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# How to calculate maximum error?

## How to calculate maximum error?

(OP)
Hi,
I am wondering how I can calculate the maximum error of a measurement chain.
If I have a voltage transducer with a accuracy of +-1%, which is wired to analogue input of a PLC (12 bit), what's the error of it?
The output of the transducer is 0-10V so as the input.

Cheers,

Lars

### RE: How to calculate maximum error?

Not easy to say. You haven't said anything about the error of the PLC input. All we have to go on is the resolution, which is 12 bit. We do no know if it is unipolar (12 bits across -10 V to +10 V) or bipolar (12 bits across 0 to 10 V). In the former case, you will have around 0.05% and in the latter case 0.025% of range resolution.

The general rule to add independent errors is RMS and that means error is sqrt(0.01^2 + 0.0005^2) or 0.01001, which corresponds to 0,01001 or 1.001% error, which means that you can forget about the influence from PLC resolution.

So, it is very important if your transducer's error is ten times or more. On the other hand, if your PLC isn't better calibrated than 1%, then your RMS error will be sqrt(1^2 + 1^2) or 1.4%. The maximimum possible error will be 1 + 1 = 2%

Then you have to decide if this is linearity only or offset plus linearity. And, then again, is your error refered to range, maximum value or actual value?

It is almost impossible to state what the error is without going into lots of details like that.

Gunnar Englund
www.gke.org
--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

### RE: How to calculate maximum error?

Just remember the rules of digital sampling. I think if you want 1% accurancy your sampling has to be 2x that accurate. That includes your sensor, how you configure that card in the plc (RPI), the task that its called from has a scan time. Just something to think about.

### RE: How to calculate maximum error?

That is more about Nyquist, isn't it? Not so much about calibration, non-linearities and offsets.

Gunnar Englund
www.gke.org
--------------------------------------
Half full - Half empty? I don't mind. It's what in it that counts.

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