The equivalent circuit model (ECM)of the folded waveguide (FW) in consistent consideration of the ohm loss on the waveguide wall was established for calculating the cold-circuit phase velocities, interaction impedance and attenuating coefficient of space harmonics of periodic TE10 mode in this slow wave structure (SWS). These results were obtained for one-dimensional (1-D) parametric model calculation of the particle-microwave interaction in the 220 GHz backward wave oscillator (BWO). When the frequency of microwave is up to terahertz regime, the ohm loss caused by surface current on rough waveguide wall is not negligible any more. Further study shows that the starting oscillation current and output power are intimately dependent upon the loss property calculation. The ECM about lossy periodic circuits was then developed from the previous loss-free model to give a more accurate analysis. Three-dimensional (3-D) Eigen mode analysis for the FW SWS was taken to verify the improved model, which shows good agreement. Additionally, based on the improved ECM, 1-D beam wave interaction calculation was conducted which is in good consistency with 3-D Particle-in-cell (PIC) method.