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166 Alternating current basics Fig. 9-1 for a simple ac wave. The period of a wave can, in theory, be anywhere from a minuscule fraction of a second to many centuries. Radio-frequency currents reverse polarity millions or billions of times a second. The charged particles held captive by the magnetic field of the sun, and perhaps also by the much larger magnetic fields around galaxies, might reverse their direction over periods measured in thousands or millions of years. Period, when measured in seconds, is denoted by T.

Earlier in this chapter, it was said that there can be an ac wave whose instantaneous amplitude remains constant, even though the polarity reverses. Does this seem counterintuitive Think some more! A square wave is such a wave. On an oscilloscope, a square wave looks like a pair of parallel, dashed lines, one with positive polarity and the other with negative polarity (Fig. 9-2A). The oscilloscope shows a graph of voltage on the vertical scale and time on the horizontal scale. The transitions between negative and positive for a theoretically perfect square wave would not show up on the oscilloscope, because they would be instantaneous. But in practice, the transitions can often be seen as vertical lines (Fig. 9-2B). True square waves have equal negative and positive peaks. Thus, the absolute amplitude of the wave is constant. Half of the time it s +x, and the other half of the time it s x (where x can be expressed in volts, amperes, or watts). Some squared-off waves are lopsided; the negative and positive amplitudes are not the same. Still others remain at positive polarity longer than they remain at negative polarity (or vice versa). These are examples of asymmetrical square waves, more properly called rectangular waves.

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In addition to the gladiatorial combat approach to sharing access to a transmission facility, a more civilized technique is known as distributed

The frequency, denoted f, of a wave is the reciprocal of the period. That is, f = 1/T and T = 1/f .Originally, frequency was specified in cycles per second, abbreviated cps. High frequencies were sometimes given in kilocycles, megacycles, or gigacycles, representing thousands, millions, or billions of cycles per second. But nowadays, the unit is known as the hertz, abbreviated Hz. Thus, 1 Hz = 1 cps, 10 Hz = 10 cps, and so on. Higher frequencies are given in kilohertz (kHz), megahertz (MHz), or gigahertz (GHz). The relationships are: 1 kHz = 1000 Hz 1 MHz = 1000 kHz = 1,000,000 Hz 1 GHz = 1000 MHz = 1,000,000,000 Hz Sometimes an even bigger unit, the terahertz (THz), is needed. This is a trillion (1,000,000,000,000) hertz. Electrical currents generally do not attain such frequencies, although electromagnetic radiation can. Some ac waves have only one frequency. These waves are called pure. But often, there are components at multiples of the main, or fundamental, frequency. There might also be components at odd frequencies. Some ac waves are extremely complex, consisting of hundreds, thousands, or even infinitely many different component, frequencies. In this book, most of the attention will be given to ac waves that have just one frequency.

do not show up on the graph. At B, the more common rendition of a square wave, showing the transitions as vertical lines.

Sometimes, alternating current has a sine-wave, or sinusoidal, nature. This means that the direction of the current reverses at regular intervals, and that the current-versus time curve is shaped like the trigonometric sine function. The waveform in Fig. 9-1 is a sine wave. Any ac wave that consists of a single frequency will have a perfect sine waveshape. And any perfect sine-wave current contains only one component frequency. In practice, a wave might be so close to a sine wave that it looks exactly like the sine function on an oscilloscope, when in reality there are traces of other frequencies present. Imperfections are often too small to see. But pure, single-frequency ac not only looks perfect, but actually is a perfect replication of the trigonometric sine function. The current at the wall outlets in your house has an almost perfect sine waveshape, with a frequency of 60 Hz.

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Some ac waves rise and/or fall in straight, sloping lines as seen on an oscilloscope screen. The slope of the line indicates how fast the magnitude is changing. Such waves are called sawtooth waves because of their appearance. Sawtooth waves are generated by certain electronic test devices. They can also be generated by electronic sound synthesizers.

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