The Equivalent Matrices of a Periodic Structure

A method to find a simple and accurate model of a periodic structure is presented using equivalent matrices. The model is simple in the sense that very few degrees of freedom (DoFs) are needed. Accuracy is based on the phase velocity and the electric field. It is applied to real structures used in traveling-wave tubes, namely, helix, helix with vanes, and folded waveguide. The method is very efficient even for broadband structures such as the helices. Accuracy better than 2% over a very broad band (first and second modes) is achieved on the phase velocity with only 16 DoFs for the helix with vanes. The accuracy on the electric field is better than 5%. However, a problem of spurious modes sometimes appears and is shown in examples.