I am planning a 220V AC to 9V DC rectifier circuit.
In order to provide a stable DC output, I've decided to put a capacitor. But how do I find the rating of the capacitor I should use?
In my circuit, the current flowing will be a maximum of 5mA, and the power will not be greater than 50mW.
Keeping these in mind, can anyone suggest what capacitor I should use?
The choice of the capacitor value needs to fulfil a number of requirements. In the first case the value must be chosen so that its time constant is very much longer than the time interval between the successive peaks of the rectified waveform:
\$ R_{load} C >> \frac{1}{f}\$
where: \$R_{load}\$ = the overall resistance of the load for the supply
\$C\$ = value of capacitor in Farads
\$f\$ = the ripple frequency - this will be twice the line frequency a full wave rectifier is used.
As there will always be some ripple on the output of a rectifier using a smoothing capacitor circuit, it is necessary to be able to estimate the approximate value. Over-specifying a capacitor too much will add extra cost, size and weight - under-specifying it will lead to poor performance.
For cases where the ripple is small compared to the supply voltage - which is almost always the case - it is possible to calculate the ripple from a knowledge of the circuit conditions:
Full wave rectifier:
\$V_{ripple} = \frac{I_{load}}{2fC}\$
Half wave rectifier:
\$V_{ripple} = \frac{I_{load}}{fC}\$
These equations provide more than sufficient accuracy. Although the capacitor discharge for a purely resistive load is exponential, the inaccuracy introduced by the linear approximation is very small for low values of ripple.
It is also worth remembering that the input to a voltage regulator is not a purely resistive load but a constant current load. Finally, the tolerances of electrolytic capacitors used for rectifier smoothing circuits are large - ±20% at the very best, and this will mask any inaccuracies introduced by the assumptions in the equations.
