## Friday, 6 September 2013

### What does equation y=mx+c got to do with specification?

Well, almost most of them. Take example, a voltmeter spec of +/-(10% of reading + 10% of range). The first term of % of reading is referred as gain error, and second term of % of range is referred as offset error.
to understand this from graphical approach,
let’s start by drawing out a x-y axis – with x being voltmeter reading and y being actual value
then draw a line with y = x (implied m=1, c=0) from –1 to +1.
Let’s try to interpret this graph

now, to further discuss this, i think it is best to throw in some number – let’s consider the gain error of +/-10%. what it means is that the line will has a slope of 10% deviation from our ideal line (m=1, c=0).
if gain error is all that we have, then we have something like below:

next let’s consider the case where gain error is zero, and +/-10% of offset error (remember that we are taking about +/-10% of measurement range offset). for this we have

Now, for the real world instrument – gain error and offset error is real and cannot be ignored.
Factor in both gain and offset error, we have resulted in a series of possible lines that the real instrument behave.

From the look of it, it seem pretty bad – as the uncertainty is high for the voltmeter reading, in fact – up to 20% of measurement range. But, what you pay is what you get, gain and offset error of 10% is chosen for the sake of our discussion here. For real voltmeter with decent pricing, you can easily get 0.1% accuracy for both offset and gain. In certain case (depend of calibration, operating temperature, pricing…) you can even get better than 0.01%! Now, that is impressive.

Note:
In this example we used a voltmeter, but most measurement / sourcing instrument (source measure unit, power supply, oscilloscope, capacitance meter….) present their spec in similar form. So you can apply this method to have a sense of what the spec mean – with graphical approach.

Sometimes, the manufacturer will give un-normalized spec for offset, which is essentially the same thing. take our example here of +/-(10% reading + 10% of range) , if the range is 10V, the equivalent un-normalized spec will be +/-(10% reading + 1V)