Rectifier circuits may be single-phase or multi-phase (three being the most common number of phases). Most low power rectifiers for domestic equipment are single-phase, but three-phase rectification is very important for industrial applications and for the transmission of energy as DC (HVDC).
In half-wave rectification of a single-phase supply, also called uncontrolled one-pulse midpoint circuit, either the positive or negative half of the AC wave is passed, while the other half is blocked. Mathematically, it is a ramp function (for positive pass, negative block): passing positive corresponds to the ramp function being the identity on positive inputs, blocking negative corresponds to being zero on negative inputs. Because only one half of the input waveform reaches the output, mean voltage is lower. Half-wave rectification requires a single diode in a single-phase supply, or three in a three-phase supply. Rectifiers yield a unidirectional but pulsating direct current; half-wave rectifiers produce far more ripple than full-wave rectifiers, and much more filtering is needed to eliminate harmonics of the AC frequency from the output.
The no-load output DC voltage of an ideal half-wave rectifier for a sinusoidal input voltage is:
Vdc, Vav – the DC or average output voltage,
Vpeak, the peak value of the phase input voltages,
Vrms, the root mean square (RMS) value of output voltage.
Full-wave rectifier, with vacuum tube having two anodes.
A full-wave bridge rectifier converts the whole of the input waveform to one of constant polarity (positive or negative) at its output. Mathematically, this corresponds to the absolute value function. Full-wave rectification converts both polarities of the input waveform to pulsating DC (direct current), and yields a higher average output voltage. Two diodes and a center tappedtransformer, or four diodes in a bridge configuration and any AC source (including a transformer without center tap), are needed. Single semiconductor diodes, double diodes with common cathode or common anode, and four-diode bridges, are manufactured as single components.
Graetz bridge rectifier: a full-wave rectifier using four diodes.
For single-phase AC, if the transformer is center-tapped, then two diodes back-to-back (cathode-to-cathode or anode-to-anode, depending upon output polarity required) can form a full-wave rectifier. Twice as many turns are required on the transformer secondary to obtain the same output voltage than for a bridge rectifier, but the power rating is unchanged.
Full-wave rectifier using a center tap transformer and 2 diodes.
The average and RMS no-load output voltages of an ideal single-phase full-wave rectifier are:
Very common double-diode rectifier vacuum tubes contained a single common cathode and two anodes inside a single envelope, achieving full-wave rectification with positive output. The 5U4 and 5Y3 were popular examples of this configuration.