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    Power Supply 1

    Types of Power Supply

    There are many types of power supply. Most are designed to convert high voltage AC mainselectricity to a suitable low voltage supply for electronics circuits and other devices. A powersupply can by broken down into a series of blocks, each of which performs a particular function.

    For example a 5V regulated supply:

    Each of the blocks is described in more detail below:

    Transformer- steps down high voltage AC mains to low voltage AC. Rectifier- converts AC to DC, but the DC output is varying. Smoothing - smooths the DC from varying greatly to a small ripple. Regulator- eliminates ripple by setting DC output to a fixed voltage.

    Power supplies made from these blocks are described below with a circuit diagram and a graphof their output:

    Transformer only Transformer + Rectifier

    Transformer + Rectifier + Smoothing Transformer + Rectifier + Smoothing + Regulator

    Dual Supplies

    Some electronic circuits require a power supply with positive and negative outputs as well aszero volts (0V). This is called a 'dual supply' because it is like two ordinary supplies connectedtogether as shown in the diagram.

    Dual supplies have three outputs, for example

    a 9V supply has +9V, 0V and -9V outputs.

    Transformer only

    http://www.kpsec.freeuk.com/#transformerhttp://www.kpsec.freeuk.com/#rectifierhttp://www.kpsec.freeuk.com/#smoothinghttp://www.kpsec.freeuk.com/#regulatorhttp://www.kpsec.freeuk.com/#tonlyhttp://www.kpsec.freeuk.com/#trhttp://www.kpsec.freeuk.com/#trshttp://www.kpsec.freeuk.com/#trsrhttp://www.kpsec.freeuk.com/#transformerhttp://www.kpsec.freeuk.com/#rectifierhttp://www.kpsec.freeuk.com/#smoothinghttp://www.kpsec.freeuk.com/#regulatorhttp://www.kpsec.freeuk.com/#tonlyhttp://www.kpsec.freeuk.com/#trhttp://www.kpsec.freeuk.com/#trshttp://www.kpsec.freeuk.com/#trsr
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    Power Supply 2

    The low voltage AC output is suitable for lamps, heaters and special AC motors. It is notsuitable for electronic circuits unless they include a rectifier and a smoothing capacitor.

    Further information:Transformer

    Transformer + Rectifier

    The varying DC output is suitable for lamps, heaters and standard motors. It is not suitable forelectronic circuits unless they include a smoothing capacitor.

    Further information:Transformer| Rectifier

    Transformer + Rectifier + Smoothing

    The smooth DC output has a small ripple. It is suitable for most electronic circuits.

    http://www.kpsec.freeuk.com/#transformerhttp://www.kpsec.freeuk.com/#transformerhttp://www.kpsec.freeuk.com/#rectifierhttp://www.kpsec.freeuk.com/#transformerhttp://www.kpsec.freeuk.com/#transformerhttp://www.kpsec.freeuk.com/#rectifier
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    Power Supply 3

    Further information:Transformer| Rectifier| Smoothing

    Transformer + Rectifier + Smoothing + Regulator

    The regulated DC output is very smooth with no ripple. It is suitable for all electronic circuits.

    Further information:Transformer| Rectifier| Smoothing | Regulator

    Transformer

    http://www.kpsec.freeuk.com/#transformerhttp://www.kpsec.freeuk.com/#rectifierhttp://www.kpsec.freeuk.com/#smoothinghttp://www.kpsec.freeuk.com/#transformerhttp://www.kpsec.freeuk.com/#rectifierhttp://www.kpsec.freeuk.com/#smoothinghttp://www.kpsec.freeuk.com/#regulatorhttp://www.kpsec.freeuk.com/#transformerhttp://www.kpsec.freeuk.com/#rectifierhttp://www.kpsec.freeuk.com/#smoothinghttp://www.kpsec.freeuk.com/#transformerhttp://www.kpsec.freeuk.com/#rectifierhttp://www.kpsec.freeuk.com/#smoothinghttp://www.kpsec.freeuk.com/#regulator
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    Power Supply 4

    Transformers convert AC electricity from one voltage toanother with little loss of power. Transformers work only with

    AC and this is one of the reasons why mains electricity is AC.

    Step-up transformers increase voltage, step-downtransformers reduce voltage. Most power supplies use a step-

    down transformer to reduce the dangerously high mainsvoltage (230V in UK) to a safer low voltage.

    The input coil is called the primary and the output coil iscalled the secondary. There is no electrical connectionbetween the two coils, instead they are linked by analternating magnetic field created in the soft-iron core of thetransformer. The two lines in the middle of the circuit symbolrepresent the core.

    Transformers waste very little power so the power out is

    (almost) equal to the power in. Note that as voltage is steppeddown current is stepped up.

    The ratio of the number of turns on each coil, called the turnsratio, determines the ratio of the voltages. A step-downtransformer has a large number of turns on its primary (input)coil which is connected to the high voltage mains supply, and a small number of turns on itssecondary (output) coil to give a low output voltage.

    turns ratio =Vp

    =Np

    andpower out = power in

    Vs Ns Vs Is = Vp Ip

    Vp = primary (input) voltageNp = number of turns on primary coilIp = primary (input) current

    Vs = secondary (output) voltageNs = number of turns on secondary coilIs = secondary (output) current

    Rectifier

    There are several ways of connecting diodes to make a rectifier to convert AC to DC. The

    bridge rectifieris the most important and it produces full-wave varyingDC. A full-wave rectifier can also be made from just two diodes if acentre-tap transformer is used, but this method is rarely used now thatdiodes are cheaper. A single diode can be used as a rectifier but it onlyuses the positive (+) parts of the AC wave to produce half-wave varying DC.

    Bridge rectifier

    Transformercircuit symbol

    TransformerPhotograph Rapid Electronics

    There is more informationabout transformers on the

    Electronics in Meccanowebsite.

    There is more informationabout rectifiers on the

    Electronics in Meccanowebsite.

    http://www.kpsec.freeuk.com/#bridgerectifierhttp://www.kpsec.freeuk.com/#singlediodehttp://www.rapidonline.com/http://www.rapidonline.com/http://www.eleinmec.com/http://www.eleinmec.com/http://www.rapidonline.com/http://www.eleinmec.com/http://www.eleinmec.com/http://www.kpsec.freeuk.com/#bridgerectifierhttp://www.kpsec.freeuk.com/#singlediode
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    Power Supply 5

    A bridge rectifier can be made using four individual diodes, but it is also available in specialpackages containing the four diodes required. It is called a full-wave rectifier because it uses allthe AC wave (both positive and negative sections). 1.4V is used up in the bridge rectifierbecause each diode uses 0.7V when conducting and there are always two diodes conducting,as shown in the diagram below. Bridge rectifiers are rated by the maximum current they canpass and the maximum reverse voltage they can withstand (this must be at least three times the

    supply RMS voltage so the rectifier can withstand the peak voltages). Please see the Diodespage for more details, including pictures of bridge rectifiers.

    Bridge rectifierAlternate pairs of diodes conduct, changing over

    the connections so the alternating directions ofAC are converted to the one direction of DC.

    Output: full-wave varying DC(using all the AC wave)

    Single diode rectifier

    A single diode can be used as a rectifier but this produces half-wave varying DC which hasgaps when the AC is negative. It is hard to smooth this sufficiently well to supply electronic

    circuits unless they require a very small current so the smoothing capacitor does not significantlydischarge during the gaps. Please see the Diodes page for some examples of rectifier diodes.

    Single diode rectifierOutput: half-wave varying DC

    (using only half the AC wave)

    Smoothing

    Smoothing is performed by a large value electrolytic capacitorconnected across the DC supplyto act as a reservoir, supplying current to the output when the varying DC voltage from therectifier is falling. The diagram shows the unsmoothed varying DC (dotted line) and thesmoothed DC (solid line). The capacitor charges quickly near the peak of the varying DC, and

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    Power Supply 6

    then discharges as it supplies current to the output.

    Note that smoothing significantly increases the average DC voltage to almost the peak value(1.4 RMS value). For example 6V RMS AC is rectified to full wave DC of about 4.6V RMS(1.4V is lost in the bridge rectifier), with smoothing this increases to almost the peak value giving1.4 4.6 = 6.4V smooth DC.

    Smoothing is not perfect due to the capacitor voltage falling a little as it discharges, giving asmall ripple voltage. For many circuits a ripple which is 10% of the supply voltage is satisfactoryand the equation below gives the required value for the smoothing capacitor. A larger capacitor

    will give less ripple. The capacitor value must be doubled when smoothing half-wave DC.

    Smoothing capacitor for 10% ripple, C =5 Io

    Vs f

    C = smoothing capacitance in farads (F)Io = output current from the supply in amps (A)Vs = supply voltage in volts (V), this is the peak value of the unsmoothed DCf = frequency of the AC supply in hertz (Hz), 50Hz in the UK

    Regulator

    There is more informationabout smoothing on theElectronics in Meccano

    website.

    http://www.kpsec.freeuk.com/acdc.htm#rmshttp://www.eleinmec.com/http://www.kpsec.freeuk.com/acdc.htm#rmshttp://www.eleinmec.com/
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    Power Supply 7

    Voltage regulator ICs are available with fixed(typically 5, 12 and 15V) or variable outputvoltages. They are also rated by themaximum current they can pass. Negativevoltage regulators are available, mainly foruse in dual supplies. Most regulators include

    some automatic protection from excessivecurrent ('overload protection') andoverheating ('thermal protection').

    Many of the fixed voltage regulator ICs have 3 leads and look like power transistors, such as the7805 +5V 1A regulator shown on the right. They include a holefor attaching a heatsink if necessary.

    Please see the Electronics in Meccano website for moreinformation about voltage regulator ICs.

    Zener diode regulator

    For low current power supplies a simple voltage regulator can bemade with a resistor and a zener diode connected in reverse asshown in the diagram. Zener diodes are rated by theirbreakdown voltage Vz and maximum power Pz (typically400mW or 1.3W).

    The resistor limits the current (like an LED resistor). The current through the resistor is constant,so when there is no output current all the current flows through the zener diode and its power

    rating Pz must be large enough to withstand this.

    Please see the Diodes page for more information about zener diodes.

    Choosing a zener diode and resistor:

    1. The zener voltage Vz is the output voltage required2. The input voltage Vs must be a few volts greater than Vz

    (this is to allow for small fluctuations in Vs due to ripple)3. The maximum current Imax is the output current required plus 10%4. The zener power Pz is determined by the maximum current: Pz > Vz Imax

    5. The resistor resistance: R = (Vs - Vz) / Imax6. The resistor power rating: P > (Vs - Vz) Imax

    Example:output voltage required is 5V, output current required is 60mA.

    1. Vz = 4.7V (nearest value available)

    2. Vs = 8V (it must be a few volts greater than Vz)

    3. Imax = 66mA (output current plus 10%)

    4. Pz > 4.7V 66mA = 310mW, choose Pz = 400mW

    5. R = (8V - 4.7V) / 66mA = 0.05k = 50 , choose R = 47

    Voltage regulatorPhotograph Rapid Electronics

    zener diodea = anode, k = cathode

    There is more informationabout regulators on theElectronics in Meccano

    website.

    http://www.kpsec.freeuk.com/components/heatsink.htmhttp://www.eleinmec.com/http://www.kpsec.freeuk.com/components/diode.htm#zenerhttp://www.rapidonline.com/http://www.eleinmec.com/http://www.rapidonline.com/http://www.kpsec.freeuk.com/components/heatsink.htmhttp://www.eleinmec.com/http://www.kpsec.freeuk.com/components/diode.htm#zenerhttp://www.eleinmec.com/
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    Power Supply 8

    6. Resistor power rating P > (8V - 4.7V) 66mA = 218mW, choose P = 0.5W

    http://www.kpsec.freeuk.com/powersup.htm

    http://www.kpsec.freeuk.com/powersup.htmhttp://www.kpsec.freeuk.com/powersup.htm
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    Power Supply 9

    Elements of a Power Supply

    Introduction

    When dealing with electronic circuits, we have to meet the basic requirement of providingelectrical power for them to work. Without that power, your circuit is no more useful or

    meaningful than a single raindrop in a hurricane.

    The basic purpose of a power supply is to provide one or more fixed voltages to the working

    circuit, with sufficient current-handling capacity to maintain the operating conditions of the

    circuit. The power source doesn't have to be fancy; the typical hand-held transistor radio uses a9-volt battery as its power source. A flashlight uses cells that are physically much larger, but

    provide a lower voltage. Major electronic appliances such as television sets, VCRs, and

    microwave ovens have electronic circuits built in that take power from a wall socket and convert

    it to the form and voltages required by the other internal circuits of the appliance.

    Although each power supply has its own individual specifications and characteristics, all power

    supplies have certain characteristics in common. We'll look at the main parts of a power supply

    on this page and see how they work together. Then, on subsequent pages, we'll take a more

    detailed look at each of the parts we haven't seen before, and explore the major variations thatare commonly used in modern power supplies.

    The Main Sections

    A basic power supply consists of three main sections, as shown in the block diagram below and

    to the right. Depending on the requirements for a given power supply, the sectionscan be very simple or extremely complex, or even left out altogether in certain

    circumstances. Each of the sections serves one or more specific purposes, as

    follows:

    Transformer. In general, the ac line voltage present in your

    house wiring is not suitable for electronic circuits. Most circuits

    require a considerably lower voltage, while a few require highervoltages. The transformer serves to convert the ac line voltage to a

    voltage level more appropriate to the needs of the circuit to be

    powered. At the same time, the transformer provides electrical isolation between the

    ac line and the circuit being powered, which is an important safety consideration.However, a line transformer is generally large and heavy, and is rather expensive.

    Therefore, some power supplies (notably for PCs) are deliberately designed to operate

    directly from the ac line without a line transformer. The output of the transformer isstill an ac voltage, but now of an appropriate magnitude for the circuit to be powered.

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    Power Supply 10

    Rectifier. The next step is to force current to flow in one direction only,

    preventing the alternations that occur in the transformer and the ac line. This processis known as rectification, and the circuit that accomplishes the task is the rectifier.

    There are many different rectifier configurations that may be used according to the

    requirements of the circuit. The output of the rectifier is a pulsating dc, which still hassome of the variations from the ac line and transformer.

    Filter. The pulsating dc from the rectifier is generally still not suitable to powerthe actual load circuit. The pulsations typically vary from 0 volts to the peak outputvoltage of the transformer. Therefore, we insert a circuit to store energy during each

    voltage peak, and then release it to the load when the rectifier output voltage drops.

    This circuit is called afilter, and its job is to reduce the pulses from the rectifier to a

    much smaller ripple voltage. No filter configuration can be absolutely perfect, but aproperly designed filter will provide a dc output voltage with only a small ac ripple.

    Each of the three sections identified above can have a number of variations even the

    transformer, which we covered in an earlier page on transformers. Regardless of thesevariations, each section performs its specific task. However, some circuits do the job more

    effectively than others, or pick different trade-offs between possible alternatives. To measure theeffectiveness of each circuit, we compare the magnitude of the remaining ac component, or

    ripple, with the dc component of the total voltage appearing at the output of that section. Theratio of ac voltage to dc voltage is known as the ripple factor. The goal of any power supply

    design is to reduce the ripple factor as much as possible, or at least to the point where the load

    circuit will not be adversely affected by the remaining ac ripple voltage.

    In the remaining pages in this group, we will examine typical circuits and variations used forrectifiers and filters, and compare their performance.

    Basic Rectifier Circuits

    Overview

    As we have noted when looking at theElements of a Power Supply, the purpose of the rectifier

    section is to convert the incoming ac from a transformer or other ac power source to some form

    of pulsating dc. That is, it takes current that flows alternately in both directions as shown in thefirst figure to the right, and modifies it so that the output current flows only in one direction, as

    shown in the second and third figures below.

    http://www.play-hookey.com/ac_theory/ac_transformers.htmlhttp://www.play-hookey.com/ac_theory/ps_elements.htmlhttp://www.play-hookey.com/ac_theory/ps_elements.htmlhttp://www.play-hookey.com/ac_theory/ps_elements.htmlhttp://www.play-hookey.com/ac_theory/ac_transformers.htmlhttp://www.play-hookey.com/ac_theory/ps_elements.html
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    Power Supply 11

    The circuit required to do this may be nothing more than a single diode, or it may be

    considerably more complex. However, all rectifier circuits may be classified into one of twocategories, as follows:

    Half-Wave Rectifiers. An easy way to convert ac to pulsating dc is to simplyallow half of the ac cycle to pass, while blocking current to prevent it from flowing

    during the other half cycle. The figure to the right shows the resulting output. Such

    circuits are known as half-wave rectifiers because they only work on half of theincoming ac wave.

    Full-Wave Rectifiers. The more common approach is to manipulate theincoming ac wave so that both halves are used to cause output current to flow in the

    same direction. The resulting waveform is shown to the right. Because these circuits

    operate on the entire incoming ac wave, they are known asfull-wave rectifiers.

    Rectifier circuits may also be further clasified according to their configuration, as we will see

    below.

    The Half-Wave Rectifier

    The simplest rectifier circuit is nothing more than a diode connected in series with the ac input,

    as shown to the right. Since a diode passes current in only one direction, only half of the

    incoming ac wave will reach the rectifier output. Thus, this is a basic half-wave rectifier.

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    Power Supply 12

    The orientation of the diode matters; as shown, it passes only the positive half-cycle of the ac

    input, so the output voltage contains a positive dc component. If the diode were to be reversed,the negative half-cycle would be passed instead, and the dc component of the output would have

    a negative polarity. In either case, the DC component of the output waveform is vp/ = 0.3183vp,

    where vp is the peak voltage output from the transformer secondary winding.

    It is also quite possible to use two half-wave rectifiers together, as shown in the second figure tothe right. This arrangement provides both positive and negative output voltages, with each

    output utilizing half of the incoming ac cycle.

    Note that in all cases, the lower transformer connection also serves as the common reference

    point for the output. It is typically connected to the common ground of the overall circuit. Thiscan be very important in some applications. The transformer windings are of course electrically

    insulated from the iron core, and that core is normally grounded by the fact that it is bolted

    physically to the metal chassis (box) that supports the entire circuit. By also grounding one end

    of the secondary winding, we help ensure that this winding will never experience evenmomentary voltages that might overload the insulation and damage the transformer.

    The Full-Wave Rectifier

    While the half-wave rectifier is very simple and does work, it isn't very efficient. It only useshalf of the incoming ac cycle, and wastes all of the energy available in the other half. For greater

    efficiency, we would like to be able to utilize both halves of the incoming ac. One way to

    accomplish this is to double the size of the secondary winding and provide a connection to itscenter. Then we can use two separate half-wave rectifiers on alternate half-cycles, to provide

    full-wave rectification. The circuit is shown to the right.

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    Power Supply 13

    Because both half-cycles are being used, the DC component of the output waveform is now

    2vp/ = 0.6366vp, where vp is the peak voltage output from halfthe transformer secondarywinding, because only half is being used at a time.

    This rectifier configuration, like the half-wave rectifier, calls for one of the transformer's

    secondary leads to be grounded. In this case, however, it is the center connection, generally

    known as the center tap on the secondary winding.

    The full-wave rectifier can still be configured for a negative output voltage, rather than positive.

    In addition, as shown to the right, it is quite possible to use two full-wave rectifiers to get

    outputs of both polarities at the same time.

    The full-wave rectifier passes both halves of the ac cycle to either a positive or negative output.This makes more energy available to the output, without large intervals when no energy is

    provided at all. Therefore, the full-wave rectifier is more efficient than the half-wave rectifier.

    At the same time, however, a full-wave rectifier providing only a single output polarity doesrequire a secondary winding that is twice as big as the half-wave rectifier's secondary, becauseonly half of the secondary winding is providing power on any one half-cycle of the incoming ac.

    Actually, it isn't all that bad, because the use of both half-cycles means that the current drain on

    the transformer winding need not be as heavy. With power being provided on both half-cycles,one half-cycle doesn't have to provide enough power to carry the load past an unused half-cycle.

    Nevertheless, there are some occasions when we would like to be able to use the entire

    transformer winding at all times, and still get full-wave rectification with a single output

    polarity.

    The Full-Wave Bridge Rectifier

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    Power Supply 14

    The four-diode rectifier circuit shown to the right serves very nicely to provide full-waverectification of the ac output of a single transformer winding. The diamond configuration of the

    four diodes is the same as the resistor configuration in a Wheatstone Bridge. In fact, any set of

    components in this configuration is identified as some sort of bridge, and this rectifier circuit issimilarly known as a bridge rectifier.

    If you compare this circuit with the dual-polarity full-wave rectifier above, you'll find that the

    connections to the diodes are the same. The only change is that we have removed the center tap

    on the secondary winding, and used the negative output as our ground reference instead. Thismeans that the transformer secondary is never directly grounded, but one end or the other will

    always be close to ground, through a forward-biased diode. This is not usually a problem in

    modern circuits.

    To understand how the bridge rectifier can pass current to a load in only one direction, consider

    the figure to the right. Here we have placed a simple resistor as the load, and we have numbered

    the four diodes so we can identify them individually.

    During the positive half-cycle, shown in red, the top end of the transformer winding is positivewith respect to the bottom half. Therefore, the transformer pushes electrons from its bottom end,

    through D3 which is forward biased, and through the load resistor in the direction shown by the

    red arrows. Electrons then continue through the forward-biased D2, and from there to the top of

    the transformer winding. This forms a complete circuit, so current can indeed flow. At the sametime, D1 and D4 are reverse biased, so they do not conduct any current.

    During the negative half-cycle, the top end of the transformer winding is negative. Now, D1 and

    D4 are forward biased, and D2 and D3 are reverse biased. Therefore, electrons move throughD1, the resistor, and D4 in the direction shown by the blue arrows. As with the positive half-

    cycle, electrons move through the resistor from left to right.

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    Power Supply 15

    In this manner, the diodes keep switching the transformer connections to the resistor so that

    current always flows in only one direction through the resistor. We can replace the resistor withany other circuit, including more power supply circuitry (such as the filter), and still see the

    same behavior from the bridge rectifier.

    Filters

    Overview

    As we have already seen, the rectifier circuitry takes the initial ac sine wave from thetransformer or other source and converts it to pulsating dc. A full-wave rectifier will produce the

    waveform shown to the right, while a half-wave rectifier will pass only every other half-cycle to

    its output. This may be good enough for a basic battery charger, although some types of

    rechargeable batteries still won't like it. In any case, it is nowhere near good enough for mostelectronic circuitry. We need a way to smooth out the pulsations and provide a much "cleaner"

    dc power source for the load circuit.

    To accomplish this, we need to use a circuit called a filter. In general terms, afilteris any circuit

    that will remove some parts of a signal or power source, while allowing other parts to continueon without significant hinderance. In a power supply, the filter must remove or drastically

    reduce the ac variations while still making the desired dc available to the load circuitry.

    Filter circuits aren't generally very complex, but there are several variations. Any given filtermay involve capacitors, inductors, and/or resistors in some combination. Each such combination

    has both advantages and disadvantages, and its own range of practical application. We will

    examine a number of common filter circuits on this page.

    A Single Capacitor

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    Power Supply 16

    If we place a capacitor at the output of the full-wave rectifier as shown to the left, the capacitor

    will charge to the peak voltage each half-cycle, and then will discharge more slowly through the

    load while the rectified voltage drops back to zero before beginning the next half-cycle. Thus,the capacitor helps to fill in the gaps between the peaks, as shown in red in the first figure to the

    right.

    Although we have used straight lines for simplicity, the decay is actually the normal exponential

    decay of any capacitor discharging through a load resistor. The extent to which the capacitorvoltage drops depends on the capacitance of the capacitor and the amount of current drawn by

    the load; these two factors effectively form the RC time constant for voltage decay.

    As a result, the actual voltage output from this combination never drops to zero, but rather takesthe shape shown in the second figure to the right. The blue portion of the waveform corresponds

    to the portion of the input cycle where the rectifier provides current to the load, while the red

    portion shows when the capacitor provides current to the load. As you can see, the outputvoltage, while not pure dc, has much less variation (orripple, as it is called) than the unfiltered

    output of the rectifier.

    A half-wave rectifier with a capacitor filter will only recharge the capacitor on every other peak

    shown here, so the capacitor will discharge considerably more between input pulses.Nevertheless, if the output voltage from the filter can be kept high enough at all times, the

    capacitor filter is sufficient for many kinds of loads, when followed by a suitable regulator

    circuit.

    RC Filters

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    Power Supply 17

    In order to reduce the ripple still more without losing too much of the dc output, we need toextend the filter circuit a bit. The circuit to the right shows one way to do this. This circuit does

    cause some dc loss in the resistor, but if the required load current is low, this is an acceptable

    loss.

    To see how this circuit reduces ripple voltage more than it reduces the dc output voltage,consider a load circuit that draws 10 mA at 20 volts dc. We'll use 100 f capacitors and a 100

    resistor in the filter.

    For dc, the capacitors are effectively open circuits. Therefore any dc losses will be in that 100

    resistor. for a load current of 10 mA (0.01 A), the resistor will drop 100 0.01 = 1 volt.Therefore, the dc output from the rectifier must be 21 volts, and the dc loss in the filter resistor

    amounts to 1/21, or about 4.76% of the rectifier output. This is generally quite acceptable.

    On the other hand, the ripple voltage (in the USA) exists mostly at a frequency of 120 Hz (there

    are higher-frequency components, but they will be attenuated even more than the 120 Hzcomponent). At this frequency, each capacitor has a reactance of about 13.26 . Thus R and C2

    form a voltage divider that reduces the ripple to about 13% of what came from the rectifier.

    Therefore, for a dc loss of less than 5%, we have attenuated the ripple by almost 87%. This is asubstantial amount of ripple reduction, although it doesn't remove the ripple entirely.

    If the amount of ripple is still too much for the particular load circuit, additional filtering or a

    regulator circuit will be required.

    LC Filters

    While the RC filter shown above helps to reduce the ripple voltage, it introduces excessive

    resistive losses when the load current is significant. To reduce the ripple even more without a lot

    of dc resistance, we can replace the resistor with an inductor as shown in the circuit diagram tothe right.

    In this circuit, the two capacitors store energy as before, and attempt to maintain a constant

    output voltage between input peaks from the rectifier. At the same time, the inductor stores

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    energy in its magnetic field, and releases energy as needed in its attempt to maintain a constant

    current through itself. This provides yet another factor that attempts to smooth out the ripplevoltage.

    In some cases, C1 is omitted from this filter circuit. The result is a lower dc output voltage, but

    improved ripple removal. The choice is a trade-off, and must be made according to the specific

    requirements in each individual case.

    For dc, the inductance has only the resistance of the wire that comprises the coil, which amounts

    to a few ohms. Meanwhile, the capacitors still operate as open circuits at dc, so they do not

    reduce the dc output voltage. However, at the basic ripple frequency of 120 Hz, a 10 Henryinductance has a reactance of:

    XL = 2 fL = 7540

    At the same time, a 100 f capacitor at the same ripple frequency has a reactance of:

    XC = 1/2 fC = 13.26

    Thus, L and C2 form a voltage divider that drastically reduces the ripple component (to less than

    0.2%) while leaving the desired dc output nearly alone. This configuration may providesufficiently pure dc for some applications, without the need for any following regulator at all.

    The drawback of this approach is that a 10 Henry inductor is as large as some power

    transformers, with a heavy iron core. It takes up a lot of space and is relatively expensive. This

    is why the RC filter circuit may be preferred to the LC filter, provided the ripple reduction issufficient and the power loss in the resistor is not excessive.

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