## Friday, 6 September 2013

### Moments of my intimate contact with electricity:Telephone Line Voltage

I like wiring – since my childhood years – guess it is just the way i am.

One of my early experience as a teenager is to extend the telephone line – essentially i just strip the wires and twist the interconnect – with my bare hand. In the middle of doing that, muscle at my upper arm started twitching involuntary – it felt kind of funny – no pain but still… seeing part of your body behaving out of your control is kind of weird…

As it turns out, telephone line is typically at 40VDC, and when it rings it can go all the way up to 90VAC.. so i guess my twitching muscle act as the incoming call detector!!

Having your body as part of current path is never a good idea, few mili ampere of current is enough to mess up your heart beat under the right condition – so give electricity some respect is what we should do..

Side notes:

IEC voltage range AC DC defining risk
High voltage (supply system) > 1000 Vrms > 1500 V electrical arcing
Low voltage (supply system) 50–1000 Vrms 120–1500 V electrical shock
Extra-low voltage (supply system) < 50 Vrms < 120 V low risk

< 120VDC is considered as low risk.

### 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)