## 4 AC/DC Converter
### Operation Principles of AC/DC Converters Architectures
#### 4.1.3 Split-N and Split-NP Topologies  
Both topologies constitute an improvement of the previous one because Split-N and split-NP, unlike the previous of the rotational parts architectures, work like a switched power converter. The MOSFET control signals are generated with a pulse width modulator (PWM) controller that uses the measurement of the output voltage level to stabilize the output voltage, thus regulating the output voltage to the required value. The split capacitor topology-based converter [47; 48] is composed of six MOSFETs (M\({}_{1}\), M\({}_{2}\), M\({}_{3}\), M\({}_{4}\), M\({}_{5}\), and M\({}_{6}\)). They are connected in the same way as in the side-diode topology and allow the bidirectional switching. The diodes (D\({}_{1}\), D\({}_{2}\), D\({}_{3}\), D\({}_{4}\), D\({}_{5}\), and D\({}_{6}\)) provide a rectifying path in each half cycle for each phase. Six capacitors (two per phase) with same capacitance value are used for charge recycling and to replace the diodes D\({}_{3}\), D\({}_{4}\), D\({}_{7}\), D\({}_{8}\), D\({}_{11}\) and D\({}_{12}\) of the side diode topology (Figure 21). Thanks to this, the diode forward voltage drop is avoided, which leads to have fewer losses and improves the system efficiency. Moreover, the output capacitor provides the required DC voltage for the resistive load. Within this type of architecture, two variations will be simulated and analyzed. * Split topology with N-type MOSFETs
* Split topology with N and P-type MOSFETs  
So called N-type Split topology is composed of six N-type MOSFETs (M\({}_{1}\), M\({}_{2}\), M\({}_{3}\), M\({}_{4}\), M\({}_{5}\) and M\({}_{6}\)). Compared with side-diode architecture, replacing diodes with capacitors in the rectification part of the circuit reduces the forward diode losses. This topology schematic is shown in Figure 25.  
Analyzing a single phase, the split N architecture works similarly to the previous architecture, a step-up or boost switched converter, with two switches instead of one; thus, it is able to operate in both the positive and negative cycles of the AC input voltage. The capacitive divider C1 and C2 provides the reference voltage allowing the correct biasing of the switches, M1 and M2, and reducing the output voltage ripple alongside the output capacitor. The higher this value, the lower the voltage ripple. The waveforms this topology presents for a continuous mode operation of the boost converter are shown in Figure 26a. The switches M1 and M2 are continuously turning on and off with the clock frequency of the switched converter, \(f_{sw}\), and a duty cycle, D, corresponding to the output voltage specified, \(V_{load}\). The average output voltage could be estimated with the following expression (22),  
Figure 25: Split N capacitor three-phase circuit. which differs slightly from that of a DC-DC boost converter because the input waveform is AC, thus it has an extra term function of the switching frequency and its duty cycle, and the AC frequency:  
\[V_{load}=\frac{V_{int1}}{(1-D)}\cdot\frac{D\cdot f_{sw}}{f_{AC}} \tag{22}\]  
Thus, the average current through the inductance is (23):  
\[I_{L}=\frac{V_{load}}{R_{load}\cdot(1-D)} \tag{23}\]  
In addition, the maximum ripple of the inductance current is obtained through (24):  
\[\Delta i_{L}(\mathfrak{t})_{max}=\frac{V_{load}\cdot D}{f\cdot L_{1}} \tag{24}\]  
where \(D\) is the duty cycle of the converter, \(V_{int1}\) is the root mean square (rms) value of the AC voltage of a single phase, \(f_{AC}\) is the frequency of the AC signal, \(L_{1}\) is the inductance of one winding and \(f\) is the switching frequency of the converter. On the positive cycle of the \(V_{in}\) signal, when the switches are on, the current flows from M1 to M2 back to the source and, when M1 and M2 are in the off state, the current flows to the load through D1, Figure 26b. On the negative cycle of \(V_{in}\), the current flow changes polarity, flowing from M2 to M1, in their conduction states. When the switches turn off, the current flows to the load through D2.