Digital Multimeter Accuracy Explained

Introduction

The digital multimeter is the most widely used test instrument in the electronics industry. It is the standard tool for electronics Technicians and it’s usually the first test/diagnosis tool that a newcomer to electronics will purchase.

Despite this, multimeter capabilities are often misunderstood or ignored. I have worked in the electronics trade for 14 years and it has been my experience that surprisingly few people actually understand (or care about) their multimeter specifications. In particular, I have discovered that a large number of Technicians and even Engineers are blissfully ignorant of their instrument’s capabilities and the implications for the measurements they make.

Digital Multimeter Specifications Explained

Modern digital multimeter accuracy specifications are actually quite easy to understand once you become familiar with all the jargon. It is important that you fully understand what is meant by counts, digits and the effects they have on instrument resolution and accuracy. In terms of resolution and accuracy, there is an important distinction to be made here as well.

Resolution, Counts and Digits

Resolution

When we talk about resolution we’re talking about the smallest possible change that the instrument can detect. In practice this means we’re looking at the least significant digit on the display. The resolution at any given time is the amount that a single count of the least significant digit is worth. So, for example, if the display is showing us ‘4.0005’ volts, then one count of the least significant digit is worth 100µV (0.0001V). And this, is its current resolution.

The resolution will change depending on what range you select, and if you are interested in accuracy then you should use the lowest possible range for the measurement being taken.

Counts

My Fluke 28II multimeter is a twenty-thousand count, 4½ digit instrument. The counts and digits refer to my instrument’s resolution. But what does it mean?

Well, the counts and digits are effectively two ways of saying the same thing, but both terminologies are in common use so it’s good to have a handle on both. First, let's talk about "Counts":

To start with, it should be noted that the practical count figure is almost always one count less than the naming convention we use to refer to it. For example, in my case (for a Fluke 28II), the practical resolution of my instrument is 19,999 counts. That is what the instrument is actually capable of. However, when we refer to the counts by name we call this “twenty-thousand count”, and this is purely because a round number is easier to say. What we mean in practice is one less than that. The instrument specifications will usually quote you the practical counts as an actual figure, so with a well written specification there should be no ambiguity:

The implications in terms of multimeter resolution are that the Fluke 28II is capable of displaying a maximum of 19999 on its screen. A point to note here is that the most significant digit can ONLY be a 0 or a 1. It can of course move a decimal point to indicate different orders of magnitude.

So if we’re measuring <2V, the instrument can display up to 1.9999V, with a resolution of 100uV.

What happens when we try to measure voltages higher than this? Well, the instrument has to abandon the most significant digit because it can’t display a ’2′. Therefore in order to display 2V it has to shift the displayed measurement to the right, and the current least significant digit gets bumped off the end of the display in the process (i.e. we lose it).

The displayed voltage would be 2.000V, and the least significant digit is now only worth 1mV.

The Fluke 28II will then maintain this 1mV resolution all the way up to 19.999V after which it’ll be forced to drop a least significant digit again and the resolution will become 10mV per count.

You can see, then, that once you know your instrument’s maximum number of counts you can use this information to determine what the maximum resolution will be for any measured voltage.

The resolution will decrease in discrete steps (these are the multimeter ranges) as the measured voltage increases. The point that the steps occur and their effect on the resolution are determined by the maximum number of counts.

Digits

So how does all this relate in terms of digits? Very simple. The multimeter is a 4½ digit instrument because it is capable of displaying four full digits (0-9) plus one half digit. The most significant digit is called a half digit in this case because it is only capable of displaying 0 or 1.

Some instruments are capable of displaying higher numbers in their most significant digit. Commonly you will see a ¾ digit quoted, and this usually refers to a digit that can display up to and including a numeric value of 3. So, for example, a 4¾ digit multimeter could display up to 39999 on its display. This would be called a “forty-thousand-count” instrument, and it is an improvement over the 19999 count display because it can go further into its range before it has to compromise its resolution by dropping a least significant digit.

There is a caveat here though – although a ¾ digit typically refers to a digit capable of displaying values between 0 and 3, this is not a safe assumption and in fact it can mean any digit up to 6. This means that there is some ambiguity surrounding the use of fractional digits to define resolution.

Counts And Digits Are Equivalent And Interchangeable

Counts and digits effectively mean the same thing. A twenty-thousand-count instrument is capable of displaying practical values of up to 19999 which is four full digits plus one half digit = 4½ digit.

Due to the uncertainty of meaning surrounding fractional (in particular ¾) digits, it is my opinion that the use of counts to define resolution is prefferable because it accurately defines the instrument’s capabilies and leaves no room for ambiguity.

The Display is not the limiting factor!

Before I leave my explanation of multimeter counts, digits and resolution, I want to clear up a common misconception. Some might reasonably question why the instrument manufacturer would choose to hamper themselves with a most significant digit that can only display a 0 or a 1. Would it not be better to have a full digit there as well, thereby avoiding the complications and maintaining better resolution for more of the range?

Well, the answer is that the display is not the limiting factor here. The display itself is almost certainly quite capable of indicating numerals from 0-9. The limiting factor is the measurement circuitry in the instrument itself. It obviously has a finite resolution, and it is this limiting factor that causes the instrument manufacturer to be tied to a smaller MSD.

Digital Multimeter Accuracy

The accuracy of a measurement refers to how closely it reflects the true value of the property being measured. Whenever you measure something in real life, the measurement you take is always an approximation of the actual property itself, and therefore there’ll be some uncertainty involved.

Today’s digital multimeters are very accurate instruments – the uncertainty in their measurements is extremely low – but even so, there will be some small error/uncertainty in any measurement that is taken.

What will the error be? Well, it’s impossible to quantify the error exactly. Otherwise, if we could determine the exact magnitude of the measurement error, then we’d just correct for it in software and then we’d have no uncertainty at all!

In practice all we can really do is provide a figure of uncertainty about the measurement which gives us a range for which the measurement can potentially be in error. The multimeter specifications give us these limits, and they’re called the accuracy specifications.

Let’s now look at some practical accuracy specifications and determine what they mean. Staying with the Fluke 28II, let’s have a look at its accuracy specifications for the VDC range:

As you can see, the Fluke 28II’s VDC voltage range is quoted as being accurate to “±(0.05% of the reading +1)″.

This means that the instrument's DC voltage range is accurate to somewhere within 0.05% of the true value +1 count. The ‘+1′ refers to an additional uncertainty in terms of ‘numbers of counts/digits’ - in other words, counts of the least significant digit. In this case we’re only talking about one count of uncertainty but some instruments suffer more than that. Notice that the +1 count is contained within the ± bracket so the actual uncertainty in terms of counts is plus or minus 1 count. The easiest way to understand what this means in terms of measurement uncertainty is to take an example:

Example: Measurement uncertainty for a known 1.8000V source with the Fluke 28II.

Let’s imagine we decide to measure a voltage reference whose true voltage is 1.8000V. The most appropriate range for measuring this value on the Fluke 28II is the 6V range, which has a resolution of 0.001V (1mV). The uncertainty in this measurement for the Fluke 28II is:

The two parts in this equation are accounting for the basic multimeter accuracy, and the uncertainty owing to 1 count. Evaluating each term:

and...

So the total uncertainty is:

So a source whose true voltage is 1.8000V could be measured as anywhere between 1.7981V and 1.8019V on the Fluke 28II Multimeter.

These accuracy specifications should help you understand why it is important to always use the most appropriate range if you care about accuracy of your measurement.

It's because of that extra "count" uncertainty on the end.

If you use a higher range to measure the value, then the resolution will be less, and hence the uncertainty in terms of counts (the least significant digit) carries much more weight!

This is particularly troublesome for less accurate instruments. For example, the Meterman 37XR has an accuracy of:

So not only is its basic accuracy worse, but it suffers an additional uncertainty of 5 counts rather than 1.

This uncertainty adds up very quickly when you use an inappropriate range and the counts carry more weight.

That's all folks!

Now we have explained Digital Multimeter Counts, Digits, Resolution and Accuracy.

Good luck, and happy measurements!