Power Electronics –BEE503

Module 1
INTRODUCTION

POWER DIODES

DIODE RECTIFIERS

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Module 1
Introduction:
 Power electronics is one of the important branch of electrical and electronics engineering.
 It deals with conversion and control of electric energy.
 Available AC voltage and current of fixed frequency is available from mains. This supply
cannot be used always directly for some of the application.
 The Power Electronics circuit converts electric energy in the other form. The block diagram
of basic conversion of energy is shown in the figure 1.1

Figure 1.1 Block diagram

 Electronic energy conversion is performed by rectifiers (with consists of power
electronics devices such as SCR, Thyristers, IGBT etc).
 Thus, Power electronic system thus performs conversion and controlling of electric
energy to be given to the output.
 The word Power mean high amplitudes of current and voltages.

1.1 Application of Power Electronics:

Power electronics has numerous applications:
1. Uninterruptible power supplies and stands by power supplies for critical loads such as
computers, medical equipment‟s etc.
2. Power control in resistance welding induction heating, electrolysis, process industry etc.
3. Power conversion for HVDC and HVAC transmission systems.
4. Speed control of motors which are used in traction drives, textile mills, rolling mills,
cranes, lifts, compressors, pumps etc.
5. Solid state power compensators, static contactors, transformer tap changers etc.
6. High voltage supplies for electrostatic precipitators, and x-ray generators, etc.
7. Power supplies for communication systems, telephone exchanges, satellite systems etc.
These are some of the important applications of power electronics.

1.1.1Advantages of Power electronics controllers

 The power electronic controllers have following advantages:
 Fast dynamic response due to static devices.
 High efficiency of conversion due to low losses in electronic devices.
 Compact size and light weight of the controllers due to electronic devices.
 Increased operating life and reduced maintenance since there are no moving parts.

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 Power electronic controllers use digital or microprocessor based control. Hence their
operation is highly flexible.
 Since solid state devices are used, the electromagnetic interference and a acoustic noise
is reduced.

1.1.2 Draw Backs of Power Electronic Controllers:

The power electronic controllers have some drawbacks also. They are as follows:
 The power electronic controllers generate harmonics. These harmonics affect the
performance of other loads.
 The power factor of some power electronic controllers is very low. Hence power factor
correction is necessary to reduce reactive power.
 For very simple conversion requirements, power electronic converters may be costly.

1.2 Block diagram of Power Electronic Controller

Figure 1.2 Block diagram of Power Electronic Controller

 The power source can be AC mains, generator or batteries.

 Power controller or converter can use thyristor (SCR), GTO, MOSFET, BJT or IGBT as
a switch. The power controller converts the input power which is suitable for the load.
 The sensing and feedback circuits monitor the load conditions.
 The control unit consists of drive circuits of the power controller. The drives of the
switches are adjusted according to feedback and the reference settings.
 The control unit adjusts the drives whenever there is difference between feedback
(actual) speed and reference speed. The control unit also accepts commands form the
user. These commands are given for the proper functioning of the power electronic
system and the load.

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1.3 Types of Power Electronics Devices

1.3.1 AC to DC Convertors

Figure 1.3(a) AC to DC Convertors Figure 1.3(b) Block diagram with Wave forms

 The input is single phase or three phase AC supply normally available from the mains.
The output is the controlled DC voltage and current.
 The AC to DC converters include diode rectifiers as well as controlled rectifiers. The
controlled rectifiers mainly use SCRs.
 Since the input is AC supply, the SCRs are turned off by natural commutation. Hence
external commutation circuits are not required. Hence AC to DC converters are also
called as line (supply) commutated converters.
 These converters are used for DC drives, UPS and HVDC systems.

1.3.2DC to AC convertors (or Invertors):

Figure 1.4(a) DC to AC Convertors Figure 1.4(b) Block diagram with Wave forms

 These converters are commonly called inverters. The input to the inverters is fixed DC
voltage. Normally this DC voltage is obtained from the batteries.
 The output of the inverter is the fixed or variable frequency AC voltage. The AC
voltage magnitude is also variable.
 Inverters are mainly used whenever mains is not available .UPS use inverters inside to
generate AC output from batteries.
 Inverters are also used for speed control of induction motors. The voltage, frequency or
both are varied by inverter to control the speed of induction motors.
 Inverters are also used in standby and emergency power supplies.

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1.3.3 DC to DC Converters (Choppers):

Figure 1.5(a) DC to DC Convertors Figure 1.5(b) Block diagram with Wave forms
 The choppers take input from fixed voltage DC supply such as battery or output of
uncontrolled rectifier. The output of the chopper is fixed or variable DC voltage.
 The choppers are normally used in DC drives. The speed of the motor can be controlled
in forward and reverse directions.
 The choppers are also used in switched mode power supplies (SMPS).

1.3.4AC to AC Convertors:
(a) AC Regulators :

Figure 1.6(a) AC Regulators

 The input to the AC regulator is fixed voltage AC mains. The output is variable AC
voltage which is suitable for load.
 Here note that the output frequency is same as input frequency. Thus AC regulators
does not change the frequency.
 The AC regulators are used for the speed control of large fans and pumps.

(b) Cyclo converters :

Figure 1.7(a) Cycloconverter Figure 1.7(b) Block diagram with Wave forms
 Cycloconverter (also known as a cyclo inverter or CCV) converts a constant voltage,
constant frequency AC waveform to another AC waveform of a different frequency.

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 A cycloconverter achieves this through synthesizing the output waveform from

segments of the AC supply.
 The line communication is more common in these convertors, through force and load
commutated cycloconverters

1.3.5 Static Switches: The power semiconductor devices can operate as static switches or
contactors. Static switches possess many advantages over mechanical and electromechanical
circuit breakers. Depending upon the input supply, the static switches are called ac static
switches.

1.4 Peripheral Effects:

Figure 1.7: Generalized power converter system.

The operations of the power converters are based mainly on the switching of power
semiconductor devices; as a result, the converters introduce current and voltage harmonics into
the supply system and on the output of the converters. These can cause problems of distortion of
the output voltage, harmonic generation into the supply system, and interference with the
communication and signalling circuits. It is normally necessary to introduce filters on the input
and output of a converter system to reduce the harmonic level to an acceptable magnitude.
Figure 1.7 shows the block diagram of a generalized power converter.
The application of power electronics to supply the sensitive electronic loads poses a
challenge on the power quality issues and raises problems and concerns to be resolved by
researchers. The input and output quantities of converters could be either ac or dc. Factors such
as total harmonic distortion (THD), displacement factor (DF), and input power factor (IPF) are
measures of the quality of a waveform. To determine these factors, finding the harmonic content
of the waveforms is required. To evaluate the performance of a converter, the input and output
voltages and currents of a converter are expressed in a Fourier series. The quality of a power
converter is judged by the quality of its voltage and current waveforms. The control strategy for
the power converters plays an important part on the harmonic generation and output waveform
distortion, and can be aimed to minimize or reduce these problems. The power converters can
cause radio-frequency interference due to electromagnetic radiation, and the gating circuits may

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generate erroneous signals. This interference can be avoided by grounded shielding. As shown in
Figure 1.7, power flows from the source side to the output side. Thewaveforms at different
terminal points would be different as they go through processingat each stage. It should be noted
that there are two types of waveforms: one at thepower level and another from the low-level
signal from the switching or gate controlgenerator. These two voltage levels must be isolated
from each other so that they donot interfere with each other.

1.5 Power Semiconductor Devices:

Figure 1.8: Classification of Power Electronic Devices.

1.6 Power Diodes:

 Power diode is uncontrolled device. Power diodes are required in
most of the power converters.
 When anode (A) is positive with respect to cathode (K), diode starts
conducting. Normally a forward bias of 1 volts is sufficient to push
the diode in conduction. Current flows from anode to cathode.
 The diode does not conduct when anode to cathode voltage is
negative. The diode is said to be reverse biased.
 The Symbolic Representation is as shown in the figure.
Figure1.9:Power Diode
1.6.1Structure of Power Diode:
Power diode consists of heavily doped 𝑛+ substrate with doping
level of 1019 /𝑐𝑚3 . This substrate forms a cathode of the diode. On 𝑛+
substrate, lightly doped 𝑛− epitaxial layer is grown.
This layer is also called drift region. The doping level of 𝑛−
layer is about 1014 /𝑐𝑚3 . Then the pn junction is formed by diffusing a
heavily doped 𝑝+region. This 𝑝+ region forms anode of the diode.

Figure 1.10: Power Diode

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The doping level of 𝑝+ region is 1019 /𝑐𝑚3 . The thickness of 𝑝+ region is 10 μm. The
thickness of 𝑛+ substrate is 250 μm . The thickness of 𝑛− drift layer depends upon the
breakdown voltage of the diode. For higher breakdown voltages, the drift region is wide. The
𝑛− drift region is absent in low power signal diodes. The drift region absorbs depletion layer of
the reverse biased 𝑝+𝑛− junction.
When power diode is forward biased, the holes will be injected from the 𝑝+ region into
the drift region. Some of the holes combine with electrons in the drift region.
Since injected holes are large, they attract electrons from 𝑛+layer. Thus, holes and
electrons are injected in the drift region simultaneously. Hence resistance of the drift region
reduces significantly. Thus diode current goes on increasing, but drift region resistance remains
almost constant.This phenomenon is called conductivity modulation of drift region

1.6.2 V-I Characteristics :

The forward biased condition, anode current increases linearly with voltage. In lower
power diodes, current increases exponentially. The linear rise takes place because of ohmic
resistance in 𝑛−layer. The 𝑛− drift region is lightly doped. Hence, it appears as low value
internal resistance of the diode. Therefore current is linearly proportional to voltage. A forward
bias of 1 V is sufficient to trigger diode into conduction.

Figure 1.11: I-V Characteristics

When the diode is reverse biased, a very small anode current flows. This current is called
leakage current.When the reverse bias is greater than reverse breakdown voltage, anode current
starts rising rapidly. Hence large power dissipation take place in the diode and it is damaged.

1.6.3: Reverse Recovery characteristics:

The Figure 1.12 depicts the reverse recovery characteristic of a power diode.
Whenever the diode is switched off, the current decays from IF to zero and further continues in

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reverse direction owing to the charges stored in the space charge region and the semiconductor
region.
This reverse current attains a peak IRR and again starts approaching zero value and
finally, the diode is off after time 𝒕𝒓𝒓 and and is measured from the initial zero crossingof the
diode current to 25% of maximum (or peak) reverse current 𝐼𝑅𝑅 .

Figure 1.12: Reverse Recovery Characteristics

From the figure 1.12,

𝑡𝑟𝑟 = 𝑡𝑎 + 𝑡𝑏
ta → time when charge from depletion region is removed
tb → time when charge from semiconductor region is removed.
The peak reverse current can be expressed in reverse di/dt as
𝑑𝑖
𝐼𝑅𝑅 = 𝑡𝑎 ---------- 1
𝑑𝑡
The Reverse recovery time 𝒕𝒓𝒓 is defined as the time between the instant forward current
reaches zero and the instant the reverse current decays to 25% of IRR. After this time the diode is
said to attain its reverse blocking capability. Variable trris dependent on the junction
temperature, rateof fall of forward current, and forward current prior to commutation, IF.

The Reverse recovery charge 𝐐𝐑𝐑 is the amount of charge carriers that flows across
the diode in the reverse direction due to changeover from forward conduction to reverse
blocking condition. Its value is determined from the area enclosed by the curve
of the reverse recovery current.
That is, 𝑄𝑅𝑅 = 𝑄1 + 𝑄2
The storage charge, which is the area enclosed by the curve of the recovery current,
is approximately
1 1 1
𝑄𝑅𝑅 = 𝑄1 + 𝑄2 = 𝐼𝑅𝑅 𝑡𝑎 + 𝐼𝑅𝑅 𝑡𝑏 = 𝐼𝑅𝑅 𝑡𝑎 ----------2
2 2 2
2𝑄𝑅𝑅
𝐼𝑅𝑅 ≅ ----------3
𝑡 𝑟𝑟
Equating 𝐼𝑅𝑅 in equation 1 to equation 3

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𝑑𝑖 2𝑄𝑅𝑅
𝑡𝑎 =
𝑑𝑡 𝑡 𝑟𝑟
2𝑄𝑅𝑅
𝑡𝑟𝑟 𝑡𝑎 = 𝑑𝑖 ---------4
𝑑𝑡
If 𝑡𝑎 is negligible as compared to ta, which is usually the case 𝑡𝑟𝑟 = 𝑡𝑎 , and equation 4
becomes,
2𝑄𝑅𝑅
𝑡𝑟𝑟 = 𝑑𝑖 ---------5
𝑑𝑡
Substituting equation 4 in 5

𝐼𝑅𝑅 = 2𝑄𝑅𝑅 𝑑𝑖 𝑑𝑡 --------6

It can be noticed from Equation 5 and 6 that the reverse recovery time 𝑡𝑟𝑟 and the peak
reverse recovery current 𝐼𝑅𝑅 depend on the storage charge QRR and the reverse (or reapplied)
di/dt. The storage charge is dependent on the forward diode current 𝐼𝐹 .
If a diode is in a reverse-biased condition, a leakage current flows due to the minority
carriers. Then the application of forward voltage would force the diode to carrycurrent in the
forward direction. However, it requires a certain time known as forwardrecovery (or turn-on)
time before all the majority carriers over the whole junction cancontribute to the current flow. If
the rate of rise of the forward current is high and theforward current is concentrated to a small
area of the junction, the diode may fail.Thus, the forward recovery time limits the rate of the rise
of the forward current andthe switching speed.

1.6.4 Types of Power Diodes:

a) General purpose diodes :

 The general-purpose rectifier diodes have relatively high reverse recovery time, typically
25 𝜇s; and are used in low-speed applications,
where recovery time is not critical (e.g., diode
rectifiers and converters for a low-input
frequency up to 1-kHz applications and line-
commutated converters).
 These diodes cover current ratings from less than
1 A to several thousands of amperes, with
voltage ratings from 50 V to around 5 kV. These
diodes are generally manufactured by diffusion.
However, alloyed types of rectifiers that are used
in welding power supplies are most cost-effective
and rugged, and their ratings can go up to 1500
V, 400 A.
Figure 1.13: Various general purpose diodes

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b) Fast-Recovery Diodes:
 The fast-recovery diodes have low recovery time, normally less than 5𝜇s. They are used
in dc–dc and dc–ac converter circuits, where
the speed of recovery is often of critical
importance.
 These diodes cover current ratings of voltage
from 50 V to around 3 kV, and from less than 1
A to hundreds of amperes. For voltage ratings
above 400 V, fast-recovery diodes are generally
made by diffusion and the recovery time is
controlled by platinum or gold diffusion.
 For voltage ratings below 400 V, epitaxial
diodes provide faster switching speeds than
those of diffused diodes. The epitaxial diodes
have a narrow base width, resulting in a fast
recovery time of as low as 50 ns. Fast-recovery
diodes of various sizes are shown in Figure 1.14.
Figure 1.14 Fast Recovery Diodes
c) Schottky Diodes:
 In Schottky diodes, the pn junction is eliminated.
 A thin film of metal is placed directly on the
semiconductor as shown in Figure 1.14
 Normally aluminumis deposited on n-type
semiconductor. The metal is anode and semiconductor
is cathode.
 Since, there is no pn junction, the storage time isabsent.
Hence, turn-off time is very small. Hence schottky
diodes have high switching frequencies.
 The drift layer is absent. Hence on-state losses are very
low. But Schottky diodes have large reverse leakage
currents.
Figure 1.15 Fast Recovery Diodes

1.6.5 Applications of Schottky diodes: Schottky diodes are used in

• Switched mode power supplies. AC to DC converters
• Radar systems
• Mixers and detectors in communication circuits.
• Feedback and freewheeling operations of power converters.

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1.6.6 Applications of Power Diodes:

Power diodes are required in almost all the power converters.Some of the applications are
mentioned below:
 Power diodes are used in uncontrolled rectifiers.
 Feedback and freewheeling operations in choppers, inverters and controlled converters
use power diodes.
 Almost all the commutating circuits for SCRs use power diodes.
 Half controlled converters and half bridge inverters use power diodes.

1.7 Silicon Carbide Diodes :

Silicon carbide (SiC) is a new material for
power electronics. Its physical properties
outperform Si and GaAs by far. For example, the
Schottky SiC diodes manufactured by Infineon
Technologies [3] have ultralow power losses and
high reliability. They also have the following
features:
 No reverse recovery time.
 Ultrafast switching behaviour.
 No temperature influence on the switching
behaviour.
Figure 1.16 Comparison of reverse recovery time.

1.7.1 Silicon Carbide Schottky Diodes:

Schottky diodes are used primarily in high frequency and fast-switching applications.
Many metals can create a Schottky barrier on either silicon or GaAs semiconductors.
A Schottky diode is formed by joining a doped semiconductor region, usually n-type,
with a metal such as gold, silver, or platinum. Unlike a pn-junction diode, there is a metal to
semiconductor junction. This is shown in Figure 1.17 a and its symbol in Figure 1.17b. The
Schottky diode operates only with majority carriers.
There are no minority carriers and thus no reverse leakage current as in pn-junction
diodes. The metal region is heavily occupied with conduction band electrons, and the n-type
semiconductor region is lightly doped. When forward biased, the higher energy electrons in the
n-region are injected into the metal region where they give up their excess energy very rapidly.
Since there are no minority carriers, it is a fast-switching diode.
The SiC Schottky diodes have the following features:
• Lowest switching losses due to low reverse recovery charge;
• Fully surge-current stable, high reliability, and ruggedness;
• Lower system costs due to reduced cooling requirements;
• Higher frequency designs and increased power density solutions.

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These devices also have low device capacitance that enhances overall system
efficiency,especially at higher switching frequencies.

Figure 1.17 Basic internal structure of a Schottky diode.

1.8 Freewheeling Diodes:

Freewheeling diode is used to protect the circuit from unusual damage caused due to
abrupt reduction in the current flowing through the circuit. It is also known as Flyback
diode and forms connection across the inductor to remove Flyback voltage generated across it.

Freewheeling diodes are also known as kickback diode, clamp diodes, commutating
diodes, suppression diodes, or snubber diode etc.

Note: Flyback is basically defined as an abrupt increase in voltage across the inductive load
when the current through the circuit shows a reduction.

1.8.1 Freewheeling Diode with RL Load:

Figure 1.18RL Circuit with freewheeling diode.

𝑉𝑠
In the figure 1.18(a) steady state current, after switch S is closed, is equal to 𝑅 . If the switch
2
1 𝑉𝑠
S is now opened, the energy stored = 𝐿 𝑅 in the inductance L will appear in the form
2

of arc at switch contacts of switch S. In order to avoid such an occurrence, a diode FD called

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freewheeling or flyback diode is connected across RL as shown in figure 1.18(a). For

understating how FD comes into play, working of circuit is divided into two modes.

Mode I:When switch S is closed in figure 1.18(a) at t=0, current flows through 𝑉𝑠 ,S,D,R and L
as shown in figure 1.18(b). In this circuit, current „i‟ is given by
𝑅
𝑉𝑠
𝑖= 1 − 𝑒 −𝐿 𝑡 ---------1
𝑅

Final value of current or steady state value of current is given by

𝑉𝑠
𝐼= 𝑅

Mode II:When switch S is opened at t=0, current in the circuit tends to decay and so a voltage
𝑑𝑖
𝐿 𝑑𝑡 is induced in L which forward biases freewheeling diode. The current is therefore,
transferred to the circuit consisting of FD, R and
L as shown figure 1.18(c).
𝑅
𝑉𝑠
In this circuit, current is given by𝑖1 = 𝑒 −𝐿 𝑡
𝑅

The current 𝑖1 will exponentially decays to zero

in mode II of figure 1.18(c). The current buildup
during mode I and current decay during mode II
are shown in figure 1.19.
Figure 1.19 Current variation in the circuit

Diode Rectifiers :
Diodes are extensively used in rectifiers. A rectifier is a circuit that converts an acsignal
into a unidirectional signal. A rectifier is a type of ac–dc converter. A rectifiermay also be
considered as an absolute value converter. If 𝑣𝑠 is an ac input voltage, thewaveform of the output
voltage 𝑣𝑜 would have the same shape, but the negative partwill appear as a positive value. That
is𝑣𝑠 = 𝑣𝑜 Depending on the type of input supply,the rectifiers are classified into two types: (1)
single phase and (2) three phases. Asingle-phase rectifier can be either a half wave or a full
wave. A single-phase half-waverectifier is the simplest type, but it is not normally used in
industrial applications. Forthe sake of simplicity, the diodes are considered to be ideal. By
“ideal” we mean thatthe reverse recovery time 𝑡𝑟𝑟 and the forward voltage drop 𝑉𝐷 are negligible.
That is,𝑡𝑟𝑟 = 0and𝑉𝐷 = 0.

1.9 Diode circuits with DC source: In this section, the effect of switching a dc source to a
circuit consisting of diode and different circuit parameters is examined. The conclusion can then
be applied to similar situations encountered later in power- electronic circuits.

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1.9.1 Diode with Resistive Load:

Figure 1.20(a) Diode circuit with R load (b) Waveforms

In the circuit shown in figure 1.20 (a), when switch S is closed, the current rises
𝑉𝑠
instantaneously to as shown in the figure 1.20 (b). Here 𝑉𝑠 is the dc source voltage and R is the
𝑅
load resistance. When switch S is opened at 𝑡1 , the current at once falls to zero, (Refer the wave
form), voltage 𝑣𝐷 across diode is zero during the time diode conducts and is equal to +𝑉𝑠 after
diode stops conducting.

1.9.2 Diode Circuits with R-L load:

Diode circuits with RL load is as shown in the figure 1.21(a) , when switch S is closed at t=0 in
the RL and diode circuit, applying KVL
𝑑𝑖
𝑅𝑖 + 𝐿 𝑑𝑡 = 𝑉𝑠 ---------1

Figure 1.21 (a) Diode circuit with R-L load (b) Waveforms
With initial current in the inductor as zero, the solution of equation 1 is
𝑅
𝑉𝑠
𝑖= 1 − 𝑒 −𝐿 𝑡 ---------2
𝑅
𝑅
𝑑𝑖 𝑉 𝑉𝑠
Initial rate of rise of current is𝑑𝑡 ⎢𝑡=0 = 𝐿𝑠 𝑒 −𝐿 𝑡 = 𝑅
𝑅
𝑑𝑖 − 𝑡
The voltage across L is 𝑣𝐿 𝑡 = 𝐿 𝑑𝑡 = 𝑉𝑆 𝑒 𝐿

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1.10 Single phase full-wave diode rectifier:

There are two types of full-wave diode rectifiers, one is centre-tapped(or mid-point) full-wave
diode rectifier and the other is full-waver diode rectifier with R and RL loads.
1.10.1 Single-phase full-wave mid-point diode rectifier:

Figure 1.22(a)Single-phase full-wave mid-point diode rectifier (b) Waveforms

A full-wave rectifier circuit with a center-tapped transformer (mid-point) is shown in Figure

1.22(a) During the positive half-cycle of the input voltage, diode D1 conducts and diode D2 is in
a blocking condition with reverse voltage of −2𝑉𝑚 . The input voltage appears across the load.
During the negativehalf-cycle of the input voltage, diode D2 conducts while diode D1 is in a
blocking condition with reverse voltage of −2𝑉𝑚 .The negative portion of the input voltage
appears across the load as a positive voltage. The waveform of the output voltage over a
complete cycle is shown in Figure 1.22(b). The output current is same input voltage with lesser
magnitude (which is not shown in the figure).Because there is no dc current flowing through the
transformer, there is no dc saturation problem of transformer core.
The average output voltage is
1𝜋 𝑉 𝜋 2𝑉𝑚
𝑉𝑜 = 𝑉𝑑𝑐 = 𝜋 0 𝑚
𝑉 𝑠𝑖𝑛𝜔𝑡 𝑑𝜔𝑡 = 𝜋𝑚 − cos 𝜔𝑡 0 = ---------1
𝜋
𝑉
Average current 𝐼𝑜 = 𝑅𝑜
1 𝜋
Rms value of Voltage 𝑉𝑟𝑚𝑠 = 𝑉 2 𝑠𝑖𝑛2 𝜔𝑡 . 𝑑𝜔𝑡
𝜋 0 𝑚
1
w.k.t 𝑠𝑖𝑛2 𝜔𝑡 = 2 (1 − 𝑐𝑜𝑠2𝜔𝑡)
𝑉𝑚 𝜋 𝑉𝑚 𝑠𝑖𝑛 2𝜔𝑡 𝜋 𝑉𝑚
𝑉𝑟𝑚𝑠 = 0
1 − 𝑐𝑜𝑠2𝜔𝑡 𝑑𝜔𝑡 = 𝜔𝑡 − = = 𝑉𝑠 ------2
2𝜋 2𝜋 2 0 2
Rms value of load current,
𝑉
𝐼𝑟𝑚𝑠 = 𝑟𝑚𝑠
𝑅
Power delivered to load = 𝑉𝑟𝑚𝑠 𝐼𝑟𝑚𝑠 =𝐼𝑟𝑚𝑠 2 𝑅
𝑉 𝐼𝑟𝑚𝑠
Input voltamperes = 𝑉𝑠 𝐼𝑟𝑚𝑠 and Input power factor = 𝑟𝑚𝑠 =1
𝑉𝐼 𝑠 𝑟𝑚𝑠

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1.10.2 Single-phase full-wave diode bridge rectifier:

Figure 1.23(a)Single-phase full-wave diode bridge rectifier (b) Waveforms

Single-phase full-wave diode bridge rectifier shown in figure 1.23(a). During the positive
half-cycle of the input voltage, the power is suppliedto the load through diodes D1 and D2.
During the negative cycle, diodes D3 and D4conduct. The waveform for the output voltage is
shown in Figure 1.23(b) . The peak inverse voltage of a diode is only −𝑉𝑚 . This circuit isknown
as a bridge rectifier and it is commonly used in industrial applicationsup to 100 kWRipple
frequency is twice thesupply frequencySimple to use in commerciallyavailable units.
The average value of the voltage
1𝜋 𝑉
𝑚 𝜋 2𝑉𝑚
𝑉𝑜 = 𝑉𝑑𝑐 = 2𝜋 0 𝑚
𝑉 𝑠𝑖𝑛𝜔𝑡 𝑑𝜔𝑡 = 2𝜋 − cos 𝜔𝑡 0 = ---------1
𝜋
𝑉
Average current 𝐼𝑜 = 𝑅𝑜

1 𝜋
Rms value of Voltage 𝑉𝑟𝑚𝑠 = 𝑉 2 𝑠𝑖𝑛2 𝜔𝑡 . 𝑑𝜔𝑡
𝜋 0 𝑚
1
w.k.t 𝑠𝑖𝑛2 𝜔𝑡 = 2 (1 − 𝑐𝑜𝑠2𝜔𝑡)
𝑉𝑚 𝜋 𝑉𝑚 𝑠𝑖𝑛 2𝜔𝑡 𝜋 𝑉𝑚
𝑉𝑟𝑚𝑠 = 0
1 − 𝑐𝑜𝑠2𝜔𝑡 𝑑𝜔𝑡 = 𝜔𝑡 − = = 𝑉𝑠 ------2
2𝜋 2𝜋 2 0 2
Rms value of load current,
𝑉𝑟𝑚𝑠
𝐼𝑟𝑚𝑠 = 𝑅
Power delivered to load = 𝑉𝑟𝑚𝑠 𝐼𝑟𝑚𝑠 =𝐼𝑟𝑚𝑠 2 𝑅
Input voltamperes =𝑉𝑠 𝐼𝑟𝑚𝑠

1.10.3 Single-phase full wave diode rectifier with RL load:

Figure 1.24(a) presents the circuit connection for a single-phase, full-wave, rectifier loaded with
a highly inductive load. Highly inductive loads are basically R-L loads where L≪ R. Therefore,
𝐿
the load time constant 𝜏 = 𝑅 is very high and can be considered infinity. Consequently, the load
current is assumed constant.

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Power Electronics –BEE503

Figure 1.24 (a)Single-phase full-wave diode bridge rectifier with RL (b) Waveforms

For one total period of operation of this circuit, the corresponding waveforms are shown in
figure 1.24(b).During the conduction of D1 and D2 simultaneously the supply voltage appears
directly across the load so that the load voltage 𝑣𝑜 (𝜔𝑡) remains the form shown in Fig.1.22 (b) (
same as the case of resistive load). Hence, the average value of the load voltage Vdc can be
calculated as follows:
𝜋
1 𝑉 2𝑉𝑚
𝑉𝑜 = 𝑉𝑑𝑐 = 𝜋 0 𝑚
𝑉 𝑠𝑖𝑛𝜔𝑡 𝑑𝜔𝑡 = 𝜋𝑚 − cos 𝜔𝑡 𝜋0 = ---------1
𝜋
𝑉 𝐼𝑜
Average current 𝐼𝑜 = 𝑅𝑜 , average value of diode current 𝐼𝑑𝑎𝑣 = 2

1 𝜋
Rms value of Voltage 𝑉𝑟𝑚𝑠 = 𝑉 2 𝑠𝑖𝑛2 𝜔𝑡 . 𝑑𝜔𝑡
𝜋 0 𝑚
1
w.k.t 𝑠𝑖𝑛2 𝜔𝑡 = 2 (1 − 𝑐𝑜𝑠2𝜔𝑡)
𝑉𝑚 𝜋 𝑉𝑚 𝑠𝑖𝑛 2𝜔𝑡 𝜋 𝑉𝑚
𝑉𝑟𝑚𝑠 = 2𝜋 0
1 − 𝑐𝑜𝑠2𝜔𝑡 𝑑𝜔𝑡 = 2𝜋
𝜔𝑡 − 2
= 2
= 𝑉𝑠 ------2
0
Rms value of load current,
𝑉𝑟𝑚𝑠
𝐼𝑟𝑚𝑠 = 𝑅
𝐼𝑜
Average value of diode current 𝐼𝐷𝐴 = 2
𝐼𝑜
Rms value of diode current, 𝐼𝐷𝑟 = 2
Power delivered to load = 𝑉𝑟𝑚𝑠 𝐼𝑟𝑚𝑠 =𝐼𝑟𝑚𝑠 2 𝑅
Input power = 𝑉𝑠 𝐼𝑠 cos ∅
Supply current 𝐼𝑠 = 𝐼𝑟𝑚𝑠
𝑉𝑟𝑚𝑠 𝐼𝑟𝑚𝑠
∴ Supply power factor cos ∅ = 𝑉𝑠 𝐼𝑟𝑚𝑠

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Question Bank
1) With neat circuit diagram, input and output wave forms, explain the different types of
power electronic converters.
2) With neat diagram, explain the different types of power electronic circuits.
3) List the application of power electronics
4) Write a shot notes on peripheral effects of power electronic circuits
5) Explain the reverse recovery characteristics of power diode, with neat waveform. And
also obtain an expression for peak reverse current.
6) Explain the operation of single phase full wave rectifier with RL load. Derive the
expression for RMS o/p current for continuous load current.
7) List the various types of power diodes indicating the differences
8) With circuit diagram and waveforms explain the working of single phase full wave
rectifier with R load
9) Discuss the major industrial application of power electronic converter circuits.
10) What is freewheeling diode? Explain its working with circuit diagram, equivalent circuits
and waveforms.
11) With circuit diagram and waveforms explain diode switched RL load with necessary
equations.
12) Compare the advantages and disadvantages of bridge rectifier and rectifier with centre
tapped transformer.

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