The increasing use of rectifier locomotives and motor-coaches has focused attention on the limitations of accepted rectifier theory in the calculation of performance of bi-phase and single-phase bridge-connected rectifier circuits. Most industrial rectifier installations exceeding a few kilowatts in rating are supplied from a 3-phase system, and are designed to operate with 6- or 12-phase output on the d.c. side, while sometimes in very large installations it is necessary to operate with up to 72-phase output. In these conventional multi-phase equipments the ripple current, which is associated with undulations in the output voltage, is superimposed on the output direct current, but is sufficiently small to permit, for the purpose of calculation, the assumption of a d.c. circuit of infinite inductance. This assumption leads to considerable simplification of the theory. Unfortunately it is not tenable in the circuits discussed in the paper, as it is found that the presence of the ripple current in the d.c. circuit has a profound effect on the operation of the whole equipment.The paper outlines the calculations for bi-phase and bridge circuits, based on the accepted ‘infinite inductance’ theory, and derives the direct voltage at the motor, ripple current in the motor circuit, power factor in the a.c. supply, harmonic currents in the a.c. supply and other related quantities. The inaccuracies in the results of these calculations are pointed out.A description follows of a new approach to rectifier problems, by means of which solutions to both transient and steady-state problems can be obtained, taking proper account of resistances, inductances and capacitances in all parts of the circuit. The problems are treated as circuit problems, the equilibrium equations being established in terms of mesh currents and expressed as simultaneous first-order differential equations. These are solved by means of a digital electronic computer, Deuce, whose logical facilities are used to take account of the valve action of the rectifying elements.Results of calculations are supported by tests which were carried out in conjunction with British Railways on the Lancaster-Morecambe-Heysham section. A description of this electrification has appeared elsewhere.12The operation of rectifier locomotives is discussed in the light of further calculations based on variations of a typical design.