## 1 Introduction  
Matrix converters are single-stage alternating current (AC/AC) power converters mainly based on power transistors with minimal passive component requirements. Since their appearance, matrix converters have been a topic of research with extensive study in topological variations, control methods/strategies, reliability and loss analysis [1]. Even though the industrial applications of matrix converters have been somewhat limited by constraints such as efficiency and semiconductor drive requirements, recent developments in semiconductor technologies combined with more affordable and powerful computation devices, such as system-on-chip technologies that combine both Field-Programmable Gate Array (FPGA) and microprocessors inside the same chip enabling the use of more complex control schemes, shape a promising future for matrix converters in a variety of applications. Matrix converters are bidirectional power topologies that allow AC/AC power conversion, without intermediate energy storage, revealing one of the most important advantages of matrix converters when compared to traditional back to back (B2B) voltage source converters (VSCs). Furthermore, the reduced filtering requirements makes the matrix converter a topology mainly dependent on power semiconductors, and as a direct consequence the matrix converter is able to achieve unparalleled power densities, an attractive feature for applications such as aerospace, aeronautics, military, electrical traction and distribution in high price real estate areas. To allow bidirectional operation, matrix converters are constructed with bidirectional power semiconductor switches. Each bidirectional switch can be operated in the four-quadrants and controlled at a frequency \(f_{s}\) much higher than the output or input fundamental frequencies \(f_{o}\), \(f_{s}\gg f_{o}\). With the use of recent power semiconductor technologies, such switches can be attained in a variety of configurations with different semiconductor technologies. Figure 1 shows different configurations of semiconductors for controlled 4-quadrant bidirectional switches. The most common configurations are both the common emitter and the common collector insulated gate bipolar transistor (IGBTs) configurations with their respective antiparallel diodes (Figure 1a,b). With the current trends on wideband-gap technologies the use of silicon carbide metal oxide semiconductor field effect transistors (SiC MOSFETs) (Figure 1c,d) allows for increased efficiencies and higher switching frequencies than the switches with silicon IGBTs. Reverse blocking IGBTs (RB-IGBTs) (Figure 1e) have also been employed in matrix converter applications in an effort to increase the converter efficiency by reducing the switch conduction losses [2,3]. Matrix converters can be divided into two different families of converters, single-stage or direct matrix converters (DMCs) and dual-stage or indirect matrix converters (IMC). Several topology variations within these two categories exist and their analysis and labeling have been extensively covered across different works [4]. Simplified structures depicting the most common topologies for DMCs and IMCs can be found in Figure 2a,b, respectively, while a common topology for a single phase matrix converter is shown in Figure 2c. Each family of topologies has their benefits and drawbacks and the appropriate selection will depend on each specific application requirements. Figure 1: Common configurations for 4-quadrant bi-directional switches: (**a**) common emitter insulated gate bipolar transistors (IGBTs), (**b**) common collector IGBTs, (**c**) common drain N-channel metal oxide semiconductor field effect transistors (MOSFETs), (**d**) common source N-channel MOSFETs, (**e**) anti-parallel reverse blocking IGBTs. Figure 2: Schemes for two matrix converter topologies families. (**a**) Direct/one stage matrix converter (**b**) indirect/dual stage matrix converters. (**c**) Single-phase matrix converter.