This study presents a high-gain broadband balanced homodyne detector, utilizing cascade amplification to generate continuous-variable quantum random numbers. The innovative approach of distributed parameter circuit analysis and optimization simulation is introduced into the circuit design of the broadband balanced homodyne detector. The objective is to enhance the transmission attributes of the ultra-high-frequency circuit. This is realized by optimally combining different elements and selecting key electronic components, guided by system stability indicators. Hence, a balanced homodyne detector was developed with a bandwidth surpassing 1.65 GHz and gain flatness of ±2 dB within the 0.2?930 MHz range. This study proposes a novel design perspective for broadband balanced homodyne detectors. The enhanced features of the detectors facilitate a more efficient derivation of continuous-variable quantum state random entropy sources, thereby propelling the rate enhancement and practical advancement of continuous-variable quantum random number generators.