The transient behaviour of uniform LC pulse forming networks

Summary form only given, as follows. It should be possible to derive exact equations that describe the transient behaviour of uniform LC ladder pulse forming networks from their impedance function as a function of s the complex frequency parameter. In practice the inversion of the Laplace transforms that describe this behaviour proves to be extremely difficult. This paper describes the progress that has been made towards achieving the correct inversion and deriving an exact solution to the problem. The problem, so far, has been split into two parts. A solution to the problem of how the shape of a voltage step changes as it propagates along a uniform LC ladder network and an analysis of the waveform that is produced when an infinite LC ladder network is discharged into a matched load. In the case of the propagating step the solution takes the form of an integrated Bessel function from which it is possible to see exactly how the shape of a voltage step is changed as it propagates along the ladder. In practice the rise-time of the step increases and an overshoot develops on the leading edge of the pulse. For the discharge of an infinite LC ladder network two solutions have been produced also in terms of integrated Bessel functions of variable order. Again the rise-time of the pulse produced and the ringing overshoot on the leading edge of the pulse are predicted with complete accuracy. It is hoped that from these two solutions a complete solution for pulse forming action by a LC pulse forming network can be deduced and that this solution will lead to new synthesis methods for pulse forming networks that can be used to design networks which generate pulses to an exact specification.