Sensor Characteristics Example Problem

• The instrument span is:

$$x_{max}-x_{min}=\frac{1.5-0[\text{V}]}{20[\text{mV/mm}]}=75\text{ mm}$$

• There are $2^8$ states, which correspond to $0,\dots ,255$. We want this to correspond to our input voltage range from $0$ to $3.3\text{ V}$. Thus, the resolution is:

$$\frac{3.3\text{ V}}{2^8}=12.89\text{ mV per LSB}$$

• The minimum voltage (LSB) we can discern is $12.89\text{ mV}$, so we want to find how many millimeters this corresponds to.

$$\frac{12.89\text{ mV}}{20\text{ [mV/mm]}}=644.5\mu \text{m}$$

• The resolution of $0.5\text{ mm}$ is much worse than $644.5\mu \text{m}$.