Editing Rectifier (section)

=== Single-phase rectifiers ===

==== Half-wave rectification ====
{{anchor|Half-wave rectification}}
In half-wave rectification of a single-phase supply, either the positive or negative half of the AC wave is passed, while the other half is blocked. 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 electric power|single-phase supply]], or three in a [[Three-phase electric power|three-phase supply]]. Rectifiers yield a unidirectional but pulsating direct current; half-wave rectifiers produce far more [[Ripple (electrical)|ripple]] than full-wave rectifiers, and much more filtering is needed to eliminate [[Harmonics (electrical power)|harmonics]] of the AC frequency from the output.

[[File:Halfwave.rectifier.en.svg|600px|thumb|left|Half-wave rectifier, 'U' denotes voltage, 'D' denotes a diode, and 'R' a resistance]]
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The no-load output DC voltage of an ideal half-wave rectifier for a sinusoidal input voltage is:<ref name=Lander93>{{cite book|last=Lander|first=Cyril W.|title=Power electronics|year=1993|publisher=McGraw-Hill|location=London|isbn=978-0-07-707714-3|edition=3rd|chapter=2. Rectifying Circuits}}</ref>

<!-- This is half-wave, not full-wave.  PLEASE DO NOT CHANGE TO SQUARE-ROOT 2.  You will be completely wrong and will be reverted. 
-->: <math>\begin{align}
V_\mathrm {rms} &= \frac{V_\mathrm {peak}}{2}\\[8pt]
V_\mathrm {dc} &= \frac{V_\mathrm {peak}}{\pi}
\end{align}</math><!-- 
This is half-wave, not full-wave.  PLEASE DO NOT CHANGE TO SQUARE-ROOT 2.  You will be completely wrong and will be reverted. -->

where:
: ''V''<sub>dc</sub>, ''V''<sub>av</sub> – the DC or average output voltage,
: ''V''<sub>peak</sub>, the peak value of the phase input voltages,
: ''V''<sub>rms</sub>, the [[root mean square]] (RMS) value of output voltage.

==== Full-wave rectification ====
{{anchor|Full-wave rectification}}
[[File:VacRect2E.png|thumb|200px|Full-wave rectifier, with vacuum tube having two anodes.]]
A full-wave 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-tapped [[transformer]], or four diodes in a [[Diode bridge|bridge configuration]] and any AC source (including a transformer without center tap), are needed.<ref>{{cite book|last=Williams|first=B. W.|title=Power electronics : devices, drivers and applications|year=1992|publisher=Macmillan|location=Basingstoke|isbn=978-0-333-57351-8|edition=2nd|chapter=Chapter 11}}</ref> Single semiconductor diodes, double diodes with a common cathode or common anode, and four- or six-[[diode bridge]]s are manufactured as single components.

[[File:Gratz.rectifier.en.svg|thumb|left|600px|Bridge rectifier: a full-wave rectifier using four diodes.]]
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For single-phase AC, if the transformer is center-tapped, then two diodes back-to-back (cathode-to-cathode or anode-to-anode, depending on 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.

[[File:Fullwave.rectifier.en.svg|thumb|left|600px|Full-wave rectifier using a [[center tap]] transformer and 2 diodes.]]
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The [[Arithmetic mean|average]] and RMS no-load output voltages of an ideal single-phase full-wave rectifier are:

: <math>\begin{align}
V_\mathrm{dc}=V_\mathrm {av}&=\frac{2 \cdot V_\mathrm{peak}}{\pi}\\[8pt]
V_\mathrm {rms}&=\frac {V_\mathrm{peak}}{\sqrt 2}
\end{align}</math>

Very common double-diode rectifier [[vacuum tube]]s contained a single common [[cathode]] and two [[anode]]s inside a single envelope, achieving full-wave rectification with positive output. The 5U4 and the 80/5Y3 (4 pin)/(octal) were popular examples of this configuration.