Editing Rectifier (section)

==== 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.