ABSTRACT
At the end of this chapter you should be able to:
• define a complex wave
• recognize periodic functions
• recognize the general equation of a complex waveform
• use harmonic synthesis to build up a complex wave
• recognize characteristics of waveforms containing odd, even or odd and even harmonics,with or without phase change
• determine Fourier
• calculate r.m.s. and of a complex wave
• calculate power
• perform calculations harmonics
• define and perform
• list and explain some
In preceding chapters a.c. supplies have been assumed to be sinusoidal, this being a form of alternating quantity commonly encountered in electrical engineering. However, many supply waveforms are not sinusoidal. For example, sawtooth generators produce ramp waveforms, and rectangular waveforms may be produced by multivibrators. A waveform that is not sinusoidal is called a complexwave. Such awaveformmay be shown to be composedof the sumof a series of sinusoidalwaves having various interrelated periodic times. A functionf (t) is said to be periodic iff (t + T )=f (t) for all values of t , where T is the interval between two successive repetitions and is called the period of the function f (t). A sine wave having a period of 2π /ω is a familiar example of a periodic function. A typical complex periodic-voltage waveform,
shown in Figure 39.1, has period T seconds and frequency f hertz. A complex wave such as this can be resolved into the sum of a number of sinusoidal waveforms, and each of the sine waves can have a different frequency, amplitude and phase. The initial, major sine wave component has a fre-
quency f equal to the frequency of the complex wave and this frequency is called the fundamental frequency. The other sine wave components are known as harmonics, these having frequencies which are integer multiples of frequency f . Hence the second harmonic has a frequency of 2f , the third harmonic has a frequency of 3f , and so on. Thus if the fundamental (i.e. supply) frequency of a complex wave is 50Hz, then the third harmonic frequency is 150Hz, the fourth harmonic frequency is 200Hz, and so on.
