摘要：In this paper, the basic equations of beam-wave interaction for designing the 220 GHz folded waveguide （FW） backward wave oscillator （BWO） are described. On the whole, these equations are mainly classified into small signal model （SSM）, large signal model （LSM）, and simplified small signal model （SSSM）. Using these linear and nonlinear one-dimensional （1D） models, the oscillation characteristics of the FW BWO of a given configuration of slow wave struc- ture （SWS） can be calculated by numerical iteration algorithm, which is more time efficient than three-dimensional （3D） particle-in-cell （PIC） simulation. The SSSM expressed by analytical formulas is innovatively derived for determining the initial values of the FW SWS conveniently. The dispersion characteristics of the FW are obtained by equivalent circuit analysis. The space charge effect, the end reflection effect, the lossy wall effect, and the relativistic effect are all considered in our models to offer more accurate results. The design process of the FW BWO tube with output power of watt scale in a frequency range between 215 GHz and 225 GHz based on these 1D models is demonstrated. The 3D PIC method is adopted to verify the theoretical design results, which shows that they are in good agreement with each other.