Characteristics of time-varying inductance

When an ac current pushes an inductor into saturation for part of each cycle, the inductor presents two values of inductance to the rest of the circuit. This situation can arise either deliberately, as in the operation of a fluxgate magnetometer, or unintentionally, as with the saturation of power transformers by geomagnetically induced currents. Analyzing such a circuit can be laborious, but often all that is required is knowledge of how the changing inductance affects slowly varying components of the current. It is shown that the effective inductance seen by slowly varying currents flowing through a time-varying inductance is given by 1/L_eff=θ/L₁ +(1-θ)/L₂, where θ is the proportion of time for which the inductance has value L₁. This expression is comparable to that for the effective inductance of two uncoupled inductors in parallel, but allowing for the proportion of time that each one is seen by the rest of the circuit. For power transformers, where the unsaturated inductance is considerably greater than the saturated inductance, the term involving the larger inductance quickly becomes negligible as the proportion of time in saturation increases. Thus, beyond very mild saturation, the effective inductance seen by slowly varying currents flowing through the transformer is inversely related to the proportion of time in saturation