Analytical formulas for calculating the electrical characteristics of multiparameter arbitrary configurational homogenous ladder networks

Abstract

SummaryMost electrical systems are represented as ladder networks made up of resistances, inductances and capacitances. Electrical characteristics of these networks, such as voltages, currents and equivalent impedance, are difficult to compute because they require solving multiple differential‐algebraic equations. Further, circuit simulator‐based modelling is a time‐consuming and tedious process for simulating large networks with multiparameters present in various configuration. This paper presents generalised analytical formulae for computing the electrical properties of any multiparameter arbitrary section homogenous ladder network that can be reduced to series and shunt impedances. Circuit principles, chain matrix decomposition and linear transformation are used to derive the symbolic expressions. Simply plugging the values of the series and shunt impedances, as well as the number of sections, into the derived expression yields the impedance. Thereafter, the calculated impedances can be used to calculate the nodal voltages and mesh currents. Simulation results of a six‐section homogeneous ladder network are presented and compared with those of other existing techniques to validate the derived expressions. The derived expressions eliminate the need for recursive relations, complex integro‐differential equations, large state‐space matrices and simulator‐based circuit modelling, which are all clearly advantageous.