# Power Losses Investigation in Direct 3 \(\times\) 5 Matrix Converter Using MATLAB Simulink
## 2 Bidirectional Switch Analysis  
The IGBT transistor is used to provide a bidirectional switch in the majority of matrix converters [6; 22; 23; 24]. Even some manufacturers, such as SEMIKRON, produce modules with IGBT switches suitable for use in matrix converters, such as the SKM150 GN12T4G or SKM400 GM17E4. The switches mentioned are only available in high-power designs, which are not suitable for low or mid-power applications due to their high cost, possibly large power losses, and low power density. However, IGBT switches are well established, dependable, and can even survive a short circuit current for a short period, which can be useful in matrix converter applications. The significant drawback, on the other hand, is the current flow distribution in the switch during positive or negative flow, as seen in Figure 1.  
As shown in Figure 1a, the current travels in a positive direction (from the power source to the load) via Q1 and then, through the internal diode of Q2. Conversely, the negative current (from the load to the power supply) flows via Q2 and then through Q1 internal diode. As previously established, current will always flow via one transistor and one diode even if both transistors are fully open. This is due to the technology utilized in IGBT transistors. The resulting conducting power losses in this sort of bidirectional switch may be represented as:  
\[P_{LOSSigbt}=I_{AV}\cdot V_{SAT}+I_{AV}\cdot V_{F} \tag{1}\]  
where \(I_{AV}\) denotes the average current flowing through the bidirectional switch and \(V_{SAT}\) and \(V_{F}\) denote the IGBT saturation voltage and internal diode forward voltage, respectively. The following characteristics can be noticed while using a random average 1200 V IGBT, such as the STGW15H120 DF2. The voltage drop at the separate sections of the IGBT is shown in Table 1.  
Figure 1: Current flow in IGBT-based bidirectional switch (**a**) Positive current flow, (**b**) Negative current flow. As can be observed, the diode voltage drop is quite substantial, which can result in high power losses, particularly at low power outputs, lowering the matrix converter's efficiency dramatically. SiC technology, on the other hand, is now quite popular in power electronics due to its benefits. They provide a very high blocking voltage while also having a low RDson of the transistor. Because the driving circuits are simple and SiC semiconductors can function at high frequencies, the overall volume of the converter's passive components may be kept to a minimum. Another feature of MOSFET-based SiC semiconductors is the channel ability to conduct current in both directions. This mode of operation is known as inverse conduction, and most manufacturers include a description of it in their product datasheet. The reverse conducting capability in matrix converter applications can have a significant impact on power losses and converter efficiency. If a negative voltage is given to the Drain-Source channel and the transistor is positively biased (VGS is positive), the channel will conduct current from Source to Drain if the following equation is true:  
\[V_{F}>I_{RMS}\cdot R_{DSOn} \tag{2}\]  
The current will pass through both the SiC channel and the intrinsic diode in the circumstance when the right side of Equation (2) is somewhat higher than the left side. If the voltage drop on the channel is less than the internal diode threshold voltage VF, current flows exclusively via the MOSFET channel. This scenario is depicted in Figure 2.  
If both transistors are positively biased and the voltage drop in the channel is less than the threshold voltage of the internal diode, Figure 2 represents both current directions (positive and negative).