In this laboratory you will get some data to work with.  First you need to be sure that you understand the instrument you use.  You will do the following for your instrument.

• Determine the smallest voltage increment that can be resolved by the instrument.
• Determine how big the A/D is in the instrument.  In other words, how many bits are in the output of the A/D?
• Be sure you know the range of the instrument.  If the instrument auto-ranges, be sure you know which range it used.

• Get a good voltage source - one that can be adjusted in small increments.
• Measure the voltage source with the instrument.
• There are a couple of strategies here, but one good one is to set the voltage and measure it repeatedly.
• In some cases you can do that by getting a measurement of the voltage over a period of time.
• The voltage won't stay precisely constant, and you can use the small changes in an almost constant source to help you determine the resolution of the instrument.
• If the source holds the output voltage absolutely constant, you can still work to change the output voltage by the tiniest amount possible and observe the values you measure.

The measurements will take on discrete values that differ by the smallest increment that can be distinguished by the instrument.  In other words, these different values differ by one or two counts.  (and never one-half count!)  You should observe that you only obtain certain discrete voltages and there are voltage values between your observations that are not measured.  In the picture above there are no measured values between the dotted lines.  Only three discrete values of voltage are observed above.

        In the example above, the middle dots come from a measurement with N counts, the higher ones from a measurement with N+1 counts, and the lower ones from N-1 counts.

        Now, let's assume that you have a set of measurements.  If you plotted those measurements, you would see something like this.  Your measurements will take on discrete values as shown in the sketch.

        What you should do is take the value for the highest dots (N+1), and subtract the value of the voltage for the middle dots (N).  That will give you a voltage increment that corresponds to the smallest difference between two voltage measurements.  You could also take the difference between the middle dots (N) and the lower values (N-1).  That difference should be the same as the first difference you measured.  Call that value DV. DV is shown on the diagram above.

        Once you have DV, then then if you know the range of the instrument, you can compute the number of bits fairly easily.

• Here's the first part of the computation.
• Estimated Number of Intervals = Range/DV
• Here's an Example.
• You measure with an A/D board that has a nominal range of -5v to +5v, for a total range of 10v.
• You measure a voltage that is supposed to be 2.0 volts.
• You get values of 2.01v, 2.00v and 1.99v, and figure DV = .01
• You estimate the number of intervals as 10/.01 = 1000.
• You calculate the number of bits as 10 since 2¹⁰ = 1024.  Ten (10) is the power of two (2) that most comes closes to the number of intervals you have observed.

• The measured values of 2.01v, 2.00v and 1.99v are surely not exact.  They are more likely the closest values that can be displayed.
• The number of steps is also probably not 1000.
• The instrument manufacturer made a choice.  Here were two possibilities for the choice made.
• Let the measured voltages run from -5.12v to +5.11v (1024 steps) and let the increments be exactly .01v.
• Let the measured voltages run from -5.00v to +5.00 (or4.99)v and with 1024 steps, the increments would be 10/1024, and the increments would be .00977v - close to .01, but not exact.

        Now, let's think a little more about this instrument.

• With voltage increments of .01v, you would not expect to find an instrument displaying a voltage like 2.039527v.
• That's just way too many decimal places.
• You would expect that 2.039527v would be read as and displayed as 2.04v, and you would probably be right.  The digital logic within the instrument would be constructed to do that.  (Although the "digital logic" might be a small computer program running inside the instrument.)
• If you have this data within a computer program, then the program saves the data in a file, you would expect it to save 2.04 - and that means it saves four characters - "2" + "." + "0" + "4".
• The program might also append (concatenate) a carriage return (CR) or a line feed (LF) or both.  That would signify that the data is the last data in a row when the data is imported into a spreadsheet.
• The program might also append a comma (,) or a tab character.  Doing that would indicate that there is more data in the row.
• In another lesson we dig just a little deeper into this topic!  Click here to go to that lesson.

A.  The DVM

       The first instrument to measure is a DVM.  (Click here for some background on DVMs.)  Note, you might have a DVM or you might have a DAU (Data Acquisition Unit).  The DAU is a DVM with the capability of measuring temperature.  Think of a DAU as a DVM +.

        Do the following.

• Connect an adjustable voltage source to your DVM.
• Observe the voltage reading.
• With a little bit of luck the voltage source/DVM combination will display 2 or 3 voltage values that are very close.  If so, record those values.
• If the DVM readings do not fluctuate, adjust the voltage source the minimum amount possible and record values.  The goal is to get several voltage readings that are separated by the minimum amount.
• If you have a program that will monitor the DVM readings and record them in a file, use that, but work to ensure that you have the kinds of readings you need.
• Follow the procedure above and calculate the number of bits in the A/D in the DVM.

        Another "instrument" you might encounter is a board that resides inside a computer.  There are numerous boards with A/Ds and D/As that are used to measure voltage with a computer and to produce output voltages with a computer (making the computer into a digital controller in a control system in many cases).  Follow the procedure above (for the DVM) after connecting an adjustable voltage source to the input terminals of the board.  Note that most of these kinds of boards come with programs that will let you monitor a voltage and record values in a file usable in a spreadsheet.  Use that method if appropriate.