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of the filtered signal to the DC or average value of the signal:
r = Vrms,AC
VDC
. (3.16)
For the simple capacitor filter, it can be shown that, for RLC
T, the ripple factor
is given by
r ≈
T
2
√3RLC = 1
2
√3fRLC (3.17)
where f is the frequency of the rectified signal. Examining this result, we see that r
decreases with increasing C, RL, and f . This is reasonable since increasing any of
these parameters will decrease the amount the capacitor discharges. It can also be
shown that, under these conditions, the DC part of the rectified signal is given by
VDC ≈ Vp − VpT
2RLC
≈ Vp − IDC
2fC (3.18)
where Vp is the peak value of the rectified signal and, in the last equality, we have
used the approximation IDC ≈ Vp/RL.
This last result draws attention to an
r = Vrms,AC
VDC
. (3.16)
For the simple capacitor filter, it can be shown that, for RLC
T, the ripple factor
is given by
r ≈
T
2
√3RLC = 1
2
√3fRLC (3.17)
where f is the frequency of the rectified signal. Examining this result, we see that r
decreases with increasing C, RL, and f . This is reasonable since increasing any of
these parameters will decrease the amount the capacitor discharges. It can also be
shown that, under these conditions, the DC part of the rectified signal is given by
VDC ≈ Vp − VpT
2RLC
≈ Vp − IDC
2fC (3.18)
where Vp is the peak value of the rectified signal and, in the last equality, we have
used the approximation IDC ≈ Vp/RL.
This last result draws attention to an
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