Reverse-Acting I/P transducer signal Calculation

A current-to-pressure transducer is used to convert a 4-20 mA electronic signal into a 3-15 PSI
pneumatic signal. This particular transducer is configured for reverse action instead of direct,
meaning that its pressure output at 4 mA should be 15 PSI and its pressure output at 20 mA should
be 3 PSI. Calculate the necessary current signal value to produce an output pressure of 12.7 PSI.
Reverse-acting instruments are still linear, and therefore still follow the slope-intercept line
formula y = mx + b. The only differences are a negative slope and a different intercept value.
Instead of y = 16x + 4 as is the case for direct-acting instruments, this reverse-acting instrument
follows the linear equation y = −16x + 20:

First, we need to to convert the pressure signal value of 12.7 PSI into a percentage of 3-15 PSI
range. We will manipulate the percentage-pressure formula to solve for x:

Next, we plug in the 12.7 PSI signal value and solve for x:

This tells us that 12.7 PSI represents 80.8 % of the 3-15 PSI signal range. Plugging this percentage
value into our modified (negative-slope) percentage-current formula will tell us how much current is
necessary to generate this 12.7 PSI pneumatic output:

Therefore, a current signal of 7.07 mA is necessary to drive the output of this reverse-acting I/P
transducer to a pressure of 12.7 PSI.