Analytical computation of any system function of a large-sized fully-coupled ladder network: A symbol-free method

Abstract

In this paper, an elegant and time-efficient computation method is proposed for obtaining the analytical expression of any system function (in Laplace-domain) of a fully-coupled, completely inhomogeneous ladder network with an arbitrary number of sections and without resorting to symbolic computations. The direct approach of performing symbolic computation using software such as Maple becomes severely restrictive, because, the memory and computational time required increases unboundedly, even for moderate-sized networks. So, handling large-sized ladder networks are ruled out. To circumvent this bottleneck, authors propose an entirely numeric approach, i.e., a symbol-free method to compute any network function (e.g. transfer or driving-point), which is time-efficient, poses no restrictions on the network-size and the number of windings that can be included. Furthermore, it includes both winding and dielectric losses and every inductor and capacitor is coupled to every other inductor and capacitor, thus making it fully-coupled. Details of its formulation are described and simulation results are presented to demonstrate its time-efficiency and applicability to both single- and three-phase winding configurations.