Handy Formula for Transmitter / Calibration (x = %Span + MNR)

This is a Handy Formula for Transmitter to Control Valve Signal [Current to Pneumatic Converter (I/P)] or when you do Calibration, that I learned back when I am still studying at the Meralco Foundation Institute (MFI), and I find it easy & useful when dealing such cases like below. Hopefully, this will also help others to do the computation a lot faster and easier.

Below is just a sample temperature loop diagram and we'll be applying this to our "Handy Formula", and with that note kindly examine below diagram. 

Probably, for the most of the training's and seminars that we have attended, below table is the commonly used illustration to show the relationship of Transmitter Milliampere (4 - 20 mA) output to Current to Pneumatic Converter (I/P or sometimes E/P), and below table is very simple and easy to understand.

But what if we are required to calculate the Transmitter mA output , I/P output and provide the percentage opening of the Control Valve based only to the actual process measurement value. See below table.

Actually, this can be solve by means of interpolation, but we can use below formula to make our calculation simple:
x = % Span + MNR
where:
x = Given value / Measured value /  Available value
% = Percentage
Span = Maximum Range - Minimum Range
MNR = Minimum Range

​Observe below diagram:

Solution:
using   x = % Span + MNR
where: 
x = 64.5 
We will look first the Percentage Value of 64.5 Deg. C to its temperature range of 0 - 100 Deg. C based on the above table.
where: 
Span = Maximum Temperature - Minimum Temperature (based on the above Temperature Range from table)
MNR = 0 
using   x = % Span + MNR
64.5 = % (100 - 0) + 0
64.5 - 0 = % 100
64.5 = % 100
64.5 / 100 = %
0.645 = %
 
We are now going to use this percentage value to compute for the actual transmitter mA output, range is 4 - 20 mA.
using   x = % Span + MNR
where: 
x = actual mA transmitter output
% = 0.645
Span = Maximum mA - Minimum mA (based on the above mA Range from table)
MNR = 4   
x = 0.645 (20 - 4) + 4
x = 0.645 (16) + 4
x = 14.32 mA is the Transmitter and Controller output going to our I/P or E/P converter
 
Now, to compute for the Current to Pneumatic Output (3 - 15 psig), we will still be using the Percentage Value of the above temperature measurement (64.5 Deg. C).
using   x = % Span + MNR
where: 
x = actual psig of Current to Pneumatic output
% = 0.645
Span = Maximum psig - Minimum psig (based on the above psig Range from table)
MNR = 3   
x = 0.645 (15 - 3) + 3
x = 0.645 (12) + 3
x = 10.74 psig is the Current to Pneumatic output going to our Control Valve or Final Element
 
Lastly, to compute for the Percentage Valve Opening, just copy or refer to the Percentage Value of the above temperature measurement (64.5 Deg. C) since range is also from 0 to 100 Deg. C. This is due to the fact that once the actual temperature measurement varies, the Control Valve opening will also varies from 0% (fully close) to 100% (fully open).
% = 0.645 x 100
% = 64.5
Therefore, the Valve Opening for the above temperature measurement is 64.5 %. 

​The above formula is not only limited to Temperature but also applicable to all other process variables (Pressure, Flow and Level) and other application similar to this one. 

You will appreciate more of this formula for complex ranges like 30 - 985 deg C or 0 to 25 deg C and just a reminder, practice more to master this technique.

Date Published: March 8, 2019
Source: Leo - MFI Alumni - Batch 23