Half Wave Rectifier | full wave bridge Rectifier | Center tapped full wave

What is a Half Wave Rectifier?

what is half wave rectifier

A half-wave rectifier can be explained as a type of rectifier that only passes one half-cycle of an AC voltage waveform to pass, blocking the remaining half-cycle. Half-wave rectifiers are normally used to convert AC power to DC power, and only require one diode to construct.

A simple Half Wave Rectifier is nothing more than a single PN junction diode which is connected in series to the load resistor. As you know a diode is to electric current like a one-way valve is to water, it passes electric current to flow in the only uni-direction. This property of the diode is very useful in developing simple rectifiers which are normally used to convert AC power to DC power.

Here the alternating current is applied as input. Input voltage is provided to a step-down transformer and the resulting reduced voltage of the transformer is supply to the diode ‘D’ and load resistor RL. The output voltage is measured across the load resistor RL.

As part of our “Basic Electronics Tutorial” series, we have seen that rectification is the most important application of a PN junction diode. The process of rectification is transferring alternating current (AC) to direct current (DC).

Half wave rectifier definition

A half-wave rectifier is a simple type of rectifier which transfers the positive half cycle (positive current) of the input signal into pulsating DC (Direct Current) output signal.

or

A half-wave rectifier is a type of rectifier that passes only half cycle (either positive half cycle or negative half cycle) of the input AC signal while the other half cycle is blocked.

For example, if the positive half cycle of the power is allowed then the negative half cycle will be blocked. Similarly, if the negative half cycle is passed then the positive half cycle will be blocked. However, a half-wave rectifier can not pass both positive and negative half-cycles at the same time.

Therefore, the half-cycle (either positive or negative) of the input power supply is wasted.

Half Wave Rectifier Theory

A rectifier is the simplest and basic form of the rectifier available. We will observe at a complete half-wave rectifier circuit later – but let’s first understand exactly what this type of rectifier is doing.

When a standard AC waveform is passed through a half-wave rectifier, only half of the AC waveform remains. Half-wave rectifiers only allow one half-cycle (positive or negative half-cycle) of the AC voltage through and will block the other half-cycle on the DC side, as seen below.

Only one diode is required to construct a half-wave rectifier. In essence, this is all that the half-wave rectifier is doing.

Since DC systems are designed to have current flowing in a single direction (and constant voltage – which we’ll describe later), putting an AC waveform with positive and negative cycles through a DC device can have destructive (and dangerous) consequences. So we use half-wave rectifiers to convert the AC input power into DC output power.

But the diode is only part of it – a complete half-wave rectifier circuit consists of main parts:

Components requirements

When designing a half-wave rectifier circuit, it is necessary to ensure that the diode is capable of providing the required performance. While there are very many parameters that define individual diodes, and these may need to be taken into account for a given design, some of the major parameters are detailed below:

AC source

The AC source supplies Alternating Current to the circuit. The alternating current is often represented by a sinusoidal waveform.

Transformer

A transformer is a device that reduces or increases the AC voltage. The step-down transformer reduces the AC voltage from high to low whereas the step-up transformer increases the AC voltage from low to high. In the half-wave rectifier, we generally use a step-down transformer because the voltage needed for the diode is very small. Applying a large AC voltage without using the transformer will permanently destroy the diode. So we use a step-down transformer in a half-wave rectifier. However, in some cases, we use a step-up transformer.

In the step-down transformer, the primary winding has more turns than the secondary winding. So the step-down transformer reduces the voltage from the primary winding to secondary winding.

Diode

A diode is a two-terminal device that allows electric current in one direction and blocks electric current in another direction.

Resistor

A resistor is an electronic component that restricts the current flow to a certain level.

•             Forward current:   It is necessary that the diode is able to handle the levels of average current and peak current flowing through it in a half-wave rectifier circuit. The current will peak as a result of the capacitor smoothing circuit. As the current only flows as the capacitor charge up, the current is in short bursts which are much higher than the average current.

•             Peak inverse voltage:   The diode must be able to reliably withstand the peak reverse or inverse voltages that appear across it. The peak voltages are not just the output voltage, but higher. The peak inverse voltage rating of the diode should be at least 2 x √2 times the RMS voltage of the input. This is because the output is normally smoothed by a capacitor, and this will take a value that is the peak of the input waveform. This will be √2 times the RMS voltage. With this voltage on the output, the input waveform on the “blocked” half of the cycle will fall and reach a peak value at the bottom of the crest of √2 times the RMS value. The maximum reverse value seen across the rectifier diode is the sum of these two voltages.

There should also be a significant margin, especially when used in a mains or line power supply. This is because voltage spikes can appear on the line.

•             Diode turn on voltage:   All diodes have a forward voltage drop needed to turn the diode on. This can be necessary for some applications. Typically a silicon diode requires is 0.7V and a germanium diode needed is 0.3V. A silicon Schottky diode is nearly about 0.2 to 0.3V. Reducing the forward voltage drop decreases power loss and in a few applications like signal detection, it makes the diode rectifier more sensitive.

•             Forward voltage drop:   Apart from the forward turn-on voltage, diodes also have a different level of resistance. As the current increase, so does the level of voltage reduces. Power diodes normally have a larger area for current conduction and therefore their voltage drop will be less at high current levels.

•             Diode capacitance:   When the diode is used in a half-wave rectifier as a signal detector, the capacitance may be a problem because the frequencies are present. Typically Schottky diodes have a very tiny junction capacitance.

Circuit precautions

When developing a half-wave rectifier circuit, it is a must to make sure there is a DC power return in the circuit. Often when using the diode rectifier for signal or peak detection it is easy to omit a DC power return. This must to be included either as a resistor or as part of a transformer or choke.

The rectifier circuit can be used to good effect. As a power rectifier, it only detects half of the waveform making smoothing an is a later problem. As a result, a full-wave system is usually used for power rectification. The half-wave rectifier is sometimes used for signal and peak detection.

Half  Wave Rectifier Operation

operation of half wave rectifer

Simply place a half-wave rectifier clips the negative half cycle of an AC input and passes only the positive cycles to creating a DC flow.

To understand the working of a half-wave rectifier exactly, you must know the theory section really well. If you are new to the concepts of a PN junction and its characteristics, I suggest you read the half-wave rectifier theory first.

The working of a half-wave rectifier is pretty easy. From the theory part, you should know that a PN junction diode conducts current only in one or single direction. In other words, a PN junction diode conducts current only when it is forward biased. The same phenomenon is made use of in a half-wave rectifier to transfer AC power to DC power. The input we supply here is alternating current. This input voltage is stepped down by a transformer. The reduced voltage is provided to the diode ‘D’ and load resistance RL. During the positive half cycles of the input wave signal, the diode ‘D’ will be forward biased and during the negative half cycles of the input wave signal, the diode ‘D’ will be reverse biased. We achieve the output across the load resistor RL. Since the diode flows current only during the one-half cycle of the input wave, we get an output as shown in the diagram. The output is positive and significant during the positive half cycles of the input supply. At the same time output is 0 or insignificant during negative half cycles of the input wave. This is known as half-wave rectification.

Explaining Half Wave Rectification in academic words!

When a one rectifier diode unit is placed in series with the load across an ac power supply, it converts the alternating voltage into a uni-directional pulsating voltage, using a one-half cycle of the applied voltage, the other half cycle being clipped due to it conducts only in a uni-direction. Unless there is an inductance or battery present in the circuit, the current will be 0, therefore, for half the time. This is known as half-wave rectification. As already told, a diode is an electronic component consisting of two elements known as cathode plate and anode plate. Since a diode current can pass in one direction only i.e. from the cathode to anode, the diode provides the unilateral conduction necessary for rectification. This is fact for diodes of all types-vacuum, gas-filled, crystal or semiconductor, metallic (copper oxide and selenium types) diodes. Semiconductor diodes, because of their inherent advantages are normally used as a rectifying device. However, for very huge voltages, vacuum diodes may be employed.

Working of a Half wave rectifier

The half-wave rectifier circuit using a semiconductor diode (D) with a load RL but no smoothing filter is provided in the figure. The diode is connected in series with the secondary side of the transformer and the load RL. The primary of the transformer is being connected to the ac main power supply.

WORKING of halfwave rectifer

The ac voltage across the secondary winding continuously changes its polarities after every half cycle of the input wave. During the positive half-cycles of the input ac voltage i.e. when the upper-end side of the secondary winding is positive w.r.t. its lower end side, the diode is forward biased and therefore conducts current at the time. If the forward resistance of the diode is assumed to be 0 (in practice, however, a small resistance exists) the input voltage during the positive half-cycles is directly supplied to the load resistance RL, making its upper-end side positive w.r.t. its lower end side. The waveforms of the output current and output voltage are of the exact same shape as that of the input ac voltage and current.

During the negative half cycles of the input ac voltage i.e. when the lower end side of the secondary winding is positive w.r.t. its upper-end side, the diode is now on reverse-biased mode and so does not conduct current. Thus during the negative half cycles of the input ac voltage, the current and the voltage across the load remains 0. The reverse current is very little in magnitude, is neglected. Thus for the negative half-cycles, no power is provided to the load.

Thus the output voltage (VL) shows across the load resistance RL  is a series of positive half cycles of alternating voltage, with intervening very little constant negative voltage levels, It is obvious from the figure that the output is not a steady dc, but only a pulsating dc wave power. To make the output wave smooth and useful in a DC power source, we must have to use a filter across the load. Since only half-cycles of the input wave are used, it is known as a half-wave rectifier. 

Half Wave Rectifier Theory

Rectification is an application of the simple PN junction diode. A half-wave rectifier is a circuite that makes use of important properties of a PN junction diode. So to understand the underlying theory behind a half-wave rectifier, you need to clearly understand the PN junction and the characteristics and properties of the PN junction diode.

Power Supply Specifications of a rectifier

The most important parameters which are needed to be specified for a power supply are the needed output dc voltage, the average current and peak currents in the diode, the peak inverse voltage (PIV) of the diode, the regulation, and the ripple factor.

A half-wave rectifier is sometimes used in practice. It is never preferred as the power supply of an audio circuit due to of the very huge ripple factor. huge ripple factor will develop noises in the input audio signal, which in turn will affect audio quality.

The advantage of a half-wave rectifier is only that it’s very cheap, simple, and easy to develop. It is cheap because of the few components involved. Simple because of the straightforwardness in circuit design. Apart from this, a half-wave rectifier has a huge number of disadvantages than advantages!

Disadvantages of Half wave rectifier

1. The output current in the load contains, in addition to the dc component, ac components of basic frequency equal to that of the input supplied voltage frequency. Ripple factor is huge and elaborate filtering is, therefore, required to give steady dc output.

2. The output power and, therefore, rectification efficiency is very low. This is because the fact that power is supplied only during the one-half cycle of the input alternating voltage source.

3. The transformer utilization factor is low.

4. DC saturation of the transformer core resulting in magnetizing current and hysteresis losses and developing of harmonics.

The  DC output provided from a half-wave rectifier is not satisfactory to make a  general power supply. However, it may be used for a few applications such as battery charging.

Half Wave Rectifier with Capacitor Filter 

The output of the half-wave rectifier is not a fixed or constant DC voltage. You can see from the output diagram that it’s a pulsating dc voltage including ac ripples. In real-life applications, we required a power supply with smooth waveforms. In other words, we want a DC power supply with a constant or fixed output voltage. A constant output voltage which comes from the DC power supply is very important as it directly impacts the reliability of the electronic device we connect to the power supply.

We can make the output of a half-wave rectifier smooth by utilizing a filter (a capacitor filter or an inductor filter) across the diode.  In some cases, a resistor-capacitor coupled filter (RC) is mostly used. The circuit diagram below shows a half-wave rectifier with a capacitor filter.

Half-wave Rectifier Characteristics

The parameters of a half-wave rectifier for the following parameters

PIV (Peak Inverse Voltage)

During the reverse biased mode, the diode must withstand because of its maximum voltage. During the negative half-cycle, zero current passe through the load. So, an all voltage appears across the diode due to there is a no-voltage drop by the load resistance.

PIV of a half-wave rectifier = VSMAX

Average current and Peak Currents in the Diode

Assuming, the voltage across the secondary side of the transformer will be sinusoidal and its peak value is VSMAX. The instantaneous voltage which is provided to the half-wave rectifier is

Vs = VSMAXSin wt

The current passes through the load resistance is

IMAX = VSMAX / (RF+RL)

Regulation of Half wave rectifier

Regulation is the difference between no-load voltage to full-load voltage with respect to the full-load voltage, and the % voltage regulation is shown as

%Regulation = {(Vno-load – Vfull-load) / Vfull-load} *100

Efficiency of half wave rectifier

The ratio of input AC to output DC is known as efficiency (?).

?= Pdc / Pac

A DC power that is delivered to the load is

Pdc = I2dc RL = (IMAX/ᴨ)2 RL

The input AC power to the transformer,

Pac=Power dissipation in load resistance + power dissipation in the junction diode

= I2rmsRF + I2rmsRL = {I2MAX/4} [RF + RL]

?= Pdc/Pac = 0.406/{1+RF/RL}

The practical efficiency of a half-wave rectifier is 40.6% when RF is neglected.

Ripple Factor of half wave rectifier (γ)

Ripple content is defined as the amount of AC component present in the output DC signal. If the ripple factor is small, the rectifier performance will be huge. The ripple factor value is 1.21 for a half-wave rectifier.

I2 = I2dc + I21 + I22+ I24 = I2dc+ I2ac

γ = Iac / Idc = (I2 – I2dc) / Idc = {( Irms / I2dc) / Idc = {(Irms /I2dc)-1} = kf2-1)

Where kf – form factor

kf= Irms / Iavg = (Imax/2)/ (Imax/ᴨ) =ᴨ/2 = 1.57

So, γ = (1.572 – 1) = 1.21

Transformer Utilization Factor (TUF)

It is defined as the ratio of AC power provided to the load and transformer secondary AC power rating. The TUF of half wave rectifier is nearly 0.287.

Power Supply Specifications of a rectifier

The most important characteristics which are needed to be specified for a power supply are the required output dc voltage, the average current and peak currents in the diode, the peak inverse voltage (PIV) of the diode, the regulation, and the ripple factor.

•            

Three Phase Half-wave Rectifier

three phase half wave rectifier

Three-phase half wave uncontrolled rectifier needs three diodes, each connected to a phase. The three-phase rectifier circuit suffers from a huge amount of harmonic distortion on both DC and AC connections. There are three distinct pulses per cycle on the DC output voltage.

All of the theory above has a deal with a single-phase half-wave rectifier. Although the phenomena of a 3 phase half-wave rectifier are the same the properties are different. The waveform, ripple factor, efficiency, and RMS output values are not the same as single-phase half-wave.

The three-phase half-wave rectifier is normally used for the transferring of three-phase AC power to DC power. Here the switches are diodes, and we know that they are uncontrolled switches. That is to say, there is no way of controlling the on and off times of these diodes.

The 3 phase half wave diode rectifier is generally designed with a three-phase power supply connected to a three-phase transformer where the secondary winding of the transformer is always connected using star connection. This is because the neutral point is needed to connect the load back to the transformer secondary windings, providing a back path for the flow of power.

A typical configuration of a three-phase half-wave rectifier supplying to a purely resistive load is shown below. Here, each phase of the transformer is used as an individual alternating source.

So we can observe from the above figure that the diode D1 conducts when the R phase has a value of the voltage that is much higher than the value of the voltage of the other two phases have, and this condition starts when the R phase is at a 30o and repeats after every complete cycle. That is to say, the next time diode DI starts to conduct is at 390o. Diode D2 takes over conduction from D1 which stops conducting at angle 150o due to this instant the value of voltage in the B phase becomes much higher than the voltages in the other two phases. So each diode conducts for an angle of 150o – 30o = 120o.

Here, the waveform of the resulting DC power signal is not purely DC as it is not flat, but rather it contains a more ripple. And the frequency of the ripple is 3 × 50 = 150 Hz.

Even though the efficiency of the 3 phase half-wave rectifier is seemingly high, it is still less than the efficiency provided by a 3 phase full wave diode rectifier. Although three-phase half-wave rectifiers are cheaper, this cost-saving is insignificant compared to the money lost in their higher power losses. As such, three-phase half-wave rectifiers are not commonly used in the industry.

Applications of Half wave rectifier

Any rectifier used to make DC power supplies. The practical application of any rectifier (be it half wave or full wave) is to be needed as a component in building DC power supplies.  A half-wave rectifier is not special as compare to a full-wave rectifier in any terms. In order to develop an efficient & smooth DC power supply, a full-wave rectifier is always preferred.  However, for applications in which a constant or fixed DC voltage is not very important, you can use power supplies with a half-wave rectifier.

Limitations

If the load resistor is very small for a given capacitor rating, a high current will pass through the load which discharges the capacitor very quickly (Because of the RC time constant) and results in much-increased ripples. As long as the RC time constant is much greater than the period, the capacitor remains almost fully charged, and we will get a perfect DC output power. To have a greater RC time constant, we need a huge value capacitor. This is not practical due to there are limits on both the cost as well as the size of the capacitor.

Also, there is zero output during the negative half cycle of wave hence half of the power is wasted which results in lower output amplitude.

Because of their major disadvantages, the half-wave rectifiers are few times used.

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FULL WAVE RECTIFIER:

In full wave rectifier, current flows through the load in the same direction for both half cycles of ac input voltage .it allows unidirectional (one way) current through the load during the entire 360 degrees of the input cycle, whereas a half-wave rectifier allows current through the load only during one half of the cycle. the result of full-wave rectification is an output voltage with frequency twice the input frequency and that pulsates every half cycle of the input. This can be obtained with two diodes working alternately. For the positive half cycle of input voltage, one diode supplies current to the load and for the negative half cycle, the other diode does so, current flows in the same direction across the load. Therefore a full-wave rectifier utilizes both half cycles of input ac voltage to produce the dc output. The number of positive alternations that make up the full rectified voltage is twice that of the half-wave voltage for the same time interval.

full wave rectifier

                                                            FIG[1]

The average voltage value is the value measured by a dc voltmeter for full-wave rectified sinusoidal voltage is twice that of the half-wave as shown in the following formula:

                                              Vavg=2Vp/π

Vavg is about  63.7% of vp for a full wave rectified voltage  .

The following two circuits are commonly  used for full wave rectification :

  1. center tap full-wave rectifier.
  2. full-wave bridge rectifier.

Center tapped full wave rectifier operation:

A center-tapped rectifier uses two crystal diodes that are connected to the secondary winding of a center-tapped transformer as shown in figure[2]. The input voltage is coupled through a transformer to the center-tapped secondary. Half of the total secondary voltage appears between the center-tapped and each end of the secondary winding.

center tapped full wave rectifier operation

                                                                   FIG[2]

During the positive half cycle of the input AC signal, point A becomes positive, and point B becomes negative and center tap is grounded (zero volts). The positive side A is connected to the anode of the diode d1 and the negative side B is connected to the cathode of the diode d2. So the diode d1 is forward biased during the positive half cycle and passes current through it. whereas diode d2 is reverse biased because the anode of diode d2 is connected to the negative side of polarity and cathode of diode d2 is connected to the positive side of polarity and blocks the current. in this way, only diode d1 supplies the dc current to the resistive load. The DC current produced at the load will return to the secondary winding through a center tap so the current only flows upper part of the circuit as the diode d2 is reverse biased so the lower part of the circuit carry no current to load. Thus, in the half positive cycle of the ac signal, only diode d1 passes the electric current whereas diode d2 blocks the electric current.

During the negative half cycle of the input AC signal, point A becomes negative, and point B becomes positive and the center tap is grounded (zero volts). The negative side of polarity is connected to the anode of the diode d1 and the positive side of polarity is connected to the cathode of the diode d1. So the diode d1 is reverse biased and does not pass the electric.

on the other hand diode, d2 becomes forward biased as the positive side of polarity is connected to the anode of diode d2 and the negative side of polarity is connected to the cathode of diode d2 in this way d2 supplies the current to load. The DC current produced at the load will return to the secondary winding through a center tap, so the current only flows lower part of the circuit as the diode d1 is reverse biased so the upper part of the circuit carry no current to load. Thus, in the half negative cycle of the ac signal, only diode d2 passes the electric current whereas diode d1 blocks the electric current. Because the output current during both the positive and negative portions of the input cycles is the same direction through the load, the output voltage developed across the load resistor is full-wave rectified dc output voltage.

what is the effect of the turn ratio on  output voltage

If the transformer’s  turns ratio is equal to one then the rectified output voltage is equal to half of the peak value of primary input voltage less the barrier potential and the                   

(vp(sec)=vp(vpri))     

vout= vp/2-0.7v

So we will define the forward voltage due to the potential barriers as a diode drop. To order to achieve output voltage peak equal to input voltage peak with less drop of potential barrier we need to use a transformer with turns ratio 1:2 in this case secondary voltage (vs) is twice the primary voltage (2vp). Due to double voltage at the secondary side, the half value of voltage will appear across the half part of the secondary winding and equal to the (Vpri)

  vout=vp(pri)-0.7

 So we concluded one point here that it does not matter what value of turn ratio is the value of rectified voltage output of the center-tapped rectifier is always half of the total secondary voltage minus diode drop or potential barrier voltage.

          Vout =(Vsec /2)- 0.7 V

Peak inverse voltage :

It is maximum voltage appear across diode when diode is in reverse biased.

As shown in figure[3]. During positive half cycle diode D1 is conducting and diode D2 is reverse biased if we apply kvl in the lower part of the circuit the  voltage across the diode D2  is denote by  vD2 is

                                                vin+vo=vD2

if diode D1 is ideal then output voltage vo is equal to vin.

therefore                           

                                                  vD2=2Vin

                                                 PIV=2Vm

when voltage drop across the diode then

                                               PIV=2Vm(out)+0.7

full wave rectifier piv

FIG[3]

Disadvantages

  1. it is difficult to locate the centre tap on the secondary winding .
  2. The dc output is small as each diode uses only one half of the  transformer secondary voltage.
  3. The diode used must have high peak inverse voltage.

full wave bridge rectifier

The bridge rectifier is another circuit to produce the full waveform output. it uses four diodes connected in a bridge configuration to produce the output .The main advantage of this bridge circuit is that it does not need a special centre tapped transformer, so minimize its size and cost. The single secondary winding is attached to one side of the diode bridge circuit and the load to the other side .

Bridge rectifier construction:

 The bridge rectifier is uses of four diodes namely D1, D2, D3, D4 and load resistor RL as shown in figure[4].The four diodes are attached in a closed loop (Bridge) configuration to efficiently change the Alternating Current (AC) into Direct Current (DC).

bridge rectifier

                                                       FIG[4]

The four diodes D1, D2, D3, D4 are set in series with only two diodes passes electric current during each half cycle. For instance, diodes D1 and D3 are considered as one pair which passes electric current during the positive half cycle whereas diodes D2 and D4 are considered as another pair that passes electric current during the negative half cycle of the input AC signal.

During the positive half cycle of the supply the end P of secondary winding becomes positive and end Q negative so this makes diodes D1 and D2  forward biased and diodes D3 and D4 are reverse biased so the diodes D1 and D3 conduct. These two diodes will be in series through load RL  and the current flows through the load as shown below in fig[5](i)

bridge rectifier current passes

                      FIG[5]

During the negative half cycle of the supply, end P becomes negative and ends Q positive. This makes diodes D2 and D 4  forward biased and diodes D1 and D3 reverse biased. so only diodes  D2 and D4 conduct. These two diodes will be in series with load RL as shown in fig[5](ii). Again current flow from A to B through the load i.e in the same direction as for positive half cycle, therefore dc output is obtained across load RL.

PEAK INVERSE VOLTAGE FOR BRIDGE RECTIFIER

Refer to the figure [6] as for the positive half cycle diodes D1 and D3 will be forward biased, considered the diodes are ideal so the diodes are replaced by wire as shown in the figure. The reverse-biased diodes D2 and D4 are parallel with the transformer secondary. therefore  PIV of each diode D2 and D4 is equal to the maximum voltage Vm across the secondary. likewise, during the next half-cycle, D2 and D4 are forward biased while D1 and D3 will be reverse biased. It is easy to see that reverse voltage across D1 and D3 is equal to VM.

fig[6]

 Advantages:

  1. In the bridge rectifier there is no need of centre-tapped transformer .
  2. The output from the bridge rectifier is twice that of the centre-tap circuit for the same secondary voltage.
  3. The peak inverse voltage is one-half that of the centre-tap circuit (for same d.c. output).

Disadvantages:

(i) It consist of four diodes.

Full-Wave Rectifier output frequency:

The output frequency from a full-wave rectifier is double the input frequency. A wave has a complete one cycle when it repeats the same pattern. In Fig[7](i), the input  AC  completes one cycle from 0° – 360°. However, the full-wave rectified wave completes 2 cycles in this period [See Fig[7] (ii). So, output frequency is twice the input frequency i.e.

                                               fout = 2 fin

fig[7]

For instance, if the input frequency to a full-wave rectifier is 50 Hz, then the output frequency will be 100 Hz.     

Efficiency of Full Wave Rectifier:

Below the figure demonstrate the process of full-wave rectification.

the waveform of full-wave rectification

Let v =VmsinѲ be the AC voltage to be rectified. Let RL and rf be the load resistance and diode resistance respectively. clearly, the rectifier will conduct current through the load in the same direction for both half-cycles of input  AC voltage. The instantaneous current i is given by :

instantaneous current

d.c. output power.

The output current from the rectifier is not a perfect dc but it is pulsating direct current. so, in order to get the d.c. power, the average current has to be found out. using the elementary knowledge of electrical engineering,



if rf is negligible as compared to RL then the efficiency will be maximum.

∴ Maximum efficiency = 81.2% . In a full-wave rectifier, the efficiency will be double as compared to the half-wave rectifier.

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Faults in Centre Tap Full Wave Rectifier

The faults in a center tap full-wave rectifier may occur in the transformer or rectifier diodes. Fig.6.36 shows the circuit of a center-tap full-wave rectifier. A fuse is connected in the primary of the transformer for protection purposes.

 Faults in Centre Tap Full Wave Rectifier

We can divide the rectifier faults into two classes viz.

1. Faults in transformer 2. Faults in rectifier diodes

Faults in the Transformer.

The transformer in a rectifier circuit can develop the following faults :


(i) A shorted primary or secondary winding.
(ii) An open primary or secondary winding.
(iii) A short between the primary or secondary winding and the transformer frame.


(i) In most cases, a shorted primary or shorted secondary will cause the fuse in the primary to blow. If the fuse does not blow, the d.c. the output from the rectifier will be extremely low and the transformer itself will be very hot.


(ii) When the primary or secondary winding of the transformer opens, the output from the rectifier will drop to zero. In this case, the primary fuse will not blow. If you believe that either the transformer winding is open, a simple resistance check will verify your doubt. If either winding reads a very high resistance, the winding is open.


(iii) If either winding shorts to the transformer casing, the primary fuse will blow. This fault can be checked by measuring the resistance from the winding leads to the transformer casing. A low resistance measurement indicates that a winding-to-case short exists.

Faults in Rectifier Diodes.

If a fault occurs in a rectifier diode, the circuit conditions will indicate the type of fault.


(i) If one diode in the center tap full-wave rectifier is shorted, the primary fuse will blow. The reason is simple. Suppose diode D2 in Fig. 6.36 is shorted. Then diode D2 will behave as a wire. When diode D1 is forward biased, the transformer secondary will be shorted through D1. This will cause excessive current to flow in the secondary (and hence in the primary), causing the primary fuse to blow.


(ii) If one diode in the center tap full-wave rectifier opens, the output from the rectifier will
resemble the output from a half-wave rectifier. The remedy is to replace the diode.


Bridge Rectifier Faults

The transformer faults and their remedies for bridge rectifier circuits are the same as for center tap full-wave rectifier. Again symptoms for shorted and open diodes in the bridge rectifier are the same as those for the center tap circuit. In the case of bridge circuit, you simply have more diodes that need to be tested.

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Nature of Rectifier Output

Nature of Rectifier:- It has already been discussed that the output of a rectifier is pulsating d.c. as shown in Fig. 6.37. In fact, if such a waveform is carefully analyzed, it will be found that it contains a d.c. component and an a.c. component. The a.c. the component is responsible for the *pulsations in the wave. The reader may wonder how a pulsating d.c. voltage can have an a.c. component when the voltage never becomes negative. The answer is that any wave which varies in a regular manner has an a.c. component.

Nature of Rectifier Output
rectifier device

The fact that a pulsating d.c. contains both d.c. and a.c. components can be beautifully illustrated by referring to Fig. 6.38. Fig. 6.38(i) shows a pure d.c. component, whereas Fig. 6.38 (ii) shows the *a.c. component. If these two waves are added together, the resulting wave will be as shown in Fig. 6.38 (iii). It is clear that the wave is shown in Fig. 6.38 (iii) never becomes negative, although it contains both a.c. and d.c. components. The striking resemblance between the rectifier output wave shown in Fig. 6.37 and the wave is shown in Fig. 6.38 (iii) may be noted. It follows, therefore, that a pulsating output of a rectifier contains a d.c. component and an a.c. component.

What is Ripple Factor

The output of a rectifier consists of a d.c. component and an a.c. component (also known as ripple). The a.c. component is undesirable and accounts for the pulsations in the rectifier output. The effectiveness of a rectifier depends upon the magnitude of a.c. component in the output; the smaller this component, the more effective is the rectifier.


The ratio of r.m.s. value of a.c. component to the d.c. component in the rectifier output is known
as ripple factor i.e.

equation of ripple factor
wave of ripple factor

Therefore, the ripple factor is very important in deciding the effectiveness of a rectifier. The smaller the ripple factor, the lesser the effective a.c. component and hence more effective is the rectifier. Mathematical analysis. The output current of a rectifier contains d.c. as well as a.c. component. The undesired a.c. the component has a frequency of 100 Hz (i.e. double the supply frequency 50 Hz) and is called the ripple (See Fig. 6.39). It is a fluctuation superimposed on the d.c. component.
By definition, the effective (i.e. r.m.s.) value of total load current is given by :

full equation of ripple factor
ripple factor value in half wave rectifier

It is clear that a.c. component exceeds the d.c. component in the output of a half-wave rectifier.
This results in greater pulsations in the output. Therefore, half-wave rectifier is ineffective for conversion of a.c. into d.c.


For full-wave rectification

In full-wave rectification,

ripple factor value in full wave rectifier

This shows that in the output of a full-wave rectifier, the d.c. component is more than the a.c.
component. Consequently, the pulsations in the output will be less than in half-wave rectifier. For
this reason, full-wave rectification is invariably used for conversion of a.c. into d.c.
Example 6.22. A power supply A delivers 10 V dc with a ripple of 0.5 V r.m.s. while the power
supply B delivers 25 V dc with a ripple of 1 mV r.m.s. Which is a better power supply?

Solution. The lower the ripple factor of a power supply, the better it is.

power supply ripple factors

Comparison of Rectifiers

comparison of rectifier

A comparison among the three rectifier circuits must be made very judiciously. Although bridge
circuit has some disadvantages
, it is the best circuit from the viewpoint of overall performance. When the cost of the transformer is the main consideration in a rectifier assembly, we invariably use the bridge circuit. This is particularly true for large rectifiers which have a low-voltage and a high-current rating.

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