I know that voltage regulation is give by
$$ V.R.= \frac{V_{nl} - V_{fl}}{V_{fl}} \cdot 100 $$
where \$V_{nl}\$ is the no load output voltage and \$V_{fl}\$ is the full load output voltage.
I can easily solve for a particular case but can I find out theoretically which one has a better voltage regulation?
Average output voltage for a 50Hz mains and half wave rectification is approximately:
\$\sqrt{2} V_{RMS} - V_F - \frac{20ms\cdot I_{OUT}}{2 C}\$ where VF(I) is the forward voltage of the rectifier, and C is the filter capacitor value
For full wave rectification it is :
\$\sqrt{2} V_{RMS} - 2V_F - \frac{10ms\cdot I_{OUT}}{2C}\$
So for a given filter capacitor, the output will change twice as much with current change. That ignores the rectifier forward voltage change with current. If the filter capacitor is doubled for the full wave (to maintain the same ripple voltage) then the full wave will have worse regulation because there are two diode drops in there and each increases with increasing current.
half-wave, full wave, 3phase rectifier on their own don't really indicate which provides the better voltage regulation.
Half wave only facilitates pulsed powerflow every half cycle. a full wave rectifier facilitates almost continuous, but pulsed powerflow. 3phase facilitates a significant continuous flow of power
The key is the DC side filter. For a large enough DClink capacitor ( C --> inf ) then all are comparable as they each would then present a stiff, well regulated voltage to the load.
The issue comes from an infinite capacitor is not an option and thus practicalities are a driver.
For a very "light load" a single diode, halfwave rectifier might be all that is required but for a high power a 3phase + L-C DClink filtering might be required.
