High-Intensity Discharge(HID) lamps are the new generation of lamps that require high DC voltage. This kind of lamp is used in cars’ headlights. The suitable input voltage varies from 120 V to 400 V. However, this value is not accessible in vehicles. Therefore, a high-gain DC-DC converter must be used beside. This study has proposed a family of high-gain converters according to the boost modifying based on the voltage multiplier cell and voltage lift technique. The input current of these converters is continuous. Consequently, the input current filter faces less current stress. Additionally, only one switch has been employed in the topologies, increasing the converter's reliability. Moreover, the load and input source common ground is present, which is essential in various applications. Despite the boost converter, the semiconductors face less than the output voltage during their inactivation mode. The proposed topology has been discussed in both the ideal and non-ideal manner. Moreover, the converter's operation requirements in the continuous conduction mode have been expressed. Finally, the experimental results of the first proposed topology have been presented, and the extracted theoretical relations have been validated. Notably, the output power was 90 W, the output current was 0.5 A, and the extracted efficiency was 90 percent.