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Unit 7. AC Waveforms and the Oscilloscope


Up to now, we've been working with dc (direct-current) circuits. In this unit we'll study the difference between dc and ac (alternating current). We'll also begin to use the oscilloscope, an important instrument for making measurements on ac circuits. Another piece of equipment that we'll start using is the function generator, which generates ac voltages and currents.

The textbook has many chapters on ac circuits, but they're too advanced for this course. (You'll study those chapters in a later course, EET 155.) Although I'm not asking you to do any reading in the book, I do give you page references below, so that you can look up these topics in the book if you wish. Most of the material in this Unit is discussed in Chapter 11 of the textbook.

Work through the e-Lesson and self-test questions below.

After completing the e-Lesson, take Quiz #7, perform Lab #7, and do Homework #7.


Unit 6 Review
  • This unit will build on material that you studied in Unit 6. So let's begin by taking this self-test to review what you learned in that unit.
  • Self-test

DC and AC
  • Direct current (dc) is current that flows in one direction only.
  • A dc voltage source is a voltage source that produces direct current.
    • Examples: Batteries and dc power supplies (such as the power supply built into the trainer that you use in lab) are dc voltage sources.
  • Alternating current (ac) is current whose direction periodically reverses.
  • An ac voltage source is a voltage source that produces alternating current.
    • Examples: Electrical outlets in the walls of your home provide alternating current. The trainer that you use in lab also contains an ac voltage source called a function generator, which you'll start using this week.
  • Wisconsin Online learning object
Waveform
  • In most dc circuits, current and voltage remain constant as time passes. But in ac circuits the voltage and current change as time passes.
  • It's possible to write down mathematical expressions that describe how the values change in time, but a simpler and more common way is to draw diagrams showing how the voltage or current changes in time.
  • Such a plot, or graph, of a current or voltage versus time is called a waveform.
  • Examples: Below are diagrams of three of the most common waveforms we'll deal with: a triangle wave, a square wave, and a sine wave. Notice that each of these diagrams plots voltage (measured in volts or millivolts) on the vertical axis, and time (measured in microseconds or milliseconds) on the horizontal axis.
    Triangle wave

    Square wave

    Sine wave
Periodic Waveform
  • A periodic waveform is a waveform whose values are repeated at regular intervals.
  • All three of the waveforms shown above are periodic waveforms.

Cycle (Floyd, p. 407)
  • The plot of a periodic waveform shows a regularly repeating pattern of values, each of which is called a cycle.
  • Example: In the picture of the sine wave shown just above, we see a little less than two full cycles. The first cycle extends from 0 ms to 50 ms, and the second (incomplete) cycle extends from 50 ms to the edge of the chart, where it is cut off.
  • Self-test
Period (Floyd, p. 408)
  • The time required for the values to rise and fall through one complete cycle is called the period of the waveform.
  • The symbol for period is T.
  • Period is measured in units of seconds, abbreviated s.
  • Example: The sine wave shown above has a period of 50 ms.
  • Self-test
Frequency (Floyd, p. 410)
  • The frequency of a periodic waveform is the number of cycles that occur in 1 second.
  • The symbol for frequency is f.
  • Frequency is measured in units of cycles per second, or Hertz, abbreviated Hz.
Relationship Between Period and Frequency (Floyd, p. 410)
  • Period and frequency are the reciprocal of each other:
    f = 1 ÷ T  
  • and
    T = 1 ÷ f  
  • Example: The sine wave shown earlier has a period of 50 ms. Therefore, its frequency is 20 Hz.
  • Self-test

Peak Value (Floyd, p. 416)
  • The maximum value reached by an ac waveform is called its peak value.
    • If the waveform is a voltage waveform, then its peak value is also called its peak voltage, abbreviated Vp.
    • If the waveform is a current waveform, then its peak value is also called its peak current , abbreviated Ip.
  • The peak value of a waveform is sometimes also called its amplitude, but the term “peak value” is more descriptive.
  • Example:The sine wave shown earlier has a peak value of 500 mVp. Notice that I write a "p" after the unit to show that I'm talking about a peak value.
  • Self-test
Peak-to-Peak Value (Floyd, p. 416)
  • The peak-to-peak value is the difference between a waveform's positive peak value and its negative peak value.
    • If the waveform is a voltage waveform, then its peak-to-peak value is also called its peak-to-peak voltage, abbreviated Vpp.
    • If the waveform is a current waveform, then its peak-to-peak value is also called its peak-to-peak current , abbreviated Ipp.
  • If the waveform is symmetrical about the time axis, then the peak-to-peak value equals twice the peak value.
  • Example: The sine wave shown earlier has a peak-to-peak value of 1 Vpp. That's the difference between the maximum positive value (which is 500 mV) and the maximum negative value (which is -500 mV). Notice that I wrote a "pp" after the unit to show that I'm talking about a peak-to-peak value.
  • Self-test
p and pp
  • As mentioned in the two examples above, we write p as the subscript of a quantity or unit to show that we're talking about a peak value, and we write pp as the subscript of a quantity or unit when we're talking about a peak-to-peak value.
  • Example: For the sine wave above, we could write

    Vp = 500 mVp

    or

    Vpp = 1 Vpp.

  • Similarly, if we were dealing with a current waveform whose peak value is 20 mA and whose peak-to-peak value is 40 mA, we could write

    Ip = 20 mAp

    or

    Ipp = 40 mApp.

  • Some other textbooks use pk (instead of p) as the abbreviation for peak values, and p-p (instead of pp) as the abbreviation for peak-to-peak values. So you may see these other abbreviations used from time to time.

Review of Electrical Quantities
  • Period and frequency are two of the electrical quantities presented in the table that you first saw in Unit 1 of this course. By now you should have learned the units of most of these electrical quantities, as well as the symbols for the quantities and their units. If you haven't already done so, be sure to play the Electrical-Units Matching Game and Electrical-Symbols Matching Game until you've got these units and symbols memorized.

Function Generator (Floyd, p. 414)
  • The function generator, or signal generator, is an instrument designed to produce ac waveforms, such as square waves, triangle waves, and sine waves. Using it, you can set the peak value and the frequency of these waveforms.
  • Here is a photo of the built-in function generator on the trainers that we use in our electronics labs. It provides the basic controls that any function generator must have:
    • an Amplitude control to set the waveform's peak value
    • Frequency and Range controls to set the waveform's frequency
    • a Function control to set the shape of the waveform.
    Lab 6 will teach you how to use these controls.
    Function generator on the trainer--click for larger photo
  • The photo below shows a professional-quality function generator made by Tektronix. It provides all of the controls discussed above, as well as more advanced features. You'll use this function generator in later courses at Sinclair.
    Stand-alone function generator--click for larger photo
Oscilloscope (Floyd, p. 443)
  • The oscilloscope is an instrument designed to display waveforms. Using it, you can measure period, frequency, peak values, peak-to-peak values, and other important quantities.
  • Shown here is a Tektronix 2213, one of the types of oscilloscopes that we have in Sinclair's electronics labs. At the left is the screen on which waveforms are displayed. To the right are the knobs and switches that you can adjust to control the waveform's appearance.
    Oscilloscope--click for larger photo
  • Below are three separate photos showing how a triangle wave, a square wave, and a sine wave look on the oscilloscope screen.
    Triangle wave displayed on the oscilloscope

    Square wave displayed on the oscilloscope

    Sine wave displayed on the oscilloscope
Using the Oscilloscope to Measure Voltage
  • The oscilloscope displays a graph of voltage versus time, with voltage plotted on the vertical axis and time plotted on the horizontal axis.
  • To measure a waveform's peak-to-peak voltage, you count how many vertical divisions (squares) the waveform covers on the oscilloscope's screen, and then you multiply this number times the setting of the oscilloscope VOLTS-PER-DIVISION knob.
  • This learning object will show you how to do it:
  • Wisconsin Online learning object
Using the Oscilloscope to Measure Period and Frequency
  • Remember, the oscilloscope displays a graph of voltage versus time, with voltage plotted on the vertical axis and time plotted on the horizontal axis.
  • To measure a waveform's period, you count how many horizontal divisions (squares) the waveform covers on the oscilloscope's screen, and then you multiply this number times the setting of the oscilloscope SECONDS-PER-DIVISION knob.
  • Once you know the waveform's period, you can use the formula f = 1 ÷ T to find its frequency.
  • This learning object will show you how to do it:
  • Wisconsin Online learning object
Oscilloscope Challenge Game
  • The oscilloscope is a complicated piece of equipment. You'll need plenty of practice to learn how to use it correctly.
  • To start learning this skill, take some time right now to play Oscilloscope Challenge. In particular, work through the game's "Study" section, which is a tutorial containing several pages of notes to help you identify and use the oscilloscope's controls. This will be a good preparation for Lab 6, in which you'll begin using a real oscilloscope to make measurements.

Unit 7 Review
  • This e-Lesson has covered several important topics related to ac waveforms, including:
    • period
    • frequency
    • peak values
    • peak-to-peak values
    • function generator and oscilloscope.
  • To finish the e-Lesson, take this self-test to check your understanding of these topics.
  • Self-test

Congratulations! You've completed the e-Lesson for this unit. What's next?

  • Take Quiz #7.
  • Perform Lab #7.
  • Do Homework #7.
  • Keep practicing your skills by playing the games on the Games page.

Then you'll be ready to go on to Unit 8's e-Lesson .


Nick Reeder | Electronics Engineering Technology | Sinclair Community College

Send comments to nick.reeder@sinclair.edu