# A High-Conversion Ratio Multiphase Converter Realized with Generic Modular Cells
## 2 Modular Multiphase Step-Down Converter  
The development of a generic cell as a basic building block is shown in Figure 2. The cell includes an inductor, a capacitor, and a pair of complementary switches. Multiple cells can be connected for increased energy processing. This unique approach of designing with a generic cell enables the extension of the converter to any number of phases, with the benefit of higher duty ratio resolution, lower voltage stress on the transistors, and inherent current balancing [51]. These benefits make the multiphase topology an ideal candidate for high output current and high conversion ratio applications. The combination of generic cells for the implementation of a high conversion ratio DC-DC converter is described and analyzed in the following sections. Throughout this paper, the concept is presented and analyzed on a configuration of three cells, namely, a three-phase buck converter, as illustrated in Figure 1. The main building block is a generic cell (Figure 2) comprised of an inductor, a capacitor, and two complementary switches. The cells connection follows a simple procedure. Port \"\(a\)\" of the cell (Figure 2) is connected to the previous cell (to \(V_{in}\) in the case of the first cell), port \"\(b\)\" of the cell is connected to the next cell, and port \"\(c\)\" is connected to the load. To complete the converter, one additional switch per converter (\(S_{2\text{-}3}\) in Figure 1) is added. It provides a discharge path for the last cell capacitor. Figure 1: Circuit diagram of three-cell buck converter. The operation of the proposed topology is described using the ideal timing diagram in Figure 3 and the sub-circuits with highlighted current paths in Figure 4. For simplicity, this analysis assumes that the voltage ripple across all capacitors is negligible compared to their DC levels. The switching period is divided into six intervals, corresponding to six states (I-VI). Odd-numbered intervals represent the charging phases for each cell, while even-numbered intervals correspond to balancing states. In this context, a \"cell\" refers to an individual building block, whereas a \"phase\" denotes the electrical components within a single cell that contributes to supplying the load current. As in typical multiphase converters, all phases deliver a continuous current to the output in an interleaved buck type connection. Since the charging and discharging of the capacitors is carried out via an inductance at all states, the charge transfer is referred to as soft charging [51; 52], which is highly advantageous in terms of efficient energy processing [53]. State I (Figure 4a) is the charging state for phase 1, and phases 2 and 3 are discharging to the load during this state. The switches \(S_{\rm 1H}\), \(S_{\rm 2L}\), and \(S_{\rm 3L}\) are turned ON, and capacitor \(C_{1}\) and inductor \(L_{1}\) are charging from the input and at the same time deliver current to the load. Inductors \(L_{2}\) and \(L_{3}\) are delivering current to the load. Figure 3: Timing diagram and idealized waveforms of a three-phase converter. Figure 2: Generic \(LC\) cell for a modular multiphase converter. States II, IV, and VI (Figure 4b) are balancing states. No phases are charged during these states. Switches \(S_{\rm 1L}\), \(S_{\rm 2L}\), and \(S_{\rm 3L}\) are ON, and all the inductors are delivering current to the load. State III (Figure 4c) is the charging state for phase 2, and phases 1 and 3 are discharging. Switches \(S_{\rm 1L}\), \(S_{\rm 2H}\), \(S_{\rm 2J}\), and \(S_{\rm 3L}\) are ON, and inductor \(L_{2}\) is charged from two parallel sources: capacitor \(C_{3}\), and a series connection of \(C_{1}\) and \(C_{2}\) (where \(C_{1}\) is connected in a positive direction, and \(C_{2}\) is connected in a negative direction).