### Dynamic Response » Transfer Functions and the Transfer-Function Diagram

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.

Generic description of a sensor where the measurand x can be steady-state as during static calibration, time-varying as during field operations. Image from NCAR/EOL.

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.