Measuring Voltage
Why Measure Voltage?
Using A Voltmeter - Intro
Voltmeters
Oscilloscopes
You are at:  Basic Concepts - Measurement - Voltage
Why Measure Voltage?
• If you are an Electrical Engineering student:
• 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:
• 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:
• 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:
• 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:
• 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:

• Given a need for a physical measurement:
• 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,
• 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:
• Be able to record voltage measurements in a computer file, and,
• 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.

• 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.
• 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.
• 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.
• 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.
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.

• Voltmeters can often measure either DC or AC voltages.
• 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, 0-3v, 0-30v, etc.  On lower ranges you will get more accuracy.  On digital voltmeters, for example these ranges are really:
• 0-3.0000 v
• 0-30.000 v
• As you go to higher ranges you will get as many significant digits in the measured value.
• 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 MW.  When you connect the voltmeter to a circuit it would be like connecting a 10 MW 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.
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.

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:
• Programming in Visual C++
• Programming in LabView
• Programming in Matlab
• Programming in Visual Basic
• 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.