Transmission Line Model for Folded Waveguide Circuits

We describe an equivalent circuit model for traveling wave structures based on folded or serpentine waveguides (F/SWs), including a beam tunnel. The model consists of a combination of transmission line segments and lumped electrical elements. Values of the five parameters that characterize the model are found by minimizing the differences between the dispersion and coupling impedance as calculated by the model and those obtained from a 3-D finite element code. We find that the model reproduces the dispersion to better than 0.1% and the coupling impedance to better than 1% over a broad frequency range in different examples in which the dependence of the impedance on frequency tends either to zero or to infinity near the band edge at 2π. The model is also able to capture the effects of asymmetric fields and misalignment of the beam tunnel. We conclude that the model can be used with confidence in codes that simulate the beam-wave interaction in FW and SW traveling wave tubes.