ECE 451 Power Electronics I
ECE 451 POWER ELECTRONICS I (3 UNITS)
Physics and characteristics of semiconductor power devices: MOSFETs, SCRthyristors, power diodes, IGBT, Power transistors. Rectifier circuits and their
characteristics. Output voltage ripple. Smoothing methods. Operation with resistive and
inductive loads. Single- and poly-phase half and full-controlled bridge rectifiers. Free
wheeling diode. Application of power switching circuit in control of ac/dc loads. Forced
commutation: definitions and classification. Protection: heat transfer and cooling
techniques in power devices, fuse protection: fuse characteristics, operation of fuses on
DC, selection of fuselinks for device protection; Over-voltage protection: suppression of
surges on ac-input side, snubber circuits, surge suppression at dc output, lightning
arrestors; Power Supplies: Uninterruptible power supplies. Regulated Power Supplies:
DC voltage regulators . Electromagnetic interference: sources of EMI; minimizing EMI
generation, EMI shielding, EMI standards.
References:
1.)
Muhammad H. Rashid, Power Electronics, circuits devices, and applications,
Prentice Hall – India, 3rd Edition, 2004.
2.)
N. Mohan, T.M. Undeland, W.P. Robbins, Power Electronics, Applications,
Converters and Design, John Wiley & Sons Inc., 3rd Ed., 2003.
3.)
Mithal G.K., Gupta M., Industrial and Power Electronics, Khanna Publishers,
19th Edition, 2006.
4.)
Sen P.C., Power Electronics, Tata Mc-Graw Hill Publishing Company Ltd.,
Delhi, 2002.
5.)
Erickson R.W., Makasimovic D., Fundamentals of Power Electronics, Kluwer
academic Publishers, Massachussets, 2002.
Lecturer: Dr. L.K. Letting
-i-
ECE 451 Power Electronics I
CHAPTER ONE
1
INTRODUCTION
1.1
Definition
Power electronics is defined as the application of solid-state electronics for the
control and conversion of electric power. The key element is the switching converter,
illustrated in Fig. 1.1. In general, a switching converter contains power input and control
input ports, and a power output port. The raw input power is processed as specified by the
control input, yielding the conditioned output power. One of several basic functions can
be performed.
 In a DC-DC converter, the dc input voltage is converted to a dc output voltage
having a larger or smaller magnitude, possibly with opposite polarity or with
isolation of the input and output ground references.
 In an AC-DC rectifier, an ac input voltage is rectified, producing a dc output
voltage. The dc output voltage and / or ac input current waveform may be
controlled.
 DC-AC inversion, involves transforming a dc input voltage into an ac output
voltage of controllable magnitude and frequency.
 AC-AC cycloconversion involves converting an ac input voltage to a given ac
output voltage of controllable magnitude and frequency.
Figure 1-1 Switching converter
1.2
Power Processing System
Fig. 1.2 shows the block diagram of a general power electronic system. The
power input to the power processor is usually, but not essentially, from the electric utility
at the line frequency (50 or 60 Hz), single phase or three phase. The phase angle between
the input voltage and the current depends on the topology and the control of the power
processor. The processed output (voltage, current, frequency and the number of phases) is
as needed by the load. If the processor’s output can be taken as a voltage source, the
output current and its phase angle relative to the output voltage is governed by the
-1-
ECE 451 Power Electronics I
requirement of the load characteristic. Ordinarily a feedback controller compares the
output of the power processor with the desired or reference value and the error between
the two is fed back to the processor as a control signal. This control signal interacts with
the input power in the processor in such a way as to minimize the error. Thus it is ensured
that proper power of desired characteristic is fed to the load. The power through such
systems maybe made reversible thereby interchanging the roles of the input and the
output.
Figure 1-2 Power Conversion system
In recent past, the field of power electronics has undergone tremendous growth.
Thus the controller in the block diagram of Fig. 1.2 consists of linear IC’s and/or digital
signal processors. This has become possible due to revolutionary advances in the microelectronic fabrication techniques. These advances in semiconductor fabrication
technology has further resulted in highly improved voltage- and current-handling
capabilities and switching speeds of power semiconductor devices constituting the power
processor of Fig. 1.2. As a result, the market for power electronic systems has expanded
significantly and a sizeable percentage of electric load is being supplied power through
power electronic systems of the basic type shown in Fig. 1.2.
1.3
Power Electronics versus Communication (or Linear) Electronics
In every power conversion process such as shown in Fig. 1.2, four factors of
importance are:
i.) small power loss i.e. high energy efficiency. This is necessary in order to
reduce the cost of wasted energy and for easy removal of heat generated
due to energy dissipation. (ii) reduced size
ii.) reduced weight and
iii.) reduced cost.
The above four objectives can not be met in most of the linear electronic systems
where semiconductor devices are operated in their linear (active) region and a line
transformer is used for electrical isolation between the utility supply and linear system.
1.4
Applications of Power Electronics
1.)
Residential. Refrigerators and freezers, air conditioning, space heating, lighting,
cooking, personal computers and other entertainment electronic equipments, light
-2-
ECE 451 Power Electronics I
2.)
3.)
4.)
5.)
6.)
7.)
1.5
dimmers, electric blankets, electric washing and sewing machines, vacuum
cleaners etc.
Industrial. Pumps and compressors, blowers and fans, arc and industrial furnaces,
industrial lasers, lighting, induction heating, welding, rolling mills, textile mills,
cement mills, excavators etc.
Commercial. Heating, ventilating and air conditioning, central refrigeration,
lighting, computer and office equipments, UPS, elevators, light dimmers and
flashers.
Transportation. Traction control of electric vehicles, electric locomotives, battery
chargers for electric vehicles, street cars and trolley buses, subways, automotive
electronics including engine control.
Aerospace. Space shuttle power supply systems, satellite power supply systems,
aircraft power supplies.
Telecommunications. Battery chargers, power supplies (dc and UPS).
Utility Systems. High voltage dc (HVDC) transmission, excitation systems, static
VAR compensation (SVC), non-conventional energy sources (solar, wind), fuel
cells, energy storage systems, induced draft fans and boiler feed water pumps,
static circuit breakers.
Classification of Power Processors
For proper study of power electronics, it is useful to classify the power processors
shown in the block diagram of Fig. 1.2 in terms of their input and output forms or
frequency. In most of the power electronic systems, the input is from the electric utility
system, either single phase or three phase. However, the output to the load may have any
of the following forms depending on the application :
1.
DC
(a) regulated (constant magnitude)
(b) adjustable magnitude
2.
AC
(a) constant frequency, adjustable magnitude
(b) adjustable frequency, adjustable magnitude.
The ac load may either be single phase or three phase. The power flow is usually
from the utility input to the output load. However, in some systems, the direction of
power flow is reversible, depending on the operating condition.
1.6
Merits and Demerits of Power Electronic Systems
Merits
i.) High efficiency due to low power loss.
ii.) High reliability.
iii.) Long life and low maintenance due to absence of moving parts.
iv.) Fast dynamic response.
v.) Small size and weight resulting in less floor space and lower installation cost.
vi.) Lower cost due to mass production of power semiconductor devices.
Demerits
i.) Tendency to generate harmonics in the supply system as well as in the load.
ii.) AC to dc and ac to ac converters operate at low input power factor under certain
operating conditions.
-3-
ECE 451 Power Electronics I
iii.)
Power electronic controllers have low overload capacity. Hence these controllers
must be designed for taking momentary overloads. This results in increased cost.
iv.) Regeneration of power is difficult in power electronic converter systems.
Merits of power electronic systems far overweigh the demerits and these converters
are extensively used in systems where power flow is to be regulated.
1.7
Types of Semiconductor Switch
The main types of semiconductor switches in common use are
1.) Diodes
2.) Power transistors
a.) Bipolar junction transistor (BJT)
b.) Metal oxide semiconductor field effect transistor (MOSFET)
c.) Insulated gate bipolar transistor (IGBT)
d.) Static induction transistor (SIT)
3.) Thyristor devices
a.) Silicon controlled rectifier (SCR)
b.) Static induction thyristor (SITH)
c.) Gate turn-off thyristor (GTO)
1.8
Characteristics and specifications of Switches
1.8.1 Ideal Characteristics
The attributes of an ideal switch may be summarized as follows:
Primary Attributes
1.)
2.)
3.)
4.)
5.)
6.)
7.)
Switching times of the state transitions between ‘‘on’’ and ‘‘off’’ should be zero.
‘‘On’’ state voltage drop across the device should be zero.
‘‘Off’’ state current through the device should be zero.
Power–control ratio (i.e., the ratio of device power handling capability to the
control electrode power required to effect the state transitions) should be infinite.
‘‘Off’’ state voltage withstand capability should be infinite.
‘‘On’’ state current handling capability should be infinite.
Power handling capability of the switch should be infinite.
Secondary Attributes
1. Complete electrical isolation between the control function and the power flow
2. Bidirectional current and voltage blocking capability
1.8.1 Characteristics of Practical Devices
During the turn-on and -off process, a practical switching device, shown in Figure
1.3(a), requires a finite delay time (td ) , rise time ( t r ), storage time ( t s ), and fall time
( t f ). As the device current isw rises during turn-on, the voltage across the device vsw ,
falls. As the device current falls during turn-off, the voltage across the device rises. The
typical waveforms of device voltages vsw and currents isw are shown in Figure 1.3(b).
The turn-on time ( ton ) of a device is the sum of the delay time and the rise time, whereas
-4-
ECE 451 Power Electronics I
the turnoff time ( toff ) of a device is the sum of the storage time and the fall time. In
contrast to an ideal, lossless switch, a practical switching device dissipates some energy
when conducting and switching. Voltage drop across a conducting power device is at
least approximately 1 V, but can often be higher, up to several volts. The goal of any new
device is to improve the limitations imposed by the switching parameters.
Figure 1-3 Typical waveforms of device voltages and currents
The average power loss, PON , is given by
PON
1

TS
t on
 p dt
(1-1)
0
where Ts denotes the conduction period and p is the instantaneous power loss (i.e.,
product of the voltage drop vsw across the switch and the conducted current isw ). Power
losses increase during turn-on and turn-off of the switch because during the transition
from one conduction state to another state both the voltage and current have significant
values.
-5-
ECE 451 Power Electronics I
CHAPTER TWO
2
CHARACTERISTICS OF POWER SEMICONDUCTOR
DEVICES
The modern age of power electronics began with the introduction of thyristors in
the late 1950s. Now there are several types of power devices available for high-power
and high-frequency applications. The most notable power devices are gate turn-off
thyristors, power Darlington transistors, power MOSFETs, and insulated-gate bipolar
transistors (IGBTs). Power semiconductor devices are the most important functional
elements in all power conversion applications. The power devices are mainly used as
switches to convert power from one form to another. They are used in motor control
systems, uninterrupted power supplies, high-voltage DC transmission, power supplies,
induction heating, and in many other power conversion applications. A review of the
basic characteristics of these power devices is presented in this section.
The ratings, specifications and characteristics of a device are of utmost
importance to the designer for designing equipment which will render lasting trouble-free
service. Choice of components for a particular service requirement and design of their
safety devices would be easier if detailed characteristics and ratings are available.
Detailed specifications and ratings are available only in manufacturers’ data sheets and
designers have to depend on them. In this chapter, some of the important characteristics
of parameters of the devices are discussed.
2.1
Power Diode
Among all the static switching devices used in power electronics (PE), the power diode is
perhaps the simplest. Its circuit symbol, shown in Fig. 2.1, is a two terminal device, and
with terminal A known as the anode and terminal K known as the cathode. If terminal A
experiences a higher potential compared to terminal K, the device is said to be forward
biased and a forward current (IF ) will flow through the device in the direction as shown.
This causes a small voltage drop across the device (<1 V), which under ideal conditions
is usually ignored. By contrast, when a diode is reverse biased, it does not conduct and
the diode then experiences a small current flowing in the reverse direction called the
leakage current. Both forward voltage drop and leakage current are ignored in an ideal
diode. In PE applications a diode is usually considered to be an ideal static switch.
The characteristics of a practical diode depart from the ideals of zero forward and infinite
reverse impedance, as shown in Fig. 2.2a. In the forward direction, a potential barrier
associated with the distribution of charges in the vicinity of the junction, together with
other effects, leads to a voltage drop. In the case of silicon this is in the range of 1 V for
currents in the normal range. In the reverse direction, within the normal voltage operating
range, a very small current flows that is largely independent of the voltage. For practical
-6-
ECE 451 Power Electronics I
purposes, the static characteristics are often represented as shown in Fig. 2.2b. In Fig.
2.2b the forward characteristic is expressed as a threshold voltage VO with a linear
incremental or slope resistance r. The reverse characteristic remains the same over the
range of possible leakage currents irrespective of voltage within the normal working
range.
Figure 2-1 Power diode: (a) symbol; (b) and (c) types of packaging.
Figure 2-2(a) Typical static characteristic of a power diode (forward and reverse have different scale).
-7-
ECE 451 Power Electronics I
Figure 2-3(b) Practical representation of the static characteristic of a power diode
2.1.1 Diode Characteristics
From the forward and reverse-biased condition characteristics, one notices that when the
diode is forward biased, current rises rapidly as the voltage is increased. Current in the
reverse-biased region is significantly small until the breakdown voltage of the diode is
reached. Once the applied voltage is over this limit, the current will increase rapidly to a
very high value limited only by an external resistance.
DC Diode parameters. The most important are the following:
 Forward voltage VF is the voltage drop of a diode across A and K at a defined
current level when it is forward biased.
 Breakdown voltage VB is the voltage drop across the diode at a defined current
level when it is beyond reverse-biased level. This is known as avalanche.
 Reverse current IR is the current at a particular voltage, and which is below the
breakdown voltage.
AC Diode parameters. Very common are the following:
 Forward recovery time tFR is the time required for the diode voltage to drop to a
particular value after the forward current starts to flow.
 Reverse recovery time tRR is the time interval between the application of reverse
voltage and the reverse current dropped to a particular value as shown in Fig. 2.2.
Parameter ta is the interval between the zero crossing of the diode current and
when it becomes IRR. On the other hand, tb is the time interval from the maximum
reverse recovery current to  0.25 I RR . The ratio of the two parameters ta and tb is
known as the softness factor SF. Diodes with abrupt recovery characteristics are
used for high-frequency switching. See Fig. 2.3 for soft and abrupt recovery.
In practice, a design engineer frequently needs to calculate reverse recovery time in
order to evaluate the possibility of high-frequency switching. As a rule of thumb, the
lower trr is, the faster the diode can be switched.
-8-
ECE 451 Power Electronics I

Figure 2-4 Diode reverse recovery process with various softness factors. (a) Soft recovery; and (b) abrupt
recovery.
trr  ta  tb
(2-1)
If tb is negligible compared to ta (which commonly occurs), then the following
expression is valid:
2QRR
trr 
di / dt
from which the reverse recovery current
di
I rr 
2QRR
dt
where QRR is the storage charged, and can be calculated from the area enclosed by the
path of the recovery current.
Diode Capacitance CD is the net diode capacitance including the junction (CJ )
plus package capacitance (CP). In high-frequency pulse switching a parameter known
as transient thermal resistance is of vital importance because it indicates the instantaneous
junction temperature as a function of time under constant input power.
EXAMPLE 2.1 The manufacturer of a selected diode gives the rate of fall of the diode
current di / dt  20 A /  s , and a reverse recovery time of trr  5 s . What value of peak
reverse current do you expect?
SOLUTION. The peak reverse current is given as:
di
I rr 
2QRR
dt
The storage charge QRR is calculated as:
1 di 2
Qrr 
trr  1/ 2  20 A /  s  (5 106 ) 2  50C
2 dt
Hence,
I rr  20 A /  s  2  50C  44.72 A
-9-
ECE 451 Power Electronics I
2.1.2 Maximum Average Forward Current
The maximum average forward current ( I f ( avg )max ) is the current a diode can safely
handle when forward biased. Power diodes are available in ratings from a few amperes to
several hundred amperes. For example, the power diode D6 described in the data
specification sheet can handle up to 6 A in the forward direction when used as a rectifier.
2.1.3 Peak Inverse Voltage
The peak inverse voltage (PIV) of a diode is the maximum reverse voltage that can be
connected across a diode without breakdown. The peak inverse voltage is also called
peak reverse voltage or reverse breakdown voltage. The PIV ratings of power diodes
extened from a few volts to several thousand volts. For example, the power diode D6 has
a PIV rating of up to 1600 V(Fig. 1.12).
2.1.4 Maximum Surge Current
The IFSM (forward surge maximum) rating is the maximum current that the diode can
handle as an occasional transient or from a circuit fault. The IFSM rating for the power
diode D6 is up to 190 A, as shown in Fig 1.12.
2.1.5 Maximum Junction Temperature
This parameter defines the maximum junction temperature that a diode can withstand
without failure. The maximum junction temperature for the power diode D6 is 180°C.
2.1.6 Testing a Power Diode
An ohmmeter can be used to test power diodes. The ohmmeter is connected so that the
diode is forward biased. This should give a low resistance reading. Reversing the
ohmmeter leads should give a very high resistance or even an infinite reading. A very low
resistance reading in both directions indicates a shorted diode. A high resistance reading
in both directions indicates an open diode.
2.1.7 Protection of Power Diodes
A power diode must be protected against over current, over voltage, and transients. When
a diode is reverse-biased, it acts like an open circuit. If the reverse bias voltage exceeds
the breakdown voltage, a large current flow results. With this high voltage and large
current, power dissipation at the diode junction may exceed its maximum value,
destroying the diode. For the diode protection, it is a usual practice to choose a diode with
a peak reverse voltage rating that is 1.2 times higher than the expected voltage during
normal operating conditions.
Current ratings for diodes are based on the maximum junction temperatures. As a safety
precaution, it is recommended that the diode current be kept below this rated value.
Electrical transients can cause higher-than-normal voltages across a diode. To protect a
diode from the transients, an RC series circuit may be connected across the diode to
reduce the rate of change of voltage.
- 10 -
ECE 451 Power Electronics I
2.2
Schottky Diode
Bonding a metal, such as aluminum or platinum, to n-type silicon forms a
Schottky diode. The Schottky diode is often used in integrated circuits for high-speed
switching applications. An example of a high speed switching application is a detector at
- 11 -
ECE 451 Power Electronics I
microwave frequencies. The Schottky diode has a voltage current characteristic similar to
that of a silicon pn-junction diode. The Schottky diode is designed to reduce the
propagation delay time of the standard TTL IC chips. The construction of the Schottky
diode is shown in Fig. 1.18a, and its symbol is shown in Fig. 1.18b.
Characteristics
The low-noise characteristics of the Schottky diode make it ideal for application in power
monitors of low-level radio frequency, detectors for high frequency, and Doppler radar
mixers. One of the main advantages of the Schottky barrier diode is its low forward
voltage drop compared with that of a silicon diode. In the reverse direction, both the
breakdown voltage and the capacitance of a Schottky barrier diode behave very much
like those of a one-sided step junction. In the one-sided step junction, the doping level of
the semiconductor determines the breakdown voltage. Because of the finite radius at the
edges of the diode and because of its sensitivity to surface cleanliness, the breakdown
voltage is always somewhat lower than theoretical predictions.
Data Specifications
The data specification sheet for a DSS 20-0015B power Schottky diode is provided as an
example in Figs. 1.19. Specifications will vary depending on the application and model of
Schottky diode.
Testing of Schottky Diodes
Two ways of testing the diodes use either a voltmeter or a digital multimeter. The
voltmeter should be set to the low resistance scale. A single diode or rectifier should read
a low resistance, typically, 2/3 scale from the resistance in the forward direction. In the
reverse direction, the resistance should be nearly infinite. It should not read near 0 Ω in
the shorted or open directions. The diode will result in a higher scale reading of resistance
as a result of its lower voltage drop. What is being measured is the resistance at a
particular low current point; it is not the actual resistance in a power rectifier circuit. The
- 12 -
ECE 451 Power Electronics I
digital multimeter will usually have a diode test mode. When using this mode, a silicon
diode should read between 0.5 to 0.8 V in the forward direction and open in the reverse
direction. A germanium diode will be in the range of 0.2 to 0.4 V in the forward
direction. By using the normal resistance range, these diodes will usually show open for
any semiconductor junction since the voltmeter does not apply enough voltage to reach
the value of the forward drop.
- 13 -
ECE 451 Power Electronics I
- 14 -
ECE 451 Power Electronics I
2.3
Thyristor
Thyristors are four-layer pnpn power semiconductor devices. These devices switch
between conducting and nonconducting states in response to a control signal. Thyristors
are used in timing circuits, AC motor speed control, light dimmers, and switching
circuits. Small thyristors are also used as pulse sources for large thyristors. The thyristor
family includes the silicon-controlled rectifier (SCR), the DIAC, the Triac, the siliconcontrolled switch (SCS), and the gate turn-off thyristor (GTO).
(a) The SCR symbol; (b) the SCR structure.
2.3.1 Two – Transistor Analogy of SCR
A thyristor can be considered as two complementary transistors, one pnptransistor, Q1 , and other npn-transistor, Q2 , as shown in Figure 2.6(a). The equivalent
circuit model is shown in Figure 2.6(b).
As I G flows into the gate, i.e. the base of the n-p-n transistor, it is amplified and
appears at the collector as  2 I G . This current then flows to the base of the p-n-p
transistor and appears at its collector as 1 2 IG . The current 1 2 IG appears at the base
of n-p-n transistor creating a regenerative system. Thus, a small gate current turns the
device ON. The ON state current through the device may be thousand times greater than
the gate current. The only requirement of the gate current is that it should be sufficiently
large to cause regenerative action to fire the device.
- 15 -
ECE 451 Power Electronics I
Figure 2-5 Two – transistor model of a thyristor
2.3.2 SCR Characteristics
The volt-ampere characteristic of an SCR is shown in Fig. 1.22. If the forward
bias is increased to the forward breakover voltage, VFBO, the SCR turns ON. The value of
forward breakover voltage is controlled by the gate current IG. If the gate-cathode pnjunction is forward-biased, the SCR is turned ON at a lower breakover voltage than with
the gate open. As shown in Fig. 1.22, the breakover voltage decreases with an increase in
the gate current. At a low gate current, the SCR turns ON at a lower forward anode
voltage. At a higher gate current, the SCR turns ON at a still lower value of forward
anode voltage.
When the SCR is reverse-biased, there is a small reverse leakage current (IR). If
the reverse bias is increased until the voltage reaches the reverse breakdown voltage
V(BR)R), the reverse current will increase sharply. If the current is not limited to a safe
value, the SCR may be destroyed.
- 16 -
ECE 451 Power Electronics I
Figure 2-6 (a) V-I characteristic of SCR connected for operation in dc circuit, (b) circuit of (a)
- 17 -
ECE 451 Power Electronics I
SCR Turn-Off Circuits
If an SCR is forward-biased and a gate signal is applied, the device turns ON. Once the
anode current is above IH, the gate loses control. The only way to turn OFF the SCR is to
make the anode terminal negative with respect to the cathode or to decrease the anode
current below IH. The process of SCR turnoff is called commutation. Figure 1.23 shows
an SCR commutation circuit. This type of commutation method is called AC line
commutation. The load current IL flows during the positive half cycle of the source
voltage. The SCR is reverse-biased during the negative half cycle of the source voltage.
With a zero gate current, the SCR will turn OFF if the turn-off time of the SCR is less
than the duration of the half cycle.
SCR Ratings
A data sheet for a typical thyristor follows this section and includes the following
information:
Surge Current Rating (IFM)—The surge current rating (IFM) of an SCR is the peak anode
current an SCR can handle for a short duration.
Latching Current (IL)—A minimum anode current must flow through the SCR in order
for it to stay ON initially after the gate signal is removed. This current is called the
latching current (IL).
- 18 -
ECE 451 Power Electronics I
Holding Current (IH)—After the SCR is latched on, a certain minimum value of anode
current is needed to maintain conduction. If the anode current is reduced below this
minimum value, the SCR will turn OFF.
Peak Repetitive Reverse Voltage (VRRM)—The maximum instantaneous voltage that an
SCR can withstand, without breakdown, in the reverse direction.
Peak Repetitive Forward Blocking Voltage (VDRM)—The maximum instantaneous
voltage that the SCR can block in the forward direction. If the VDRM rating is exceeded,
the SCR will conduct without a gate voltage.
Nonrepetitive Peak Reverse Voltage (VRSM)—The maximum transient reverse voltage
that the SCR can withstand.
Maximum Gate Trigger Current (IGTM)—The maximum DC gate current allowed to turn
the SCR ON.
Minimum Gate Trigger Voltage (VGT)—The minimum DC gate-to-cathode voltage
required to trigger the SCR.
Minimum Gate Trigger Current (IGT)—The minimum DC gate current necessary to turn
the SCR ON.
2.5
The DIAC
A DIAC is a three-layer, low-voltage, low-current semiconductor switch. The
DIAC symbol is shown in Fig. 1.24a. The DIAC structure is shown in Fig. 1.24b. The
DIAC can be switched from the OFF to the ON state for either polarity of applied
voltage.
The volt-ampere characteristic of a DIAC is shown in Fig. 1.25. When Anode 1 is
made more positive than Anode 2, a small leakage current flows until the breakover
voltage VBO is reached. Beyond VBO, the DIAC will conduct. When Anode 2 is made
more positive relative to Anode 1, a similar phenomenon occurs. The breakover voltages
for the DIAC are almost the same in magnitude in either direction. DIACs are commonly
used to trigger larger thyristors such as SCRs and Triacs.
2.6
The Triac
The Triac is a three-terminal semiconductor switch. It is triggered into conduction in both
the forward and the reverse directions by a gate signal in a manner similar to the action of
an SCR. The breakover voltage of the Triac can be controlled by the application of a
positive or negative signal to the gate. As the magnitude of the gate signal increases, the
breakover voltage decreases. Once the Triac is in the ON state, the gate signal can be
removed and the Triac will remain ON until the main current falls below the holding
current (IH) value.
- 19 -
ECE 451 Power Electronics I
- 20 -
ECE 451 Power Electronics I
Fig. Triac characteristics
2.7
Silicon-Controlled Switch
The SCS is a four-layer pnpn device. The SCS has two gates labeled as the anode gate
(AG) and the cathode gate (KG). An SCS can be turned ON by the application of a
negative gate pulse at the anode gate. When the SCS is in the ON state, it can be turned
OFF by the application of a positive pulse at the anode gate or a negative pulse at the
cathode gate.
- 21 -
ECE 451 Power Electronics I
2.8
Gate Turn-Off Thyristor
The GTO is a power semiconductor switch that turns ON by a positive gate signal. It can
be turned OFF by a negative gate signal. The GTO voltage and current ratings are lower
than those of SCRs. The GTO turn-off time is lower than that of SCR. The turn-on time
is the same as that of an SCR.
2.9
ASSIGNMENT
Read and make notes on Power Bipolar Junction Transistors (BJTs), IGBTs, and Metaloxide-semiconductor field effect transistors (MOSFETs).
- 22 -
ECE 451 Power Electronics I
CHAPTER THREE
3
UNCONTROLLED RECTIFIERS
Rectification refers to the process of changing alternating current to direct current.
It is extensively used in charging batteries, supplying dc motors, supply of arc lamps,
electrochemical processes and radio and television receivers at home.
Rectifying circuits can be classified as uncontrolled rectifiers which deliver a
constant output voltage, or as controlled rectifiers in which the output voltage can be varied
by the controlling action of a silicon controlled rectifier. The type of load in a rectifier
circuit has an important effect on the behaviour of the circuit and on the duty imposed on
the rectifier elements. For example, the load may consist solely of resistance or a storage
battery or a motor load, or it may consist of combination of resistance, inductance and
capacitance such as in rectifiers having smoothing filters. Each type of load offers a
different problem in the application of a rectifier circuit
3.1
Half – Wave Rectifier with Resistive Load
The basic single-phase half-wave rectifier circuit with a resistance load is the
simplest and is shown in Fig. 3.1.
Figure 3-1 Single – phase half-wave rectifier with resistive load
The diode begins to conduct as soon as its anode potential becomes greater than that
of the cathode, i.e. when the voltage at terminal A is positive with respect to B , current
- 23 -
ECE 451 Power Electronics I
starts flowing through the load resistance and a voltage is developed across it. The
conduction continues throughout the positive half- cycle, till the terminal B becomes
positive with respect to A . At this condition, the diode becomes reverse biased and only a
small leakage current flows through the load resistance. Since this current is negligibly
small compared to the forward current, it is taken as zero for all practical purposes. This
non-conducting state continues throughout the negative half-cycle and no voltage is
developed across RL . Therefore, a voltage is developed across the load for alternate halfcycles of the supply voltage. The voltage waveform is shown in Fig. 3.2. The voltage drop
across the diode is neglected.
3.1.1 Load – Side Quantities
Let,
(3-1)
vs  Vmsint  2Vs sin t
where,
Vs = r.m.s. voltage across the secondary of the transformer
Vdc = average voltage across the load
Vrms = r.m.s. voltage across the load
The relationship between Vs , Vdc , Vrms , can be obtained from the following equations.
Vdc 
1
2

Vm


2




V
sin

t
d
(

t
)

0 d (t ) 
 m




0

 0.318Vm
(3-2)
1/ 2
Vrms
2
 1  2 2

    Vm sin t d (t )   0 d (t ) 

 2  0

Vm
(3-3)
 0.5Vm
2
The components of load current may be found in a similar way. By the use of Eqts.
3.2 and 3.3, these components may be found directly from the voltage components. If the
load resistance is RL , then the average value of load current I dc is
V
V
(3-4)
I dc  dc  m
R R
and the r.m.s. value is
V
V
I
(3-5)
I rms  rms  m  m
R
2R 2
The peak value of load current,
V
V
(3-6)
I m  m  dc
R
R
The form factor (FF) of the load voltage is the ratio of the r.m.s. value of the load voltage
to the average value.

- 24 -
ECE 451 Power Electronics I
Vrms I rms
(3-7)

 1.57
Vdc
I dc
In the half-wave configuration, the r.m.s value of the transformer secondary current is the
same as I rms . Therefore, power delivered by the transformer secondary,
FF 
(3-8)
Pac  Vrms I rms
and, in terms of dc values,
V
Pac  dc 1.57 I dc
2
(3-9)
 3.49Pdc
The dc power developed across the load is Pdc  Vdc I dc . The power to be supplied by the
transformer is Pac  3.49Pdc . Therefore, utility factor of the transformer is, by definition,
Pdc
P
TUF 
 dc  0.29
trasformer VA rating Vs I s
It is also desired that a rectifier produces direct current and minimizes the losses owing to
the flow of ac harmonics in the load. The efficiency with which alternating current is
converted into direct current is measured by the term efficiency of rectification, and is
given by,
dc load power
(3-10)

100%
ac load power  rectifier loss
If the rectifier forward resistance is neglected as in an ideal case, then,
P
(3-11)
  dc 100%
Pac
where Vs and I s are the r.m.s. voltage and r.m.s. current of the transformer secondary
respectively. For the half-wave rectifier the rectification efficiency is 40.6% .
Since both the current supplied to the load and the voltage developed across it have
the half-sinusoidal waveform shown in Fig. 3.2, the ultimate purpose of the rectifier - to
produce a steady output voltage and current from the sinusoidal voltage source - is but
imperfectly achieved. A measure of the ripple voltage and current, i.e. the waviness or lack
of smoothness of the waveform, is given by the ripple factor (RF). This is defined as
effective value of ac components
of voltage (or current )
RF 
direct or average value of voltage
(or current )
1/ 2
2
Vrms
 Vdc2 

Vdc
2
V 
(3-12)
  rms   1  FF 2  1
 Vdc 
For the half-wave rectifier the ripple factor is 1.21. The ideal value of the ripple factor is
zero, for an undistorted steady dc output. The value 1.21 for half-wave rectification is
undesirably large and is unacceptable for many applications.
The peak inverse voltage is another important factor in rectifier circuit design. The
peak inverse voltage, PIV, limits the permissible voltage that may be applied to the rectifier
element, which is the maximum instantaneous voltage that appears across the diode in the
- 25 -
ECE 451 Power Electronics I
blocking state. In the half - wave rectifier, PIV is the peak value of the transformer
secondary voltage appearing across the rectifier in the negative half-cycle, as is evident
from Fig. 3.1. Therefore,
(3-13)
PIV  1.414E
3.1.2 Supply-Side Quantities
In the series circuit Fig. 3.1 the supply current is also the load current. Equations
(3.4) and (3.5) therefore also define the supply current. Because the diode is presumed
ideal, the input power from the supply is equal to the power dissipated in the load resistor.
From the supply side, the circuit of Fig. 3.1 is nonlinear; that is, the impedance of the diode
plus resistor cannot be represented by a straight line in the voltage-current plane. When a
sinusoidal voltage supplies a nonlinear impedance the resulting current is periodic but nonsinusoidal. Any function that is periodic can be represented by a Fourier series, which
enables one to calculate values for the harmonic components of the function.

a
i(t )  0   (an cos nt bn sin nt )
2 n 1

a
(3-14)
 0   (cn sin(nt n )
2 n 1
Where,
cn  an2  bn2
(3-15)
 an 

 bn 
When function i(t ) is periodic in 2 the coefficients of (3.14) are given by
n  tan 1 
a0
1

2 2
an 
bn 
1

1

(3-16)
2
 i(t ) d (t )
(3-17)
0
2
 i(t ) cos nt d (t )
(3-18)
0
2
 i(t )sin nt d (t )
(3-19)
0
The Fourier coefficient a0 / 2 defines the time average or dc value of the periodic function.
The fundamental (supply frequency) components are obtained when n  1 in Eqts. (3.16)
and (3.17). The supply current of Figure 3.1 is defined by
2
1
a1   i(t ) cos t d (t )

0

E
 m  sin t cos t d (t )  0
R 0
Similarly
b1 
1

2
 i(t ) cos t d (t )
0
- 26 -
(3-20)
ECE 451 Power Electronics I


Em
E
sin 2 t (t )  m

R 0
2R
(3-21)
The peak amplitude c1 of the fundamental frequency sine wave component of Fig. 3.1 is
therefore
E
(3-22)
c1  a12  b12  m
2R
Angle 1 defines the displacement angle between the fundamental component of i(t ) and
the supply current origin. In this case
a 
1  tan 1  1   0
(3-23)
 b1 
Equation (3.23) shows that the fundamental component of current is in time phase with the
supply voltage.
3.1.3 Power Factor
The power factor of any circuit is the factor by which the apparent voltamperes
must be multiplied to obtain the real or time average power. For the supply side of Fig. 3.1,
the power factor is given by
P
(3-24)
PF 
Vs I s
where P is the average power and Vs and I s are r.m.s values of the supply voltage and
current. The universal definition of Eqt. (3.24) is independent of frequency and of
waveform.
In most nonlinear circuits supplied by a sinusoidal voltage the supply current
contains a supply frequency component (or fundamental harmonic component) of r.m.s
value I s1 that is phase displaced from the supply voltage by angle 1 . This is illustrated in
Figure 3.2. The average input power P can then be written as
P  Vs I s1 cos 1
(3-25)
Combining Eqts. (3.14) and (3.15) gives
I
(3-26)
PF  s1 cos 1
Is
The ratio I s1 / I s is the current distortion factor and arises because of the nonlinear load
(i.e., rectifier) impedance. The term cos 1 in Eqt. (3.26) is called the displacement factor
(DF) and may be partly or wholly attributable to reactive components of the load
impedance. The harmonic factor (HF) also known as the total harmonic distortion (THD)
is a measure of the distortion of a waveform. It is defined as:
1/ 2
 I  2 
THD   s   1
 I s1 

(3-27)
- 27 -
ECE 451 Power Electronics I
Figure 3-2 Waveforms for input voltage and current
For the half-wave rectifier circuit of Fig. 3.1 the Fourier coefficients of the
fundamental current wave showed that the displacement angle 1 is zero [Eqt. (3.23)]. This
means that the displacement factor, cos 1 , is unity. The power factor, in this case, is
therefore equal to the distortion factor and is due entirely to the nonlinear rectifier
impedance. Substituting values from Eq. (3.1) and (3.5) into Eq. (3.24), noting that
Vm  2Vs gives the result
PF 
1
2
(3-28)
N.B.
I s  I rms  I m / 2;
I s1  I m1 / 2;
But I m1  I m / 2 from Eqt. (3.22).
For a resistive load the PF can also be obtained using
P
PF  ac
Vs I s
Example 3-1
The rectifier of Fig. 3.1 (a) has a purely resistive load R . Determine
(a) the efficiency
(40.5%)
(b) the FF,
(1.57)
(c) the RF,
(1.21)
(d) the TUF, (0.286)
(e) the PIV of the diode D1 , (Vm )
(f) the THD, and
(1.0)
(g) the input PF.
(0.707)
- 28 -
(3-29)
ECE 451 Power Electronics I
3.2
Single – Diode circuit for Battery Charging
A simple diode circuit containing a current limiting resistance R can be used to
charge a battery of e.m.f E from a single-phase supply (Fig. 3.3). The battery opposes the
unidirectional flow of current so that the net driving voltage is vs  E . Neglecting any
voltage drop on the diode (which is likely to be of the order 1–2 V) the current is therefore
v  E Vm sin t  E
for   t  
(3-30)
i0  s

R
R
where  and  define the current pulse in Fig. 3.3. Current flows only in the positive
voltage direction when e vs  E  0 . Angles  and  are defined by
vs  E  Vm sin   E  0
(3-31)
Therefore,
 E

 Vm 
  sin 1 
Figure 3-3 Battery Charger
- 29 -
(3-32)
ECE 451 Power Electronics I
By symmetry,
   
(3-33)
The average value I dc of the battery charging current is defined by
2
1
i(t ) d (t )
2 0
Substituting Eqt. (3.30) into the above defining integral expression gives

1
I dc 
(Vm sin t  E ) d (t )
2 R 
I dc 
1
Vm (cos   cos  )  E (   )
2 R
Eliminating  between Eqs. (3.34) and (3.35) gives
1
I dc 
 2Vm cos   E (2   )
2 R

(3-34)
(3-35)
(3-36)
Example 3-2
An ideal single-phase source, 240 V, 60 Hz, supplies power to a load resistor R  100 via
a single ideal diode. Calculate the average and rms values of the current and the power
dissipation. What must be the rating of the diode?
Solution
The circuit is shown in Fig. 3.1. The specified voltage of 240 V is the r.m.s value. The
average circuit current, from Eq. (3.4), is
V
240 2
I dc  m 
 1.08 A
 R 100
The r.m.s value of the current is given by Eq. (3.5)
V
240 2
I rms  m 
 1.70 A
2 R 2(100)
In the circuit of Fig. 3.1 power dissipation takes place only in the load resistor and is given
by
2
Po  I rms
R  1.72 (100)  289W
The diode must be rated in terms of a peak inverse voltage and a mean forward current.
PIV  Vm  240 2  339.41V
A convenient commercial rating would be to choose a diode rated at 400 V. Either the r.m.s
or the mean (average) current could be used as a basis of current rating. Since I rms  1.7 A a
convenient commercial rating would be 2 A.
Example 3-3
In the battery charger circuit, Fig. 3.3, the supply voltage is given by vs  300sin t and
resistor R  10 . Calculate the average charging current if E  150V . What is the
operating power factor?
Solution
From Eqs. (3.32) and (3.33),
- 30 -
ECE 451 Power Electronics I
 150 
o
  30 ;
 300 
      150o
Substituting values Vm  300V , E  150V , R  10,    / 6 , into Eq.(3.36) gives
I dc  3.27 A .
The r.m.s current is given by integrating Eq. (3.30)
2
1
I 02 
i02 (t ) d (t )
2 0
  sin 1 

1
(Vm sin t  E ) 2 d (t )
2 
2 R 
from which it is found that, with      then

 Vm2

Vm2
2

E
(


2

)

sin 2  4Vm E cos  


2

 2

Substituting numerical values gives
I 0  4.79 A
The total power delivered to the circuit from the ac supply is
P  I o2 R  I dc E
In this application the power factor is therefore
I 2 R  EI dc
P
PF 
 o
Vs I o
 Vm 

 Io
 2
Now
P0  I 02 R  229.4W
The total power delivered by the supply is
P  229.4  (3.27)(150)  720W
The power factor as seen from the supply is
720
PF 
 0.71
 300 

 (4.79)
 2
I 02 
1
2 R 2
- 31 -
ECE 451 Power Electronics I
3.3
Single-Phase Fullwave Rectifier
A full-wave rectifier circuit with a center-tapped transformer is shown in Figure 3.4(a).
Each half of the transformer with its associated diode acts as a half-wave rectifier and the
output of a full-wave rectifier is shown in Figure 3.4(b). Because there is no dc current
flowing through the transformer, there is no dc saturation problem of transformer core. The
average output voltage is

2V
2
Vdc   Vm sin t d (t )  m
(3-37)

0

Figure 3-4 Single-phase rectifier with centre-tapped transformer
Instead of using a centre-tapped transformer, four diodes can be used as shown in
Fig. 3.5. During the positive half-cycle of the input voltage, the power is supplied to the
load through diodes D1 and D2. During the negative cycle, diodes D3 and D4 conduct. The
waveform for the output voltage is shown in Figure 3.5(b) and is similar to that of Figure
3.4(b). The peak-inverse voltage of a diode is only Vm. This circuit is known as a bridge
rectifier, and it is commonly used in industrial applications.
- 32 -
ECE 451 Power Electronics I
Figure 3-5 Full-wave bridge rectifier
Example 3-4 Finding the Performance Parameters of a Full-Wave Rectifier with CenterTapped transformer
If the rectifier in Figure 3.4(a) has a purely resistive load of R, determine (a) the efficiency,
(b) the FF, (c) the RF, (d) the TUF, (e) the PIV of diode D1, and (f) the CF of the input
current.
Solution
Vdc 
2

V

m
sin t d (t ) 
2Vm

0
; I dc 
Vdc
;
R
1
Vrms
2 
2 V
V
   (Vm sin t ) 2 d (t )   m ; I rms  rms ;
R
2
 0

a)  
Pdc Vdc2 / R 4Vm2 /  2
8
 2

 2  0.8105
2
Pac Vrms / R
Vm / 2

b) FF 
Vrms Vm / 2



 1.1107
Vdc
2Vm /  2 2
c) RF  FF 2  1  0.4834
d) TUF 
Pdc
4Vm2 /  2 R
4 2

 2  0.5732
Vs I s
2Vm / 2  0.5Vm / R  


- 33 -
ECE 451 Power Electronics I
N.B. The transformer secondary current Is ( r.m.s. current through each diode) is
determined from the power consideration. Since the two diodes supply the total load power,
then
2
2 I s2 R  I rms
R;  I s 
I rms
2

Vm
2R
e) PIV  2Vm
f) I s ( peak ) 
I s ( peak )
Vm
V
; I s  m ;crest factor CF 
 2
R
Is
2R
g) The input PF for a resistive load can be found from
PF 
Pac Vrms I rms
V2 /2
2

 2m

VA
Vs I s
2
Vm / 2
Example 3-5 Finding the Input Power Factor of a Full-Wave Rectifier
A single-phase bridge rectifier that supplies a very high inductive load such as a dc motor
is shown in Figure 3.7a. The turns ratio of the transformer is unity. The load is such that the
motor draws a ripple-free armature current of ‘a as shown in Figure 3.6b. Determine (a) the
THD of input current, and (b) the input PF of the rectifier.
Figure 3-6 Full-wave bridge rectifier with dc motor load
Solution
Normally, a dc motor is highly inductive and acts like a filter in reducing the ripple current
of the load.
- 34 -
ECE 451 Power Electronics I
a.) The waveforms for the input current and input voltage of the rectifier are
shown in Figure 3.7b. The input current can be expressed in a Fourier series
as

is (t )  I dc    an cos nt  bn sin nt 
n 1
1
I dc 
2
an 
1

2
1
0 is (t )d (t )  2
2
2
 I d (t )  0
a
0
 is (t ) cos nt d (t ) 
0
2


I
a
cos nt d (t )  0
0
0, n  even 


bn   is (t )sin nt d (t )   I a sin nt d (t )   4 I a

 0
 0
, n  odd 

 n

1
2

2
The r.m.s. value of the fundamental component of input current is
I s1 
4I a
 2
 0.90 I a .
The r.m.s. value of input current I s  I a
1
 1
2
THD  

1
  0.4843
2
 (0.90)

b.) The displacement angle   0 and DF  cos   1 .
I
PF  s1 cos   0.90 lagging
Is
- 35 -
ECE 451 Power Electronics I
3.4
THREE-PHASE BRIDGE RECTIFIERS
A three-phase bridge rectifier is commonly used in high-power applications and it is
shown in Figure 3.13. This is a full-wave rectifier. It can operate with or without a
transformer and gives six-pulse ripples on the output voltage. The diodes are numbered in
order of conduction sequences and each one conducts for 1200. The conduction sequence
for diodes is D1 - D2, D3 - D2, D3 - D4, D5 - D4, D5 D6, and D1 – D6. The pair of diodes
which are connected between that pair of supply lines having the highest amount of
instantaneous line-to-line voltage will conduct. The line-to-line voltage is 3 times the
phase voltage of a three-phase Y-connected source. The waveforms and conduction times
of diodes are shown in Figure 3.7.
If Vm is the peak value of the phase voltage, then the instantaneous phase voltages
can be described by
van  Vm sin t; vbn  sin(t  120o ), vcn  sin(t  240o )
Figure 3-7 Three-phase bridge rectifier
Because the line-line voltage leads the phase voltage by 30o, the instantaneous line-line
voltages can be described by
vab  3Vm sin(t  30o ); vbc  3Vm sin(t  90o ); vca  3Vm sin(t  210o )
The average output voltage is found from (using vab )
1
Vdc 
 /3

3 3

2 /3


3Vm sin t d (t ) 
/3
2


Vm   cos
 cos 

3
3

3 3
Vm  1.654Vm
(3-38)
where Vm is the peak phase voltage. The r.m.s. output voltage is
 1
Vrms  
 / 3
2 /3
2 2 /3
m

 9V
3Vm2 sin 2 t d (t )   
/3

 2


 9V   1
4 1
2

 sin
  sin
3 2
3
 2  3 2
2
m
1
2
/3

   1.6554Vm

- 36 -

 1  cos 2t  d (t ) 

1
2
(3-39)
ECE 451 Power Electronics I
If the load is purely resistive, the peak current through the diode is I m  3Vm / R and the
r.m.s. value of the diode current is
 2
Ir  
 2
2 /3

 /3
1
2
I m2 sin 2 t d (t )   0.5518I m

Figure 3-8 Waveforms and conduction time of diodes
The r.m.s. value of the transformer secondary current is,
 4
Is  
 2
2 /3

 /3
1
2
I m2 sin 2 t d (t )   0.7804 I m

Where I m is the peak secondary current.
Example 3-6 Finding the Performance Parameters of a Three-Phase Bridge Rectifier
A three-phase bridge rectifier has a purely resistive load of R. Determine (a) the
efficiency, (b) the FF, (c) the RF, (d) the TUF, (e) the peak inverse (or reverse) voltage
(PIV) of each diode, and (f) the peak current through a diode. The rectifier delivers
I dc  60 A at an output voltage of Vdc = 280.7 V and the source frequency is 60 Hz.
- 37 -
ECE 451 Power Electronics I
Solution
a.) From Eq. (3.38), Vdc =1.654Vm and Idc = 1.654Vm/R. From Eq. (3.39), Vrms  1.6554Vm
and I rms  1.6554Vm / R ., Pdc  (1.654Vm )2 / R;

Pac  (1.6554Vm )2 / R; the efficiency
(1.654Vm )2
 99.83%
(1.6554Vm )2
b) FF  1.6554 /1.654  100.08%
c) RF  1.0082  1  4%
d) r.m.s. voltage of transformer secondary Vs  0.707Vm ; I s  0.7804 I m  0.7804  3
Vm
R
The VA rating of the transformer,
VA  3Vs I s  3  0.707Vm  0.7804  3
TUF 
Vm
R
1.6542
 0.9542
3  3  0.707  0.7804
e) Vm  280.7 /1.654  169.7V ; PIV  3Vm  293.9V
f) The average current through each diode is
4
Id 
2
 /6
I
m
cos t d (t ) 
0
2

I m sin

6
 0.3183I m ;
The average current through each diode is I d  60 / 3  20 A ; therefore, peak current is
20
Im 
 62.83 A
0.3183
Example 3-7 Finding the Diode Ratings from the Diode Currents
A three-phase bridge rectifier supplies a highly inductive load such that the average load
current is I dc  60 A and the ripple content is negligible. Determine the ratings of the
diodes if the line- to-neutral voltage of the Y-connected supply is 120 V at 60 Hz.
Solution
The currents through the diodes are shown in Figure 3.20. The average current of a diode
I d  60 / 3  20 A . The r.m.s current is
 1
Ir  
 2

1
2 I
2
 /3 I dc d (t )  dc3  34.64 A
The PIV  3Vm  3  2 120  294V
- 38 -
ECE 451 Power Electronics I
Figure 3-9 Current through diodes
- 39 -
ECE 451 Power Electronics I
CHAPTER FOUR
4
CONTROLLED RECTIFIERS
We have seen in Chapter 3 that diode rectifiers provide a fixed output voltage
only. To obtain controlled output voltages, phase-control thyristors are used instead of
diodes. The output voltage of thyristor rectifiers is varied by controlling the delay or
firing angle of thyristors. A phase-control thyristor is turned on by applying a short pulse
to its gate and turned off due to natural or line commutation; and in case of a highly
inductive load, it is turned off by firing another thyristor of the rectifier during the
negative half-cycle of input voltage.
These phase-controlled rectifiers are simple and less expensive; and the efficiency
of these rectifiers is, in general, above 95%. Controlled rectifiers are used extensively in
industrial applications, especially in variable-speed drives, ranging from fractional
horsepower to megawatt power level.
The phase-control converters can be classified into two types, depending on the
input supply: (1) single-phase converters, and (2) three-phase converters. Each type can
be subdivided into (a) semiconverter, (b) full converter, and (c) dual converter. A
semiconverter is a one-quadrant converter and it has one polarity of output voltage and
current. A full converter is a two-quadrant converter and the polarity of its output voltage
can be either positive or negative. However, the output current of full converter has one
polarity only. A dual converter can operate in four quadrants; and both the output voltage
and current can be either positive or negative. In some applications, converters are
connected in series to operate at higher voltages and improve the input power factor (PF).
The method of Fourier series similar to that of diode rectifiers can be applied to
analyze the performances of phase-controlled converters with RL loads. However, to
simplify the analysis, the load inductance can be assumed sufficiently high so that the
load current is continuous and has negligible ripple.
4.1
Principle of phase-controlled converter operation
Consider the circuit in Fig. 4-l(a) with a resistive load. During the positive half-cycle of
input voltage, the thyristor anode is positive with respect to its cathode and the thyristor is
said to be forward biased. When thyristor T1 is fired at t   , thyristor T1 conducts and
the input voltage appears across the load. When the input voltage starts to be negative at
t   , the thyristor anode is negative with respect to its cathode and thyristor T1 is said
to be reverse biased; and it is turned off. The time after the input voltage starts to go
positive until the thyristor is fired at t   is called the delay or firing angle  . Fig.
4.l(b) shows the region of converter operation, where the output voltage and current have
one polarity. Fig. 4.lc shows the waveforms for input voltage, output voltage, load
current, and voltage across T1. This converter is not normally used in industrial
applications because its output has high ripple content and low ripple frequency.
- 40 -
ECE 451 Power Electronics I
However, it explains the principle of the single-phase thyristor converter. If f s is the
frequency of input supply, the lowest frequency of output ripple voltage is f s .
Figure 4-1 Single-phase thyristor converter with a resistive load
If Vm , is the peak input voltage, the average output voltage Vdc can be found from

Vm
V

  cos t   m (1  cos  )
2
2
Vdc   Vm sin t d (t ) 

(4-1)
Vdc can be varied from Vm /  to 0 by varying  from 0 to  . The average output
voltage becomes maximum when   0 and the maximum output voltage Vdm is
V
Vdm  m
(4-2)

The r.m.s. output voltage is given by
1
Vrms
1
 1  2 2
 2  Vm2 
2
   Vm sin t d (t )     (1  cos 2t ) d (t ) 
 2 

 4 


Vm
2
1 
sin 2  
       2 

 
1
2
- 41 -
(4-3)
ECE 451 Power Electronics I
Example 4-1 Finding the Performances of a Single-Phase Thyristor Converter
If the converter of Fig. 4.la has a purely resistive load of R and the delay angle is
   / 2 , determine (a) the rectification efficiency, (b) the form factor (FF), (c) the
ripple factor (RF), (d) the TUF, and (e) the peak inverse voltage (NV) of thyristor T1.
Solution
a) Rectification efficiency
Pdc (0.1592Vm )2


 20.27%
Pac (0.3536Vm )2
b) the FF
V
0.3536Vm
FF  rms 
 2.221
Vdc 0.1592Vm
c) RF  FF 2  1  1.983
d)
The
r.m.s.
voltage
of
the
Vs  Vm / 2  0.707Vm ; I s  I rms  0.3536Vm / R
Pdc
0.15922
TUF 

 0.1014
Vs I s 0.707  0.3536
e) PIV  Vm
- 42 -
transformer
secondary,
ECE 451 Power Electronics I
4.2
Single-Phase Full Converters
The circuit arrangement of a single-phase full converter is shown in Figure 4.2a with a
highly inductive load so that the load current is continuous and ripple free. During the
positive half-cycle, thyristors T1 and T2 are forward biased; and when these two
thyristors are fired simultaneously at t   , the load is connected to the input supply
through T1 and T2. Due to the inductive load, thyristors T1 and T2 continue to conduct
beyond t   , even though the input voltage is already negative. During the negative
half-cycle of the input voltage, thyristors T3 and T4 are forward biased; and firing of
thyristors T3 and T4 applies the supply voltage across thyristors T1 and T2 as reverse
blocking voltage. T1 and T2 are turned off due to line or natural commutation and the
load current is transferred from T1 and T2 to T3 and T4. Figure 4.2b shows the regions of
converter operation and Figure 4.2c shows the waveforms for input voltage, output
voltage, and input and output currents.
During the period from  to  , the input voltage vs and input current is are positive;
and the power flows from the supply to the load. The converter is said to be operated in
rectification mode. During the period from  to    , the input voltage vs is negative
and the input current is is positive; and reverse power flows from the load to the supply.
The converter is said to be operated in inversion mode. This converter is extensively used
in industrial applications up to 15 kW. Depending on the value of  , the average output
voltage could be either positive or negative and it provides two- quadrant operation.
The average output voltage can be found from
 
V
2V
1
 
Vdc 
(4-4)
 Vm sin t d (t )  m   cos t   m cos 




Vdc can be varied from 2Vm /  to 2Vm /  by varying  from 0 to  . The r.m.s. output
voltage is given by
1
1
 1   2 2
 2  Vm2  
 2 Vm
Vrms    Vm sin t d (t )   
(1

cos
2

t
)
d
(

t
)
 Vs
 

2
 

 2 

With a purely resistive load, thyristors T1 and T2 can conduct from  to  , and
thyristor T3 and T4 can conduct from    to 2 .
- 43 -
(4-5)
ECE 451 Power Electronics I
Figure 4-2 Single-phase full-converter
Example 4-2 Finding the Input Power Factor of a Single-Phase Full Converter
The full converter in Figure 4.2a is connected to a 120-V, 60-Hz supply. The load current
I a is continuous and its ripple content is negligible. The turns ratio of the transformer is
unity. (a) Express the input current in a Fourier series; determine the HF of the input
current, DF, and input PF. (b) If the delay angle is    / 3 , calculate Vdc , Vrms , HF
(THD), DF, and PF.
Solution
a). The waveform for input current is shown in Figure 4.2c and the instantaneous input
current can be expressed in a Fourier series as
- 44 -
ECE 451 Power Electronics I
- 45 -
ECE 451 Power Electronics I
4.3
Single-Phase Semi-converter
The circuit arrangement of a single-phase semiconverter is shown in Figure 4.3a
with a highly inductive load. The load current is assumed continuous and ripple free.
During the positive half-cycle, thyristor T1 is forward biased. When thyristor T1 is fired
at t   , the load is connected to the input supply through T1 and D2 during the period
a   t   . During the period from   t  (   ) , the input voltage is negative and
the freewheeling diode Dm is forward biased. Dm conducts to provide the continuity of
current in the inductive load. The load current is transferred from T1 and D2 to Dm ; and
thyristor T1 and diode D2 are turned off. During the negative half-cycle of input voltage,
thyristor T2 is forward biased, and the firing of thyristor T2 at t     reverse bias
Dm . The diode Dm is turned off and the load is connected to the supply through T2 and
D1.
Figure 4.3b shows the region of converter operation, where both the output
voltage and current have positive polarity. Figure 4.3c shows the waveforms for the input
voltage, input current, and currents through T1, T2, D1, and D2. This converter has better
PF due to the freewheeling diode and is commonly used in applications up to 15 kW,
where one quadrant operation is acceptable.
The average output voltage can be found from

V
V
1

Vdc   Vm sin t d (t )  m   cos t   m (1  cos  )
(4-6)




and Vdc can be varied from 2Vm /  to 0 by varying  from 0 to  . The r.m.s. output
voltage is found from
- 46 -
ECE 451 Power Electronics I
1
Vrms
 1  2 2  Vm  1 
sin 2   2
   Vm sin t  







2  
2  
 

(4-7)
Figure 4-3 Single-phase semiconverter
Example 4-3 Finding the Fourier Series of the Input Current and Input PF of 1Phase Semiconverter
The semiconverter in Figure 4.3a is connected to a 120-V, 60-Hz supply. The load
current I a can be assumed to be continuous and its ripple content is negligible. The turns
ratio of the transformer is unity. (a) Express the input current in a Fourier series;
determine the input current HF (or THD), DF, and input PF. (b) If the delay angle is
   / 2 , calculate Vdc ,Vrms , HF, DF, and PF.
- 47 -
ECE 451 Power Electronics I
Solution
- 48 -
ECE 451 Power Electronics I
- 49 -
ECE 451 Power Electronics I
4.3
Principle of Three-Phase Half-Wave Converters
Three-phase converters provide higher average output voltage, and in addition the
frequency of the ripples on the output voltage is higher compared with that of singlephase converters. As a result, the filtering requirements for smoothing out the load
current and load voltage are simpler. For these reasons, three-phase converters are used
extensively in high-power variable-speed drives. Three single-phase half-wave converters
in Figure 4.la can be connected to form a three-phase half-wave converter, as shown in
Figure 4.4a.
Figure 4-4 Three-phase half-wave converter
When thyristor T1 is fired at t   / 6   , the phase voltage van appears across the load
until thyristor T2 is fired at t  5 / 6   . When thyristor T2 is fired, thyristor T1 is
- 50 -
ECE 451 Power Electronics I
reverse biased, because the line-to-line voltage, vab ( van  vbn ) , is negative and T1 is
turned off. The phase voltage vbn appears across the load until thyristor T3 is fired at
t  3 / 2   . When thyristor T3 is fired, T2 is turned off and vcn appears across the
load until T1 is fired again at the beginning of next cycle. Figure 4.4b shows the v  i
characteristics of the load and this is a two-quadrant converter. Figure 4.4c shows the
input voltages, output voltage, and the current through thyristor T1 for a highly inductive
load. For a resistive load and    / 6 , the load current would be discontinuous and each
thyristor is self-commutated when the polarity of its phase voltage is reversed. The
frequency of output ripple voltage is 3 f s . This converter is not normally used in practical
systems, because the supply currents contain dc components. However, this converter
explains the principle of the three-phase thyristor converter.
If the phase voltage is van  Vm sin t , the average output voltage for a continuous
load current is
- 51 -
ECE 451 Power Electronics I
Example 4-4 Finding the Performances of a Three-Phase Half-Wave Converter
- 52 -
ECE 451 Power Electronics I
4.3
Three-Phase Full-Wave Converters
Three-phase converters are extensively used in industrial applications up to the 120-kW
level, where a two-quadrant operation is required. Figure 4.5a shows a full- converter
circuit with a highly inductive load. This circuit is known as a three-phase bridge. The
thyristors are fired at an interval of  / 3 . The frequency of output ripple voltage is 6 f s
and the filtering requirement is less than that of half-wave converters. At t   / 6   ,
thyristor T6 is already conducting and thyristor T1 is turned on. During interval
( / 6   )  t  ( / 2   ) , thyristors T1 and T6 conduct and the line-to - line voltage
vab ( van  vbn ) appears across the load. At t   / 2   , thyristor T2 is fired and
thyristor T6 is reversed biased immediately. T6 is turned off due to natural commutation.
During interval ( / 2   )  t  (5 / 6   ) , thyristors T1 and T2 conduct and the lineto-line voltage vac appears across the load. If the thyristors are numbered, as shown in
Figure 4.5a, the firing sequence is 12, 23, 34, 45, 56, and 61. Figure 4.5b shows the
waveforms for input voltage, output voltage, input current, and currents through
thyristors.
If the line-to-neutral voltages are defined as
- 53 -
ECE 451 Power Electronics I
Figure 4-5 Three-phase full converter
- 54 -
ECE 451 Power Electronics I
Figure 4.5b shows the waveforms for    / 3 . For    / 3 , the instantaneous
output voltage vo has a negative part. Because the current through thyristors cannot be
negative, the load current is always positive. Thus, with a resistive load, the instantaneous
load voltage cannot be negative, and the full converter behaves as a semiconverter.
Example 4-5 Finding the Performances of a Three-Phase Full-Wave Converter
Repeat Example 10.5 for the three-phase full converter in Figure 4.5a.
- 55 -
ECE 451 Power Electronics I
Example 4-6 Finding the input Power Factor of a Three-Phase Full Converter
The load current of a three-phase full converter in Figure 4.5a is continuous with a
negligible ripple content. (a) Express the input current in Fourier series, and determine
the HF of input current, the DF, and the input PE (b) If the delay angle    / 3 ,
calculate Vn , HF, DF, and PF.
- 56 -
ECE 451 Power Electronics I
Note: If we compare tie PF with that of Example 4-5, where the load is purely resistive,
we can notice that the input PF depends on the PF of the load.
- 57 -
ECE 451 Power Electronics I
5 INVERTERS
An inverter is a circuit which converts d.c. power into a.c. power at the desired
voltage and frequency. In most of the inverters, both voltage and frequency are required
to be controlled. Earlier, inverters used thyratrons, ignitrons, and mercury arc rectifiers.
However for most of the applications, these devices have been replaced by thyristors
(silicon controlled rectifiers) used as switches, in conjunction with capacitors or inductor
or both as energy storage elements.
Uses of Inverters
i.) For variable speed a.c. motor drives
ii.) For induction heating
iii.) For aircraft power supplies
iv.) As uninterrupted power supplies (UPS) in computers or domestic power
supplies.
Requirements of a Practical Inverter
i.) Ability to operate into an inductive load
ii.) Provision for overcurrent protection
iii.) Controllable output
iv.) Close proximity of output waveform to sinusoidal waveform
v.) Ability to work with load disconnected
vi.) Drive rating should not be exceeded.
Thyristor Commutation
Once a thyristor is switched into conducting state, the gate loses all control.
Hence commutation i.e. interruption of current flow in a conducting thyristor is required
to be done by some other means. The simplest way to commutate a thyristor is to
interrupt the current by a mechanical switch. While conducting, thyristor contains high
concentration of holes and electrons, which recombine on interruption of current.
Thyristor then regains its forward blocking ability. However, such a commutation is not
possible for high frequency operation. In high frequency circuits, thyristor current is
interrupted by applying a reverse anode-to-cathode voltage across the thyristor. The
reverse voltage reduces the forward current to zero and simultaneously produces a large
pulse of reverse current of extremely short duration, a few microseconds. This reverse
current sweeps the current carriers at the extreme junctions J1 and J3 out of the device.
The reverse anode current then falls to zero and the reverse biased end junctions then
block the inverse voltage. But the thyristor is still not able to block forward voltage since
current carriers are still present at the middle junction J2. These charge carriers take a
definite interval to recombine naturally and permit the device to regain forward blocking
capability.
Turn-off time
It is defined as the time interval between the reduction of the anode current to
zero and the regaining of the forward blocking capability. The magnitude of forward
- 58 -
ECE 451 Power Electronics I
current before commutation influences the turn-off time since the charges trapped at
junction J2 are directly proportional to this current. The turn-off time typically lies
between 3 s and 100 s . If a forward voltage is reapplied before recombination is
complete, the thyristor immediately reverts to the conducting state.
Types of Commutation
Commutation may be natural or forced. In an a.c. circuit, when the current in the
thyristor goes through a natural zero, a reverse voltage automatically appears across the
thyristor. Such a commutation is said to be natural commutation. No additions are
required for turning off the thyristor. In a d.c. circuit, on the other hand, it is necessary
that the forward current be forced to zero to turn off the thyristor with the help of an
external circuit.
Forced Commutation using Capacitor
Fig. 4-1 (a) gives the basic circuit arrangement. Here capacitor C, previously
charged in the polarity shown, is switched in across the conducting thyristor. This switch
S may be a transistor or another thyristor triggered to conduct at the desired instant. Fig.
4-1 (b) shows the waveforms of current and voltage for the main thyristor TH. Prior to
the initiation of commutation, the anode-to-cathode voltage of thyristor is simply the
forward conducting voltage drop, about 1 volt. On switching in the charged capacitor C,
the forward current takes some time to drop to zero. Subsequently a small reverse current
flows limited by the stray inductance of the circuit. This reverse current removes the free
charges from the end junctions J1 and J3 with a corresponding reduction in the charge on
the capacitor. This is called the carrier storage effect. This drop in capacitor voltage is,
however, small. The capacitor voltage is then blocked by the two end junctions J1 andJ3
of the thyristor and appears as a reverse bias on the thyristor.
Figure 5-1 Forced commutation of thyristor by capacitor
The d.c. supply voltage V charges the capacitor C in the opposite polarity. After
some time, capacitor voltage reverses and the thyristor is again subjected to a forward
voltage. However, the thyristor does not conduct provided that the recombination is
complete at the middle junction J2. This junction J2 then regains its forward blocking
- 59 -
ECE 451 Power Electronics I
capability. The time interval t0 from the instant t1 of current reduction to zero to the
instant t2 of reapplication of forward voltage i.e. time interval ( t2  t1 ), is called the
circuit turn-off time or the commutation time ( t0 ). The circuit commutation time t0 must
be kept greater than the thyristor turn-off time to avoid commutation failure. The value of
capacitor C is selected to ensure that sufficient turn-off time is allowed for the largest
expected current to be commutated.
Classification of Inverters
Inverters may be classified in a number of ways as below:
(A) According to the number of phases:
i.) Single phase inverters
ii.) Three phase inverters.
(B) According to the nature of driving d.c. source whether voltage source or current
source.
i.) Voltage Source Inverter (VSI)—d.c. voltage source has very small internal
resistance.
ii.) Current Source Inverter (CSI)—d.c. source has large internal resistance.
Single Phase Inverters
The following are the basic single phase inverters:
i.) using centre tapped d.c. supply
ii.) using centre tapped load
iii.) bridge type
(a) Single Phase Inverter Using Centre Tapped DC Supply
Fig. 4-2. (a) gives the basic circuit. The gating circuit and the commutating circuit
have been omitted for clarity, Fig. 4-2 (b) gives the waveforms of the output voltage v0
and the load current. Two thyristors T1 and T2 are connected across the complete d.c.
supply with centre tap of d.c. supply connected to junction of the two thyristors through
the load impedance. Two feedback diodes D1 andD2 are connected across T1 and T2
respectively in inverse parallel. These feedback diodes are necessary to provide path for
return of reactive energy, from reactive (inductive or capacitive) loads to the d.c. supply.
In the case of a purely resistive load, these feedback diodes are not needed.
- 60 -
ECE 451 Power Electronics I
Figure 5-2 Single-phase thyristor inverter with inductive load
(b) Single Phase Inverter Using Centre-Tapped Load.
Fig. 4-3 (a) gives the basic circuit. Fig. 4-3 (b) gives the waveform of output
voltage assuming ideal performance of the inverter. Here again feedback diodes D1 and
D2 are connected across thyristors T1 and T2 respectively in inverse parallel. These
feedback diodes are needed to provide path for return of reactive energy from reactive
(usually inductive) load to the d.c. supply.
Figure 5-3 Single-phase thyristor inverter using centre tapped load
(c) Single Phase Bridge Inverter
- 61 -
ECE 451 Power Electronics I
Fig. 4-4 (a) gives the basic circuit. Four thyristors are connected in a bridge circuit
form with four diodesD1 to D4 across the respective thyristors in inverse parallel. These
feedback diodes are needed to provide paths for return of reactive energy from inductive
or capacitive loads to the d.c. supply.
The entire bridge may be considered into two parts, the part to the left’ of the load
impedance and connected to node A and part to the right of the load impedance and
connected to node B. It is evident that the two thyristors in the same part of the inverter
must never conduct simultaneously since this would short circuit the d.c. supply. Thus
thyristor T1 and T2 or T3 and T4 must not conduct simultaneously. Further the
commutating circuit must ensure that a thyristor is always turned off before its series
partner is gated in.
Figure 5-4 Single-phase bridge inverter
Waveform Control
For most of the applications, the inverter output waveform is required to be
sinusoidal instead of a square wave. Thyristor produces a square wave. Any periodic
waveform may be considered to be consisting of a fundamental sine-wave of frequency
equal to the frequency of periodic wave and harmonics. Departure of any waveform may
be expressed by its harmonic distortion defined as percentage harmonic distortion:
1
V 2  2
  t 2  100
V1 
(5-1)

where
Vt 2  Vn2( rms )
(5-2)
n 1
Vn ( rms ) = r.m.s. value of the nth harmonic.
Sometimes, typically in the case of a.c. motor loads, individual harmonic becomes
important instead of total harmonic content. Individual harmonic voltage v(t ) at
frequency  may be expressed as:

a
(5-3)
v(t )  0   (an cos nt  bn sin nt )
2 n1
- 62 -
ECE 451 Power Electronics I
where,
an 
bn 
1

1


 v(t ) cos nt d (t ), (n=0, 1, 2, ..)
(5-4)


 v(t )sin nt d (t ), (n=0, 1, 2, ..)
(5-5)

For square wave of amplitude V, v(t )  V and further if t  0 is chosen such
that v(t ) is symmetrical about t  0 , then
an 
2


 V cos nt d (t ) 
0
4V
 /2

 cos nt d (t )
0
4V
n
sin
n
2
bn  0; a0  0;

Hence,

v(t )   an cos nt
(5-6)
n 1
Consider the square wave of width reduced from 180o to say  and again placed
symmetrical w.r.t. t  0 as shown in Fig. 4-5.
Figure 5-5
For such a square wave,
 /2
4V
4V
n
an 
cos nt d (t ) 
sin( )

 0

2
4V
Hence v(t ) 
n

n
 sin( 2 ) cos nt
(5-7)
n 1
Methods of Obtaining Sinewave Output from an Inverter
A few common methods are considered below:
(a) Resonating the Load Impedance
This utilizes a series LC circuit to produce sinusoidal output. This method,
however, suffers from severe limitation of inverter frequency range.
- 63 -
ECE 451 Power Electronics I
(b) Harmonic attenuation filter
In this method, the harmonics in. the inverter output are attenuated or filtered out
by providing shunt path for the harmonic currents and providing a series impedance
across which harmonic voltages develop instead of developing across the load
impedance. However, low frequency harmonics require long size filter elements. Fig. 4-6
shows a typical filter, called the Ott filter, for harmonic attenuation.
Figure 5-6 Ott filter
(c) Harmonic attenuation by Pulse Width Modulation
Pulses of shorter duration than the usual 180o results in elimination of certain
harmonics and attenuation of others. Thus with pulse width   120o , the third harmonic
gets eliminated. Pulse width of   130o , results in minimum
- 64 -
ECE 451 Power Electronics I
6 COOLING OF POWER SEMICONDUCTOR
DEVICES
6.1 Heat Transfer
When current flows in a semiconductor junction, a small voltage drop occurs resulting in
the conversion of some of the electrical energy into heat. Degradation or failure will
occur if this heat is not removed from the junction at a sufficient rate to prevent the
excessive temperature. It is important to note that the damage is caused by the
temperature and not by heat, power or current. It is, therefore, essential to provide
adequate heat transfer path and other mechanisms to protect each application.
Heat is generally termed as the thermal energy that flows from one substance to another
owing to a temperature difference between them. Heat flows in the direction from higher
to lower temperatures. Thus, heat flow is analogous to the current flow in an electrical
circuit. The temperature difference is comparable to the voltage drop, the rate of heat
flow with the current and the thermal resistance with ohmic resistance.
Most heat transfer problems encountered in electronics are concerned with time rate.
Therefore, it is more convenient to speak of heat rate instead of heat. Now, the energy
balance of a semiconductor component will determine how much of the electrical power
is converted to heat rate for steady state operation, i.e. energy storage is zero. To do this,
it is necessary to evaluate the energy balance equation with proper electrical power
expressions, as well as heat transfer relations that determine the energy balance.
There are three modes of heat transfer, viz, conduction, convection and radiation.
6.1.1 Conduction
Heat is transferred through a solid by conduction. The equation for steady state
conduction is
A
(6-1)
q  K (T1  T2 )
L
where
q = heat rate
K = thermal conductivity
A = area
L = length
(T1  T2 ) = temperature difference
6.1.2 Convection
Heat transfer in gases and liquids occurs by a combination of conduction and fluid
motion. The motion may be due to buoyancy within the fluid, or external forces. The
former is called natural convection, and the later is called forced convection. In both
cases, the equation of heat transfer is
q  hA(T1  T2 )
(6-2)
where
h = convection heat transfer coefficient
T1 = temperature of the surface with area A
- 65 -
ECE 451 Power Electronics I
T2 = temperature of a point in the fluid
6.1.3 Radiation
Thermal energy is transmitted by electromagnetic radiation from the surface. The
radiated heat transfer rate is given by
(6-3)
q   A(T14  T24 )
Where
 = Stefan – Boltzman constant
 = surface property depending on material, finish and temperature
T1 and T2 = absolute temperatures
The permissible internal dissipation for a device suspended in still air depends upon the
total thermal resistance between junction and case (  JC ), and between case and
surroundings. The latter component is reduced by the use of additional cooling
provisions, but the internal thermal resistance is beyond control. Thus, a dissipation
greater than TJ max  TA  /  JC cannot be achieved, where TJ max is the maximum device
junction temperature, TA is the ambient temperature, and  JC is the thermal resistance
between the junction and the case. The above figure is frequently quoted for TA  25o C
and the 'infinite heat sink' rating of the device. This represents the condition where the
thermal resistance between the case and the surroundings has been reduced to zero so that
the case is at ambient temperature whatever the internal power dissipation is. The infinite
heat sink rating is obviously an impractical figure, but is significant in indicating the
improvement that can be achieved over the free air rating. It is, in fact, a combined
expression of thermal resistance and the maximum junction temperature. If  JC is large,
the proportionate improvement over the free air rating produced by a given area of heat
sink will be less than when  JC is small.
The maximum heat dissipating junctions of power devices are attached directly to the
case for rapid conduction of heat from the semiconductor wafer to the case. In
dispersing the heat energy from the case to the surroundings, conduction to the surface
layer of air and subsequent convection are the major contributors. At the surface
temperature involved, the contribution by radiation is usually small, even when the
emissivity of the surface approaches unity. By attaching a cooling fin or heat sink, the
effective surface area of the case is increased giving a considerable improvement in the
speed of transfer of heat to the air. The effectiveness of a particular heat sink depends
upon the following factors:
i.) thermal conductivity of the metal
ii.) its surface area
iii.) its surface condition
iv.) thickness of the metal
v.) its orientation and situation
vi.) means of attaching to the case of the device
vii.) whether convection is free or forced
In addition, for transistors, an electrical insulation is placed between the collector and ,
the heat sink to isolate it electrically from the sink. This considerably reduces the rate at
which heat is transferred to the heat sink. To avoid this, sometimes a transistor is
directly attached to the heat sink, and the heat sink itself is isolated from the chassis.
- 66 -
ECE 451 Power Electronics I
For high-power SCRs, liquid cooling and vapour phase cooling are used to solve the
heat transfer problems.
.
There are generally four types of mounting arrangements for the high-power
semiconductor devices, viz. stud-mounted, press-fit, flat base and press-pack or icehockey puck. Mounting of the device on the heat sink is very important because in
order to perform optimum cooling, the semiconductor package must be mounted not
only in a good location on the heat sink, but also in such a manner as to achieve low
thermal resistance to heat flow from the case to the heat sink. It is obvious that when
the device is mounted on the heat sink, the thermal resistance between the junction and
the air becomes the total value of the thermal resistance between the junction and the
case (  JC ), between the case and the heat sink ( CS ), and between the heat sink and the
air (  SA ) i.e  JA   JC  CS   SA .
CS is chiefly in the pressure contact interface between the device base and the heat sink.
Hence, to minimize the contact resistance, the contact surfaces should be clean, smooth,
and flat, and the case of the device should have no projections capable of impairing
uniform total contact with the heat sink. The surface of the heat sink should also have no
projections or depressions on the surface. The two mating surfaces should be lubricated
with a substance to improve the thermal heat transfer from the case of the device to the
heat sink by filling any air space, and must remain stable under wide variations of
temperature and environmental condition. Thus, the formation of corrosion products,
galvanic products or oxides between the two surfaces can be prevented. For this purpose,
a Dow Corning silicore grease (number DC-200) is widely used.
The effective thermal resistance  SA of the heat sink varies according to material and the
distance that the heat must travel before it can be dissipated. This is also a function of
coolant properties and magnitude of power dissipation according to equation for
convection (Eq. 6.2). Again, if the electrical overload surges of the medium and the large
power devices are of duration less than 0.5 s, the transient heat will not have time to flow
from the device into the heat exchanger. In that case, the transient properties of the device
and the steady state properties of the heat sink are of major importance. For overloads
longer than 0.5 s, the thermal storage capacity of the heat sink becomes important.
Though the heat storage capacity per unit volume of nickel is the highest, it is generally
not used as heat sink because of large weight and cost. Aluminium is very suitable for
heat exchange purposes because it has the highest value of the heat storage capacity, and
the highest thermal conductivity per unit volume. The cost is also moderate. Copper fins
are sometimes used for medium power devices because it has higher thermal conductivity
and heat storage capacity than aluminium, but its application is limited to medium power
devices from economical considerations.
The maximum power dissipation in a particular heat sink depends on its surface area but
the relation is not linear. It shows saturation as shown in Fig. 6.1. This is due to the fact
that the thermal resistance of the heat sink becomes much less than the internal thermal
resistance of the device at a certain area of the sink, and any further increase in area does
not improve the dissipation at the same rate.
The heat sinks may be either flat or block type with parallel radiators, as shown in Fig.
6.2. The thermal resistance varies with the area of the heat sink.
- 67 -
ECE 451 Power Electronics I
Fig. 6-1 Curve showing maximum permissible dissipation vs. area of heat sink
Fig. 6-2 Types of heat sinks
6.2
Electrical Equivalent Thermal Model
The heat path from the chip to the heat sink can be modeled by one analogous to the
electrical transmission line shown in Figure 6.3. Thermal resistance and thermal
capacitance per unit length are needed for exact characterization of the thermal
properties. The electrical power source P(t) represents the power dissipation (heat flow)
occurring in the chip in the thermal equivalent.
Rth and Cth are the lumped equivalent parameters of the elements within a device. These
can be derived directly from the structure of the element when it basically exhibits onedimensional heat flow. Figure 6.4 shows the thermal equivalent elements of a typical
transistor in a package with solid cooling tab (e.g.,TO-220 or DPak). The thermal
equivalent elements can be determined directly from the physical structure. The structure
is segmented into partial volumes (usually by a factor of 2 to 8) with progressively larger
thermal time constants  Rth,i , Cth,i  in the direction of heat propagation.
If the heat-inducing area is smaller than the heat-conducting material cross section, a
"heat-spreading" effect occurs, as shown in Figure 6.4. This effect can be taken into
account by enlarging the heat-conducting cross-section A .Thermal capacitance Cth
depends on the specific heat c and the mass density  . For heat propagation in
- 68 -
ECE 451 Power Electronics I
homogeneous media, it is assumed that the spreading angle is about 40° and subsequent
layers do not obstruct the heat propagation with low-heat conductivity. The size of every
volume element must be determined exactly because its thermal capacitance has a
decisive influence on the thermal impedance of the system when power dissipation
pulses, with a very short duration, occur. Table 6.1 shows the thermal data for common
materials.
One can also use the finite element analysis (FEA) method to calculate the heat flow. The
FEA method divides the entire structure, which sometimes covers several tens or hundred
thousand finite elements, into suitable substructures to determine lumped equivalent
elements. Unless this process is supported by standard FEA software tools, this solution
is too complex for most applications.
Fig. 6-3 Electrical transmission line equivalent circuit for modeling heat conduction
Fig. 6-4 Thermal equivalent elements for modeling heat conduction
- 69 -
ECE 451 Power Electronics I
Table 6-1 Thermal data for common materials
- 70 -