The theory of the static frequency-changer is developed and a number of expressions of a simple character are obtained which enable the performance to be calculated for any loading conditions.It is shown that, knowing the magnetization characteristic of the iron, the maximum attainable output per unit volume of iron for unity-power-factor conditions in the load may be calculated for the ideal transformer from a simple formula.It is found theoretically that if the load is of suitable impedance and leading power factor an output from a given weight of iron is obtainable which is many times that obtainable when the load is of unity power factor. The power factor of the input is also improved.Experimental work, confirming the theoretical work, is described.Finally, design particulars are given of a 550-kW unit, changing from 50 cycles to 150 cycles with an efficiency of 94 per cent and output power factor of 0–53 leading. The input power factor of the unit as designed is 0–38 lagging, but this may be increased by the use of additional capacitative kVA on the higher-frequency side.