### Relationship between Input and Output Ranges

In Table 2 and Figure 3-1 we see the relationship between input range and output range for a transmitter.  The graph of Figure 3-1 shows that the relationship is linear.

 Input Range 100 - 500ÂºC % Output Range 3 – 15 psi Output Range 4 – 20 mA 100 0 3 4 200 25 6 8 300 50 9 12 400 75 12 16 500 100 15 20
Table 2

Refer to Figure 3-2 as you follow the examples.  This figure shows a temperature control loop

Figure 3-2     A Temperature Control Loop

Figure 3-2     A Temperature Control Loop

What if the temperature was 250ÂºC?  How can we find out what the output should be?
First, find the temperature as a percentage of spans.

Use the following equation for the calculation of percentage input or output span values.
Therefore:
Next find the value of output signal for a 37.5% input value.  Remember that a transmitter is linear.  A 37.5% input produces a 37.5% output.
To convert a percentage to an actual output signal value, first calculate the percentage span and then add the zero value using the equation below.
Therefore, to find 37.5% of 3 to 15psi:
Or in the case of a 4 to 20mA signal system, we have:

If the output signal is not 7.5 psi in the case of a pneumatic transmitter or 10mA for an electronic transmitter; then the transmitter needs calibrating.
Let’s convert from a known output value to a process variable value for the same temperature transmitter.  We know the transmitter range is 100ÂºC - 500ÂºC.
A pressure gauge on the output indicates 10 psi for a pressure transmitter and 13.3 mA for an electronic transmitter.
What should the input temperature be?
Find 10 psi as a percentage of spans.
Next find 58.33% of 500ÂºC - 100ÂºC
The actual temperature should be 333.32ÂºC at the input.  If it is not, then the transmitter requires calibration.

Let’s look at another example with a pneumatic transmitter.  The transmitter has a range of 0 to 600 psi.  The actual pressure is 450 psi.  What should the value of the output signal be?
First find 450 psi as a percentage of span.
Next find 75% of 3 to 15 psi
If the output signal is not 12 psi, the transmitter requires calibration.
When working with an electronic transmitter the Span in the equation becomes
16 mA and the Live Zero is 4 mA.