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As long as a wave has a definite period, and as long as the polarity keeps switching back and forth between positive and negative, it is ac, no matter how complicated the actual shape of the waveform. Figure 9-6 shows an example of a complex ac wave. There is a definable 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 ascertain the period. This is because the wave has two or more components that are of nearly the same amplitude. When this hap-
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9-6 An irregular waveform.
pens, the frequency spectrum of the wave is multifaceted. That means the wave energy is split up more or less equally among multiple frequencies.
Frequency Spectrum
An oscilloscope shows a graph of amplitude as a function of time. Because time is on the horizontal axis and represents the independent variable or domain of the function, the oscilloscope is said to be a time-domain instrument. But suppose you want to see the amplitude of a complex signal 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. Its horizontal axis shows frequency as the independent variable, ranging from some adjustable minimum frequency (at the extreme left) to some adjustable maximum frequency (at the 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 frequency. But many, if not most, ac waves contain harmonic energy along with energy at the fundamental frequency. A harmonic frequency is a whole-number multiple of the fundamental frequency. For example, if 60 Hz is the fundamental frequency, 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; the 240-Hz wave is the fourth harmonic; and so on.
Frequency Spectrum 149
In general, if a wave has a frequency equal to n times the fundamental (where n is some whole number), then that wave is called the nth harmonic. In Fig. 9-7B, a wave is shown along with several harmonics, as it would look on the display screen of a spectrum analyzer. Square waves and sawtooth waves contain harmonic energy in addition to energy at the fundamental frequency. Other waves can get more complicated. The exact shape of a wave depends on the amount of energy in the harmonics, and the way in which this energy is distributed among them. Irregular waves can have any imaginable frequency distribution. Figure 9-8 shows an example. This is a spectral (frequency-domain) display of an amplitude-modulated (AM) voice radio signal. Much of the energy is concentrated at the center of the pattern, at the frequency shown by the vertical line. That is the carrier frequency. There is also plenty of energy near, but not exactly at, the carrier frequency. That s the part of the signal that contains the voice.
9-7 At A, a spectral diagram
of a pure, 60-Hz sine wave. At B, a spectral diagram of a 60-Hz wave with three harmonics.
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9-8 A spectral diagram of a
modulated radio signal.
Fractions of a Cycle
Engineers break the ac cycle down into small parts for analysis and reference. One complete cycle can be compared to a single revolution around a circle.
Degrees One method of specifying the phase of an ac cycle is to divide it into 360 equal parts, called degrees or degrees of phase, symbolized by a superscript, lowercase letter o ( ). The value 0 is assigned to the point in the cycle where the magnitude is zero and positive-going. The same point on the next cycle is given the value 360 . The point one-fourth of the way through the cycle is 90 ; the point halfway through the cycle is 180 ; the point three-fourths of the way through the cycle is 270 . This is illustrated in Fig. 9-9. Degrees of phase are used mainly by engineers and technicians.
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