The use of digital computers in obtaining solutions to electric-circuit problems involving switching operations

The analysis of electric circuits by matrix methods is well established as a means for obtaining differential equations relating the electric quantities to the impedance properties of the circuit. A brief summary is given of the mesh method of circuit analysis and a procedure is derived for expressing the resulting equations as simultaneous first-order differential equations. Reference is made to a digital-computer programme by which equations of this type are solved using a step-by-step method; non-linear features are dealt with by supplementing the programme with a set of special instructions. Ideal rectifying elements are regarded as switches whose opening and closing are either partly or entirely dependent on currents and voltages; the difficulties introduced by their presence in a network are discussed in general terms. Two special programmes are described which were made for the computer Deuce, dealing respectively with problems associated with 3-phase and 2-phase power-rectifier installations. An example is given of the calculation of the input and output currents of a 2-phase rectifier operating under steady-state conditions; another programme is used to make a harmonic analysis of the results. The need is discussed for a general programme incorporating certain non-linear features and capable of dealing with rectifier circuits for which there are less than a certain number of equations. A description is given of an iterative method for dealing with rectifying elements. The method is capable of yielding solutions of any desired accuracy, and mathematical justification is given. A scheme for a general programme based on the method is described and the range of possible applications is discussed.