Obtaining impedance matrices of RF structures using the joining and subtraction formulae

We present a computationally efficient method for the calculation of impedance (Z-) matrices and optimization of a large class of standing and traveling wave structures used in klystrons, traveling wave tubes, and other vacuum-electronic devices. We apply the joining formulas by which the Z-matrix of a structure may be constructed from the Z-matrices of its component parts without additional finite element (FE) simulations. For the inverse operation, we apply the subtraction formulas that define the Z-matrix of a structure from which a selected section has been removed. We also derive and show how to use the joining and subtraction formulas for computing the Z-matrix of a modified structure, without re-computing the entire structure Z-matrix. The obtained Z-matrices are suitable for the large signal 1D and 2D beam-wave interaction codes CHRISTINE-CC and TESLA-Z. Application of the techniques described here greatly facilitates the accurate Z-matrix calculations and optimization of large, complex circuits that are difficult or impossible to model whole in a single FE simulation.