We use differential equations to model dynamic performance. If the instrument or sensor responds linearly, its response can be characterized by a linear differential equation. Consider an instrument that uses a sensor to produce a signal M when exposed to a measurand x. Calibration of a sensor consists of determining the static relationship between M and x, often plotted as a transfer curve showing the relationship as discussed in the section on static response. A sensor can be depicted generically using a diagram like that below, where H(x) will be called the transfer function.
The transfer curve characterizes this relationship under static conditions (M given x), but we are often interested in applications where the measurand x varies in time. The simple box-description of the sensor still applies, but now the output M will depend not only on the present value of x but also on its past history.