| Digital Voltmeters |
Digital Voltmeters (DVMs)
are a special case of
A/Ds. DVMs are voltmeters - i.e. they measure voltage - and are general
purpose instruments commonly used to measure voltages in labs and in the field.
DVMs display the measured voltage using LCDs or LEDs to display the result in a
floating point format. They are an instrument of choice for voltage
measurements in all kinds of situations.
Obviously, if voltage measurements are
taken and the results are displayed digitally with LED or LCD displays, the
instrument has to contain an A/D converter. Digital voltmeters have some
characteristics that you might need to understand.
Digital voltmeters usually
have scales that are 0-0.3v, 0-3v, 0-30v, 0-300v, etc.
It is not clear why those ranges were chosen but they
are commonplace. Now, consider some of the implications of these facts.
Example
E1
Consider a voltmeter built around a 10 bit A/D converter. We will assume the
following.
Then, with 10 bits we can draw these
inferences.
Ten bits will produce 210
intervals. That's 1024 intervals. If there are 1024 intervals
over a range of 3v, each interval will be 3/1024 = .00293v. It is easier to compute the
displayed voltage if the interval is adjusted to .003v.
That would make the range
0-3.072v. (That's .003 x 1024.) If you are measuring a
voltage that varies around 3v, that would allow you to keep the range
the same, but still change the range (if the instrument also has a 0-30v
range, for instance) when the voltage got large enough. Manufacturers
like to build in a little "hysteresis" to prevent constant range changes
in situations like that and it might be especially hard on auto-ranging
meters.
If you wanted to measure
negative voltages and have the range be from -3v to +3v, you would have
intervals of .006v, and the meter would measure from -3.072v to +3.072v. If you wanted to measure
voltages on a 0-30v scale, you would probably use a voltage divider or some
other way to reduce the voltage by a factor of (exactly) 10 (i.e., multiply
it by exactly 0.1) and then use the same converter as on the 0-3v scale.
If we could use a 12 bit A/D, then
some conclusions would change.
Twelve bits will produce 212
intervals. That's 4096 intervals. If there are 4096 intervals
over a range of 3v, each interval will be 3/4096 = .000732v. It is easier to compute the
displayed voltage if the interval is adjusted to .0075v.
That would make the range
0-3.072v - just as it was in the case of the 10 bit converter, That produces the same
advantages as you had with the 10 bit converter.
If you wanted to measure
negative voltages and have the range be from -3v to +3v, you would have
intervals of .0015v, and the meter would measure from -3.072v to +3.072v.
A Note on Voltmeter Specifications
In the example you saw a few typical
voltmeter possibilities. For some reason voltmeters have had scales like 0-3v,
0-30v, etc. for a long time. You might have expected 0-1v and 0-10v, etc. to be
more common. However, that's not the way it is, and it probably won't change
any time soon. That situation has led to some interesting ways to specify
voltmeters.
If you had a voltmeter that had a 0-1v
range, and it had ten bits, it would probably be designed to have a range from
0-1.024v, and it would measure voltages in steps of .001v. Then, the
measurement results would be things like 0.314v or 0.582v, things like that.
Displayed values would all have exactly three decimal places, and the instrument
would be referred to as a 3 digit meter. If you
use the same converter on a 0-10v scale (and put the voltage through a 0.1x
voltage divider!), then the results would be things like 3.14v or 5.82v. You
would get exactly the same number of significant figures, and you would still
refer to the meter as a 3 digit meter.
Let's think about this situation.
If you have a voltmeter with
a 0-1v scale that can read increments of .001v the meter is a 3 digit meter. If you have a voltmeter with
a 0-1v scale that can read increments of .0001v the meter is a 4 digit
meter. If you have a voltmeter with
a 0-10v scale that can read increments of .001v the meter is a 4 digit
meter. If you have a voltmeter with
a 0-100v scale that can read increments of .001v the meter is a 5 digit
meter.
Now, what if you have a meter that has a 0-3v scale
that can read increments of .001v? How many digits is that meter?
The Number Of Digits In A DVM
You need to be able to answer the question in the last section. When you buy a meter it may tell you the number of digits and you need to know what that means, especially when the scales are 0-3v, etc. Here is the story.
A meter that reads in
increments of .001v and has a 0-1v range is a 3 digit meter. A meter that reads in
increments of .001v and has a 0-10v range is a 4 digit meter. A meter that reads in
increments of .001v and has a 0-100v range is a 5 digit meter.
Notice the logarithmic nature of the
relationship, summarized in this table.
Range (v)
|
Digits
(for .001v)
|
0-1
|
3
|
0-10
|
4
|
0-100
|
5
|
If the high limit of the scale is
3, that's almost halfway between 1 and 10 on a logarithmic scale. (The mid
point is really at the square root of ten.) A meter that has a range of 0-3v is
said to be a 3 1/2 digit meter when it has intervals of .001v. That's halfway
between 3 and 4 digits.
There is another way to
look at the question of digits. If you have a meter that has a 0-10v scale that
reads in increments of .01v that's a 3 bit meter. That meter has 1000 steps,
and 1000=103. Let's repeat the table from above, but include
the log10 of the number of steps.
Range
|
Digits
(for .001v)
|
#Steps
|
log10(#Steps)
|
0-1v
|
3
|
1000
|
3
|
0-10v
|
4
|
10,000
|
4
|
0-30v
|
4.5?
|
30,000
|
4.47
|
0-100v
|
5
|
100,000
|
5
|
We included an extra row
for a 0-30v meter. We also included the number of steps and a suggestion for
the number of digits we can claim for the meter. It looks reasonable to call a
0-30v meter with 30,000 steps a 4.5 digit meter, and that's the way they are
sold.
That's it for digits in a
voltmeter. That's the way that they are specified, and that's what you pay for
when you buy a DVM. The number of digits is determined by the number of bits in
the A/D, and we need to look at that idea just a little bit more.
|
