Abstract: The group-delay characteristics and gap impedance of the newly-designed output structure with three-gap coupling cavity, for the X-band extended interaction klystron (EIK) beam-wave interaction system, were mathematically modeled, theoretically analyzed and numerically simulated with CST and PIC software for design optimization. The influence of the input power on the output power, gain and efficiency was investigated. In addition, the high frequency interaction circuit for EIK was designed; and the output, with a fairly large bandwidth, of the entire high-frequency system was stabilized with the effective measures, such as loading, misalignment and stagger tuning. The simulated results show that the high frequency EIK system with the optimized output structure has a 3 dB instantaneous bandwidth of 11. 5%, an output power of 1. 43 MW, a gain of 38. 54 dB and an efficiency of 28. 52%, when operating in X-band at a frequency of f₀ GHz and at an input power of 200 W.