Linear Transducer Scaling

How to calculate Scale and offset for a Linear Transducer

The most common type of output signals are volts, current and frequency and questions often arise about conversion to actual units. In this example, I am going to discuss conversion from current to pressure units or PSI.

For this example, I have chosen a 3000 PSI pressure sensor that outputs current as low as 4mA and as high as 20mA depending on the pressure. The output current needs to be converted to units so that my data makes sense; and to do this I will show how to solve two simultaneous line equations in the form of y = mx + b

To begin, I am using a device that has differential inputs, which means that each input has two connections – one (+) and one (-). In order to convert current to a voltage a resistor is installed into the loop completing the current loop of the sensor – refer to the configuration below for signal hookup.

Figure 1: Basic Current Loop Circuit

Doing the math (Ohm’s Law) the resistor will produce values between 1 and 5 volts. Knowing this I setup my two equations as follows

Applying the equation to both ends of the pressure sensor’s range (substitute 3000 and 0 for the y parameter) and voltage equivalents (substitute 5 and 1 for the m parameter), yields:

3000 = 5X + B and 0 = 1X + B

Using substitution, solve for variable B in the second equation: B = –X

Substitute that into the first equation: 3000 = 5X + B

Yields: 3000 = 5X -X

3000= 4X

X =3000/4 or 750 (this is the scaling parameter)

Plug that answer back into the other equation: 0 = 1X + B

And solve for B: B = 0 – 1X

Where X = 750

B = -1 * 750 or -750 (this is the offset)

Using some rearranging yield the transfer function in the form of y=mx+b or y = 750x - 750

Let’s test it:

Given values from the pressure sensor in volts (X) of 1V, 3V and 5V we convert those readings to pressure (y):

x (voltage measured) = (750x) – 750 (apply scaling) Y (converted back to pressure)
1V 1 *750 - 750 0
3V 3* 750 - 750 1500
5V 5* 750 - 750 3000

In this example, scale and offset turned out to be opposites of each other, but that is not normally the case.

The basic equation is y = mX + B, where X is the scaling or multiplier, and B is the offset. Using a little basic algebra I can apply this same set up to calculate scale and offset of any linear sensor or device with a linear output.