APPLICATION OF DIFFERENCE EQUATIONS IN DC CIRCUITS (In Press)

Abstract

This study explores the application of difference equations in modelling and analysing electrical circuits, specifically 4-mesh DC, RL, and RLC topologies. With the increasing integration of discrete-time simulation and digital control in engineering systems, traditional methods such as mesh analysis may be limited by computational complexity. Difference equations offer a discrete framework to simulate circuit dynamics using time-stepped recurrence relations. First- and second-order difference equations are applied and derived from RL and RLC circuit models in continuous time using discrete-time approximations. Solution of ladder circuits is through characteristic equation for second-order recurrence relations, whereas recursive formulations are adopted to analyse transient responses in RL and RLC circuits. The study defines complexity in terms of equation count and compares it across methods to demonstrate improved scalability. Realistic component values are selected to reflect conditions in actual electrical systems, such as inductive startup loads and resonant filter behaviour. The resulting current responses demonstrate convergence and system stabilization over time. Stability is confirmed analytically through characteristic roots and time-step considerations. These visualizations reinforce the suitability of difference equations for modelling dynamic responses in power electronics, sensor systems, and digital control applications. The findings highlight how difference equations provide a viable alternative for efficient and scalable analysis in modern electrical engineering.