The form factor of a half wave rectified sine wave is defined as the ratio of its RMS (root mean square) value to its average value. In the case of a half wave rectified sine wave, the form factor is typically calculated by dividing the RMS value by the average value of the rectified waveform.
For a standard sine wave, the RMS value is given by:
RMS = (peak value / √2)
When half wave rectified, the negative half of the sine wave is removed, resulting in a waveform that only contains the positive half of the original sine wave. The average value of this rectified waveform can be calculated by integrating the positive half of the sine wave over a half-cycle and then dividing by the time period of that half-cycle.
For a standard sine wave, the average value is zero because it is symmetric about the x-axis. However, for a half wave rectified sine wave, the average value can be determined by integrating the positive half of the sine wave over the half-cycle (from 0 to π) and then dividing by the half-cycle duration (π radians). The integral of the positive half of the sine wave from 0 to π is (2/π), and dividing by the half-cycle duration of π radians gives an average value of (2/π) * (1/π) = (2/π^2).
Therefore, the form factor of a half wave rectified sine wave is:
Form Factor = RMS value / Average value = ((peak value / √2) / (2/π^2)) = (π / 2√2) ≈ 1.11
So, the form factor of a half wave rectified sine wave is approximately 1.11.