A general theory of phase transformation by means of static pulsating-flux transformers is presented, i.e.mtonphases on ak-limbed transformer,m,n, andkbeing integers greater than unity. This is derived from the requirements of e.m.f. and m.m.f. balance. Except in the so-called 2-phase case, freedom of choice in selecting the winding elements in each phase always exists and it is always possible to produce a phase transformer for any required transformation ratio and phase shift. It is shown that the effective phase-turns are in general complex and that the ratio of voltage transformation is different from that for current transformation, both being complex and having equal and opposite phase-angles. Equality of primary and secondary power factors is thus established.In the examples given, the Scott and Leblanc connections for 2- to 3-phase transformation are shown to be duals. Two 3- to 4-phase connections are worked out in detail, and the symmetrical phasetransformers used with mercury-arc supplies are discussed briefly.