The modes of operation of the various circuits employed in vibratory converters are briefly described and a more detailed analysis is then made. Formulae are derived for use in design and in most instances these are presented graphically. The paper includes calculation of the transformer flux density, the buffer capacitance, and the no-load (constant) losses, together with load characteristics for a.c. outputs with resistive or inductive load, and d.c. outputs employing full-wave, half-wave or voltage-doubling rectifying circuits. The ripple voltage across d.c. outputs is calculated and its harmonic content analysed. Formulae for input current, current in the transformer windings, and copper loss are also included, and are utilized to compare the power ratings for a given size of transformer operating in any of the various circuits. The paper deals mainly with conventional circuits for low or medium power, up to about 50 watts; however, one section analyses some special circuits for d.c. outputs of high power in which the current pulses in the transformer are so shaped that the vibrator contacts open at virtually no load.