A control theory approach on the design of a Marx generator network

A Marx generator is a well-known type of electrical circuit first described by Erwin Otto Marx in 1924. It has been utilized in numerous applications in pulsed power with resistive or capacitive loads. To-date the vast majority of research on Marx generators designed to drive capacitive loads relied on experimentation and circuit-level modeling to guide their designs. In this paper we describe how the problem of designing a Marx generator to drive a capacitive load is reduced to that of choosing a diagonal gain matrix F that places the eigenvalues of the closed-loop matrix A+BF at specific locations. Here A is the identity matrix and B characterizes the elements of the Marx generator and depends on the number of stages N. Due to the special structure of matrix F, this formulation is a well-known problem in the area of feedback control and is referred to as the structured static state feedback problem. While the problem is difficult to solve in general, due to the specific structures of matrices A and B, various efficient numerical algorithms exist to find solutions in specific cases. In a companion paper by Buchenauer it is shown that if certain conditions hold, then setting the natural frequencies of the circuit to be harmonically related guarantees that all the energy is delivered to the load capacitor after a suitable delay. A theorem formalizing this result is presented. Earlier aspects of this research have been published in two theses.