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You can estimate capacitor value in a rectifier circuit by considering what your maximum ripple voltage and frequency is, and assuming that the input AC is actually a pulse train.

Lets look at frequency first. In a 60 Hz application, there is 16.7 ms between charge pulses in half wave mode, or 8.3 ms in full wave mode.

Now look at ripple voltage. Lets say you have a regulator that will tolerate a ripple voltage of 3 volts. Divide that by the period, 16.7 ms or 8.3 ms, and you get 180 v/s or 361 v/s.

Now, consider your load. Lets say you have a 4 amp supply. Go back to the equation of a capacitor,

dv/dt = i/c

and plug in what you know...

180 v/s = 4/c

and solve for c...

c = 0.0222 farads, or 22,200 microfarads.

You need half of that in the full wave application.

Now, that is an estimate. Since the input AC is sinusoidal, instead of pulse, the actual time between charge pulses is less that 16.7 ms or 8.3 ms, so this calculation is conservative.

One thing you do have to consider for large electrolytic capacitors is that they have a limit on current, usually specified as an RMS current value. You need to go back and figure out what that is, based on the fact that the charge/discharge curve is actually sawtooth, not sinusoidal, and figure that out so you don't overload the capacitor. I will leave that to you as a separate exercise.

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