The transient behaviour of ladder networks of the type representing transformer and machine windings

Abstract

The theory of the transient behaviour of certain ladder networks, having a finite number of sections, when subjected to a unit-function voltage surge is developed rigorously. The networks chosen are those usually employed to represent a coil or winding in which each section has inductance L; capacitance to earth C_g and capacitance between sections C_s. Solutions for the transient voltages produced in such a network when the end is open or short-circuited are obtained using the Laplace transform.The solutions are general and show that only certain frequencies are excited in such a network. In particular, the treatment indicates errors in the earlier work of Rudenberg which are important since they lead to inaccuracies concerning the stresses to be expected in a machine or transformer.Calculations show how the important ratio C_g/C^s affects the voltage distributions and stresses, and how special cases of engineering importance (transformer, machine, choke, artificial line) can be derived by selecting appropriate values of C_g/C_s.Finally, by allowing the number of sections to become infinite, solutions are obtained for continuous windings and for a transmission line.