A half-wave rectifying circuit using an input sine wave gives an average d.c. value of
V=Vpeak/(pi)
I=Ipeak/(pi)
Vrms=Vpeak/2
Irms=Ipeak/2
A full-wave rectifying circuit using an input sine wave gives
V=2Vpeak/(pi)
I=2Ipeak/(pi)
Vrms=Vpeak/1.414
Irms=Ipeak/1.414
Smoothing capacitors with very large values draw very large peak current through rectifying diodes, which can destroy them.
If we approximate the current pulses that charge the capacitor as a rectangle with a height Icharge and width tcharge, and the discharge current as a rectangle with height Idc and width tdischarge, we have:
Qcharge=Qdischarge
Icharge x tcharge = Idc x tdischarge
or
Icharge = Idc x (tdischarge\tcharge)
So Icharge can be many times the load current. This current is called the peak repetitive forward current IFM(rep) or repetitive surge current.
Often a surge limiting resistor is inserted between the bridge rectifier and smoothing capacitor. The value of this resistor is equal to the peak input voltage divided by the surge current value of the diodes.
Ripple factor, r = rms ripple current / load current
or r = rms ripple voltage / load voltage
For a smoothing cap the ripple is approximately triangular with an rms value of
Vrms = Vripple(p-p) / (2 * (3^0.5))
Sometimes the ripple factor is expressed as a percentage
r = (rms ripple voltage / dc average voltage) x 100%
Power Supplies are usually designed to limit output current. This prevents damage to the supply, and can help to prevent damage to the load. If the reason for excess current is due to a fault in the load, limiting the current can sometimes help to prevent further damage to the load. The safest method of limiting current is known as 'foldback': not only does the current limit, but it is 'turned down' to a low, safe level. The diagram below illustrates this: diagram (a) shows simple current limiting, whilst diagram (b) shows foldback current limiting. Less power is dissipated in the supply during short circuit conditions in the foldback configuration.