Sensor Transfer Function

A transfer function, in the context of sensors, expresses output as a function of input. In SYDE 252 or filters, “transfer functions” means something specific.

Units for a transfer function are:

$$\left[\frac{\text{output state}}{\text{input state}}\right]$$

which could be [V/kPa], [Hz/N], etc.

For example, a resistive pressure sensor could have:

$$A=10\left[\frac{\text{k}\Omega }{\text{kPa}}\right]$$

this means that its resistance is $10\text{ k}\Omega$ for every $\text{kPa}$ of applied pressure. This notation $A$ is mimics the gain of an op-amp.

These can be often be much more complex, such as:

$$R_{out}=10P_{\text{kPa}}+0.02P_{\text{kPa}}^2+7[\text{k}\Omega ]$$

Transfer functions can include frequency effects, like lowpass behaviour.

Transfer functions can be a general way to relate one state to another – similar to gain for Op-amps and Sensor Transfer Function.

For example, for a voltage divider, the transfer function would be:

$$\frac{V_{out}}{V_{in}}=\frac{R_2}{R_1+R_2}[\text{V}/\text{V}]$$

Applies to linear systems.

For a formalization, see Transfer Function.