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Introduction Electrical measurements often come down to either measuring current or measuring voltage. Even if you are measuring frequency, you will be measuring the frequency of a current signal or a voltage signal and you will need to know how to measure either voltage or current. In this short lesson, we will examine those two measurements - starting with measuring voltage. However, first we should note a few common characteristics of the meters you use for those measurements. Many times you will use a digital multimeter - a DMM - to measure either voltage or current. Actually, a DMM will also usually measure frequency (of a voltage signal) and resistance. You should note the following about typical DMMs. •

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Polarity is important. Usually the terminals of the DMM will be coded to indicate polarity. Often that polarity is indicated by a red terminal (positive) and a black terminal (negative). In other cases, the polarity could be indicated by printed notes on the terminals. Often one of the terminals on the DMM may be connected to the ground. That would normally be the black terminal, or it may be indicated with a ground symbol.

With that in mind, let's get on to measuring voltage. Measuring Voltage Voltage is one of the most common quantities measured. That's because many other variables - like temperature, for example - are measured by generating a voltage with a sensor. So, even if you want to measure temperature you might end up having to measure a voltage and convert that reading into the temperature reading you wanted. Voltage is measured with a voltmeter. However, digital multimeters (DMMs) which can function as voltmeters - often have considerably more capability and can measure current, resistance and frequency. And, there are other instruments like oscilloscopes - that measure voltage and should be thought of as voltmeters. No matter what the instrument is, if it measures voltage you have to treat the instrument as a voltmeter. When you measure voltage you have to remember that voltage is an across variable. When you measure voltage you have to connect the voltmeter to the two

points in a circuit where you want to measure voltage. Here is a circuit with a voltmeter connected to measure the voltage across element #4.

Note the following about this measurement. • •

Notice that the voltmeter measures the voltage across element #4, +V4. (And, the plus sign is important. Remember the polarity issue.) Notice the polarity definitions for V4, and notice how the red terminal is connected to the "+" end of element #4. If you reversed the leads, by connecting the red lead to the "-" terminal on element #4 and the black lead to the "+" end of element #4, you would be measuring -V4.

And, remember this as well. •

When you measure voltage, the voltmeter should not disturb the circuit where you are attempting to measure the voltage. In the circuit above, that disturbance is the current drawn by the voltmeter. You want that current to be as close to zero as it can possibly be. That means that you need to have the resistance of the voltmeter as large as possible. There's more discussion of that effect in the lesson on measuring voltage. Ideally, the resistance of a voltmeter would be infinite.

There are numerous different instruments, and we have a separate lesson just on measuring voltage that discusses some of those instrument, and you can get to that lesson by clicking here. Measuring Current Current is measured with an ammeter. While voltage is a more common measurement, it is often necessary to measure current. When measuring current, it is important to remember that current is a flow variable. Current flows through

electrical elements, and if you want to measure current you have to get it to flow through the ammeter. Here's the same circuit we used in the example above. Consider what we would have to do to measure the current flowing through element #4.

If we want to measure the current through element #4, we have to get that current to flow through the ammeter. Here's a way to insert an ammeter into the circuit to measure that current.

However, this doesn't give the whole picture. Remember that polarity is important. In the circuit the polarity for the voltage across element #4 is defined, but the current polarity is not defined. In the diagram below, we have defined the direction of that current, and given it an algebraic name, Im.

As with the voltmeter, you need to pay attention to the polarity, and you also want to remember this. •

When you measure current, the ammeter should not disturb the circuit where you are attempting to measure the current. In the circuit above, that disturbance is the voltage across the ammeter. You want that voltage to be as close to zero as it can possibly be. That means that you need to have the resistance of the voltmeter as small as possible. Ideally, the resistance of an ammeter would be zero.

Links to Related Lessons •

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Lessons o Introduction to Electrical Measurements o Measuring Voltage o Measuring Frequency o Digital Voltmeters o Oscilloscopes o Interfaces - A/D Converters Labs

Why Measure Voltage? •

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If you are an Electrical Engineering student: o Voltage is a fundamental quantity that is important in every phase of electrical engineering from power systems to voltages inside VLSI chips. If you are an Mechanical Engineering student: o You will want to measure things like temperature. If you do that, you will use some sort of temperature sensor, and the odds are high that it will produce a voltage that you have to measure. If you are a Chemical Engineering student: o You will want to measure things like pH. If you do that, you will use some sort of pHsensor, and the odds are high that it will produce a voltage that you have to measure. If you are a Civil Engineering student: o You will want to measure things like strain. If you do that, you will use a strain gage in an electrical circuit, and you will need to know how to measure voltage, and quite possibly you will need to know how to set up the circuit. If you are a Bioengineering student: o You may want to measure voltages produced by nerve cells.

Whatever your engineering persuasion, you will need to make measurements that will invariably require you to deal with a voltage from a sensor. You might not need to be the world's greatest expert on how to measure voltage, but you will need to be knowledgable even if you just want to talk to the person who designs the measurement system. (And, click here if you need to review basic ideas about voltage.) That leads us to the question of what you should know at the end of this lesson. Consider the following: •

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Given a need for a physical measurement: o Be able to select and use basic sensors to measure temperature, strain, etc. Given a voltage output from a sensor:

To be able to connect a voltmeter - or other voltage measurement instrument - to the circuit at proper points, o

Be able to use a voltmeter, oscilloscope or A/D card to measure the voltage

Eventually, you will also want to do the following - even though it is not explicitly covered in this lesson. •

Given a voltage measurement problem: o Be able to record voltage measurements in a computer file, and, o Be able to use that file in an analysis program, including Mathcad, Matlab or Excel.

The conclusion that you have to come to is that everyone who makes measurements - of almost any physical variable - is going to deal with voltages, voltage measurements and digital representations of voltages, whether they are a biologist, a mechanical engineer, an automobile mechanic or any number of other occupations. Voltage is ubiquitous, and you have to deal with it - whether you want to or not. You may not want to be an electrical enginer, but you will probably need to understand enough about basic electrical measurements to be able to use modern sensors, instruments and analysis programs in your work. Using a Voltmeter In this section we'll look at how you use a voltmeter. Here's a representation of a voltmeter.

For our introduction to the voltmeter, we need to be aware of three items on the voltmeter. •

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The display. This is where the result of the measurement is displayed. You meter might be either analog or digital. If it's analog you need to read a reading off a scale. If it's digital, it will usually have an LED or LCD display panel where you can see what the voltage measurement is. The positive input terminal, and it's almost always red.

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The negative input terminal, and it's almost always black.

Next, you need to be aware of what the voltmeter measures. Here it is in a nutshell. •

A voltmeter measures the voltage difference between the positive input terminal of the voltmeter and the negative input terminal.

That's it. That's what it measures. Nothing more, nothing less - just that voltage difference. That means you can measure voltage differences in a circuit by connecting the positive input terminal and the negative input terminal to locations in a circuit. We'll show a voltmeter connected to the circuit diagram - a mixed metaphor approach. Forgive us for that, but let's look at it.

This figure shows where you would place the leads if you wanted to measure the voltage across element #4. • •

Notice that the voltmeter measures the voltage across element #4, +V4. Notice the polarity definitions for V4, and notice how the red terminal is connected to the "+" end of element #4. If you reversed the leads, by connecting the red lead to the "-" terminal on element #4 and the black lead to the "+" end of element #4, you would be measuring -V4.

There are some important things to note about taking a voltage measurement. The most important point is this. •

Voltage is an across variable. o That means that when you measure voltage you measure a difference between two points in space.

There are other variables of this type. For example, if you use a pressure sensor, you measure the pressure difference between two points, much like you measure a voltage difference. o There are other kinds of variables. For example, there are numerous variables that are flow variables. Current and fluid flow variables are example of flow variables. They usually have units of something per second. (Current is couloumbs/sec, while water flow might be in gallons/sec. - for example.) When you measure a voltage the two terminals of the voltmeter (in the figure, the red terminal and the black terminal) are connected to the two points where the voltage appears that you want to measure. One terminal say it is the red terminal - will then be at the same voltage as one of the points, and the other terminal - the black terminal - will be at the same voltage as the other point. The meter then responds to the difference between these two voltages. o

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Let's look at an example. Here are three points. These points could be anything and may be located in a circuit, for example. Wherever they are, there is a voltage difference between any two of these points, and you could theoretically measure the voltage difference between any two of these points. There are actually three different choices for voltage differences. (Red/Green, Green/Blue, Blue/Red) Then, for each difference, there are two different ways you can connect the voltmeter - switching red and black leads.

Let's check to see if you understand that. Here are the same three points, but now they are points within a circuit. In this particular circuit, the battery will produce a current that flows through the two resistors in series.

This circuit has a schematic representation shown below.

And, here is the same circuit with the measurement points (see above) marked.

Now, if you want to measure the voltage across Rb, here is a connection that will do it.

And, the physical circuit would look like this one.

Now, the reason for taking this so slowly is that students often have trouble moving between circuit diagrams and the physical circuit and understanding how to translate between them. What looks clear on a circuit diagram is not always as clear in the physical situation. We'll get a little closer to physical reality in this exercise. Exercise 1 Here's a portion of a circuit board. You want to measure the voltage across R27. Click on both places where you should put the voltmeter leads.

When you measure a voltage difference - whatever the instrument you use you will always have two leads coming from the instrument that will have to be connected to the two points in your circuit across which the voltage appears. And, remember, the voltage might be any of the folowing. • •

The voltage might be across an element embedded in a circuit. The voltage might be the output of a transducer measuring some physical variable like temperature, pH, rotational velocity (a tachometer), etc.

Instruments for Measuring Voltage In the material above, we assumed that you would measure voltage with a voltmeter. Actually, there are often numerous options for the instruments you use to measure voltage. Here are three common options. • • •

A Voltmeter An Oscilloscope An A/D card in a computer

We will examine each of these options separately in the next section. Before we get there, however, note these common points for each of these three instruments. • •

Each measures voltage. To measure voltage, remember that voltage is an "across" variable. Each instrument will therefore have two leads to be connected to the circuit where you want to measure voltage, and those leads should be placed across the two points defining the voltage you want to measure.

Internal Resistance Voltmeters (including oscilloscopes, etc. as voltmeters) will have an effect on any circuit when they are used. Any time you take a measurement - no matter what the measurement is - you disturb the thing you are measuring. Attaching a voltmeter to a circuit will change the circuit - i.e. disturb the circuit - and modify the voltage you are trying to measure. You just have to ensure that the disturbance is negligible. That's what we want to look at here. Let's examine measuring the outut voltage of a voltage divider circuit. Here is the circuit.

Now, the voltmeter is really equivalent to a resistor, so we can - for purposes of analysis - replace the voltmeter by its equivalent resistance. Here is the circuit with the voltmeter equivalent resistance. (Rm is the resistance of the voltmeter.)

Now, you should be able to see that this isn't the same circuit that you thought you were measuring. The addition of the voltmeter resistance changes the circuit and the changed circuit will have a different output voltage than the original circuit. The question is whether the output voltage of the changed circuit is significantly different from the output voltage of the original circuit. To determine if the output voltage has changed, you need to consider that the voltmeter and the resistance, Rb, are now in parallel. That means that the output of the voltage divider is different. However, you can compute the output without the meter and with the meter. Vout = Vin Rb/( Ra + Rb) - without the meter and Vout = Vin Re/( Ra + Re) - with the meter, and Re = Rm Rb/( Rm + Rb) These two expressions are very similar, and the how the close the two voltages will be depends upon how close the equivalent resistance and the original resistance are. Note that the equivalent parallel resistance is: Re = Rm Rb/( Rm + Rb) Re = Rb [Rm/( Rm + Rb)] So, if the factor multiplying Rb is close to one, there won't be much difference between the original voltage and the voltage you have when you attach the voltmeter. In order to be sure that is true, we need to have the factor multiplying Rb as close to one as possible.

[Rm/( Rm + Rb)] = 1 or at least get as close to 1 as we can. That's going to happen when the meter resistance is much larger than Rb. The conclusion that you come to is that you want the resistance of a voltmeter - any voltmeter, including osciloscopes, etc. - to be as large as possible. We'll look at typical values for instruments that are sold as we examine individual instruments. Voltmeters Voltmeters are perhaps the commonest or most widely used instruments for measuring voltage. While there are still many analog voltmeters, most voltmeters today have digital displays, so that you get an LCD display with several digits of resolution. If an instrument has other capabilities (for example being able to measure current and/or resistance) then it is a multimeter. If it is a digital multimeter it is often referred to as a "DMM". A digital voltmeter can be referred to as a DVM. There are several things you will need to worry about when using a voltmeter or DMM. •

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Voltmeters can often measure either DC or AC voltages. o When measuring AC voltages, a voltmeter will give you values for the RMS value - not the peak value of the sine wave. And, if the signal isn't sinusoidal, you may have trouble getting the measured value(s) you want. In many instances, it is possible to connect the voltmeter to a computer. That allows you to import your data into a computer and then use analysis programs like Mathcad, Matlab, spreadsheets, etc. to extract information from your data. You may need to learn how to use those kinds of connections. Voltmeters have range settings. Some common range settings are 0-0.3v, 03v, 0-30v, etc. On lower ranges you will get more accuracy. On digital voltmeters, for example these ranges are really: o 0-3.0000 v o 0-30.000 v

As you go to higher ranges you will get as many significant digits in the measured value. o If you want more significant digits in a meter the cost will go up, and each additional digit is more expensive. Voltmeters are not ideal. The most common aspect of a voltmeter that you need to take into account is the resistance of the voltmeter. Typically a DMM will have a resistance of 10 MΩ. When you connect the voltmeter to a circuit it would be like connecting a 10 MΩ resistance to the circuit. In many circuits that won't be a problem because that will be a negligible disturbance to the circuit. Voltmeters measure voltages that are constant or at least do not change rapidly. A typical digital voltmeter will measure voltage and display the results, then hold the results long enough for you to see the number. o

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The last point in the bullets above has a hidden question. That question is "What if you have a voltage that changes rapidly and you want to see details as it changes?". If you have that situation, a voltmeter may not be your instrument of choice. You may need an oscilloscope or an A/D card in a computer. That's what we will examine next. Oscilloscopes Oscilloscopes can measure time-varying voltages and give you a graph of voltage vs. time. When you think about how to connect them to a circuit, they are exactly like voltmeters. You connect an oscilloscope across the two points where you want to measure the voltage. However, what you get from an oscilloscope is not what you get from a voltmeter. When you measure a signal with an oscilioscope, you get a scaled picture of the voltage time-function. That picture might look like this one if you were measuring a sinusoidal voltage.

Currently oscilloscopes will also perform some computations using data taken from the voltage waveform that is presented on the oscilloscope face. These usually include things like the following. • • • •

The The The The

RMS value of the waveform. average value of the waveform. peak-to-peak value of the waveform. frequency of the waveform.

Also, once those signal parameters are computed and are in numerical form within the oscilloscope, they can be transmitted - using a variety of ways - to a computer where you can use a program to compute other properties you might be interested in. For example, you might capture a transient temperature and measure the time it takes your temperature control system to reach a steady state by computing a time constant. You could use any number of analysis programs for that including Mathcad, Matlab and spreadsheets. If you want a more complete description of oscilloscopes, you can go to the lesson on oscilloscopes by clicking here. (That lesson has a number of interesting simulations you can try, so that you can learn a little before you go into lab. It also has links to laboratories that help you learn to use oscilloscopes.) A/D Boards You can purchase numerous A/D (short for Analog-to-Digital Converter) (Click here to go to the lesson on A/D converters.) converters that come on boards that plug into computers. And, there are numerous ways to interface with such boards including at least the following. • • •

Pre-written programs you can buy Programming in C or C++ Programs that allow you to build good-looking GUIs (That's Graphical User Interfaces) including: o Programming in Visual C++ o Programming in LabView o Programming in Matlab o Programming in Visual Basic o and others!

The ability to use these boards to get data into a computer allows you to use analysis programs like Mathcad, Matlab and spreadsheets to analyze your data, plot it, and to extract other information from your data. In many cases you may have soft instruments on the computer. Soft instruments are computer programs that simulate voltmeters and oscilloscopes. In other words, they look and feel like instruments (except that they are interactive images on a computer screen). They are often designed to look and act like real instruments as much as possible. Links to Related Lessons •

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Lessons o Introduction to Electrical Measurements o Measuring Voltage o Measuring Frequency o Digital Voltmeters o Oscilloscopes o Interfaces - A/D Converters Labs

Introduction When you measure frequency, you are often measuring the frequency of a voltage signal, so the first thing you need to remember is that you are making a voltage measurement, so that everything that is important to a voltage measurement will be important when you measure a frequency. In particular, you need to remember the following. •

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When you measure a voltage the two terminals of the voltmeter (in the figure, the red terminal and the black terminal) are connected to the two points where the voltage appears that you want to measure. One terminal say it is the red terminal - will then be at the same voltage as one of the points, and the other terminal - the black terminal - will be at the same voltage as the other point. The meter then responds to the difference between these two voltages. When you measure voltage, the voltmeter should not disturb the circuit where you are attempting to measure the voltage. In the circuit above, that disturbance is the current drawn by the voltmeter. You want that current to be as close to zero as it can possibly be. That means that you need to have the resistance of the voltmeter as large as possible. There's more discussion of that effect in the lesson on measuring voltage. Ideally, the resistance of a voltmeter would be infinite.

In most cases, when you measure frequency you take the above into consideration, and then you adjust the meter to take a frequency measurement. That's usually just a matter of a adjusting a single control on the instrument. If you want to measure frequency, there are some things to understand about that kind of measurement. Measuring Frequency When you measure the frequency of a voltage signal, the typical instrument will do the following. •

First, the instrument is connected like a voltmeter, and set to measure frequency.

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When the measurement is taken, the instrument counts the signal. It might count zero crossings of the signal, or it might just assume that the signal is a sequence of pulses, and count the pulses. In either case, the instrument counts for a predetermined length of time, T (which you might be able to control). Then, the frequency is computed by dividing the count by the time period, T. o The computation of frequency cannot have a resolution better than one count. For example, if the instrument counts for one second, a count of ten would compute as 10 Hz, and a count of 11 would compute as 11 Hz. You couldn't get a good measurement of 10.5 Hz, and would always be off by 0.5 Hz. What you got would depend upon the timing of the count - when it started. o The resolution is probably not a problem if you are interested in a 20KHz signal and the instrument counts for a second, but you have to be cognizant of what is taking place. That's the one thing you need to be cognizant of when you take a frequency

measurement. Remember that and the instrument won't fool you.

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. •

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. o That would make the range 0-3.072v. (That's .003 x 1024.) o 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

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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. • • •

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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. o That would make the range 0-3.072v - just as it was in the case of the 10 bit converter, o 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. Click here for a lab exercise that gets you thinking about the topic. Problems o o o

Interface Problem ConvDVMP01 - Properties of a DVM Interface Problem ConvDVMP02 - Properties of a DVM Interface Problem ConvDVMP03 - Properties of a DVM

Lab Exercises

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Interface Laboratory ConvAD1 - Getting the Number of Bits in an Instrument's A/D