Rectifier Ripple Formulas: Capacitor Filter

Rectifier ripple formulas: peak voltage, ripple voltage of a capacitor filter for half-wave and full-wave rectifiers, and the capacitor for a ripple target.

The formulas

I is the DC load current in amperes, f the mains frequency in hertz and C the capacitance in farads. The formulas assume a constant current load and a short conduction time, so they are an estimate, a little pessimistic for a large capacitor. Allow for the mains tolerance, the capacitor tolerance and the diode and transformer resistance. A full-wave rectifier has a ripple frequency of 2 × f.

Worked example: bridge rectifier, 12 V RMS, 0.5 A, 4,700 µF

A 50 Hz supply and two diode drops of 0.7 V each.

1. Vpk = 12 × √2 = 16.97 V, so Vp = 16.97 − 2 × 0.7 = 15.57 V
2. ΔV = 0.5 / (2 × 50 × 0.0047) = 1.064 V
3. The minimum voltage is 15.57 − 1.064 = 14.51 V and the average is about 15.04 V
4. The RMS ripple is 1.064 / (2 × √3) = 0.3071 V

Worked example: capacitor for 0.5 V ripple

1. C = 0.5 / (2 × 50 × 0.5) = 10,000 µF

Ripple at 0.5 A and 50 Hz

Frequently asked questions

Why is a full-wave rectifier better for ripple?

It refills the capacitor twice per mains cycle, so the capacitor discharges for half as long and the ripple is half that of a half-wave circuit with the same capacitor.

How much capacitance do I need?

Enough that the minimum voltage stays above what the regulator or load needs. Use C ≈ I / (2 × f × ΔV) and round up to the next standard value, allowing for the capacitor tolerance.

What is ripple current in the capacitor?

The capacitor charges in short pulses, so its RMS ripple current is several times the DC load current. Check the ripple current rating on the data sheet.

Does a regulator remove the ripple?

A linear regulator reduces it by its ripple rejection, but the input must stay above the dropout voltage at the lowest point of the ripple.

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