**1. Introduction**

It is a fact that magnetic components are an essential part of our lives. We can find them in almost anything of quotidian use, from simple things such as cell phone charges [1] to TVs and home appliances. However, they have become more relevant in the development of electric and hybrid vehicles, electric machines [2], renewable energy systems [3–6], and recently in implanted electronics [7,8] to open the possibility to micro-scale neural interfaces [9]. Inside these devices and systems, a power stage is conformed by magnetic and electronic components.

A few years ago, these power stages used to be bigger and heavier, and they had considerable energy losses making them less efficient. Nowadays, silicon carbide (SiC) and gallium nitride (GaN) switching devices have improved power electronics, making them smaller and faster [10,11]. Notwithstanding, magnetic components oppose miniaturization; these remain stubbornly large and lossy [12]. In a modern power converter, magnetics are approximately half of the volume and weight , and they are the main source of power losses [13,14].

The trend in power electronics has two explicit purposes for the design of magnetic components. The former is to make maximum use of magnetics capabilities, achieving multiple functions from a single component [12]. The latter consists of minimizing the size of magnetic components substituting ferrite (the leading material in their fabrication) with ferromagnetic materials [15]. Those materials have a higher saturation point than ferrite, high permeability and are based on iron (Fe) and metallic elements (Si, Ni, Cr, and

**Citation:** Rodriguez-Sotelo, D.; Rodriguez-Licea, M.A.; Araujo-Vargas, I.; Prado-Olivarez, J.; Barranco-Gutierrez, A.-I.; Perez-Pinal, F.J. Power Losses Models for Magnetic Cores: A Review. *Micromachines* **2022**, *13*, 418. https://doi.org/10.3390/mi13030418

Academic Editor: Jürgen J. Brandner

Received: 3 February 2022 Accepted: 25 February 2022 Published: 7 March 2022

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

Co). Some examples of these kinds of material are Fe-Si alloys, powder cores, amorphous materials, and nanocrystal material [16–18].

The design of magnetic components is the key to achieving two purposes. The design parameters are intimately dependent on geometric structure, excitation conditions, and magnetic properties such as power losses that determine if a core magnetic is suitable to be part of a magnetic component [19]. Power losses in magnetic components are important design parameters; which limit many high-frequency designs.

Power losses in a magnetic component are divided into two core power losses and winding power losses. Core power losses are related to the selection of the material to make the core of inductors and transformers; in this case, parameters such as frequency operating range, geometric shape, volume, weight, temperature operating range, magnetic saturation point, and relative permeability must be considered [20]. On the other hand, winding losses are related to phenomena such as skin effect, direct current (DC) and alternating current(AC) resistance in a conductor, and proximity effect [19,21,22]. Those phenomena increase the volume of a winding structure [23]. One way to overcome this kind of loss is by using Litz wire [24].

Nowadays, there are several models for studying, predicting, and analyzing the power losses in the ferromagnetic cores of magnetic components. However, many of them have been developed to work in a limited frequency range , temperature and low magnetic flux [25]. Usually, the ferromagnetic cores' manufacturers provide the graphs of the core losses in their datasheets, which it is commonly obtained with sinusoidal signal tests and for specific values of frequency (*f*) and magnetic flux (*B*) [26].

There are many ways to calculate the power losses in magnetic materials. The original Steinmetz equation is one of them; however, to the best of the author's knowledge, it is not always the best option. In the author's opinion, selecting a method to calculate power core losses must be based on its versatility to vary their measurement's parameters [27].

This document aims to provide the reader with a general panorama about the core power losses in ferromagnetic materials, emphasising the diverse models found in the literature, announcing their characteristics, advantages, and limitations. Besides, it will present a relationship about magnetic materials and tested models. Any magnetic component designer must know the basic methods, core losses' models, the conditions at which they are valid, and their mathematical fundamentals. Magnetic and thermal losses, calculus and modelling are open research areas due to the non-linear features of ferromagnetic materials, the complexity of developing a unique power core losses model for the overall ferromagnetic materials, and their respective validations.

The organization of this work consists of the following sections. In Section 2, the reader will find information about the characteristics of each ferromagnetic material. Losses in magnetic components are reviewed in Section 3. In Section 4, general core losses models are mentioned as empirical core losses proposals. Features of Finite Element Method software are given in Section 5. The design process of a magnetic component is discussed in Section 6; on the other hand, the importance of the core losses methods in miniaturization of magnetic devices is summarized in Section 7. The discussion of this work is presented in Section 8, and finally, in Section 9, conclusions are provided.
