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Technical Engineering Dictionary
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Half-Wave Rectifier. A circuit that uses one cycle in an alternating current to produce direct current. A Half-Wave rectifier circuit only generates DC from either the positive or negative cycle of the AC input, but not both. Note that the Half-wave Rectifier circuit does not require a center tap transformer.
Other Rectifier circuits; Full-wave Rectifier [center tap transformer]. Types of Full-Wave Bridge Rectifier Circuits
Full-wave Bridge Rectifier Components [four diode].

The full wave diode rectifier produces dc voltage with only a small amount of ripple. A half-wave rectifier produces pulsating DC which requires a large amount of filtering to stabilize the output voltage [as seen in the output waveform]. In a half wave rectifier the dc voltage is only present for half the time, the output is zero voltage for the remainder of the time.

Half-Wave Rectifier Circuit

The half-wave rectifier circuit is not used that often in electrical circuitry. As the graphic shows the output is far from a steady state DC output and would require a large amount of filtering. However by using a full-wave circuit [link above] the output is DC with only a small amount of ripple voltage [after a small amount of filtering]. No industrial grade power supply or commercial grade power supply would use a half-wave rectifier circuit.
In fact a half-wave rectifier circuit will only be found [if used] in a low current linear power supply, switching power supplies use a completely different approach. Note that a full-wave rectifier circuit [2-diodes] will handle twice the amount of current because the current is split between the two diodes.

1-Diode Half Wave Rectifier Circuit

This schematic shows the same 1-diode rectifier using an LC Choke. The inductor of the filter attempts to keep the current constant while the capacitor attempts to keep the output voltage steady.

Neither of the circuits above show a surge resistor, however they are sometimes used. When the diode conducts there may be nothing in the circuit to limit the amount of current through the diode. In this case a surge resistor [Rs] is added in series with the diode to the limit the maximum amount of current. However ever the load resistance may be enough to protect the diode of over-current. In addition the output winding of the transformer will offer resistance to the current flow. In the case of the second circuit, the choke will offer is more resistance to the current flow, and in most cases will negate the requirement for any additional surge resistor.

In any case the applied voltage, the resistance in the circuit, the resulting current and the selected diode will determine if a surge resistor is required.

Normally the diode used would be a 1N4004 or similar type.
Diode Numbers [Part numbers by Function]

Definition of Diode Types
Listing of Manufacturers of diodes
Listing of Manufacturers of Transformers
Listing of Manufacturers of Power Supplies