Theory and Performance of Parametric Transformers

The theory of parametric power transformers is developed, and it is shown that the secondary side of the transformer operates as a parametric power oscil lator and is described by a non-l inear second-order differential equation with periodic coefficientsof the Hill's -Mathieus type. In developing the theory, attention is focused on the secondary inductance as the variable circuit parameter responsible for the oscillations. The double frequency variation in the inductance necessaryforparametric excitation is produced by the primary flux and is looked at as a modulating effect. The saturation of the secondary core also affects the secondary inductance and leads to the appearance of the non-linear term in the equation which is necessary to limit the amplitude of oscillations that otherwise tends to grow without bound.