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# Zero & Span error

## Zero & Span error

(OP)
Could someone give me a proper definition of the two for a temperature transmitter. I know how a thermocouple works however calibrating it I'm not to sure on. Could you correct me if I'm wrong but i think zero error is when your expected zero is not reading zero and is either higher or lower depending on the system and span is when the zero is correct but further up the line the span is not correct. Could you give me a proper definition for future reference, thank you

Martyn 2nd Year instrument apprentice.

### RE: Zero & Span error

If you plot the output of any instrument against what true value should be (temperature reading versus true temperature), you will get a straight line with a slope of one, which passes through zero.

Adjusting the zero of the instrument will move the line up or down. Adjusting the span will change the slope of the line.

### RE: Zero & Span error

"Zero" is the offset error. e.g. the temperature is 30° and your instrument is measuring 29°. It's often called offset as in many cases you don't care about 'zero".

"span" often called "gain error" is where your instrument is amplifying the measured quantity in some manner so as the signal gets larger its perceived value is larger yet, of course the gain error can also result in the opposite where the perceived value gets progressively smaller.

The instrument's calibration adjustments usually provide for a finely adjustable offset voltage to be added/subtracted from the unknown and also an adjustment to the input amplifier's gain.

Where things get confusing is when the instrument's error is not linear. Typically the error is parabolic or bowl shaped. This means it could actually be correct at 0° and at, say, 100° but be, in fact, off by 2° at 50° that would be 1° off at 25° and 75°. This is where the instrumentation tech needs to earn their keep. The decision needs to be made as to how to calibrate the instrument to "optimize the process" that the instrument is observing.

An example of this would be drawing a glass optical fiber. The correct pull for the fiber's fine structure would likely need the glass temperature to be held very accurately at some temperature between 3,452°F and 3,992°F lets say 3,500°F. Your instrument is going to have offset and gain error - it just is! You have only a single offset and gain adjustment. The error is probably going to be non-linear to some extent.

Do you trot out your ice bath for calibration? NO! Zero is going to be nearly 4,000°F away from the area of interest. Ideally you would want to set the offset and gain corrections using values in "the region of interest". This means you need proper calibration standards for the process you're trying to calibrate for. You want the maximum error free region centered in the process's area of interest. You will do that at the expense of the regions of no interest. Your calibration efforts may greatly increase error in regions of no interest as a good trade for increased accuracy in the region or regions of interest.

It should also be noted that the instrument's error could be worse than a non-linear curve as mentioned. BTW the aforementioned curve is called a second order or X2 function. Another favorite error is a third order error or X3 which describes an "S" shape. This would mean in the example above you might be "dead nuts on" at zero and 100° AND at 50° but be -1° off at 25° and +1° off at 75°. As an instrument tech you need to take all this into account and make the calls needed to "calibrate for the process".

The best way to discover these non-linear issues is to check calibration over several points "in the area of interest" as this will show you what kind of error is present and will allow you to calibrate intelligently as needed.

Of course, other instrument tech decisions need to be made as to the cost of the calibrations. If you are running an incinerator that burns waste the only real issue may be that the incineration temp is at least 'so high' and the normal procedure is to run 20° higher than that. Obviously in this case nothing really needs tight calibration so a check that confirms the readings are within a generous error band is probably all that's required.

One last point. Because lots of calibrations may focus on some areas at the expense of others there should be consensus with others in the process to make sure everyone is on board with how the calibrations are done. Logs should always be fastidiously kept as they will help immensely in understanding the instrument and the sensors, how they age, and can provide the clues as to how a process may be going off-the-rails in troubleshooting. Good logs will also help if the calibration method needs to change down the road, as well as tell you when the sensor will fail next so it can be changed out before wrecking a production cycle.

Keith Cress
kcress - http://www.flaminsystems.com

### RE: Zero & Span error

(OP)
Thank you both for your explanation. This has now answered my question, can often get quite confusing when there is so much instrumentation knowledge to be learnt, thank you.

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