We're not going to give you any more simulators with more bits.  Actually, we've almost reached the resolution limit for the screen.  The simulators with the "nudge buttons" just nudge the controls by a single pixel, and that is too much for a twelve bit converter, for example.

E3  A popular A/D board gives a count and requires you to perform the computation shown in the line of C code shown below.  The variable binary is the count value that is returned.

The A/D converts voltages from -10v to +10v.  We can conclude the following.

• The converter has 12 bits.  You get that conclusion by noting that the count can vary from 0 to 4095.  When the count is 0, MeasuredVolts = 0.

        Let's sum up a few points.

• More is better when it comes to bits in an A/D.  The indicated voltage will be closer to the actual value of the voltage being measured when there are more bits.

• More is pricier when it comes to bits in an A/D.  It takes more parts, and they have to be made more accurately if there are more bits.

How Does An A/D Work?

        While we have discussed A/D converters above, we haven't yet given you any insight into how you could build an A/D.  Here we will discuss a simple way to build an A/D.  This might not be the fastest A/D possible, but it will start to give you some insight into what happens inside an A/D.

        The circuit is shown in the simulator below.

Sim 5  This simulator is a four bit A/D, and it consists of the following components.

• A pulse generator that produces a sequence of 0's and 1's.

• A counter which counts the pulses and produces an increasing count.

• The counter has a "Stop" input.  When that input goes high, the counter ceases to count.

• A D/A which produces an analog signal proportional to the count output from the counter.

• An adjustable input voltage source.

• A comparator which produces a "1" when the D/A output is larger than the input voltage.

• The output of the comparator is used to stop the counter.

Here is how the A/D Simulator works.

• First, set a DC voltage from the adjustable source.

• Second, click the "Convert" button.

• The counter begins counting, and the count is displayed on the LEDs and the numerical value of the count is displayed.

• The digital count signals (four bits of signals in this case) form the input to a D/A converter which produces an output voltage proportional to the count.

• The output voltage from the D/A is compared to the input voltage.

• When the output voltage from the D/A becomes larger than the input voltage the comparator develops a "Stop" signal that is used to stop the counter.

• The count that remains in the counter is a digital representation of the input voltage.

Try the simulator, using different voltages within the allowable range, i.e. 0-5v.

       The simulator lets you see the inner workings of one type of A/D converter.  Note the following about any A/D converter.

• The conversion takes time.  In the simulator, there is a variable amount of time until the counter reaches the correct count.  We have slowed down the simulator so you can see what happens, but even in the best A/Ds there is some time that must elapse between the start of a conversion and the end of a conversion.  That time limits how many conversions can be done per second.  People have worked on that problem and there are other kinds of converters that convert more quickly.

• The conversion is not exact, and the accuracy depends upon the number of bits in the counter.

• The result of the conversion is an integer, and that integer still must be translated into an equivalent voltage (although the conversion isn't hard to do).

Practical A/Ds

        Now, consider what happens in a typical application of an A/D.  We'll look at a voltmeter.  In a voltmeter, this is what happens.

• A voltage is applied to the voltmeter, and an A/D converts the voltage to a count.

• The count is converted to a floating point number.

• The floating point number is displayed on an LCD or LED display.

If the voltmeter is connected to a computer (say through an IEEE-488 bus) the following also takes place.

• The floating point data is converted to a character representation to transmit over an IEEE-488 or internet connection.

        You can see that there are a few conversions that have to take place in this process.  There are a number of other considerations here as well.

• The number of bits in the A/D converter will affect the accuracy of the voltmeter.  There is a lot of legend and lore in that area.

• You need to be aware of how to make conversions.  Actually, you need to become knowledgeable about the different representations as well as how to program those conversions in various programming environments like C, C++, Visual Basic and LabView.

         A/D converters are found in many places - including places where you might not think that you would find them.  Here are a few.

• Voltmeters are digital today.  To display a digital result for a voltage measurement the voltage is first converted to digital form in an A/D, and then it is changed to a decimal format to be displayed.

• A/Ds are used in digital thermometers, so if you've spent some time in the hospital, you've used an A/D.

And, you get the idea.

        However, there is an important situation where you need to dig deeper into how A/Ds operate, and how they interface with the software and hardware that is often used in measurement and control situations.  Let's think about a few typical situations.

• Assume that you are recording temperature at four points in a heat-treating oven.  You need to do the following.

• You need to get the data into a computer and you need to compute and record the average temperature (the four temperature data points).

• You have three tanks used for chemical processing.  You need to control the level of the liquid in the three tanks.  Each tank has a small computer with an A/D board that measures and controls the liquid level in each tank and also measures the temperature.  Each computer has a network card that connects it to an Ethernet LAN.  There is a central computer on the LAN and you need to send information from each of the control computers to the central computer.

• You need to take the data at each computer and you need to transmit it over the network to the central computer so that it can be recorded there and be available for any computations that might be necessary.

        In both of these situations you need to consider how to manipulate the data that you measure and want to store.  Here are some of the considerations.

• If you take data with an instrument connected to a computer (like a data acquisition unit or a voltmeter) the instrument may be connected to the computer with an IEEE-488 (GPIB) connection.   IEEE-488 connections have some considerations.

• Most IEEE-488 instruments convert data into strings of characters and those strings are transmitted to the computer.

• If you send data over a network, you must send strings of characters.

        The conclusion that you need to reach is that you need to be aware of how data has to be converted in these kinds of situations.  Let's look at the sequence of operations you might face.

• The A/D converter gets some raw data or information and it is in the form of an integer count.  Often it is simply a binary number represented with some fixed number of bits.

• The count could be a number like 10001000 (or 129 in decimal numbers).

• If the A/D converter has eight (8) bits or less, the data will take a single byte.

• If the A/D converter has more than eight bits (which is typical) the data will take more than one byte.  Usually, for most converters, the data will take two bytes, since most converters are 10, 12 or more bits.

• The count is converted to a number that represents the voltage (or possibly some other physical variable).  That takes some computer code (And there will probably be some sort of computing chip in the instrument.) and the process results in a number that is probably a floating point number.

• The floating point number might be something like 3.1416v.

• If you transmit that floating point number you need to generate a string of characters.

• The string of characters might be something like a "3", a period ("."), a "1", a "4", etc.

• In many cases you may need to add one or more characters to signal the end of a string.  That could be a carriage return and a line feed, for example.

Representing Instrument Data

        Taking data with an instrument immediately leads you to consider several things about data.  Here is a sample.

• If you take a lot of data, you need to know how the data is represented.

• If you take a lot of data, you need to know how the data is transmitted from the instrument to a computer.

• If you take a lot of data, you need to know how the data you get will be stored if you store it in a computer file.

Digital Voltmeters

       Digital Voltmeters are a special case of A/Ds.  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.

You need to learn a little terminology and the reasons for the terminology.  Let's take a look at a sample voltmeter.

E4   Consider a voltmeter built around a 10 bit A/D converter.  We will assume the following.

• The range of the voltmeter is from 0-3v, and it does DC voltage measurements.  It does not measure negative voltages.

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 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.

        At this point, you should have a good idea about how the number of bits in an A/D converter determines the accuracy of the converter - i.e. the resolution of the converter.

        You also need to learn how to determine the resolution of an instrument in the laboratory, and relate the resolution of lab instruments to what you know about the number of bits in a converter.