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Sinusoids

In the circuit analysis, the term AC refers to a sinusoidal current or voltage signal. Sinusoids or sine waves are arguably the most significant class of waveforms in electrical engineering. A common example is the mains voltage which is sinusoidal. Generally, any periodic waveform can be generated by using a combination of sinusoidal signals of varying frequencies and amplitudes. The 2 most important parameters of a sine wave are the amplitude of it, Vm and frequency, f or time period, T.

Figure (a) shows a sinusoid and related parameters Vm and T. The frequency is given by the reciprocal of the time period that is f = 1/T . Note that 2 complete cycles are plotted which clearly shows the periodic nature of a sine wave.

Peak to peak amplitude is occasionally used given as 2 times the peak amplitude. Another parameter which is vital for AC analysis is the phase, φ of the sine wave. This is normally measured with respect to the reference waveform as shown in Figure (b). It is significant to point out that sinusoidal generally refers to either cosine or sine waveform where the cosine wave has the same shape but is 900 out of phase with respect to the sine wave.


Mathematically, a sinusoidal signal can be given by the general form

68_Sinusoids.png 

Parameters of a sine wave (a) Amplitude and time period, (b) Phase

1768_Sinusoids1.png

 

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