# Calibration curves

Sometimes we need to characterize the behavior of a sensor for its measurements to be useful. This is especially true in the world of strain gages that output a millivolt signal proportional to the voltage input based on the amount of stress they are placed under. For our example, today we are going to look at creating a calibration curve for a 2 mV/V-100 PSI pressure transmitter.

# Gather Data

First, we will apply pressure and record the output millivolt readings. We will also monitor the excitation voltage throughout the process since knowing the millivolt per volt value relies on the voltage part of the equation. We will enter this data into an excel spreadsheet, leaving column A blank because it will make the graph we will be using later easy to set up.

# Calculate the mv/v

To calculate the mV/V readings we will concoct a small formula in excel to subtract the mV reading at zero PSI from the pressurized reading and divide it by the excitation voltage. This gives us our mV/V at each of the pressure test points.

# Calculate zero & span

The reported value for full-scale mV/V is simply the value we calculated for the full-scale pressure reading. To obtain the zero value divide the mV/V value by the excitation voltage.

# Graphing the data

Select the data.

Insert a line graph. Having the mV/V data to the left of the pressure data saves us the step of having to flip the axis around.

Right click on the line on the graph and click on “Add Trendline…” This will add a trendline to the graph. The default trendline is “linear,” and that matches our data well.

# Calibration Curve Formula

When we added the trend line to the graph, the “format trend line” dialog will appear to the right of the screen in excel. Near the bottom check the box that says “display equation on chart.” Given the simplicity of the data we are dealing with you could choose to perform the calculation manually, but since excel will do it for me, I stick with excel. The formula will appear on the graph in the form of a *y=mx+b* format. Since we have the mV/V plotted on the “x” axis we can plug in our reading divided by the excitation voltage to calculate the pressure reading.

# What if the function is not “linear”?

Here is some data that has a curve to it when plotted. What should we do in this case?

We can go back to the “Format Trendline” dialog and choose one of the other trend line styles. In this case I chose polynomial, and it matches the data fairly well. We can compare the dotted trend line to our actual data in the chart.

# How can we use this DATA?

Most modern data acquisition systems allow us to plug these formulas in and use them to interpret data from sensors. By building calibration curves for inexpensive sensors, we can use them to make measurements that might have been reserved for more expensive scalable sensors in the past.