Abstract: In order to improve the voltage gain of boost converters, the number of boost inductors should be increased. A systematic method to derive the single-switch multi-inductor high gain boost converters is proposed in this paper by summarizing the construction rule of boost cell in five typical single-switch dual-inductor boost converters. This method is to replace the diodes in the switched-inductor with capacitors, and to prevent the voltage of boost inductors from being clamped by the capacitors. A family of single-switch triple-inductor high gain boost converters is derived based on this method. One topology in this family is selected as the example to analyze the working principles and steady state characteristics in detail. The correctness of the theoretical analysis is verified by a 300 W/100 kHz prototype. The results show that the proposed derivation method is feasible.