Error of % + digits?

Jun 18, 2020 125 Replies

Hi,

I'll try to explain that with a simplified model of a digital meter (please everybody correct me if it's oversimplified and wrong):

The typical digital meter consist of some kind of processing of the signal to be measured and an A/D-converter that converts it's analog input signal to a number that is displayed.

The input processing serves to transform the quantity to be measured into an analog signal that is properly adapted to cover the range of possible input signals of the A/D-converter.

Let's say we want to measure an AC current of 10A with a clamp meter like yours. Let the display of the meter have 3 1/3 digits, so the range of displayable numbers goes from 0000 to 1999 with an additional decimal point somewhere.

The A/D-converter will not be able to directly convert a 10A current, so we pickup the current to be measured with a transformer, the wire carrying your 10A current being the primary and a coil internal to the clamp assembly being the secondary winding.

An AC current flow through the wire will induce an AC voltage in the secondary winding. Since the A/D-converter may not directly accept AC voltages, further processing may be required, such as amplification or voltage division and e.g. True-RMS detection of the AC voltage. All this processing will end up in a voltage that is suitable for the A/D-converter - say, 1V DC for 10A of AC current.

All the (analog) signal processing described here will not be free of unwanted influences and processing errors. The transformer at the input could e.g. pick up unwanted magnetic fields, the amplifier could exhibit noise and nonlinearities, the TRMS detection could exhibit some errors.

All these error sources or influences may be described in the meter's specification as a percentage - e.g. the +/- 1.9% you mentioned.

Now, the A/D converter converts the analog input voltage into a number. One method to do this, when speed is not a critical factor, is (dual) slope integration.

Let's assume for a moment that the input voltage is static, i.e. the 1V DC mentioned before.

Basically, the conversion works by comparing the input voltage (to be measured) to a linearly rising voltage (ramp). Similar to a stopwatch, a counter starts when the reference voltage begins to rise and a comparator stops it when the ramp voltage is equal to the input voltage.

In our example with 1V input, the counter may stop at a count of 1000. With the knowledge that, by means of the input processing and the calibration of the meter, this corresponds to 10A AC current. The meter would probably display 10.00 (A).

But: At some time in the process, the counter will switch from 999 to 1000 in a very short (almost zero) time. That means, that the input voltage may just be a tiny little bit less and the counter is stopped at 999, not at 1000.

That means, that for any input signal, you always have +/-1 digit display uncertainty because you cannot know whether the counter maybe was just before switching to the next count.

With a specification of +/-3 digits, the A/D converter has a greater uncertainty when counting. For example, even at a constant input of 1V, the internal counter may be less precise and stop at 997, 998, 999, 1000, 1001, 1002 or 1003, even if the input signal doesn't change. You can think of this as a stopwatch that may be off some counts each time you make a measurement.

This type of error is not related to the input signal processing, so it is not very meaningful to express the error as a percentage of the measured value. It is usually expressed as a number of digits, because the error is mainly caused by the process of converting input signals to numbers.

Of course, I know that this very simple single slope integration is not used in meters, dual slope is the least you can do. Also, the A/D conversion may contribute to the percentage error spec. The (over)simplification is just a means to explain why there are two numbers in the specification.

Just my two cents,

Dieter

What if your caliper had a resolution of 1 mil +/- 3 counts on the last digit? That's the issue with multimeters that have completely bogus digits at the end. Those number are just noise and serve no purpose at all. They don't even compare to all bullets missing the target but landing in the same wrong spot.

agreed. The problem with the bullets and the target story is that when explained, we somehow perfectly know where the bullets are- be in on target or a small grouping somewhere else. Cheapo meters won't give CONSISTENT or REPEATABLE results, not matter how "precise" they pretended to be, or how accurate the spec sheet claims, especially considering the last digit(s) may be totaly wrong, and random. It's like having crappy or dirty test leads or a component. You'll get all the digits in the world, but they keep changing. You won't even be able to pick a reading.

Keep in mind that "calibrated" equipment doesn't even have to be precise or accurate. An example would be an adjustable power supply with digital readout. Say it's always reads high by 0.7 volts. It's not precise or accurate, but by knowing the offset it can used with success and may even have great regulation.

On the other hand say you have an alibaba special power supply that's "accurate" to +/- 0.35 volts, with terrible regulation that oscillates.

What power supply is better?

So the point is cheapo equipment can have lots of bogus digits and readings that flop up and down, while better equipment can be more consistently wrong, which can be compensated for. Precision and accuracy mean little by themselves if you need multiple readings.

If the goal was keep the needle on their marks it does't have to mean anything was precise. Maybe your guages had no faces, or read mA instead of degrees, and bent needles. As long as your +/- 3 degree thermocouples and controllers did not jump up and down + and then -3 degrees all the time, you were good.

It's like the zener diode or voltage standard that came up in this thread. Those have no precision. They may not even be accurate. They might be consistent though. Accuracy and precision by themselves can be useless where time or multiple readings are needed.

You seem intent on picking an argument by inserting a statement that agrees with the following sentences. BTW, my caliper is not digital, so the matter of +/- count is irrelevant.

One good example of what we had is this.

In a vat of material is a test hole. In that hole is a rod about 3/8 inch in diameter and a foot long. At the end there are two thermocouples and two RTDs. The thermocouples wires go about 100 feet to a PLC (similar to a computer) card that converts the milivolts to digital that is then displayed on a compute screen. The RTDs go about

10 feet to a converter that converts the change in resistance to a 4 to 20 miliamp signal. That goes to a card on the PLC and then to the computer display.

While the computer will display to 3 decimal places at 300 deg C from the lowest to the highest temperature shown on the display can be around

3 deg differnet and all 3 be within the limits of the equipmnet.

At a certain time a sample is sent to the lab and one of the computer displays is set as a standard and the object of the PLC is to keep the actual temperature , whatever it actually is, to that 'standard'. Not too accurate as to temperature, but very precice. The operators only needed to keep that one computer display as close to that 'mark' as they can if for some reason the PLC messes up and they have to adjust the control manual.

What's the control loop if the PLC dies? How do people control temperatures manually? Is there a foot pedal to stomp on to switch the heaters on and off?

There's a couple machines I fuss with that use platinum junction RTDs and we have alarm limits set. If the machine drifts into an alarm state, outside of a warmup period that's pretty much the end of the day and everything stops until it can be fixed. The loops on these machines are tuned to maintain and hold a set point of less than 1 degree F. The displays are all wrong, show fake levels of precision, and read in C, but are wrong by several degrees, even if you do the math. We gave up trying to calibrate the displays against what the real temperature with the offset features when the probes were last changed. It just isn't worth the time. Those machines are not accurate, they're not precise (as measured with their own instrumentation), but they will absolutely hold a stable temperature if you can determine the set points yourself.

electronic test equipment is digital these days, so my question is very valid.

How would you feel if your vernier or thimble readouts on your hand tools had number that randomly moved around? That's the goofiness of how these digital integrating meters work. It makes very little sense when directly translated into the physical word.

Take a 100 foot surveyor's tape measure. Those are simple to read. You have feet and inches, and they're all in order. Let's our 100 foot tape is accurate to 3inches over that 100 feet. Not great, but fine for us.

Now go digital, with the analog feel. Say the tape is now a long e-ink display and has no factory printed numers on it like a conventional tape. Every time you pull the tape out it redisplays tape measure printing and you get stuff like this:

... 12ft 1in 2in 4in 5in 3in 6in 7in 8in 9in 11in 10in 13ft ...

How would that feel?

It makes absolutely no sense unless you understand the silly types of errors that are display on devices where we expect direct read out of numbers.

crappy meters can lack "snug" readings.

The process has two PLCs running all the time. There are two or more computers hooked to the data stream for the PLCs One PLC is the so called hot backup. It is not controlling, but if the primary one quits, the secondary one will either switch over automatically or it can be manually switched.

One thermocouple is connected to the control loop. If that TC goes bad, there are other TCs that give the temperature readout and the operators switch the control screen for that temperature to manual and they have to keep an eye on it and manually enter on the computer keyboard what percentage of valve opening is needed to mantain the correct temperature.

OK, so if a PLC croaks, the operators can switch to the redundant one. If a probe of whatever you have between it and the current loop or whatever it was fails, it's 100% manual control? How do you share the reading from one problem? Not trying to pole holes in theory here, just actually curious.

One thing annoying about the probes I deal with is it seems no two are alike. Never been able to swap one for another, even with short leads, even with three lead compensation and get the same behavior on the same controller.

Ha. There has to be some goverment lab, somwhere with cal stickers on construction levels or a plumb bob.

Here is sort of how it works. One PLC quits. The second PLC takes over automatically or can be switched manually at any time.

A TC feeding the PLCs fails. An alarm is sounded as the PLC thinks the process has gone out of limits. The operator is at a computer (was running a graphics program on Win XP when I left) , He calls up the control screen and puts the control in manual and sets the signal to the valve to where it was before the device fails. There is a secondary temperature TC. The operator looks back in the history of the read outs and sees that the primary control TC was showing 300.2 deg C when the lab said the process was on target. At the same time the secondary TC was showing 301.6 deg C. So the operator now has the control in manual and adjusts the output of the contoler to try and keep the process at

301.6 deg C showing on the readiout now.

When the bad TC is replaced and the process is checked out by the lab, The new setting may come back as 301.1 deg C. So that will be the new target.

The vessels are large enough , around 10 feet tall and 5 feet in diameter so the temperature change takes a long time.

The process is making polyester material. We put in a powder that looks like flour and a liquid Glycol. It is heated to about 300 deg C. There are 5 vessels in the process and it is continious. The powder and liquid are put in the first vessel and at the bottom is a pipe that conveys it to the next one. The process is repeated and small ammouts of other chemicals are added at each stage. It is extruded after the last vessel to what looks like string. It takes about 15 hours for the material to make it from start to finish. We make about 3000 pounds to 10,000 pounds of material each hour depending on the size of the process line.

About 2 years ago the plant that had around 3000 people 20 years ago went out of business. Mostly because of other countries makeing the material much cheaper.

Bullshit, I'm one of the least OCD people there is. Just look at my grammar.

So should I assume the cheaper ones are lying? Or have they just made a rough estimate adding the two errors?

Interesting.

I met an engineer who worked at Eastman decades ago. He had good stories about the complexity of starting a new production line of chemicals or plastics whatever they were making at the time. The amusing part was none of the people that designed the new systems could never get the first batches to work at full scale. They'd have an old timer operator figure it out for them after they all gave up. This process could take days.

The final "say" on the machines I deal with are the colors of test strips that run through the entire process.

might be both. I dug out my first DMM, a Wavetek DM2, circa 1990s. It might have been from a raffle or something like that.

The DC voltage specs range from 0.8% +1 digit (not bad really) over to the AC ranges which are "1.2% RDG +10 Digits". If I had new leads, I'd trust it with outlet voltage, but would stay away from 208volts. The meter has 3.5 digits or max display of 1999. I'm figuring a real 100volt AC reading could be 99 to 101 plus another error of +/- 1 volt for the 10 digits tolerance on the display or count. so 100volts from your Japanese outlet reference might read 98 to 102 volts. So while in the ballpark, it's better than you can read off a Simpson 260 meter in the AC voltage range. I could be wrong on this too.

It's a pretty decent meter for poking at DC circuits for the tens of dollars is must have cost when new.

More likely they simply invested less effort in measuring their respective meters accuracy. And a generally safe assumption is that lower cost often equates to less accurate.

This is likely, but without being able to ask the maker, anything we surmise here is just a guess anyway.

It seems that maybe due to modern manufactoring the meters are more accurate than they were 20 years ago. I bought some DC voltmeters from China. They display 3 digits. They read from 0 to 99.9 volts. I coulg get 4 of them for less than $ 15 including the shipping. I hooked all 4 of them in parallel with a Fluke 87 . Three of them tracked right along with the Fluke with the last digit sometimes being one high or low from

0 to 24 volts. The fourth one was off by an average of 2 on the last digit. I found an adjustment screw on the back of the meter and tweaked it and re ran the test. It then fell in line with the other meters.

I had 3 or 4 of the Harbor Freight 'free' multimeters. The ones that usually sell for around $ 5. They seem to be reasonable accurate for the money. Plenty accurate for the home user to test things around the house. I do admit that the safety issue of putting them across the 120 or 240 volt power wires is somewhat doubtful. I sure would not use one where I worked to put across the 480 volt 3 phase system that is fused with 200 amps.

Have you run this test with AC? That seems to be where the wheels come off. I brought up this thread to a friend and he mentioned his quest to repair some sort of HP true RMS meter that uses a thermocouple and heater to properly measure complex waveforms. I can't even guess how slow such a meter might be.

I'm pretty timid with anything upstream from a plain outlet. I had an edison base fuse burst in my hand once. Never seen one come apart before. It was just a 120v lighting circuit, but right off the service panel. There's way more excitement near those things.

The heaters used in thermal printers manage a speed better than 10mS stuff done in a microchip (like LT1088) could be even faster.

Jasen.

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