A numerical method for calculation of transients in electric circuits

The present paper describes a numerical method for calculation of transients in electric circuits, using a step by step approach. For a small interval of times Δt=const, for each branchj of circuit one calculatesa j =R j +L j /Δt+Δt/C j ,β j =R j +Δt/C j andθ=Δt/C j . After that, for each interval Δt the current increments Δi jk , the currentsi jk =i jk−1+Δi jk and the capacitor's voltageu cjk =u cjk−1+Δu cjk are calculated. The values of Δi jk are the roots of a system of simultaneous linear equations. The results of numerical calculation of transients by the proposed method do not differ from those obtained by analytical ones. The proposed method can be applied to a large number of problems in electrical engineering. A similar approach can be used for the calculation of transients in non-linear electric circuits and in other engineering disciplines (mechanics, thermodynamics, hydraulics etc.). Several numerical examples show how the proposed method can be applied.