How to Size a Filter Capacitor for Ripple Voltage
After a rectifier turns AC into pulsating DC, a filter (reservoir) capacitor smooths that waveform by supplying the load's current in the gaps between charging pulses. "Sizing" the capacitor means finding the smallest capacitance that keeps the leftover ripple voltage below a level you can tolerate — big enough to work, without paying for a needlessly oversized part.
Deriving the C = I ÷ (f × Vripple) formula
A capacitor's charge, voltage, and capacitance are related by Q = CV, and current is the rate of charge flow, I = Q/t. Between charging pulses, the capacitor alone supplies the load current I for a time t, so it loses charge ΔQ = I × t, which produces a voltage drop (the ripple) of ΔV = ΔQ/C = I × t/C. Solving for C, and noting that the time between pulses is t = 1/f (where f is the ripple frequency), gives the standard sizing formula:
- C = I ÷ (f × Vripple) — minimum capacitance (farads) for load current I (amps), ripple frequency f (hertz), and maximum allowed peak-to-peak ripple Vripple (volts).
- This is an approximation that assumes the load current stays roughly constant during discharge — accurate enough for most linear power-supply design, but real ripple is a decaying exponential, not a straight line.
Full-wave vs. half-wave rectification
The ripple frequency depends on how the AC is rectified, not just the line frequency:
- Full-wave (bridge) rectifier: both halves of the AC cycle are used, so the capacitor is recharged twice per cycle. Ripple frequency = 2 × line frequency (120 Hz on 60 Hz mains, 100 Hz on 50 Hz mains).
- Half-wave rectifier: only one half of the AC cycle is used, so the capacitor recharges once per cycle. Ripple frequency = line frequency, and the required capacitance roughly doubles for the same ripple target.
Practical capacitor selection notes
- Round the calculated minimum up to the next standard capacitor value (e.g., 4700 µF, 6800 µF, 10000 µF) and add the safety margin — electrolytic capacitors commonly carry -20%/+80% tolerance and lose capacitance with age and heat.
- Choose a voltage rating at least 1.25-1.5× the peak DC voltage across the capacitor, not just the ripple amplitude, to leave headroom for line-voltage swings and load transients.
- Equivalent series resistance (ESR) adds its own voltage spike on top of the calculated ripple, especially at higher load currents — low-ESR or multiple parallel capacitors help in high-current supplies.
- For switching (not linear) power supplies, the ripple frequency is the switching frequency (often tens of kHz), which is why switch-mode supplies can use much smaller filter capacitors.