This paper presents a comprehensive study and the analysis of a topology of a no isolated DC-DC intituled Double Quadratic Boost converter with high static gain. This converter has the main advantage of high static gain and low voltage stress on its switches. The article will first present the theoretical analysis of the converter operating in an open loop. The objective of the work is the mathematical modeling and the control strategy of the converter, as well as the validation through closed-loop experimental results. Besides, we presented the practice test results to demonstrate the operation of the converter, such as the static gain experimental curve, the practice efficiency of the converter, and the control of the output voltage, as well as the capacitor voltage balance control. The authors designed a prototype for 1 kW, with a switching frequency of fs=50kHz, with FPGA-based command and modulation.