## Process Signal Scaling

Many times during instrument calibration, loop checkout, or loop troubleshooting you will need to check the scaling of a process sensor, transmitter, or converter. You’ll need to know the output value for an input value or what input value is required to produce a particular output value.

There are many smartphone apps and websites that have simple and easy to use signal conversion calculators. The trouble with these is the user doesn’t need to know how they work or if the results are correct.

I would prefer that E&I students learn and use formulas for conversions like temperature conversion and signal scaling.  They need to be able to think about whether the answers are reasonable. Online calculators don’t do this.

I don’t want students to rely on apps that may not be accurate or available when they need them. For signal conversion, I teach why and how to use the following two formulas and suggest that they test formulas with min, max, and mid-scale values to see if the results are reasonable.

mA Loop Signal Scaling

PV = (mA -4 ) / 16 X FSO

mA = (PV / FSO X 16) + 4

In the first formula, you subtract the 4 mA offset from mA input signal, then divide the 16 mA span, this is a ratio, and multiply by the full scale output (in process units) to calculate the equivalent process variable output.

In the second formula, you divide the process variable (in engineering units) by the full scale output (in engineering units), this is a ratio, then multiply by 16 mA output span and lastly add the 4 mA offset to calculate the 4-20 mA equivalent output.

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