Abstract :
The classical mathematical method of calculating the wave-form of rectified currents is applicable to rectifiers whose volt-ampere characteristic consists of two interesting straight lines. It is based on the observed fact that there is for each rectifier a conducting phase and an insulating phase. If the characteristics for each are linear, the differential equations are linear and can be solved for each separetely. The discontinuities between the two conditions are bridged by transient terms in the integrated equations. To evaluate the harmonics, Fourier´s theorem is necessary. Even for the simplest circuit the labour of calculation is very great, although the result is mathematicallly exact. A new method is proposed which treats the rectifier characteristic as a continuous curve having an equation E=f(I) In every part of the circuit except the rectifier the harmonics are independent, since the coefficients L.R.C are assumed constant. It is therefore an easy matter in any given circuit to calculate each harmonic of E in terms of the harmonics of I. The voltage and current must, however, at every instant of time satisfy the characteristic equation of the rectifier, and this leads to sufficient equations for a solution by successive approximation. The method is applicable to cases of biphase rectification, and, like the classical method, has its simplest application for ideally perfect rectifiers having a characteristic equation EI=0 The paper shows the method of reducing the equations to tractable form for solution by successive approximations, using the algebra of plane vectors, and it is shown by means of a numerical example how the approximations converge on the true value deduced by the classical method.
