Efficient Calculation of Impedance Matrices for Vacuum Electronic Device Circuit Structures

We present a computationally efficient method for the calculation of impedance matrices of a large class of standing- and traveling-wave structures used in klystrons, traveling-wave tubes, and other vacuum electronic (VE) devices. By treating the gaps as “lumped ports,” this method avoids the time and disk spaces consuming steps employed in [1], which required postprocessing the electromagnetic fields from a finite-element (FE) simulation. By applying analytical transformations to the impedance matrix, we show that it may be cast in a form suitable for the large-signal 1-D and 2-D beam-wave interaction codes CHRISTINE-CC [4], [5] and TESLA-Z [1]. These transformations are formulated in a way to avoid numerical errors near structure resonance frequencies (singularity points). We also derive and apply formulas by which the impedance matrix of a structure may be constructed from the impedance matrices of its component parts, without additional FE simulations; by inverting the algebraic operations, we show that the impedance matrix of a structure from which a selected subsection has been removed may also be computed. Application of these formulas greatly facilitates the accurate calculation of the impedance matrices of large complex circuits that are difficult or impossible to model whole in a single FE simulation.