Compute optimal smoothing capacitor (filter capacitor) for rectified DC supplies. Determine required capacitance from load current and acceptable ripple, or estimate ripple voltage from existing capacitor. Supports half‑wave and full‑wave rectifiers (50/60 Hz).
In linear power supplies, a rectifier (half‑wave or full‑wave) converts AC to pulsating DC. A smoothing capacitor (also called filter capacitor or reservoir capacitor) stores charge during the rectifier conduction period and releases it to the load when the rectified voltage drops. This reduces the ripple voltage – the residual periodic variation in DC output.
For a constant current load, the fundamental ripple equation is:
Vripple(p-p) = Iload / (fripple · C)
or equivalently: C = Iload / (fripple · Vripple(p-p))
Where fripple = line frequency for half‑wave rectifier (50/60 Hz) and 2× line frequency for full‑wave (100/120 Hz).
This formula assumes ideal capacitor, negligible ESR, and constant load current. It provides excellent first‑order approximation for bulk capacitor sizing in most linear and basic switch‑mode pre‑regulators. The derivation comes from the capacitor discharge equation: ΔV = (I·Δt)/C, where Δt is the discharge time (approximately half the ripple period for full‑wave, full period for half‑wave).
Requirement: Load current = 1.2A, allowable ripple = 0.2Vp-p, full‑wave bridge rectifier with 50 Hz mains.
Calculation: fripple = 100 Hz, C = 1.2 / (100 × 0.2) = 0.06 F = 60,000 µF.
Practical selection: Use 68,000 µF / 25V electrolytic capacitor (derated for 18V peak).
Resulting actual ripple: Vrip = 1.2/(100×0.068) ≈ 0.176 Vp-p → better than required. The interactive simulation confirms the waveform.
| Parameter | Half‑Wave Rectifier | Full‑Wave Bridge |
|---|---|---|
| Ripple frequency | fline (50/60 Hz) | 2× fline (100/120 Hz) |
| Capacitance for same ripple (I=1A, Vrip=0.5V) | C = 1/(50×0.5) = 40,000 µF | C = 1/(100×0.5) = 20,000 µF |
| Transformer utilization | Poor (~0.28) | Good (~0.62) |
| Typical applications | Very low‑cost, battery chargers | Most DC power supplies, audio, industrial |
Capacitor ESR (Equivalent Series Resistance): Real capacitors have ESR that increases ripple and heating. For high‑ripple currents, use low‑ESR types (e.g., electrolytic capacitors designed for switching supplies). The theoretical formula provides a baseline; for precision designs, simulate with ESR.
Peak Current & Inrush: Larger capacitance causes higher peak diode currents and inrush at startup. Add a soft‑start or NTC thermistor for high power (>100W).
Voltage Derating: Always select capacitor voltage rating at least 20-30% above peak AC voltage (e.g., for 12VAC transformer → peak ≈ 17V → use 25V or 35V capacitor).