Sinusoidal Parameters

Mean or Average Value

Given a discrete sequence of signals like 1, 2, 3, 4, 5 the average value is computed as follows
 

For the continuous periodic waveform like a sinusoid, the mean value can be found by taking the average of all the instantaneous values during one cycle. This can be given by
 

Clearly, the average value of a complete sine wave is 0 because of equal positive and negative half cycles. This is regardless of peak amplitude.

The average value of a fully rectified sine wave by taking the absolute value of a sine wave, a fully rectified waveform can be produced. In practise, this can be achieved by employing the bridge circuit shown in Figure (a) with sine wave as the excitation signal. The output waveform across the load,R_L is depicted in Figure (b) with a time period of T/2 where T is the time period of a normal sine

wave. Therefore
  
Figure A bridge rectifier and the resulting fully rectified sine waveform



A bridge rectifier circuit is common in DC power supplies and is basically employed to convert an AC input signal to a DC output.

Average value of a half rectified sine wave A half wave rectification circuit is depicted in Figure (a) and the resulting waveform is shown in Figure (b). In this case, the negative half cycle of the sine wave is clipped to zero and thus the time period T of the waveform remains the same. Therefore,
 

Figure -A half wave rectification circuit and the resulting output.

A half wave rectifier is commonly employed in DC power supplies for AC to DC conversion. This requires only 1 diode as opposed to four in a bridge rectifier. However, the average value is half of the full wave as given by Equation.

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