From AC to DC
A linear power supply turns the transformer’s AC output into DC with a rectifier and smooths it with a large reservoir capacitor. The capacitor charges to the peak of each half cycle and discharges into the load between peaks, leaving a sawtooth ripple on top of the DC.
The formulas
- Peak voltage: V_peak = V_rms × √2 − diode drops (2 for a bridge, 1 for a center-tap or half-wave rectifier)
- Ripple frequency: twice the mains frequency for full-wave rectifiers, equal to it for half-wave
- Ripple (peak to peak): V_r ≈ I_load ÷ (f_ripple × C)
- Average DC: about V_peak − V_r ÷ 2
- Capacitor for a target ripple: C = I_load ÷ (f_ripple × V_r)
Example
A 12 V AC transformer feeding a bridge rectifier, with 0.7 V per diode, 4,700 µF and a 1 A load on 60 Hz mains:
| Item | Value |
|---|---|
| Peak voltage | 15.57 V |
| Ripple frequency | 120 Hz |
| Ripple | 1.77 V |
| Average DC | 14.7 V |
| Lowest voltage | 13.8 V |
| Capacitor for 1 V ripple | 8,333 µF |
On 50 Hz mains the same circuit ripples by 2.1 V, so supplies designed for Europe need about 20% more capacitance.
Choosing parts
- Regulator headroom: the lowest point of the ripple must stay above the regulator’s output plus its dropout voltage (about 2 V for a 7805 or LM317, less for an LDO).
- Capacitor voltage: choose a rating at least 25% above the no-load peak, and remember that mains voltage can be 10% high.
- Ripple current: the capacitor carries large charging pulses; check its ripple current rating, or it will overheat and age quickly.
- Diodes: use parts rated for the repetitive peak current, often several times the DC load current.
Limits of the estimate
The formula assumes a constant load current and a short charging pulse. It slightly overestimates ripple at light loads and underestimates it when the transformer’s resistance is significant. For low-noise audio or precision circuits, follow the capacitor with a regulator or an RC or LC filter.
Safety
Mains-powered circuits can kill. Work on the low-voltage side of an enclosed, fused, certified transformer, and discharge large capacitors before touching them.