Assessing instrument indication errors

[Skywave]

This thread predominately refers to analogue-indicating measuring instruments, electronic.
And, for me, it is a difficult one to carefully write.

Preliminary comments.
Occasionally, I check the calibration of certain items of my test equipment. Now I do realise that this can be a bit of a minefield for many reasons, which is one of the reasons why having such done by professional test houses is often very expensive. However, my viewpoint is that with the few items of test equipment that I feel do have 'reasonably accurate' calibrations, I use those to check other items. (A 'small' error is better than a 'big' one!) With that idea in mind, any serious deviations from indication accuracy will be readily detected - and hopefully corrected.
I've said all that in the hope that replies to the question in this thread do not stray into the above area. (Which can always be discussed in another thread). I realise that this topic can be quite controversial and would like it not to go off-topic. Your co-operation with that will be much welcomed - as will any relevant replies: thank you.

My method.
I select a certain FSD range of an analogue-indicating instrument and input a signal (or voltage, current, etc.) according to that FSD. I then do ditto at half FSD, recording the indications in each case. My method of assessing the error is as follows.
Let known input = C (for 'correct'); let resultant indication = I.
Then error = (I - C) / C, expressed as a percentage.

So to the 'question': is that bit of arithmetic a valid method of assessing calibration accuracy? If not, what do you do - or suggest?

Al.

[GMB]

There are more errors to consider...

So for meter movements, you need to repeat in different orientations, checking zero each time.

You also need to check the reading approached from different directions, both slowly and fast.

Don't forget temperature!

And a wee tap or two to settle the movement. As a general rule if three (different) meters read about the same they are good enough. This is good enough for fly by wire aircraft that use three different computers, if two agree that's what the thing does.

[Bazz4CQJ]

Doesn't your method need to have a calibrated signal source Al?

Now that I no longer have access to calibrated instruments on a daily basis, I too tend to compare three (multimeters, analogue or digital) and expect to see results "adequate" for my purposes.

B

[Skywave]

Originally Posted by GMB

There are more errors to consider... . . etc.

Yes, there are indeed. So, if I do take a series of measurements as you suggest and find the mean value, would the equation which I wrote be valid, since that is the raison d'etre of my thread.

Al.

[Skywave]

Originally Posted by merlinmaxwell

And a wee tap or two to settle the movement. As a general rule if three (different) meters read about the same they are good enough.

And if all three read different - but with very close results - if I take the mean value, is my equation then valid to estimate mean the error?

Al.

[The Philpott]

Using (I-C)/C (expressed as a percentage) is certainly what i use, ie %age discrepancy of the reading, not %age expressed as a proportion of FSD.

If we're looking at a D'arsonval movement (which i guess we usually are) the loss in magnetic flux and the loss of spring tension associated with temperature increase tend to cancel each other out to an acceptable degree, leaving the change in resistance of the actual coil as the main source of temperature error.

The other noticeable source of error with such analogue movements is the non-linearity of the readings when low deflections are compared with high deflections. At higher deflections the meter can get more 'optimistic'.. thus accurate calibration depends somewhat on the preference of the owner/end user! Taking an Avo 8 as an example of this, you might find that on DC voltage the meter reads 4v correctly at 20Celsius, but when shown 8v @ 20C will give a slight over-read. In this example it can be found that this error amounts to up to one third of one percent of FSD. On a Universal Avominor with it's much smaller moving parts, this error in this example is found be up to one HALF of one percent of FSD (which incidentally i find quite impressive) It is interesting to note that the Precision Avometer is not immune from this non-linearity; it is still noticeable although acceptably small.

I understand the typical approach to calibration is to feed the meter with a source that accords to FSD, then all the lower deflections can take care of themselves.. I don't always do this, and if i have a source that approximates to 70% or 80% of FSD i am happy to use that as a bench-mark.

In summary i think your (I-C)/C is the most sensible way of expressing error.

Dave

[Skywave]

Originally Posted by Bazz4CQJ

Doesn't your method need to have a calibrated signal source, Al?

I covered that in my O.P. I quote:
. . my viewpoint is that with the few items of test equipment that I feel do have 'reasonably accurate' calibrations . . .
(Italic added for emphasis).

Originally Posted by Bazz4CQJ

Now that I no longer have access to calibrated instruments on a daily basis, I too tend to compare three (multimeters, analogue or digital) and expect to see results "adequate" for my purposes.

Multi-instrument results: my response to merlinmaxwell's post covers that, q.v.

But you raise a valid side-issue: to what degree is a measurement error acceptable? For myself, the answer lies in the context of what is being measured and how critical the measured quantity is.

However, methodology aside, any thoughts on my equation?

Al.

[Skywave]

Originally Posted by The Philpott

Using (I-C)/C (expressed as a percentage) is certainly what I use, i.e. %age discrepancy of the reading, not %age expressed as a proportion of FSD.
. . . .
In summary, I think your (I-C)/C is the most sensible way of expressing error.

Re: your first sentence - that is exactly the basis of my error calculation, i.e., not involving FSD.
And thank you for your opinion about that formula. It's somewhat comforting to know that at least one person agrees with me.

Al.

[Bazz4CQJ]

OK, may I suggest that (I-C) looks nice as ∆ (positive or negative), so ∆/C as a percentage seems right. However, you're only dealing the the FSD and FSD/2 and I think reproducibility comes in somewhere?

When I was getting Ia v Vg data to produce "standard" valves, I always started by winding Vg up over 5 values and then winding it back down again over the same 5 values and then put it in to Excel, the graphical presentation usefully highlighting anomalies. The inconsistencies in those runs could be quite surprising; sometimes the data was highly reproducible and sometimes it wasn't. Then, of course, you have the quandary of having to decide if you are going be selective about which data you might exclude .

B

[GMB]

would the equation which I wrote be valid

Well it depends on what you are trying to express, and what "valid" means here.

The problem is that there is always a constant error component. So on digital meters there is always the one digit error that cannot be escaped. With an analogue meter there is something equivalent - the thickness of the pointer adds a constant uncertainty to the reading and if there is no mirror behind it you get the added parallax which relates to the height above the scale. Slack bearings will mean that reading the same value produces different answers depending on how you get there.

These are offset errors so the % they represent varies with the reading. Worst case is if you find that the meter is not showing exactly zero with nothing applied, that would be an infinite error by your equation.

I suspect that what is typically quoted is the worst error as a percentage of FSD. A better description in my opinion would be to give separate values for the absolute accuracy, the linearity and the offset error.

[The Philpott]

I took valid to mean 'most useful'

Using an Avo as the example again, an unrepeatable unstable needle zero does indeed cause all V & I readings to lose credibility, but would allow the reversed logarithmic R scale to be trustworthy if a solid FSD with shorted leads could be achieved by twiddling. Where the R scale is not reversed (eg RCA Voltohmyst..?) this would not apply.

An equation to express all factors including inherent non-linearity of a PMMC movement might look like the scribblings on the professor's blackboard in 'The Day The Earth Stood Still' !

Dave

[David Simpson]

Al,
A similar topic ran for a while, a year or two ago. Some keen calibration folk mentioned owning NPL standard cells, resistors, etc. My suggestion was for such folk to take along these high grade items to BVWS Swapmeets, NVC, R & TV Museum meets & auctions, etc. So that other folk could get their beloved AVO 8's, other analogue MM's, DMM's, & so on, checked out, calibration-wise. A small fee could be donated to the Museum, or whatever. Those fortunate folk could then return to their home town locality, and then, in turn, check other vintage chum's metering. A winner all round.

Regards, David

[GMB]

It is not particularly costly to buy resistors and precision voltage references with way more guaranteed accuracy than an AVO can possibly claim.

[Skywave]

Originally Posted by Bazz4CQJ

OK, may I suggest that (I-C) looks nice as ∆ (positive or negative), so ∆/C as a percentage seems right? However, you're only dealing the the FSD and FSD/2 and I think reproducibility comes in somewhere?

The reason I chose FSD/2 was an attempt to recognise linearity as a concept in verifying calibration. To me, 'calibration accuracy' needs to be viewed in context: for one particular measurement, a small error may be inconsequential; for another, it might be substantially significant. It is customary for many analogue instrument manufacturers to state accuracies in the form ± x% of FSD, so 'good' linearity is thus assumed. Often, when checking calibration, I check FSD, FSD/2 and a reading close to zero deflection. Sometimes I've chosen even more measurement points than that.

Al.

[Skywave]

Skywave, post #1:

. . . the equation which I wrote be valid . . .

Originally Posted by GMB

Well it depends on what you are trying to express, and what "valid" means here.

Point taken: I should have been more explicit, but my OP was excessively long and somewhat tedious to read before that extract, (because I was hoping thereby to restrict responses to my specific question), so I made efforts to try to condense the essence of what I was asking. So, yes, I could have done better.

For "valid", I was thinking of 'validity' in the strict mathematical sense, but in practical applications, 'validity' has much wider implications - as you rightly point out. Instead of 'valid', perhaps I should have written "adequate for practical purposes, depending on the conditions of the measurement, what is being measured, and why" (phew!) - and perhaps even that is inadequate.

Al.

[pmmunro]

Originally Posted by GMB

It is not particularly costly to buy resistors and precision voltage references with way more guaranteed accuracy than an AVO can possibly claim.

I would agree for direct voltage sources. Alternating voltage references are more of a problem if only because waveform as well as voltage needs to be considered.

My procedure for checking analogue multimeters is to check the fsd accuracy on the most sensitive range direct current range, then at each cardinal point on the scale, again on the most sensitive range. This defines the basic accuracy of the movement. Each range can then be checked at fsd and will track the basic range over the rest of the scale. The procedure is the repeated on direct voltage and unless there is some voltage dependent resistance in the circuit, which has a low probability, each range will track the most sensitive one.

Alternating ranges are checked in the same way, but here the chances of non-linear components are higher so some intermediate checks on the higher ranges are advisable.

I would certainly agree that accurate resistors are readily available and above possibly 100 ohms direct comparison should be sufficient. Towards the lower end of the scale, resistance measurement is likely to need special care and techniques as the resistance of connections becomes significant.

Reading technique is important. An anti-parallax mirror is helpful and some high class instruments have several arcs to each scale with a diagonal line between each scale division allowing very precise reading at the point where pointer, diagonal and arc cross. The width of the pointer limits the highest possible accuracy, provided some other factor such as bearing quality/suspension characteristics is not dominant.

Some limitations to home checking/calibration arise at high values of current and voltage. How many of us can provide a dependable current much above 5A, perhaps as high as 10 or even 30A? High voltages too raise problems, if only considerations of safety, especially when working alone.

PMM

[The Philpott]

I sourced what i believe to be a reasonably accurate and clean sine wave ACV reference from a cheap inverter generator. Although it is a cheap and basic assembly i do trust it to supply a steady 230v on a light load through the alternator-rectifier-smoothing-inverter chain. My more dependable meters tend to agree -give or take a volt.

Dave