Educational approach to transient analysis of electric circuits by simulating equations

Abstract

When studying an electric circuit, one can describe the circuit using equations. The equations can be coded into a computer program and iterated with fixed time step through time of interest, which generates simulation results. A specific methodology is needed for the purpose. The methodology of simulation of equations is developed and presented. Using this approach there is no black box (a general-purpose simulation tool) between the student or an engineer who is simulating the circuit, and the circuit itself. The use of “black boxes” – general-purpose simulators – is of great value when optimising circuits, but they can leave “black holes” when it is about understanding circuit principles and/or exploring new circuit ideas. Simulating equations leaves no space for “simulation noise”. The circuit is DC-wise analysed at sequential moments in time. Equations, which describe circuit components that store energy (capacitors and inductors), connect in time sequential DC analyses. The simulation of equations adds to the understanding of existing circuits and it has potential in the creation of new circuits. Time- and/or signal- and/or environment-dependent devices can be easily included in the simulation of equations. Test cases show a perfect match between simulated and known results for the analysed circuits. Programming efforts for the simulation of equations are at a manageable level for even a moderately proficient programmer.