The extended interaction klystron (EIK) consists of several reentrant multi-gap coupled cavities. The demand for high-power microwave sources in the millimeter-wave region promotes the development of a Ka-band The extended interaction klystron (EIK). In this study, The real part of the impedance of the three-gapcoupled output cavities composed by three uniform gap cavities was derived by using equivalent circuit theory and field analysis method ,respectively.The basic parameters of the broad band output circuit were obtained by using equivalent circuit theory . Filter loaded three-gap coupled output cavities with band width of 4.6% were designed by using field analysis method .It lays a solid foundation for the development of the broad band EIK.