Question 5.16: Find the peak, peak-to-peak, and average values of the perio......
Find the peak, peak-to-peak, and average values of the periodic input and output
waveforms in Figure 5–37 of a half-wave rectifier.
The input waveform is a sinusoid whose amplitude descriptors are
V_{pp} = 2V_{A} V_{p} = V_{A} V_{avg} = 0
The output waveform is obtained by clipping off the negative half-cycle of the input sinusoid. The amplitude descriptors of the output waveform are
V_{pp} = V_{p} = V_{A}
The output has a nonzero average value, since there is a net positive area under the waveform. The upper limit in Eq. (5–30) can be taken as T_{0}/2, since the waveform is zero from T_{0}/2 to T_{0}.
V_{avg} =\frac{1}{T_{0}} \int ^{T_{0}/2}_{0}V_{A}\sin(2\pi t/T_{0})dt = -\frac{V_{A}}{2\pi} \cos(2\pi t/T_{0})|^{T_{0}/2}_{0}
=\frac{V_{A}}{π}
V_{avg} =\frac{1}{T}\int_{t}^{t+T}v(x)dx (5–30)
The signal processor produces an output with a dc value from an input with no dc component. Rectifying circuits described in electronics courses produce waveforms like the output in Figure 5–37.