McHenry 2020 TMC Core Losses in Co-rich Inductors with Tunable Permeability

[3] Baradiaran, Vaquez 1989 Distribution of the magnetic anisotropy in amorphous alloys ribbons

[4] JC Sun, K.Seitenbecher 2020 dust vs. ferrite bodopower march edition

[5] L. Varga 2020 Tailoring the magnetization linearity of Finemet type nanocrystalline cores by stress induced anisotropies

[6] J. Rivas 1981 Simple approximation for Magnetization Curves and Hysteresis Loops

#### About the Author

**JC Sun** is the founder of Bs&T Frankfurt am Main GmbH, a company located in the north of the metropolis Frankfurt am Main and specializes in the development and manufacture of integrated hyster loop measuring systems. He worked for two decades as a development engineer in power electronics; developing various soft magnetic materials and was a project manager for various companies.

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