# Is magnetic hysteresis present even with a DC bias?

Consider the following circuit: With Vin(t) = A sin(ωt) for some given frequency ω.

The relationship between Vin and Vout is certainly non-linear, because of the effect of hysteresis in L's magnetic core.

My question: is hysteresis non-linearity present even if Vin(t) = A sin(ωt) + B, where B is greater (possibly much greater) than A?

My intuition is that since the polarity of the current through L does not change, then there is no hysteresis. An alternative intuition tells me that maybe it is the sign of the derivative of the current what counts; i.e., the current rises through one curve, and lowers through a different curve (different sections of the magnetization curve), thus causing non-linearity. However, I'm not sure that the math checks out with this alternative intuition, in that the output (the value of the y-axis) would diverge if you repeatedly go down at a low slope and then go back up at a higher slope.

• Cheap tape recorders used to rely on hysteresis in the presence of DC bias. (Better ones used AC bias)
– user16324
Apr 6, 2021 at 14:01

The linear relationship of $$\B = \mu H\$$ is only an approximation in this case. 