Sinusoidal Alternating Waveforms

The analysis thus far has been limited to dc networks, networks in which the currents or voltages are fixed in magnitude except for transient effects. We will now turn our attention to the analysis of networks in which the magnitude of the source varies in a set manner. Of particular interest is the time-varying voltage that is commercially available in large quantities and is commonly called the ac voltage. (The letters ac are an abbreviation for alternating current.)
Alternating waveforms
Fig. 1: Alternating waveforms.
To be absolutely rigorous, the terminology ac voltage or ac current is not sufficient to describe the type of signal we will be analyzing. Each waveform of Fig. 1 is an alternating waveform available from commercial supplies.
The term alternating indicates only that the waveform alternates between two prescribed levels in a set time sequence
To be absolutely correct, the term sinusoidal, square wave, or triangular must also be applied. The pattern of particular interest is the sinusoidal ac waveform for voltage of Fig. 1. Since this type of signal is encountered in the vast majority of instances, the abbreviated phrases ac voltage and ac current are commonly applied without confusion. For the other patterns of Fig. 1, the descriptive term is always present, but frequently the ac abbreviation is dropped, resulting in the designation square-wave or triangular waveforms.
One of the important reasons for concentrating on the sinusoidal ac voltage is that it is the voltage generated by utilities throughout the world. Other reasons include its application throughout electrical, electronic, communication, and industrial systems. In addition, the chapters to follow will reveal that the waveform itself has a number of characteristics that will result in a unique response when it is applied to the basic electrical elements. The wide range of theorems and methods introduced for dc networks will also be applied to sinusoidal ac systems. Although the application of sinusoidal signals will raise the required math level, most of the concepts introduced in the dc chapters can be applied to ac networks with a minimum of added difficulty.
The increasing number of computer systems used in the industrial community requires, at the very least, a brief introduction to the terminology employed with pulse waveforms and the response of some fundamental configurations to the application of such signals. Chapter 23 will serve such a purpose.