math to determine accuracy of analog AI?

Hello guys; I'm ashamed to admit it but I can't wrap my head around the proper math to tell a customer what type of accuracy I can get between analog inputs on a micro 1100 "on board" AI or moving to a IF4 exp card. AB states on board is 10 bit with raw data 0-1023. IF4 is 15 bit with 0-32767.

If my input is 0-10VDC from a pressure transducer with scaled engineering units (SCP) of 0-4500PSI what will be my best +/- PSI for each option???

Thanks in advance for any help you can provide.

g.robert said:

Hello guys; I'm ashamed to admit it but I can't wrap my head around the proper math to tell a customer what type of accuracy I can get between analog inputs on a micro 1100 "on board" AI or moving to a IF4 exp card. AB states on board is 10 bit with raw data 0-1023. IF4 is 15 bit with 0-32767.

If my input is 0-10VDC from a pressure transducer with scaled engineering units (SCP) of 0-4500PSI what will be my best +/- PSI for each option???

Thanks in advance for any help you can provide.

Click to expand...

Any Digital System can only be accurate to +/- one Count. There are other factors which are listed in the Manual, usually as Percent of Full Scale.

Is your question really about Accuracy, or Resolution?

If it is Resolution, it is basically the Full Scale Engineering Units divided by the Counts or Number for Full Scale. In this case;

4500PSI/1024 = 4.39453125 or +/- 4.39 PSI for the ML1100

4500PSI/32768 = 0.1373291015625 or +/- 0.14 PSI for the IF4

Quite a difference, obviously you get much better Resolution with the IF4, but not necessarily more Accurate. You will have to look at the Analog Specifications for them in their respective Manuals.

Stu....

In addition to what Stu mentions, also keep in mind there are calibration considerations as well. The more calibration points you take the closer you accuracy will approach your resolution. Obviously at the expense of cost and complexity. Using a simple SCP you are really only doing a two point calibration curve. But like Stu points out, the device itself normally has some degree of non-linearity as a percentage of full scale. It may also have some hysteresis and temperature stability aspects as well. Breaking up the curve into smaller segments and taking readings a more points can help close the gap between the accuracy and the resoltuion.

Thanks guys; I guess I am trying to determine the accuracy. By doing so we can mathmatically determine if we can use the "on board" AI and meet the customer's desired accuracy (what ever it might be).

Assume the transmitter is 100% accurate for our purposes. How much will the increased resolution of the 15 bit increase the accuracy.

What I mean is if the transmitter says it is 50% or 2250 PSI for an ouput of 5VDC how accurate will each option be +/- a PSI? Is it still;
4500PSI/1024 = 4.39453125 or +/- 4.39 PSI for the ML1100
4500PSI/32768 = 0.1373291015625 or +/- 0.14 PSI for the IF4

Thanks again for any input / resolution you can provide...

I'm not sure that there's any difference in terms of accuracy. The difference should be in resolution because the 15 bit analog breaks the data down into smaller bits.

Accuracy and resolution are not the same thing, as Stu and Damian have tried to point out.
Imagine a perfect world where the output at 0 PSI is zero volts and the output at 4,500 PSI was 10 volts and those voltages were exact and noiseless and the PLC input A to D is perfect. Then think of the output of the transducer being an exact straight line plotted between those points on a graph as a ramp. None of which, I shouldn't need to say are actually possible.
The resolution you're talking about would turn the ramp into steps like a stairway. Each step of the 10-bit input would convert to another 4.4 PSI in the PLC and each step of the 16-bit would be 0.14 PSI. That means that say at 5 volts in our perfect world your PLC would evaluate as 2,250 PSI. Then as the pressure increased slowly, the PLC would continue to read 2,250 PSI until the transmitter read about 5.005 volts, then the PLC would change to 2,254.4 PSI, then as it continued to 5.015 volts, the PLC would change to 2,258.8 PSI, and so on...
I hope I'm explaining adequately and the math is unverified but you should get the idea I'm trying to illustrate.
In the real world, actual accuracy as far as what a precision, calibrated instrument will measure on the fluid vs. what digits you convert to in the PLC will never reach the 16-bit resolution of the A to D, but a human looking at a digital display doesn't like to see numbers dithering in increments of 4 PSI that you would have with the 10-bit.
Your wiring methods and the environment will affect the accuracy as well.
This may make your decision easier or harder....

Just to add a bit more to the discussion..

Nothing you add to a signal path will increase the resolution or the accuracy. Everything you add decreases both.

If your transmitter has a 4-20ma signal and is rated at +/- 0.5% accuracy, that is the upper limit on system accuracy. If you use high resolution input cards with good accuracy, you will not degrade the signal quality much. But nothing you do on the input card can improve the accuracy.

In the analog realm, if your transmitter is 0.5% accuracy and you run it through a signal converter that is 1.0% accuracy, the result is 0.995 * 0.99 = 0.985 or +/- 1.5%.

If you then run that into a input card that is 15 bits resolution (let's assume it's accuracy is perfect for the moment), your resolution is 1/32768 or 0.003%.

Thanks for all the answers. I have firm grasp on it now.