In this paper, a simplified nonlinear Eulerian beam-wave interaction theory model for helix traveling wave tubes is developed. Next, derived from the nonlinear model, a second-order Eulerian large-signal analytic solution is obtained by the method of successive approximation. Then, the analytic solution of AM/PM conversion is obtained and the relationship between AM/PM conversion and electron phase is also found. Finally, the Eulerian large-signal analytic solution and the analytic solution of AM/PM conversion are compared to a Lagrangian beam-wave interaction theory model and traditional Eulerian nonlinear models. All the simulations are conducted on a set of millimeter-wave traveling wave tube parameters which are based on a single pitch section of a Q-Band traveling wave tube. It is found that the gain, phase and AM/PM conversion of Eulerian large-signal analytic solution agree well with Lagrangian beam-wave interaction theory model before saturation occurs. The maximum error of gain is less than 8.5% near saturation. The Eulerian large-signal analytic solution gain more accuracy than traditional Eulerian models. The present Eulerian large-signal analytic solution can describe saturation effects which is caused by electron overtaking that cannot be found by traditional Eulerian analysis. Results validate the correctness and effectiveness of our Eulerian large-signal analytic solution and the analytic solution of AM/PM conversion. The analytic model of AM/PM conversion is expected to be useful as a first-hand design and simulation tool of AM/PM conversion for millimeter-wave traveling wave tubes.