Frequency spectrumAn oscilloscope shows a graph of magnitude versus time. Because time is on the hori-zontal 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 afunction of time. This can be done with a spectrum analyzer. It is a frequency-do-main instrument with a cathode-ray display similar to an oscilloscope. Its horizontalaxis shows frequency, from some adjustable minimum (extreme left) to some ad-justable maximum (extreme right).An ac sine wave, as displayed on a spectrum analyzer, appears as a single “pip, “ orvertical line (Fig. 9-7A). This means that all of the energy in the wave is concentratedat one single frequency.Many ac waves contain harmonic energy along with the fundamental, or main, fre-quency. A harmonic frequency is a whole-number multiple of the fundamental fre-quency. 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 waveis the third harmonic.In general, if a wave has a frequency equal to n times the fundamental, then thatwave is the nth harmonic. In the illustration of Fig. 9-7B, a wave is shown along withseveral harmonics, as it would look on the display screen of a spectrum analyzer.The frequency spectra of square waves and sawtooth waves contain harmonic energyin addition to the fundamental. The wave shape depends on the amount of energy in theharmonics, and the way in which this energy is distributed among the harmonic frequen-cies. A detailed discussion of these relationships is far too sophisticated for this book.Irregular waves can have practically any imaginable frequency distribution. An ex-ample is shown at Fig. 9-8. This is a display of a voice-modulated radio signal. Much ofthe energy is concentrated at the center of the pattern, at the frequency shown by thevertical line. But there is also plenty of energy “splattered around” this carrier fre-quency. On an oscilloscope, this signal would look like a fuzzy sine wave, indicating thatit is ac, although it contains a potpourri of minor components.170 Alternating current basics9-6An irregular waveform.