Calibration function

A calibration function in LSA is synonymous to a transfer function. In the context of hysteresis compensation, the calibration function refers to the anhysteretic current-to-field transfer function.

Derivative of a transfer function

For the $I\to B$ transfer function we can express it generically as

$$B=f(I)$$

Where $f$ is the piecewise linear transfer function.

This means that for the derivative we use the chain rule

$$\begin{array}{rl}\dot{B}& =\text{dv}t\left(f(I)\right)\\ & =\text{dv}fI\text{dv}It\\ & =\text{dv}fI\dot{I}\end{array}$$

Which means that to derive $\dot{B}$ from $\dot{I}$, we need to scale them by the derivative of the transfer function $f(I)$ w.r.t. $I$.

Similarly for the inverse relationship we reach

$$\dot{I}=\text{dv}{f}^{-1}I\dot{B}$$