Taking this thread back to the beginning, there is a simple formula for calculating the minimum value of smoothing capacitance required to give a required value on a supply.
For a simple (rectifier - capacitor - resistive load) type power supply
Capacitance = (load current x period)/ripple voltage
Where:
Capacitance is in uF
Load Current is in mA
Ripple Voltage is in Volts (peak to peak)
Period is the period of the ripple frequency in milli - seconds
So if we have a load of 500mA, the ripple must be less that 100mV p-p, and the supply frequency is 50hz.
The ripple period will be 10ms for a full wave rectifier.
The smoothing capacitor must be:
C = (500 x 10)/0.1 = 50,000uF
A rather large capacitor, in a practical circuit, you may decide that you can live with a bit more ripple, use a smaller capacitor and a voltage regulator.
JimB
Edit:
On reading some of shaneshanes posts, the expression "smoothing out" appears a couple of times.
The problem is that you have to define how smooth is "smooth".
Without specifying the ripple voltage, the amount of capacitance to use is anyones guess.