The filtering process is the process of smoothing a pulsating signal to bring it closer to a stable DC voltage.
At the output of the diode bridge, we have what we call pulsating DC. The voltage rises to a value close to the peak and drops towards zero one hundred times per second, if we start from a 50 Hz mains and use full-wave rectification.
A resistive load would receive power in pulses. In an amplifier, this ripple can appear as a 100 Hz hum; a digital circuit can reset if the voltage drops below its minimum operating level.
The solution is to place a component capable of storing energy when there is excess and releasing it when it is lacking. That component is the Electrolytic Capacitor connected in parallel.
The effect of the capacitor
The operation is very intuitive if we use the hydraulic analogy of a tank:
Charging (Rising wave):
When the rectifier voltage is higher than the capacitor voltage, current flows into the capacitor and charges it up to the peak value (
Discharging (Falling wave):
When the rectifier wave starts to drop towards zero, the diode becomes reverse-biased (because the voltage across the capacitor is higher than the mains voltage).
At that moment, the rectifier stops supplying the circuit, and the capacitor takes over. It starts to discharge into the load (
The Cycle repeats: Before the capacitor fully discharges, the next pulse from the rectifier arrives, charges it back to the maximum, and the cycle begins anew.
The ripple voltage
The result of this process is not a perfect straight line. It is a line that is high overall but has small “sawtooth” or shark fin patterns.
The capacitor discharges a little between pulses. This small voltage variation is called Ripple Voltage.
: The peak voltage (minus the diode drops). : The minimum voltage the capacitor drops to before being recharged. : The peak-to-peak difference ( ).
Calculation of the filter capacitor
To design a basic linear power supply, we can use this approximation, derived from
Where:
: The current drawn by our device (in Amperes). : The frequency of the rectified wave. - Note: In full-wave rectification (Graetz bridge), the frequency is double the mains frequency. In Europe, 50Hz x 2 = 100Hz.
: The capacitance in farads.
The formula assumes an approximately constant current and a small ripple. In a real design, you must also check the Equivalent Series Resistance (ESR), the allowable ripple current, and the peak currents through the diodes.
Practical Example
We want to design a power supply for a circuit that draws 1 A, and we want the ripple to be at most 1 V. We solve for C:
Converting to microfarads: 10,000 µF. This is a rather large capacitor (a sizable “can”).
In classic linear power supplies, it is common to estimate about 1000 µF - 2200 µF per Ampere of load for acceptable filtering before a regulator.
The Inrush Current
Looking at the formula, you might think, “Well, I’ll just use a 1 Farad capacitor, and the ripple will be 0!”. Well no, I’m sorry to say things don’t work like that.
An uncharged capacitor initially behaves like a Short Circuit.
If you use a gigantic capacitor, when you turn on the power supply (
- This inrush current can blow fuses or damage the rectifier bridge if it is not limited and properly rated.
- A balance must be found: enough capacitance to filter, but not so much as to destroy the input.
You must also choose a voltage rating with sufficient margin, respect the polarity of electrolytic capacitors, and remember that a large capacitor can hold a dangerous charge after the circuit is disconnected.
The bridge and capacitor deliver a DC voltage with ripple, not an exact value. If you later add a regulator, you must leave it sufficient input headroom even at the ripple valley and check its power dissipation.
