Editing Rectifier (section)

== {{anchor|Smoothing capacitor|Reservoir capacitor}}Rectifier output smoothing ==
{{see also|Ripple (electrical)#Ripple voltage}}
{{unreferenced section|date=October 2017}}
[[File:Half-wave rectifier waveform.png|thumb|right|The AC input (yellow) and DC output (green) of a half-wave rectifier with a smoothing capacitor. Note the ripple in the DC signal. The significant gap (about 0.7V) between the peak of the AC input and the peak of the DC output is due to the forward voltage drop of the rectifier diode.]] While half-wave and full-wave rectification deliver unidirectional current, neither produces a constant voltage. There is a large AC [[ripple (electrical)|ripple]] voltage component at the source frequency for a half-wave rectifier, and twice the source frequency for a full-wave rectifier.  Ripple voltage is usually specified peak-to-peak. Producing steady DC from a rectified AC supply requires a smoothing circuit or [[electronic filter|filter]]. In its simplest form this can be just a capacitor (functioning as both a smoothing capacitor as well as a reservoir,<ref name="Sinclair_1987">{{cite book |title=Electronics for Electricians and Engineers |chapter=Rectification |author-first=Ian Robertson |author-last=Sinclair |publisher=[[Industrial Press Inc.]] |date=1987 
|edition=illustrated |isbn=978-0-83111000-0 |page=151 |chapter-url=https://books.google.com/books?id=Epf47B0MKgwC&pg=PA151 |access-date=2022-06-23}}</ref><ref name="Smith_2013">{{cite book |title=Mechanical Engineer's Reference Book |chapter=2.3.17. Power supplies |author-first=Edward H. |author-last=Smith |edition=expanded 12th |publisher=[[Butterworth-Heinemann]] |date=2013 |isbn=978-1-48310257-3 |page=2/42 |url=https://books.google.com/books?id=2ck0AwAAQBAJ |access-date=2022-06-23}}</ref> buffer or bulk capacitor), choke, resistor, Zener diode and resistor, or voltage regulator placed at the output of the rectifier. In practice, most smoothing filters utilize multiple components to efficiently reduce ripple voltage to a level tolerable by the circuit.
[[File:RC filter.svg|thumb|400px|Full-wave diode-bridge rectifier with parallel RC shunt filter]]

The filter capacitor releases its stored energy during the part of the AC cycle when the AC source does not supply any power, that is, when the AC source changes its direction of flow of current.

===Performance with low impedance source===
[[Image:Reservoircapidealised.gif]]

The above diagram shows the voltage waveforms of the reservoir performance when supplied from a voltage source with near zero [[Electrical impedance|impedance]], such as a mains supply.  Both voltages start from zero at time t=0 at the far left of the image, then the capacitor [[voltage]] follows the rectified AC voltage as it increases, the capacitor is charged and [[Electric current|current]] is supplied to the load. At the end of the mains quarter cycle, the capacitor is charged to the peak value Vp of the rectifier voltage. Following this, the rectifier input voltage starts to decrease to its minimum value Vmin as it enters the next quarter cycle.  This initiates the discharge of the capacitor through the load while the capacitor holds up the output voltage to the load.

The size of the capacitor C is determined by the amount of ripple r that can be tolerated, where r=(Vp-Vmin)/Vp.<ref>{{cite journal|last1=Cartwright|first1=Kenneth|last2=Kaminsky|first2=Edit|title=New equations for capacitance vs ripple in power supplies|journal=Latin American Journal of Physics Education|date=2017|volume=11|issue=1|pages=1301–01 1301–11|url=http://www.lajpe.org/mar17/1301_Kenneth_2017.pdf}}</ref>

These circuits are very frequently fed from [[transformer]]s, which may have significant [[Electrical impedance|internal impedance]] in the form of [[Electrical resistance|resistance]] and/or [[Electrical reactance|reactance]]. Transformer internal impedance modifies the reservoir capacitor waveform, changes the peak voltage, and introduces regulation issues.

=== Capacitor input filter ===
{{Main|Capacitor-input filter}}
For a given load, sizing of a smoothing capacitor is a tradeoff between reducing ripple voltage and increasing ripple current. The peak current is set by the rate of rise of the supply voltage on the rising edge of the incoming sine-wave, reduced by the resistance of the transformer windings.  High ripple currents increase I<sup>2</sup>R losses (in the form of heat) in the capacitor, rectifier and transformer windings, and may exceed the ampacity of the components or VA rating of the transformer.  Vacuum tube rectifiers specify the maximum capacitance of the input capacitor, and SS diode rectifiers also have current limitations.  Capacitors for this application need low [[Equivalent series resistance|ESR]], or ripple current may overheat them.   To limit ripple voltage to a specified value the required capacitor size is proportional to the load current and inversely proportional to the supply frequency and the number of output peaks of the rectifier per input cycle. Full-wave rectified output requires a smaller capacitor because it is double the frequency of half-wave rectified output.  To reduce ripple to a satisfactory limit with just a single capacitor would often require a capacitor of impractical size. This is because the ripple current rating of a capacitor does not increase linearly with size and there may also be height limitations. For high current applications banks of capacitors are used instead.

=== Choke input filter ===
It is also possible to put the rectified waveform into a choke-input filter.  The advantage of this circuit is that the current waveform is smoother: current is drawn over the entire cycle, instead of being drawn in pulses at the peaks of AC voltage each half-cycle as in a capacitor input filter.  The disadvantage is that the voltage output is much lower – the average of an AC half-cycle rather than the peak; this is about 90% of the RMS voltage versus <math>\sqrt 2</math> times the RMS voltage (unloaded) for a capacitor input filter.  Offsetting this is superior voltage regulation and higher available current, which reduce peak voltage and ripple current demands on power supply components.  Inductors require [[Magnetic core|cores]] of iron or other magnetic materials, and add weight and size.  Their use in power supplies for electronic equipment has therefore dwindled in favour of semiconductor circuits such as voltage regulators.<ref>H. P. Westman et al., (ed), ''Reference Data for Radio Engineers Fifth Edition'', 1968, Howard W. Sams pp. 12-14, 12-15, 12-16</ref>

=== Resistor as input filter ===
In cases where ripple voltage is insignificant, like battery chargers, the input filter may be a single series resistor to adjust the output voltage to that required by the circuit.  A resistor reduces both output voltage and ripple voltage proportionately.  A disadvantage of a resistor input filter is that it consumes power in the form of waste heat that is not available to the load, so it is employed only in low current circuits.

=== Higher order and cascade filters ===
To further reduce ripple, the initial filter element may be followed by additional alternating series and shunt filter components, or by a voltage regulator.  Series filter components may be resistors or chokes; shunt elements may be resistors or capacitors.  The filter may raise DC voltage as
well as reduce ripple.  Filters are often constructed from pairs of series/shunt components called RC (series resistor, shunt capacitor) or LC (series choke, shunt capacitor) sections.  Two common filter geometries are known as Pi (capacitor, choke, capacitor) and T (choke, capacitor, choke) filters.
Sometimes the series elements are resistors - because resistors are smaller and cheaper - when a lower DC output is desirable or permissible.  Another
kind of special filter geometry is a [[series resonant choke]] or tuned choke filter.  Unlike the other filter geometries which are low-pass filters, a resonant choke filter is a band-stop filter: it is a parallel combination of choke and capacitor which resonates at the frequency of the ripple voltage, presenting a very high impedance to the ripple.  It may be followed by a shunt capacitor to complete the filter.

=== Voltage regulators ===
A more usual alternative to additional filter components, if the DC load requires very low ripple voltage, is to follow the input filter with a voltage regulator. A voltage regulator operates on a different principle than a filter, which is essentially a voltage divider that shunts voltage at the ripple frequency away from the load. Rather, a regulator increases or decreases current supplied to the load in order to maintain a constant output voltage.

A simple passive shunt voltage regulator may consist of a series resistor to drop source voltage to the required level and a [[Zener diode]] shunt with reverse
voltage equal to the set voltage. When input voltage rises, the diode dumps current to maintain the set output voltage.  This kind of regulator is usually employed only in low voltage, low current circuits because Zener diodes have both voltage and current limitations.  It is also very inefficient, because it dumps excess current, which is not available to the load.

A more efficient alternative to a shunt voltage regulator is an [[Voltage regulator#Active regulators|active voltage regulator]] circuit. An active regulator employs reactive components to store and discharge energy, so that most or all current supplied by the rectifier is passed to the load. It may also use negative and positive feedback in conjunction with at least one voltage amplifying component like a transistor to maintain output voltage when source voltage drops. The input filter must prevent the troughs of the ripple dropping below the minimum voltage required by the regulator to produce the required output voltage.  The regulator serves both to significantly reduce the ripple and to deal with variations in supply and load characteristics.