Accurate parametric modeling of folded waveguide circuits for millimeter-wave traveling wave tubes

In this paper, results of different models are compared for calculating effective, cold-circuit (beam-free) phase velocities and interaction impedances of folded waveguide (FW) slow wave circuits for use in millimeter-wave traveling wave tubes (TWT). These parameters are needed for one-dimensional (1-D) parametric model simulations of FW traveling wave tubes (FWTWTs). The models investigated include approximate analytic expressions, equivalent circuit, three-dimensional (3-D) finite difference, and 3-D finite element. The phase velocity predictions are compared with experimental measurements of a representative FW circuit. The various model results are incorporated into the CHRISTINE1D code to obtain predictions of small signal gain in a 40-55 GHz FWTWT. Comparing simulated and measured frequency-dependent gain provides a sensitive, confirming assessment of the accuracy of the simulation tools. It is determined that the use of parametric 1-D TWT models for accurate, full band predictions of small signal gain in FWTWTs requires knowledge of phase velocity and impedance functions that are accurate to <0.5% and <10%, respectively. Saturated gain predictions, being approximately half as sensitive to these parameters, appear to require correct specification of phase velocity and interaction impedance to within ∼1% and 20%, respectively. Although all models generate sufficiently accurate predictions of the interaction impedance, not all generate sufficiently accurate predictions of the effective axial phase velocity.