A new theorem for active networks

A theorem is proved which states that any network with three accessible terminals can be replaced by a star or delta of certain e.m.f.´s and impedances. This is an extension of Kennelly´s star-delta theorem, and Thévénin´s theorem. The theorem is applied to find the equivalent network of a transformer and a 3-phase alternator (with coupling between windings and unequal e.m.f.´s) The sensitivity of an impedance bridge, in which a 3-winding transformer is used, is also found by the help of the theorem. Finally, the theorem is used to find the errors in voltage measurement due to earth capacitances. An important result which emerges is that, in measurements of attenuation in balanced systems, an unbalance of capacitance that occurs after the attenuation pad causes an error in the measured voltage which is not attenuated by the pad. This is in contradiction to accepted theory, but agrees with practice.