An analysis is made of the operation of magnetic amplifiers or non‐linear transformers. Open circuit output voltages are calculated for transformers driven by a sinusoidal primary current, and also for sinusoidal primary current plus a direct current bias. The case of a loaded secondary is also considered and it is shown that there exist conditions for instability or resonance. A subsequent paper will consider Barkhausen noise as a limiting condition on the sensitivity of these devices.