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In Fig. 9-3, one form of sawtooth wave is shown. The positive-going slope (rise) is extremely steep, as with a square wave, but the negative-going slope (fall or decay) is gradual. The period of the wave is the time between points at identical positions on two successive pulses.
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9-2 At A, a perfect square wave. At B, the more common rendition of a square wave.
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9-3 Fast-rise, slow-decay sawtooth.
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Another form of sawtooth wave is just the opposite, with a gradual positive-going slope and a vertical negative-going transition. This type of wave is sometimes called a ramp, because it looks like an incline going upwards (Fig. 9-4). This waveshape is useful for scanning in television sets and oscilloscopes. It tells the electron beam to move, or trace, at a constant speed from left to right during the upwards sloping part of the wave. Then it retraces, or brings the electron beam back, at a high speed for the next trace.
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Complex and irregular waveforms 169
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Slow-rise, fast-decay sawtooth, also called a ramp.
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You can probably guess that sawtooth waves can have rise and decay slopes in an infinite number of different combinations. One example is shown in Fig. 9-5. In this case, the positive-going slope is the same as the negative-going slope. This is a triangular wave.
9-5 Triangular wave.
Complex and irregular waveforms
The shape of an ac wave can get exceedingly complicated, but as long as it has a definite period, and as long as the polarity keeps switching back and forth between positive and negative, it is ac. Fig. 9-6 shows an example of a complex ac wave. You can see that there is a period, and therefore a definable frequency. The period is the time between two points on succeeding wave repetitions. With some waves, it can be difficult or almost impossible to tell the period. This is because the wave has two or more components that are nearly the same magnitude. When this happens, the frequency spectrum of the wave will be multifaceted. The energy is split up among two or more frequencies.
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9-6 An irregular waveform.
Frequency spectrum
An oscilloscope shows a graph of magnitude versus time. Because time is on the horizontal axis, the oscilloscope is said to be a time-domain instrument. Sometimes you want to see magnitude as a function of frequency, rather than as a function of time. This can be done with a spectrum analyzer. It is a frequency-domain instrument with a cathode-ray display similar to an oscilloscope. Its horizontal axis shows frequency, from some adjustable minimum (extreme left) to some adjustable maximum (extreme right). An ac sine wave, as displayed on a spectrum analyzer, appears as a single pip, or vertical line (Fig. 9-7A). This means that all of the energy in the wave is concentrated at one single frequency. Many ac waves contain harmonic energy along with the fundamental, or main, frequency. A harmonic frequency is a whole-number multiple of the fundamental frequency. For example, if 60 Hz is the fundamental, then harmonics can exist at 120 Hz, 180 Hz, 240 Hz, and so on. The 120-Hz wave is the second harmonic; the 180-Hz wave is the third harmonic. In general, if a wave has a frequency equal to n times the fundamental, then that wave is the nth harmonic. In the illustration of Fig. 9-7B, a wave is shown along with several harmonics, as it would look on the display screen of a spectrum analyzer. The frequency spectra of square waves and sawtooth waves contain harmonic energy in addition to the fundamental. The wave shape depends on the amount of energy in the harmonics, and the way in which this energy is distributed among the harmonic frequencies. A detailed discussion of these relationships is far too sophisticated for this book. Irregular waves can have practically any imaginable frequency distribution. An example is shown at Fig. 9-8. This is a display of a voice-modulated radio signal. Much of the energy is concentrated at the center of the pattern, at the frequency shown by the vertical line. But there is also plenty of energy splattered around this carrier frequency. On an oscilloscope, this signal would look like a fuzzy sine wave, indicating that it is ac, although it contains a potpourri of minor components.
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