# Design Considerations of Multi-Phase Buck DC-DC Converter
###### Abstract
This paper primarily focuses on the design of a 1.5 kW two-stage polyphase switched capacitor converter characterized based on high efficiency (above 98%) and high power density. The authors of [26] propose a methodology for sizing magnetic components and devising a novel multi-phase split-duty-cycle variant integrated with a cascaded converter. This configuration is well-suited for bidirectional operation, particularly when the low-voltage port requires a multi-phase step-down stage. The validity of the chosen magnetic components in the coupled inductor is confirmed through a combination of simulation and experimental results. A four-phase interleaved buck-boost converter with changed load connection (CLC-FIBC) for fuel cell (FC) application is proposed, analyzed, and designed in [27]. A simple structure, a wide range of input current change, high input, and output current levels, and low ripple characterize the proposed structure. In [28], a novel multi-phase synchronous zero-voltage step-down converter (ZVT) with pulse-width modulation (PWM) is presented. With an auxiliary circuit, all buck converter switches can operate under soft-switching conditions. A 2 kW two-phase ZVT-PWM synchronous step-down converter is verified, and the experimental efficiency is given compared to a conventional two-phase step-down converter. In [29], a detailed design and analysis of a multi-phase step-down converter based on a magnetic core solenoid inductor is observed. Additionally, it introduces an optimization framework for efficiently designing multi-phase step-down converters with magnetic core solenoid inductors tailored to specific specifications. Simulation results demonstrate that the multi-phase converter designed using the proposed methodology achieves 92.8% efficiency and 0.5 mV voltage ripple. In [30], a multi-phase interleaved bidirectional DC-DC converter structure is proposed. This structure brings about reductions in input current ripple, switch voltage, output voltage ripple, and passive component sizes. Improved transient dynamic response and enhanced reliability are notable advantages of using such a structure. The steady in [31] presents a novel multi-phase DC-DC converter characterized by modularity, simple control and structure, additional gain, continuous input current, and low normalized switch/diode voltage. This configuration is particularly well-suited for tracking the maximum power point in photovoltaic (PV) power generation applications. The authors of [32] present a comparative study of single-phase and multi-phase DC-DC converters for controlling Li-Fi systems. The comparison includes the converter design, efficiency, and maximum achievable bitrates of each topology. From the comprehensive analysis of the state of research in the field of multi-phase DC-DC converters, it is evident that this topic remains highly relevant, driven by a continually expanding array of applications. The enhancement of converter characteristics and the assurance of their performance metrics are primarily founded on several key methodologies:optimal synthesis of control (most often digital); use of new topologies with better qualities compared to classical ones; optimal design of the magnetic components; and optimal design of the entire power circuit. However, it is worth noting that the published sources lack studies that determine the optimal number of phases for multi-phase buck converters and the associated relationships between converter efficiency, the number of phases, and the specific input-output parameters of the design task. In this regard, the present work aims to present a rational methodology for determining the optimal number of phases of multi-phase step-down DC-DC converters depending on specific needs. The work is organized as follows: In Section 2, the main types of losses in the circuit of the studied converter are considered and analytical dependences for their calculation are presented. The output and input current ripples in the multi-phase converter are analyzed.