DEVELOPMENT OF A FOUR QUADRANT DC-DC SEPIC CONVERTER
By
M D . MA I DU L I S LAM
MASTER OF SCIENCE IN ELECTRICAL AND ELECTRONIC
ENGINEERING
BUET
DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING
BANGLADESH UNIVERSITY OF ENGINEERING AND TECHNOLOGY (BUET)
SEPTEMBER 2014
DEVELOPMENT OF A FOUR QUADRANT DC-DC SEPIC CONVERTER
By
M D . MA I DU L I S LAM
A thesis submitted to the
Department of Electrical and Electronic Engineering
in partial fulfillment for the degree of
Master of Science in Electrical and Electronic Engineering
DEPARTMENT OF ELECTRICAL AND ELECTRONIC ENGINEERING
The thesis titled “DEVELOPMENT OF A FOUR QUADRANT DC-DC SEPIC
CONVERTER”, submitted by M d. M a idu l Is l am , Roll No: 1009062083, Session
: October 2009 has been accepted as satisfactory in partial fulfillment of the
requirement for the degree of master of science in electrical and electronic
engineering on September 27, 2014.
Board of Examiners
Dr. Mohammad Ali Choudhury
Professor
Department of Electrical and Electronic Engineering, BUET
Dr. Taifur Ahmed Chowdhury
Professor and Head
Department of Electrical and Electronic Engineering, BUET
Dr. Mohammad Jahangir Alam
Professor
Department of Electrical and Electronic Engineering, BUET
Dr. Md. Ashraful Haque
Professor
Department of Electrical and Electronic Engineering, IUT, Gazipur
Chairperson
(Supervisor)
Member
(Ex-Officio)
Member
Member
(External)
Candidate’s Declaration
I hereby declare that this thesis has been prepared in partial fulfillment of the
requirement for the degree of Master of Science in Electrical and Electronic
Engineering at the Bangladesh University of Engineering and Technology
(BUET), Dhaka and has not been submitted anywhere else for any other degree.
Signature of Candidate
Md. Maidul Islam
Student No.1009062083
EEE,BUET,Dhaka
Dedicated
to
My parents
Abbreviations
Vin = The input voltage
Va = The average output voltage
Vst = peak of the saw tooth waveform
Vrepetitive =The voltage of repetitive waveform
Vcontrol = peak of the control waveform
TON = Turn on time.
TOFF = Turn off time.
T = TON + TOFF.= Time period
D = Duty cycle = T ON / T.
io = The load current
I LB =Average inductor current
f = Switching frequency
L = Inductor
C = Filter capacitance
vi
Acknowledgement
All praises goes to Allah for blessing me with the knowledge and ability to do the
present study. My indebt gratitude must be to the most benevolent and merciful for
everything what I have from Him.
It is the greatest pleasure to acknowledge my deepest gratitude to my supervisor Dr.
Mohammad Ali Choudhury, Professor, Department of Electrical and Electronic
Engineering, Bangladesh University of Engineering and Technology (BUET), Dhaka,
for his continuous guidance, cooperation, valuable suggestions and encouragement at
all stage of this work.
I would like to express my sincere thanks and regards to all faculty members of the
department especially the thesis examination committee members for valuable
suggestions to improvement of the thesis.
I wish to convey my sincere thanks to all of my well wishers for their constant
encouragement, sympathetic co-operation and mental support as well as backing at all
stages of my thesis work.
Heartfelt appreciation goes to my family. My family is the crypt of my all muse,
ethics and values. My little effort to this study is just a reflection of that.
Finally, I express my thanks to the librarian and all staffs of the Department of
Electrical and Electronic Engineering, BUET, for their cordial help and assistance.
vii
Abstract
In this thesis, a new topology of four quadrant DC-DC sepic converter has been
developed to provide four quadrant operation of a high frequency dc-dc converter
having one supply source and proper control of the converter.
The investigation started with modifying single quadrant dc-dc SEPIC converter
circuit for two quadrant operation. This required a dc-dc SEPIC converter with two
switches. Two quadrant dc-dc SEPIC converter has been investigated with variable
duty cycle operation for verifying the buck-boost gain characteristics of the voltage
and also the circuit has been investigated with input/output dc sources for two
quadrant operation as the duty cycle is varied from near zero to near one.
One quadrant SEPIC dc-dc converter is similar to a buck-boost converter, but it has
advantages of having non-inverted output and continuous input current. Connecting a
switch across the diode of the one quadrant SEPIC dc-dc converter in parallel has
made the converter operate in two quadrants. Proper differential connection of two 2Q
SEPIC dc-dc converter has resulted in a four quadrant dc-dc converter with buckboost gain characteristics having positive output voltage.
The result is a single source topology switched by conventional ON/OFF duty cycle
control as used in other high power chopper circuits. The combined topology has been
analyzed and studied by spice simulation. Conversion efficiency and gain data has
been taken from simulation result and the performance has been analyzed and studied
by Tecplot10 Software.
viii
Chapter-One
Introduction
1.1 Introduction
Development in the field of power electronics has constituted one of the great success
stories of the 20th century. As manufacturing technology has improved, the cost of the
semiconductor devices has decreased. It is often said that solid-state electronics brought
in the first electronics revolution, whereas solid-state power electronics is the second
electronics revolution. It is interesting to note that power electronics blends the
mechanical, electrical and electronic era [1].
A high level productivity of the industries and product quality enhancement is not
possible by using non power electronic systems. Today, power electronics is an
indispensable tool in any country’s industrial economy [2]. It is necessary that some
converters are to be used to improve the quality of power supply. Power semiconductor
devices are making it possible for utilities to use a variety of power control equipment to
raise power quality level and enhance performance and efficiency.
The DC– DC converter, also known as chopper, is a converter which transforms a D.C. to
another D.C. The average value of a chopper’s output voltage can be modified between
zero and the full voltage. This can be done using the “Pulse Width Modulation (PWM)”
principle of constant frequency pulses. There are schemes of chopper operating in one to
four quadrants. The H bridge converters are widely utilized in adjustable electrical drives
with d.c. motors. An arm of this bridge is obtained by series connection of two
controllable power switches. Each switch has an anti-parallel diode, called “freewheeling diode”. The two switches of an arm structure work in anti-phase.
1
1.2 Overview of DC Choppers
Silicon control rectifier (Thyristor, SCR) based DC Choppers were introduced in the
early 1960’s. SCRs were constrained to operate at low chopping frequencies. The advent
of power MOSFET’s and IGBT’s allow power switches to operate at high frequency [3].
Conventional switch mode dc-dc converters (SMPS) operate either in single quadrant or
in two quadrants [4-5]. A switch mode DC-DC power supply is switched at very high
frequency. Conversion of both step down and step up dc with small filter size having
facility of feedback regulation is possible in an SMPS.
The output voltage in DC-DC converters is generally controlled by using a switching
concept, as illustrated in Figure 1.1. Early DC-DC converters were known as choppers
with silicon-controlled rectifiers (SCRs) used as the switching device. Modern DC-DC
converters classified as switch mode power supplies (SMPS) employ insulated gate
bipolar transistors (IGBTs) and metal oxide silicon field effect transistors (MOSFETs).
The switch mode power supply has several functions [6]:
1. Step down an unregulated DC input voltage to produce a regulated DC output voltage
using a buck or step-down converter,
2. Step up an unregulated DC input supply to produce a regulated DC output voltage
using a step-up converter,
3. Step down and then step up an unregulated DC input voltage to produce a regulated
DC output voltage using a buck–boost converter,
2
Figure 1.1 Basic DC-DC converter.
Figure 1.2 DC-DC converter voltage waveform.
3
Figure 1.3 Pulse width modulation concept.
4. Invert the DC input voltage if necessary and
5. Produce multiple DC outputs using a combination of SMPS topologies and multiple
transformer secondary operating at high frequency
The regulation of the average output voltage in a DC-DC converter is a function of the
on-time Ton of the switch, the pulse width, and the switching frequency fs as illustrated
in Figure 1.2. Pulse width modulation (PWM) is the most widely used method of
controlling the output voltage. The PWM concept is illustrated in Figure 1.3. The output
voltage control depends on the duty ratio D. The duty ratio is defined as,
D
TON Vcontrol

Ts
Vrepetitive
1.1
based on the on-time ton of the switch and the switching period Ts . PWM switching
involves comparing the level of a control voltage Vcontrol to the level of a repetitive
waveform as illustrated in Figure 1.3. The on-time of the switch is defined as the portion
of the switching period, where, the value of the repetitive waveform is less than the
control voltage. The switching period (switching frequency) remains constant while the
control voltage level is adjusted to change the on-time and therefore the duty ratio of the
switch. The switching frequency is usually chosen above 20 kHz so the noise is outside
4
the audio range [7]. DC-DC converters operate in one of two modes depending on the the
characteristics of the inductor current:
1. Continuous conduction and
2. Discontinuous conduction
The continuous-conduction mode is defined by continuous inductor current (greater than
zero) over the entire switching period, whereas the discontinuous conduction mode is
defined by discontinuous inductor current, zero during any portion of the switching
period
There are two main designs for the DC power supplies:
1. Linear Power Supply and
2. Switching Power Supply.
The traditional linear power supplies are typically heavy, durable, and have low noise
across low and high frequencies. For this reason they are mostly suitable for lower power
applications, where, the weight does not pose a problem. The switching power supplies
are light weight, efficient and durable. The switching power supplies are not suitable for
audio frequency and high power applications. The two types are swappable for various
applications, and they cost about the same.
Linear regulator is used to maintain a steady voltage across the load. The resistance of a
linear regulator varies in accordance with the load resulting in a constant output voltage.
The regulating device is made to act like a variable resistor, continuously adjusting a
voltage divider network to maintain a constant output voltage dissipating power due to
the difference between the input and regulated voltages as waste heat. By contrast, a
switching regulator uses an active device that switches on and off to maintain an average
value of output. Because the regulated voltage of a linear regulator must always be lower
than input voltage, efficiency is limited and the input voltage must be high enough to
always allow the active device to drop voltage across the device. Linear regulator may be
5
preferred for light loads or where the desired output voltage approaches the source
voltage. In such cases, the linear regulator may dissipate less power than a switcher. The
linear regulator also has the advantage of not requiring inductors. Linear regulators are
simple to design and implement than switch mode dc-dc converters. Linear regulators
using only transistors, diodes and resistors. They are easy to fabricate into an integrated
circuit and on PCBs.
When the output regulated voltage must be higher than the available input voltage, linear
regulator will not work. In this situation, a switching regulator of the "boost" type may be
used.
A conventional DC-DC SMPS consists of a rectifier fed directly from line voltage, a
filter and a static switch. The SMPS is switched by control circuitry at high frequency to
step down or step up dc voltage by on/off ratio (duty cycle) control. The filter and the
feedback circuit are the other components of a DC-DC SMPS. Figure-1.4 shows the
block diagram of a DC-DC SMPS.
Main components of a dc-dc SMPS are:
1.
Power circuit
2.
Control circuit
3.
Magnetic circuit.
The control circuit of an SMPS generates high frequency gate pulses for the switching
device to control the dc. Switching is performed in multiple pulse width modulation
(PWM) according to feedback error signal from the load to serve two purposes,
1.
Produce high frequency switching signal,
2.
Control ON/OFF period of switching signal to maintain constant voltage
across the load.
6
Power circuit
3.
Input
Input filter
Output
Switch
Output
filter
Gating Signal
generator
Reference
Feedback
control
circuit
Controller Unit
Figure 1.4: Block Diagram of SMPS.
High frequency switching reduces filter size at the input/output sides of the converter.
Simplest PWM control uses multiple pulse modulations generated by comparing a dc
with a high frequency carrier triangular wave.
7
V
Vin
BJT
+
_
Vin
Diode
Vout
Vout
R
t
t
Figure 1.5: Switch mode (non dissipative) power conversion circuit.
The circuit of Figure 1.5 illustrates the basic principle of a dc-dc switch mode power
conversion. The controlling device is a switch. By controlling the ratio of the time
intervals spent in on and off positions (defined as duty ratio), the power flow to the load
can be controlled in an efficient way. Ideally this method is 100% efficient. In practice,
the efficiency is reduced as the switch is non-ideal and losses occur in power circuits.
The dc voltage to the load can be controlled by controlling the duty cycle of the
rectangular waveform supplied to the base or gate of the switching device. When the
switch is fully on, it has only a small saturation voltage across it. In the off condition the
current through the device is zero.
The output of the switch mode power conversion control (Figure 1.5) is not pure dc. This
type of output is applicable in cases such as oven heating without proper filtration. If
constant dc is required, then output of an SMPS has to be smoothed out by the addition of
a low-pass filter. Switches are required as basic components for efficient electric power
conversion and control. Inductors and capacitors are used to smooth the pulsating dc
originating from the switching action.
V
Vin
+
_
Diode
Vin
C
Vout
R
Vout
t
Figure 1.6: Typical switch mode power conversion circuit.
8
Although the conversion would be 100% efficient in the ideal case of lossless
components (Figure 1.6), in practice all components are lossy. Thus, efficiency is
reduced. Hence, one of the objectives in switch mode power conversion is to realize
conversion with the least number of components to have better efficiency and reliability.
The purpose of a DC-DC converter is to supply a stepped-down or stepped-up regulated
DC output voltage to a load from a DC input voltage. In many cases the DC input voltage
is obtained by rectifying a line voltage that changes in magnitude. DC-DC converters are
commonly used in applications requiring regulated DC power, such as in computers,
medical instrumentation, communication devices, television receivers and battery
chargers [7, 8]. DC-DC converters are also used to provide a regulated variable DC
voltage for DC motor speed control applications.
1.3 Specific aims and possible outcomes
The objective of the thesis is to propose and investigate a high frequency switching four
quadrant dc-dc converter with improved performance.
A single topology that can provide Buck-Boost operation with positive output having
four quadrant operation is not available in literature. Luo [7-10] has proposed
incorporation of voltage lift techniques in conventional switch mode circuits to obtain
better voltage gain and higher efficiency in wide range of duty cycle variation. Luo also
suggested four quadrant operation of switching dc-dc converter using two separate
circuits. None of the Luo converters operate in single source circuit configuration in all
four quadrants. Single source circuit configuration combining two separate circuits by
differential connection of the load at the output fed by same source has been proposed in
reference [11]. The proposed circuit of [11] used Buck-Boost topology for the purpose.
The new topology is developed out of switching dc-dc converters based on SEPIC
topology (modified Ĉuk topology having positive output) with improved performance. Its
operational range is wide at high conversion efficiency, whereas, the present four
quadrant switching dc-dc converters’ conversion efficiency decreases around the
9
operation of a particular duty cycle. It is expected that this study will yield an effective
design strategy of a four quadrant switching dc-dc converter and higher efficiency which
can be fabricated economically making it commercially viable.
1.4 Thesis Outline
This thesis consists of three chapters. Chapter-1 is the introduction chopper with brief
overview of DC-DC Converter. It also describes the objective and goal of the
thesis.Chapter-2 deals with introduction to DC Choppers, review of DC Choppers.
Chapter-3 includes the study of Four Quadrant DC-DC converters based on SEPIC
topology. In reference [12] two separate switch mode dc-dc converters with voltage lift
circuits, one working in two quadrant forward mode and the other working in two
quadrant reverse mode have been switched by complex gate pulses to obtain the four
quadrant dc-dc operation. Two sources are necessary for such circuit. Combining the two
circuits to have single source topology would result in mal-operation due to overlapping
switches. In this research investigation have been started with modifying single quadrant
dc-dc SEPIC converter circuit for two quadrant operation. This has introduced a dc-dc
SEPIC converter with two switches. Two quadrant dc-dc SEPIC converter has been
investigated with variable duty cycle operation for verifying the buck-boost gain
characteristics of the voltage and also the circuit has been investigated with input/output
dc sources for two quadrant operation as the duty cycle is varied from 0 to near one.
Connecting a switch across the diode of the one quadrant SEPIC dc-dc converter in
parallel makes the converter operate in two quadrants. Proper differential connection of
two 2Q SEPIC dc-dc converter has resulted in a four quadrant dc-dc converter with buckboost gain characteristics having positive output voltage.
Chapter-4 concludes the thesis with summary, achievements and suggestion on future
works.
10
Chapter-Two
DC-DC Converter
2.1 Choppers
Choppers are DC-DC converters that are used for transferring electrical energy from a
DC source to another DC source or to a load. These converters are widely used in
regulated switching power supplies and DC motor drive applications. DC-DC converters
that are discussed in this section are one-quadrant, two-quadrant, and four-quadrant
choppers. Step-down (buck) converter and step-up (boost) converters are basic onequadrant converter topologies. The two-quadrant chopper, which is a current reversible
converter, is the combination of the two dc-dc basic topologies. The full-bridge converter
four quadrant is derived from two quadrant boost and the step-down buck converter.
One-Quadrant Choppers
In one-quadrant choppers, the average DC output voltage is usually kept at a desired
level, as there are changes in input voltage and output load. These choppers operate in
first quadrant of v–i plane, where output and input voltages and currents are always
positive. Therefore, these converters are called one-quadrant choppers. One method of
controlling the output voltage employs switching at a constant frequency, i.e., a constant
switching time period (T= t ON + t OFF ), and adjusting the on-duration of the switch to
control the average output voltage. In this method, which is called pulse-width
modulation (PWM), the switch duty ratio is defined as the ratio of the on-duration to the
switching time period.
d
t ON
T
2.1
In the other control method, both the switching frequency and the on-duration of the
11
switch are varied. Choppers can have two distinct modes of operation, which have
significantly
different
characteristics:
continuous-conduction
and
discontinuous-
conduction modes. In practice, a converter may operate in both modes. Therefore,
converter control should be designed for both modes of operation.
2.2 Buck Converters
The buck or step-down converter regulates the average DC output voltage at a level lower
than the input or source voltage. The buck converter is used to provide a variable DC
voltage to the armature of a DC motor for variable speed drive applications. This is
accomplished through controlled switching where the DC input voltage is turned on and
off periodically, resulting in a lower average output voltage. The buck converter is
commonly used in regulated DC power supplies like those in computers and
instrumentation.
2.2.1 Ideal Buck Circuit
The circuit that models the basic operation of the buck converter with an ideal switch and
a purely resistive load is shown in Figure 2.1. The output voltage equals the input voltage
when the switch is in position 1 and the output voltage is zero when the switch is in
position 2. The average output voltage level is varied by adjusting the time the switch is
in position 1 and 2 or the duty ratio. The resulting average output voltage Vo is given in
terms of the duty ratio and the input voltage Vi by Eq. (2.2) [13].
Vo D Vi
T
Where, D is the duty cycle =
2.2
ON
T
. TON is the on time of the rectangular base/gate pulse,
whereas the T is the period of switch pulse. The rectangular wave output voltage for the
ideal circuit of the buck converter contains an undesirable amount of voltage ripple. The
circuit is modified by adding an inductor L in series and a capacitor C in parallel with the
load resistor as shown in Figure 2.2. The inductor reduces the ripple in the current
through the load resistor, while the capacitor directly reduces the ripple in the output
12
voltage. Since the current through the load resistor is the same as that of the inductor, the
voltage across the load resistor (output voltage) contains less ripple. The current through
the inductor increases with the switch in position 1. The current through the inductor
increases with the switch in position 1. As the current through the inductor increases, the
energy stored in the inductor increases. When the switch changes to position 2, the
current through the load resistor decreases as the energy stored in the inductor decreases
Figure 2.1 Ideal buck converter.
Figure 2.2 Buck converter with LC filter .
13
Figure 2.3 Rise and fall of load current in buck converter.
Figure 2.4 Buck converter with practical switch.
The rise and fall of current through the load resistor is linear if the time constant due to
the LR combination is relatively large compared with the on- and off-time of the switch
as shown in Figure 2.3 [14]. A capacitor is added in parallel with the load resistor to
reduce the ripple content in the output voltage. The combination of the inductor and
capacitor reduces the output voltage ripple to low levels. The circuit in Figure 2.2 is ideal.
A practical realization of the switch is designed using a diode and power semiconductor
switch as shown in Figure 2.4. A freewheeling diode is used with the switch in position 2
since the inductor current freewheels through the switch. The switch is controlled by a
scheme such as pulse width modulation.
14
2.2.2 Continuous-Conduction Mode
The continuous-conduction mode of operation occurs when the current through the
inductor in the circuit of Figure 2.2 is continuous. This means that the inductor current is
always greater than zero. The average output voltage in the continuous-conduction mode
is the same as that shown in Eq. (2.2) for the ideal circuit. As the conduction of current
through the inductor occurs during the entire switching period, the average output voltage
is the product of the duty ratio and the DC input voltage. The operation of this circuit
resembles a DC transformer according to Eq. (2.3) based on the time-integral of the
inductor voltage equal to zero over one switching period.
Figure 2.5 Buck converter switch states: (a) switch in position 1; (b) switch in position 2.
Figure 2.6 Inductor voltage and current for continuous mode of buck converter.
15
D=
Vo I i

Vi I o
2.3
The operation of the circuit in steady state consists of two states as illustrated in Figure
2.5 [14]. The first state with the switch in position 1 has the diode reverse-biased and
current flows through the inductor from the voltage source to the load. The switch
changes to position 2 at the end of the on-time and the inductor current then freewheels
through the diode. The process starts again at the end of the switching period with the
switch returning to position 1. A representative set of inductor voltage and current
waveforms for the continuous-conduction mode is shown in Figure 2.6.
2.3.3 Discontinuous-Conduction Mode
The discontinuous mode of operation occurs when the value of the load current is less
than or equal to zero at the end of a given switching period. Assuming a linear rise and
fall of current through the inductor, the boundary point between continuous- and
discontinuous-current conduction occurs when the average inductor current over one
switching period is half of the peak value, as illustrated in Figure 2.7. The average
inductor current at the boundary point is calculated using Eq. (2.4).
DTS
1
I LB  i L (peak) 
(Vi  Vo )
2
2L
2.4

16

Figure 2.7 Inductor current at boundary point for discontinuous mode of buck converter.
The input voltage or output voltage is kept constant depending on the application. If the
input voltage remains constant, then the average inductor current at the boundary is
calculated by replacing the output voltage in Eq. (2.4) with Eq. (2.2), which yields the
expression in Eq. (2.5) [15].
I LB 
DTS
(Vi )(1  D )
2L
2.5
The voltage ratio is now defined according to Eq. (2.6):
VO

Vi
D2
IO
1
D2  (
)
4 I LB (max)
2.6
If the output voltage remains constant, then the average inductor current at the boundary
is calculated by replacing the input voltage in Eq. (2.4) with Eq. (2.2), which yields the
expression in Eq. (2.7) [15]:
I LB
T
 S (Vo )(1  D )
2L
2.7
17
The duty ratio is defined according to Eq. (2.8) by manipulating Eq. (2.6) [13]:
IO
VO
D 
(
Vi
2.8
I
LB (max)
V
1 ( O )
Vi
)
1
2
2.3 Boost Converters
A boost converter regulates the average output voltage at a level higher than the input or
source voltage. The boost converter is referred to as a step-up converter or regulator. The
DC input voltage is in series with an inductor acting as a current source. A switch in
parallel with the current source and the output is turned off periodically, providing energy
from the inductor and the source to increase the average output voltage. The boost
converter is commonly used in regulated DC power supplies and regenerative braking of
DC motors.
2.3.1 Ideal Boost Circuit
The circuit that models the basic operation of the boost converter is shown in Figure 2.8
[15]. The ideal boost converter uses the same components as the buck converter with
different placement. The input voltage in series with the inductor acts as a current source.
The energy stored in the inductor builds up when the switch is closed. When the switch is
opened, current continues to flow through the inductor to the load. Since the source and
the discharging inductor are both providing energy with the switch open, the effect is to
boost the voltage across the load. The load is in resistor in parallel with a filter capacitor.
The capacitor voltage is larger than the input voltage. The capacitor is large to hold
output voltage and acts to reduce the ripple in the output voltage.
18
2.3.2 Continuous Conduction Mode
The continuous-conduction mode of operation occurs when the current through the
inductor in the circuit of Figure 2.8 is continuous with the inductor current always greater
than zero. The operation of the circuit in steady state consists of two states, as illustrated
in Figure 2.9 [15]. The first state with the switch closed has current charging the inductor
from the voltage source. The switch opens at the end of the on-time and the inductor
discharges current to the load with the input voltage source still connected. This results in
an output voltage across the capacitor larger than the input voltage.
Figure 2.8 Basic boost converter.
Figure 2.9 Basic boost converter switch states: (a) switch closed; (b) switch open.
19
Figure 2.10 Inductor voltage and current waveforms for continuous mode of boost
converter.
The output voltage remains constant if the RC time constant is significantly larger than
the on-time of the switch. A representative set of inductor voltage and current waveforms
for the continuous conduction mode is shown in Figure 2.10 [15]. The voltage ratio for a
boost converter is derived based on the time-integral of the inductor voltage equal to zero
over one switching period. The voltage ratio is equivalent to the ratio of the switching
period to the off-time of the switch as illustrated by Eq. (2.9) [13].
2.9
V
I
T
Ts
T
D= o  i  s 

V
I
t
Ts  t
1 D
off
off
i
o
The current ratio is derived from the voltage ratio assuming that the input power is equal
to the output power, as with ideal transformer analysis.
20
Figure 2.11 Inductor current at boundary point for discontinuous mode of boost
converter.
2.3.3 Discontinuous-Conduction Mode
The discontinuous mode of operation of boost dc-dc converter occurs when the value of
the inductor current is less than or equal to zero at the end of a given switching period.
Assuming a linear rise and fall of current through the inductor, the boundary point
between continuous- and discontinuous-current conduction occurs when the average
inductor current over one switching period is half the peak value, as illustrated in Figure
2.11 [15]. The average inductor current at the boundary point is calculated using Eq.
(2.10) [15].
1
DVO Ts
I LB  iL(peak) 
( D)(1  D )
2
2L
2.10
21
The output current at the boundary condition is derived by using the current ratio of Eq.
(2.9) in Eq. (2.10) with the inductor current equal to the input current. This results in Eq.
(2.11) [13]:
I OB 
Vo Ts
( D )(1  D ) 2
2L
2.11
For the boost converter in discontinuous mode, the output voltage Vo is generally kept
constant while the duty ratio D varies in response to changes in the input voltage Vi. The
duty ratio is defined as a function of the output current for various values of the voltage
ratio according to Eq. (2.12) [15]:
I
4 VO VO
D  [
(
 1) O ]1 / 4
27 V i V i
I i
2.12
2.4 Ĉuk Converter
The Ĉuk converter is a dc-dc converter named after the inventor Dr. Slobodan Ĉuk. The
basic non-isolated Ĉuk converter shown in Figure 2.12 is designed based on the principle
of using buck and boost converters to provide an inverted DC output voltage [16]. The
advantage of the basic non-isolated Ĉuk converter over the standard buck–boost
converter is to provide regulated DC output voltage at higher efficiency with identical
components due to an integrated magnetic structure, reduced ripple currents, and reduced
switching losses [17, 18]. The integrated magnetic structure of an isolated Ĉuk converter
consists of the isolation transformer and the two inductors in a single core. As a result,
the ripple currents in the inductors are driven into the primary and secondary windings of
the isolation transformer. Also, the single core results in reduced flux paths, which
improve the overall efficiency of the converter.
22
2.4.1 Non isolated Operation
The basic non-isolated Ĉuk converter is a switching power supply with two inductors,
two capacitors, a diode, and a transistor switch as illustrated in Figure 2.12 [16, 17]. The
transfer capacitor Ct stores and transfers energy from the input to the output. The average
value of the inductor voltage for steady-state operation is zero. As a result, the voltage
across the transfer capacitor is assumed to be the average value in steady state and is the
sum of the input and output voltages. The inductor currents are assumed to be continuous.
Figure 2.12 Non-isolated Ĉuk converter.
Figure 2.13 Ĉuk converter switch states: (a) switch open; (b) switch closed.
23
Figure 2.14 Inductor 1, voltage and current waveforms for Ĉuk converter.
The operation of the basic non isolated Ĉuk converter in the steady state consists of two
transistor states, as illustrated in Figure 2.13 [16, 17]. In the first state when the transistor
is off, the inductor currents flow through the diode and energy is stored in the transfer
capacitor from the input and the inductor L1 . The energy stored in the inductor L2 is
transferred to the output. As a result, both of the inductor currents are linearly decreasing
in the off-state. In the second state when the transistor is on, the inductor currents flow
through the transistor and the transfer capacitor discharges while energy is stored in the
inductor L1 . As the transfer capacitor discharges through the transistor, energy is stored
in the inductor L2 . Consequently, both of the inductor currents are linearly increasing in
the on-state. A representative set of inductor voltage and current waveforms for the non
isolated Ĉuk converter are shown in Figures 2.14 and 2.15 [16]. The voltage and current
ratio for the non isolated Ĉuk converter can be derived by assuming the inductor currents,
which correspond to the input current and output current, are ripple-free [16]. This results
in an equal charging and discharging of the transfer capacitor during the off-state and the
on-state. The charging and discharging are defined in Eq. (2.13) in terms of the product
of current and time [16].
I L1t off  I L 2t on
2.13
24
The resulting current ratio is expressed in Eq. (2.14) by substituting I L = I I , I L 2 = I o ,
t off = (1 -D) Ts , and t on = D Ts into Eq. (2.13) [16].
Figure 2.15 Inductor 2, voltage and current waveforms for Ĉuk converter.
Io 1  D

Ii
D
2.14
If the input power is equal to the output power for the ideal case, the voltage ratio in Eq.
(2.15) is determined as the inverse of the current ratio using the analysis of an ideal
transformer.
Vo
D

Vi
1 D
2.15
2.5 Buck–Boost Converter
A schematic of the buck–boost converter circuit is shown below in Figure 2.16.The main
power switch is shown to be a bipolar transistor, but it could be a power MOSFET, or
any other self commuted switching device that could be turned on in a controlled fashion.
This converter processes the power from a DC-biased source to a DC output.The DC
output voltage value can be chosen to be higher or lower than the input DC voltage. This
circuit processes power from input to output with “square wave” technology, that is, the
25
circuit produces waveforms that have sharp edges (such as those shown in Figure 2.17).
The waveforms in Figure 2.17 have a square-wave (or semi-square-wave) appearance and
are indicative of current waveforms in a typical DC-DC converter. The iL waveform is of
similar shape as that of inductor (L) current in the buck–boost converter of Figure 2.16,
iD represents the diode current and iC , the capacitor current. The operation of this
converter is nonlinear and discrete; however, it can be represented by a cyclic change of
power stage topologies. The three modes for this converter, the equations for those
topologies, and the small-signal transfer functions are presented in this section.
Figure 2.16 Buck–boost converter
26
Figure 2.17 Typical current waveforms in a buck–boost converter.
2.5.1 Continuous-Conduction Mode
Figure 2.17 illustrates the topology, where the main power switch is on and the diode is
reverse-biased; thus, it is off. For the purpose of illustration the semiconductor devices
are assumed to be ideal. There are two independent state variables that contain the
information describing the operation of this circuit: the inductor current, iL , and the
capacitor voltage, vc . Two differential equations in terms of these variables, the output
voltage, vo , and the source voltage, v S , for the designated mode 1 are shown below.
diL v S

dt
L
2.16
v
dVc
 o
dt
RL C
2.17
27
The inductor gets energy from the source and charges up. The capacitor discharges into
the output load, RL and output voltage falls. Figure 2.19 shows the change in topology
when the main power switch turns off. The inductor maintains current flow in the same
direction so that the diode is forward-biased. The differential
Figure 2.18 Topology 1 for the buck–boost converter.
Figure 2.19 Mode 2 for the buck–boost converter.
equations for the designated mode 2 are shown below. The inductor transfers energy it
has obtained from the source into the capacitor. The capacitor charges up as the inductor
is discharged, and the output voltage rises.
28
di L
v
 C
dt
L
2.18
dvc i L
v
  o
dt
C RL C
2.19
Another mode change will occur if the inductor has transferred all of its energy out into
the capacitor. In that case the inductor current will fall to zero. Initially the inductor
current is assumed to be nonzero. The power stage analysis is linear for each interval.
However, for the complete operational cycle, it becomes a piecewise linear problem. The
on-time or off-time of the main power switch may vary from cycle to cycle. Various
modeling schemes have been proposed using nonlinear techniques that would in essence
“combine” these equations. Basically there are two approaches: numerical and analytical
techniques. In analytical technique, a closed-form expression representing the operation
of the converter is obtained, enabling a qualitative analysis to be performed [19]. The
numerical technique uses various algorithms to produce accurate quantitative results.
Simple relations among the system parameters are not easily obtainable. Analytical
techniques can be divided into two different system descriptions, discrete and continuous.
The discrete system description makes no assumption on the basis of converter
application. This description could be used in any application, where, the linearization of
a periodically changing structure is sought. This method is accurate, but very
complicated. The derived expressions are complex, which impedes its practical
usefulness, and physical insight into the system operation is not easily obtainable. An
important continuous analytical technique is the averaging technique proposed by Wester
and Middlebrook [20].
It is easy to implement and gives physical insight into the
operation of a buck–boost converter. Through circuit manipulation, analytical
expressions were derived to determine the appropriate expressions. Middlebrook and
Ĉuk[21] modified the technique to average the state space descriptions (variables) over a
complete cycle. Shortt and Lee [22–24] used a discrete sample of the average state space
29
representation to develop a modeling technique that would enable a judicious control
selection to be made. Vorpérian et al. [25] developed an equivalent circuit model for a
pulse width modulation (PWM) switch that can be used in the analysis of this converter.
For the averaging technique each interval in the cycle is described by its state space
representation (differential equation). Figure 2.20 shows the waveform of the continuous,
instantaneous inductor current (that is,
Figure 2.20 Continuous inductor current.
iL does not equal zero at any point in time) and the average inductor current for the
buck–boost converter (Figure 2.18). The instantaneous current is cyclic with a time
period equal to TP s; the main power switch is on for TON s and off for TOFF s. The
equations are averaged to give a single period representation, as shown below:
i L  d 
vC
v
d s
L
L
2.20
vc  d 
iL
v
 o
C RL C
2.21
To study the small signal behavior, the time-varying system described in Eqs. (2.20) and
(2.21) can be linearized using small signal perturbation techniques. By using these
techniques, the inputs are assumed to vary around a steady-state operating point. Taking a
first-order Fourier series approximation, the inputs are represented by the sum of a DC or
steady-state term and an AC variation or sinusoidal term. Introducing variations in the
line voltage and duty cycle by the following substitutions
30
v S  VS  vˆs, d D dˆ,
dD– dˆ
cause perturbations in the state and output, as shown below. In the above and following
equations the variables in capital letters represent the DC or steady-state term; and the
variables with the symbol “ ” above them represent the AC variation or sinusoidal term.
iL ˙ = I L ˙+ iL ˙, iL = IL +iˆL, vC ˙ = V ˙C +vCˆ
Figure 2.21 shows the type of change that is being modeled for an inductor current
perturbation of Figure 2.22. Note the TON and TOFF slowly change from cycle to cycle,
which produces a slight change in the inductor current from cycle to cycle. The derivative
of a DC term is zero, so the above equations can be simplified to the following:
i˙L = iLˆ , iL =IL +iˆL, vC =VC +v ˆc ,
Substituting these equations into (2.27) and (2.28), separating the DC (steady-state) terms
and the AC (sinusoidal) terms results in the following:
Figure 2.21 Inductor current perturbation.
DC terms:
DVC DVs

0
L
L
2.22
D LL
V
 O 0
C
RL C
2.23
31
AC terms (neglecting the higher-order terms):
iˆL 
DvˆC Dvˆ S VS  VC ˆ


d
L
L
L
2.24
vˆ
D iˆL
I
 o  L dˆ
C
RL C C
2.25
v̂C 
The equation
Vc D

Vs D 
is derived from Eq. (2.22). From Figure 2.16, putting VC = VO and substituting
this into the previous equation results in:
VO D

Vs D
2.26
Equation (2.26) states that the ratio of the DC output voltage to the DC input voltage is
equal to the ratio of the power switch on-time to the power switch off-time. The
expression for the DC inductor current term is
iL  
VO
DR L
2.27
Equations (2.24) and (2.25) constitute the small signal model of a buck–boost converter.
Another method that is utilized to extract the small signal model is to realize an
equivalent circuit model from Eqs. (2.20) and (2.21). Figure 2.22 is the average circuit
model of the buck–boost converter.
32
Figure 2.22 Average circuit model of the buck–boost converter.
Figure 2.23 The small signal circuit model.
Figure 2.24 Discontinuous inductor current.
33
Figure 2.25 Topology 3 for the buck–boost converter (discontinuous inductor current).
Introducing perturbations into the state and output, removing the DC conditions,
neglecting the small nonlinear terms, and simplifying the structure, results in Figure 2.23.
2.5.2 Discontinuous-Conduction Mode
Figure 2.26 shows the waveform of the discontinuous inductor current for the buck–boost
converter (Figure 2.18 where, inductor current is equal to zero for TF2s. An additional
(third) mode change is shown in Figure 2.25. Since the inductor current is zero for this
portion of the switching cycle, there is only one state equation that can be determined.
dv c
v
 o
dt
RL C
2.28
This equation indicates that the capacitor discharges its energy into the load resistor, RL ,
and the while output voltage falls.
34
Figure 2.26 General form of discontinuous inductor current.
In the discontinuous conduction mode, the inductor current does not behave as a true
state variable, since d iL /dt = 0, thereby reducing the system order by one. Figure 2.26
illustrates the general form of the inductor current. The equations for the Ton time
interval are the same as Eqs. (2.16) and (2.17), except iL = i R + iL , where i R represents
the DC level at which the inductor current begins and , the value of the time-varying
inductor current. The equations for the TOFF interval are the same as Eqs. (2.18) and
(2.24) except iL = i R + iL , where iL represents the value of the time-varying inductor
current. By combining these sets of equations with Eq. (2.24) by the averaging technique,
the equations listed below are obtained.
diL
1

dt Tp
Ton

0
Vs
1
dt 
L
Tp
Ton TOFF

ton
(
 vc
)dt  0
L
2.29
For the buck–boost converter case I R = 0; also, from Figure 2.26,
Ton TOFF
 iL * dt  (
ton
1 vs
TON )TOFF  i AV TOFF
2 L
2.30
The variable i AV is the average value of the inductor during the TON + TOFF time, but not
for the whole cycle. Substituting into Eqs. (2.29) and (2.30) results in the following:
35
dvc
dt

T
i
T
v
TF 2vC
TonVc
 OFF AV  OFF C 
TpR L C
TPC
TP R LC
T p R LC
2.31
Let
d1 
Toff
Ton
T
d3  F 2
d2 
Tp ,
Tp
Tp ,
and substitute into the above equation.
vC  d 2
i AV
v
 C
C RL C
2.32
Figure 2.27 Buck–boost converter small signal model for the discontinuous mode.
Where d1 + d2 + d3 = 1 and
i AV 
1 vs
Ton
2 L
2.33
At this point, the same perturbation techniques, as presented previously, are used to
obtain the small signal model. Introducing variations in the line voltage and duty cycle
produce perturbations in the state and output; separating the DC and AC terms and
simplifying results in
36
vc 
vˆ c
T
V
T V
T T
 OFF S dˆ 1  ON S dˆ 2  ON OFF vˆ s
R LC
2 LC
2 LC
T P 2 LC
2.34
Where
TON
V

VS
TOFF 
2 LT p
2.35
RL
2 LT p
2.36
RL
VC D1

VS D2
2.37
A circuit model (Figure 2.27) can be realized from the above equations. The above small
signal model is used to derive them.
2.6 Two-Quadrant Choppers
A two-quadrant chopper has the ability to operate in two quadrants of the (v–i) plane.
Therefore, input and output voltages are positive; however, input and output currents can
be positive or negative. Thus, these converters are also named current reversible
choppers. They are composed of two basic chopper circuits.
Figure 2.28 A current reversible chopper.
37
Figure 2.29 Output current of a two-quadrant chopper.
Usually, a two-quadrant DC-DC converter is achieved by a combination of two basic
chopper circuits, a step-down chopper and a step-up chopper, as is shown in Figure 2.28.
The step-down chopper is composed of S1 and D1, electric energy is supplied to the load.
The step-up chopper is composed of S2 and D2; electric energy is fed back to the source.
Reversible current choppers can transfer from operating in the power mode to operating
in the regenerative mode smoothly by changing the control signals for S1 and S2, without
using any mechanical contacts. Figure 2.29 depicts the output current of a two-quadrant
chopper. d1 and d 2 = 1  d1 are the duty ratios of step-down and step-up converters,
respectively. By changing d1 and d 2 , not only the amplitude of the average of the output
current changes, but it can also be positive and negative, leading to two-quadrant
operation. Figure 2.30 (vo, ave./vin, ave.)- io, shows the characteristic of a two-quadrant
converter in continuous- and discontinuous-conduction modes of operation. As is shown
in Figure 2.30, for changing the operating mode both from step-down to step-up
operation and in the opposite direction,
38
Figure 2.30 ( vo,ave / vin,ave - io ,ave ) characteristic of a two-quadrant converter.
Figure 2.31 A full-bridge four-quadrant chopper.
By applying d 2 = 1  d1 , the operating point will never move into the discontinuousconduction region of the two basic converters. In Figure 2.30, the broken lines indicate
passage from step-down operation to step-up operation, and vice versa. Because of
specific command—the relation between the two duty ratios—the converter operating
point always stays in the continuous-conduction mode.
39
2.7 Four-Quadrant Choppers
In four-quadrant choppers, not only can the output current be positive and negative, but
the output voltage also can be positive and negative. These choppers are full-bridge DCDC converters, as shown in Figure 2.31. The main advantage of these converters is that
the average of the output voltage can be controlled in magnitude as well as in polarity. A
four-quadrant chopper is a combination of 2 two quadrant choppers in order to achieve
negative average output voltage and/or negative average output current. The fourquadrant operation of the full-bridge DC-DC converter, as shown in Figure 2.32, for the
first two quadrants of the (v–i) plane is achieved by switching S1 and S2 and considering
D1 and D2 like a two-quadrant chopper. For the other two quadrants of the (v–i) plane,
the operation is achieved by switching S3 and S4 and considering D3 and D4 as another
two-quadrant chopper, which is connected to the load in the opposite direction of the first
two-quadrant chopper.
Figure 2.32 Four-quadrant operation of a full-bridge chopper.
40
Chapter Three
Four Quadrant SEPIC Converter
3.1 One Quadrant SEPIC converter [26-27]
Single-ended primary-inductor converter (SEPIC) is a type of DC-DC converter allows
the electrical potential (voltage) at its output to be greater than, less than, or equal to that
at its input. The output of a SEPIC dc-dc converter can be controlled by the duty cycle of
the semiconductor switch used with converter.
A SEPIC converter has gain characteristics similar to a traditional buck-boost converter.
It has advantages of having non-inverted output (the output has the same voltage polarity
as the input) and use of a series capacitor for energy transfer from the input to the output.
SEPIC converters are useful in applications in which a source voltage can be above and
below that of the regulator's intended output.
Figure 3.1: Schematic Circuit diagram of SEPIC converter.
41
Circuit operation
The schematic circuit diagram of a basic SEPIC dc-dc converter is shown in Figure 3.1.
Like other dc-dc converter, the SEPIC converter exchanges energy between the
capacitors and inductors in order to convert voltage and current. The amount of energy
exchanged is controlled by switch S1, which is typically a semiconductor switch such as
a MOSFET. MOSFETs offer high input impedance and lower voltage drop than bipolar
junction transistors (BJTs). BJTs require current drive whereas MOSFET switching is
controlled by gate source voltage differences.
A SEPIC dc-dc converter is in continuous-conduction mode ("continuous mode") if the
current through the inductor L1 does not fall to zero. During a SEPIC's steady-state
operation, the average voltage across capacitor C1 (VC1) is equal to the input voltage
(Vin). Because the capacitor C1 blocks the direct current (DC), the average current across
it (IC1) is zero, making inductor L2 the only source of load current. Therefore, the
average current through inductor L2 (IL2) is the same as the average load current and
hence independent of the input voltage.
Looking at average voltages, the following can be written:
3.1
Because the average voltage of VC1 is equal to VIN, VL1 = −VL2. The two inductors can be
wound on the same core. Since the voltages are the same in magnitude, their effects of
the mutual inductance will be zero. Also, since the voltages are the same in magnitude,
the ripple currents from the two inductors will be equal in magnitude. The average
currents can be summed as follows:
42
When switch S1 is turned on, current IL1 increases and the current IL2 increases in the
negative direction. (Mathematically, it decreases). The energy to increase the current IL1
comes from the input source. Since S1 is a short while closed, and the instantaneous
voltage VC1 is approximately VIN, the voltage VL2 is approximately −VIN. Therefore, the
capacitor C1 supplies the energy to increase the magnitude of the current in IL2 and thus
increase the energy stored in L2 . The easiest way to visualize this is to consider the
voltages of the circuit in a d.c. state, then close S1.
Figure 3.2: With S1 closed current increases through L1 (green) and C1 discharges
increasing current in L2 (red)
When switch S1 is turned off, the current IC1 becomes the same as the current IL1. The
current IL2 will continue in the negative direction. It can be seen from the diagram that a
negative IL2 will add to the current IL1 to increase the current delivered to the load. Using
Kirchhoff's Current Law, it can be shown that ID1 = IC1 - IL2. It can then be concluded,
that while S1 is off, power is delivered to the load from both L2 and L1 . C1 , however is
being charged by L1 during this off cycle, and will in turn recharge L2 during the on
cycle.
43
Figure 3.3: With S1 open current through L1 (green) and current through L2 (red)
produce current through the load
The potential (voltage) across capacitor C1 may reverse direction every cycle. A nonpolarized capacitor should therefore be used.
The capacitor CIN is required to reduce the effects of the parasitic inductance and internal
resistance of the power supply. The boost/buck capabilities of the SEPIC are possible
because of capacitor C1 and inductor L2 . Inductor L1 and switch S1 create a standard
boost converter, which generates a voltage (VS1) that is higher than VIN, whose magnitude
is determined by the duty cycle of the switch S1. Since the average voltage across C1 is
VIN, the output voltage (VO) is VS1 - VIN. If VS1 is less than 2VIN, then the output voltage
will be less than the input voltage. If VS1 is greater than 2VIN, then the output voltage will
be greater than the input voltage.
Ideal Voltage and Current Gain Equations of 1Q SEPIC DC-DC converter:
The one quadrant SEPIC DC-DC converter in switch ON and switch OFF states are
shown in Figures 3.2 and 3.3. In these figures following volt-sec balance for each
switching cycle may be carried out to yield ideal voltage and current gain equation of the
converter.
44
For inductor L1 ,
Vin DT  (Vin  Vc  Vo )(1  D)T  0
3.2
Which yield ,
VC 
Vin
 VO
1 D
And I C 
1 D
 IO
I in
3.3
3.4
For inductor L2 ,
 VC DT  VO (1  D)T  0
3.5
Which yields,
VC 
VO
 VO
D
And I C  DI O  I O
3.6
3.7
From equations (3.3) and (3.6)
Vin
V
 VO  O  VO
1 d
D
Or, VO 
D
Vin
1 D
3.8
And from equation(3.4) and (3.7)
45
1 D
 I O  DI O  I O
I in
3.9
IO 1  D

I in
D
Equations (3.8) and (3.9) indicates that ideal SEPIC DC-DC converter has Buck-Boost
voltage and current gain relationship.
3.1.1 Simulation Results of One Quadrant SEPIC DC-DC Converter
Initially a 1-Q SEPIC DC-DC converter as shown Figure 2.4 which is controlled by a
pulse waveform as shown in Figure 2.5 is studied for input voltage 24V and load
resistance 20 ohm.
APT30G100BN
R12
L1
.001
10mH
D130
C1
MR2406F
20u
V+
R13
.001
D139
Z1
V1
gate1
C2
MR2406F
20u
R1
20
24Vdc
L2
gnd1
R3
5mH
V-
SEPIC CONVERTER(QUADRANT ONE
MODE)
1meg
0
Figure 3.4 One Quadrant SEPIC Chopper
Typical waveforms of an One Quadrant SEPIC Chopper of Figure 3.4 with resistive load
for gate pulse of Figure 3.5 are shown in Figures 3.6-3.7. Figures 3.6-3.7 show typical
waveforms of circuit of Figure 3.4, both Load Current and voltage are positive with
changing duty cycle.
46
Figure 3.5 Gate Signal of the one quadrant SEPIC dc-dc converter.
47
Figure 3.6: Load Current and voltage are positive of circuit of Figure 3.4 for gate signal at DC level 3V (Quadrant-I).
48
Figure 3.7: Load Current and voltage are positive of circuit of Figure 3.4 for gate signal at DC level 6V (Quadrant-I).
49
3.1.2 Typical Result of Duty cycle variation of 1-Q SEPIC DC-DC converter
The duty cycle variation of control pulse of the switch of 1-Q SEPIC DC-DC converter
of Figure 3.4 has been carried out for D=.10 to .98 and the values of voltage gain and
efficiency of the converter has been obtained as tabulated in Table 3.1 and 3.2.These
results are graphically shown Figure 3.8 and 3.9 respectively.
Table 3.1:
The Value of Voltage with changing Duty Cycle for 1-Q SEPIC DC-DC converter of the
Circuit of Figure 3.4
Duty Cycle(%)
Input Voltage(Vin),V
Output Voltage(Vo),V
Voltage Gain(Vo/Vin)
0.10
24
5.05
0.210
0.20
24
7.78
0.324
0.30
24
11.02
0.459
0.40
24
15.44
0.643
0.50
24
21.75
0.906
0.60
24
32.47
1.353
0.70
24
51.86
2.161
0.80
24
85.58
3.566
0.90
24
138.53
5.772
0.92
24
156
6.500
0.94
24
174
7.250
0.96
24
155
6.458
0.98
24
82
3.417
50
Table 3.2:
The Value of Power with changing Duty Cycle for One quadrant Chopper of Circuit of
the Figure 3.4
Duty Cycle Input Voltage(Vin)
Input Power(Pin)
Output Power(Po)
Efficency(%)
0.10
24
0.453
0.329
0.7263
0.20
24
0.98
0.764
0.7796
0.30
24
1.72
1.55
0.9012
0.40
24
3.41
3.07
0.9003
0.50
24
6.66
6.11
0.9174
0.60
24
13.94
13.44
0.9641
0.70
24
34.89
34.08
0.9768
0.80
24
97
90
0.9278
0.90
24
320
251
0.7844
0.92
24
430
320
0.7442
0.94
24
595
413
0.6941
51
Figure 3.8 Characteristics Curve Gain Vs Duty Cycle for One quadrant Chopper for the
Data Table 3.1
52
Figure 3.9 Characteristics Curve Efficiency Vs Duty Cycle for One quadrant Chopper for
the Data Table 3.2
53
The simulation results tabulated in table 3.1 and 3.2, and graphically represented in
Figures 3.8 and 3.9 indicate,
i) Voltage gain(Vo/Vin) of the converter increases with duty cycle increase. The voltage
gain peaks to 6.3 at duty cycle .89 as equation for output voltage,
VO 
D
Vin
1 D
increases with duty cycle
ii) After the peak is reached, the voltage gain decreases with increase of duty cycle
Results i) and ii) above are expected of practical dc-dc converter, whereas efficiency of
ideal dc-dc converter are 100% or unity and for SEPIC converter the voltage gain less
than 1 for duty cycle D<.5 and higher than 1upto infinity for D>.5
54
3.2 Two Quadrant SEPIC converter
The 1-Q SEPIC converter shown Figure 3.4 has been extended to a 2-Q SEPIC dc-dc
converter in the quest for development of a 4Q SEPIC dc-dc converter. The Circuit used
for 2-Q SEPIC dc-dc converter which has been derived from 1-Q SEPIC dc-dc converter
is shown in Figure 3.10(a). The Circuit has an extra switch across output diode and an
anti parallel diode across switch.
Figure 3.10(a) Two Quadrant SEPIC Chopper
55
The operation of the 2-QSEPIC converter in the forward direction is the same as the
circuit of Figure 3.4 which is shown in Figure 3.10(b).
Figure 3.10(b) Two Quadrant SEPIC converter in forward direction (left to right).
The operation of the 2-Q SEPIC converter of Figure 3.10(a) in the reverse direction can
be understood from Figure 3.10(c)-(d).
56
Figure 3.10(c): Two Quadrant SEPIC converter in Reverse direction (right to left)
Figure 3.10(d) Two quadrant SEPIC converter in Reverse direction (right to left) as
combination of a Buck-Boost (right box part) and lift circuit (left box part)
57
The operation in the reverse direction does not use the switch 1 and diode 1(as shown
dotted) as shown in Figure 3.10(c). The Circuit of Figure 3.10(c) can be identified as an
Buck-Boost converter of the right box of Figure 3.10(d) with the output at the capacitor
as shown. The left box part of circuit acts as a lift circuit that transfers the capacitor
charge to appear as +ve voltage at the output at the left side as in SEPIC converter.
In simulation the converter is switched by two pulse as shown in Figure 3.11
Figure 3.11: Gate pulse of switches of Circuit of Figure 3.10(a).
Typical waveforms of Two Quadrant SEPIC Chopper connected (+ve) EMF of circuit of
Figure 3.10(a) are shown in Figures 3.12-3.13. Figures 3.12-3.13 show typical
waveforms of circuit of Figure 3.10(a), Load Current changes positive to Negative with
changing duty cycle.
58
3.2.1 Simulation Result two Quadrant SEPIC DC-DC Converter
If we choose for gate signal at DC level 5V than duty cycle of S1 will be greater than
duty cycle of S2, Energy transfer in Forward direction (from A side to B side) that is
shown in Figure 3.12
Figure 3.12: Current is Positive at B side for Positive output of circuit of figure 3.10 for
gate signal at DC level 5V (Quadrant-I)
59
If we choose for gate signal at DC level 2V than duty cycle of S2 will be greater than
duty cycle of S1, Energy transfer in Reverse direction (from B side to A side) that is
shown in Figure 3.13
Figure 3.13: Current is Negative at B side for Positive Voltage of circuit of figure 3.10(a)
for gate signal at DC level 2V (Quadrant-II).
60
3.2.2 Typical Result of Duty cycle variation of 2-Q SEPIC DC-DC converter
The duty cycle variation of control pulse of the switch of 2-Q SEPIC DC-DC converter
of Figure 3.10(a) has been carried out for D=.10 to .90 and the values of voltage gain and
efficiency of the converter has been obtained as tabulated in Table 3.3. These results are
graphically shown Figure 3.14 and 3.15.
Table 3.3:
The Value of Power with changing Duty Cycle for Two quadrant Chopper of the Circuit
of Figure 3.10(a)
Duty Cycle
Voltage(Va)
Power(Watt)AT A side
Power(Watt) at B side
0.1
24
24.88
-54.77
0.2
24
18.89
-30.43
0.3
24
8.37
-10.83
0.4
24
-3.49
2.56
0.5
24
-32.52
25.62
0.6
24
-79.33
46.19
0.7
24
-127.18
63.2
0.8
24
-149.54
76.74
0.9
24
-184.46
92.82
61
Figure 3.14 Characteristics Curve of Power at A side Vs Duty Cycle for Two quadrant
Chopper for the Data Table 3.3
Figure 3.14 show that the value of Power at A side changes positive to negative at near
36% duty cycle. Before duty cycle 36%, Power at A side is positive means power is
supplied from B side to A and after 36% duty cycle, Power at A side is negative means
power is supplied from A side to B.
62
Figure 3.15 Characteristics Curve of Power at B side Vs Duty Cycle for Two quadrant
Chopper for the Data Table 3.3
Figure 3.15 show that the value of Power at A side changes positive to negative at near
37% duty cycle. Before duty cycle 37%, Power at B side is negative means power is
supplied from B side to A and after 37% duty cycle, Power at B side is positive means
power is supplied from A side to B.
63
From above discussion about Circuit figure 3.10(a), that Converter has bi-directional
energy transfer (Energy is transferred from A side to B side and also B to A side).
So, Our assumption is justified that it is 2-Q SEPIC dc-dc converter.
The duty cycle variation of control pulse of the switch of 2-Q SEPIC DC-DC converter
of Figure 3.10(a) has been carried out for duty cycle above 37% to 90% than Energy is
transferred into forward direction (From A to B side) and the values of power and
efficiency of the converter has been obtained as tabulated in Table 3.4. These results are
graphically shown Figure 3.14.
Table 3.4:
Efficiency with changing Duty Cycle for Two quadrant Chopper of the Circuit of Figure
3.10(a)(Forward operation)
Duty Cycle
Voltage(Va)
Power(Watt) at A
side
Power(Watt) at B side
Efficiency(%)
0.40
24
-3.49
2.56
0.733524355
0.50
24
-32.52
25.62
0.787822878
0.60
24
-79.33
46.19
0.582251355
0.70
24
-127.18
63.2
0.49693348
0.80
24
-149.54
76.74
0.513173733
0.90
24
-184.46
92.82
0.503198525
64
Figure 3.16 Characteristics Curve of Efficiency Vs Duty Cycle for Two quadrant
Chopper for the Data Table 3.4.
65
The duty cycle variation of control pulse of the switch of 2-Q SEPIC DC-DC converter
of Figure 3.10(a) has been carried out for duty cycle above 10% to 35% than Energy is
transferred into reverse direction (From B to A side) and the values of power and
efficiency of the converter has been obtained as tabulated in Table 3.5. These results are
graphically shown Figure 3.15.
Table 3.5:
Efficiency with changing Duty Cycle for Two quadrant Chopper of the Circuit of Figure
3.10 (Reverse operation)
Duty Cycle
Voltage(Va)
Power(Watt)AT A
side
Power(Watt) at B side
Efficiency(%)
0.10
24
24.88
-54.77
0.454263283
0.15
24
23.66
-43.7
0.541418764
0.20
24
18.89
-30.43
0.620768978
0.25
24
16.93
-25.69
0.659011288
0.30
24
8.37
-10.83
0.772853186
0.35
24
5.35
-6.6
0.810606061
66
Figure 3.17 Characteristics Curve of Efficiency Vs Duty Cycle for Two quadrant
Chopper for the Data Table 3.5.
The simulation results tabulated in table 3.4 and 3.5, and graphically represented in
Figures 3.16 and 3.17 indicate,
i) Duty cycle from above .37 to .90 (Energy transfer in forward direction), Efficiency of
the converter decreases with duty cycle increase. The efficiency peaks to 78% at duty
cycle .50 and
ii) Duty cycle from above 0 to .37 (Energy transfer in reverse direction), Efficiency of the
converter increases with duty cycle increase. The efficiency peaks to 81% at duty cycle
.34
67
3.3 Four Quadrant SEPIC converter
The 2-Q SEPIC converter shown Figure 3.10(a) has been extended to a 4-Q SEPIC dc-dc.
The Circuit used for 4-Q SEPIC dc-dc converter which has been derived from 2-Q SEPIC
dc-dc converter is shown in Figure 3.22. Two 2-Q SEPIC converter dc-dc converter has
been connected with differential connection to obtain 4-Q SEPIC dc-dc converter shown
Figure 3.22.Here A indicates input side and B indicates output side.
Figure 3.18: Four Quadrant SEPIC Chopper
68
In simulation among four gate pulses, using gate1, gate11 same signal and gate2, gate22
same signal for the converter of circuit figure 3.20 is switched shown in Figure 3.19
Figure 3.19 Typical Gate pulses of four quadrant SEPIC dc-dc Converter.
Voltage and Current Gain Equations of Four Quadrant SEPIC DC-DC converter:
The ideal voltage and current Gain Equations of Four Quadrant SEPIC DC-DC converter
may be obtained from the difference of 2Q DC-DC converter and current gain
expressions where one side converter operates at D and the other side converter operates
at 1-D
Hence,
VO  VO1  VO 2
69
D
1 D
Vin 
Vin
1 D
1  (1  D )
D
1 D

Vin 
Vin
1 D
D
D 2  (1  D ) 2

Vin
D(1  D )

D 2  (1  2 D  D 2 )

Vin
D (1  D)
VO 
2D  1
Vin
D (1  D )
3.10
Similarly,
IO 
D (1  D )
I in
2D 1
3.11
70
3.3.1 Simulation Result of 4-Q SEPIC Converter switching by rectangular wave
signal
Four Quadrant SEPIC Chopper with output positive DC voltage shown Figure 3.20 at B
side a 30V DC voltage source is a differential connected load. Typical waveforms of four
Quadrant SEPIC Chopper connected (+ve) EMF of circuit of Figure 3.20 are shown in
Figures 3.21-3.29. Figures 3.21-3.29 show typical waveforms of circuit of Figure 3.20,
Current at B side changes positive to Negative with changing duty cycle from .10 to .90.
Figure 3.20: Four Quadrant SEPIC Chopper with output positive DC voltage.
71
72
Figure 3.22: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width .04ms.
73
Figure 3.23: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width .06ms.
74
Figure 3.24: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width .08ms.
75
Figure 3.25: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width .10ms.
76
Figure 3.26: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width .12ms.
77
Figure 3.27: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width .14ms.
78
Figure 3.28: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width .16ms.
79
Figure 3.29: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.20 for pulse width .18ms.
80
Four Quadrant SEPIC Chopper with output negative DC voltage shown Figure 3.34 at B
side a 30V DC voltage source is a differential connected load. Typical waveforms of four
Quadrant SEPIC Chopper connected (-ve) EMF of circuit of Figure 3.34 are shown in
Figures 3.35-3.43. Figures 3.35-3.43 show typical waveforms of circuit of Figure 3.34,
Current at B side changes positive to Negative with changing duty cycle from .10 to .90.
Figure 3.30: Four Quadrant SEPIC Chopper with output negative DC voltage.
81
Figure 3.31: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width .02ms.
82
Figure 3.32: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width .04ms.
83
Figure 3.33: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width .06ms
84
Figure 3.34: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width .08ms.
85
Figure 3.35: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width .10ms
86
Figure 3.36: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width .12ms
87
Figure 3.37: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width .14ms
88
Figure 3.38: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width .16ms
89
Figure 3.39: Current at B side of Four Quadrant SEPIC Chopper of circuit of Figure 3.30 for pulse width .18ms
90
3.3.2 Typical Result of Duty cycle variation of 4-Q SEPIC DC-DC Converter
The duty cycle variation of control pulse of the switch of 4-Q SEPIC DC-DC Converter
of Figure 3.20 and Figure 3.30 has been carried out for D=.10 to .90.The control pulse
of Gate1, 11 and Gate2, 22 are opposite pulse. So if Duty Cycle of control pulse of
Gate1, 11 is decreases Duty Cycle of control pulse of Gate2, 22 is increases. The value of
output current with direction of current flow has been obtained from output Figure 3.21
to 3.29 for the circuit of Figure 3.24 as tabulated in Table 3.6 and from output Figure
3.31 to 3.39 for the circuit of Figure 3.30 as tabulated in Table 3.6 and 3.7.
Table 3.6:
The value output current changing with Duty Cycle for four quadrant Chopper of the
Circuit of Figure 3.20
Output
Voltage
(+30V)
Output
Current(B
side)(A)
Sl
no.
Simulated
Figure No.
01
Figure 3.25
.90
.10
+30
+40
I
02
Figure 3.26
.80
.20
+30
+24
I
03
Figure 3.27
.70
.30
+30
+32
I
04
Figure 3.28
.60
.40
+30
+18
I
05
Figure 3.29
.50
.50
+30
+9
I
06
Figure 3.30
.40
.60
+30
+2.5
I
07
Figure 3.31
.30
.70
+30
-2.5
II
08
Figure 3.32
.20
.80
+30
-2
II
09
Figure 3.33
.10
.90
+30
-6
II
Duty Cycle
(Gate 1,11)
Duty Cycle
(Gate2,22)
Quadrant
91
The simulation results for the Four Quadrant SEPIC converter of circuit figure 3.20 with
positive output voltage source from Figure 3.21 to 3.29 tabulated as in Table 3.6 indicate,
i) Output voltage is always positive, the output current changes positive to negative with
duty cycle changing.
ii) When Duty cycle for gate pulse 1, 11 >Duty cycle for gate pulse 2, 22 output current
always positive so our four Quadrant SEPIC converter working as Quadrant-I
operation
iii) When Duty cycle for gate pulse 1, 11 <Duty cycle for gate pulse 2, 22 output current
always negative so our four Quadrant SEPIC converter working as Quadrant-II
operation
So, Four Quadrant SEPIC converter of circuit Figure 3.20 is justified as Two Quadrant
DC-DC Converter (as working Quadrant-I and Quadrant-II).
92
Table 3.7:
The value output current changing with Duty Cycle for four quadrant Chopper of the
Circuit of Figure 3.30
Sl
no.
Simulated
Figure No.
Duty Cycle
(Gate 1,11)
Duty Cycle
(Gate2,22)
Output
Voltage
(-30V)
Output
Current(B
side)(A)
01
Figure 3.35
.90
.10
-30
+5
IV
02
Figure 3.36
.80
.20
-30
+2
IV
03
Figure 3.37
.70
.30
-30
+1.8
IV
04
Figure 3.38
.60
.40
-30
-3.6
III
05
Figure 3.39
.50
.50
-30
-10
III
06
Figure 3.40
.40
.60
-30
-20
III
07
Figure 3.41
.30
.70
-30
-32
III
08
Figure 3.42
.20
.80
-30
-28
III
09
Figure 3.43
.10
.90
-30
-41
III
Quadrant
The simulation results for the Four Quadrant SEPIC converter of circuit figure 3.30 with
positive output voltage source from Figure 3.31 to 3.39 tabulated as in Table 3.7 indicate,
i) Output voltage is always of four Quadrant SEPIC converter negative, the output current
changes positive to negative with duty cycle changing.
ii) When Duty cycle for gate pulse 1, 11 >Duty cycle for gate pulse 2, 22 output current
always positive so our four Quadrant SEPIC converter working as Quadrant-IV
operation.
93
iii) When Duty cycle for gate pulse 1, 11 <Duty cycle for gate pulse 2, 22 output current
always negative so our four Quadrant SEPIC converter working as Quadrant-III
operation.
So, Four Quadrant SEPIC converter of circuit Figure 3.30 is justified as Two Quadrant
DC-DC Converter (as working Quadrant-IV and Quadrant-III).
From above discussion, Proposed circuit of Figure 3.18 is justified as FOUR
QUADRANT DC-DC CONVERTER.
94
3.3.3 Simulation Result of Four Quadrant SEPIC Converter switched by sine PWM
wave
Figure 3.40: Four Quadrant SEPIC Chopper with differentially connected R-L load.
Four quadrant chopper circuits perform dc-dc conversion. With inductive load, inverter
output voltage and load current clearly demonstrate four quadrant operation for R-L, RL-EMF and R-L-C loads. The SEPIC converter developed in this investigation has been
studied with sine PWM gate pulse to operate the inverter(dc-ac conversion) mode. The
SEPIC 4Q dc-dc converter is shown in Figure 3.40.Typical sine PWM gate pulse for
switching the converter is shown in Figure 3.41.
95
Figure 3.41: Typical PWM gate pulses of Four Quadrant SEPIC DC-DC converter
Typical waveforms of the Four Quadrant SEPIC Chopper connected to an R-L load
circuit of Figure 3.40 are shown in Figure 3.42. Figure 3.42 shows that the value of
output voltage amplitude and current are alternating (periodic with average=0). Also it is
seen in the Figure 3.42 that while the output voltage is +ve, both +ve and –ve load current
are present when the output voltage is –ve, load current is both +ve and –ve are available.
96
Figure 3.42: Load Current and voltage at B side in forward and reverse direction operation of circuit of figure 3.40 with
(R=50ohm,L=100mh)
97
The investigation is replaced for Four Quadrant SEPIC Converter of circuit Figure 3.18
using Pulse Width Modulation switching Scheme. Interchanging between R-L load and
voltage source, R-L load is differentially connected at the Four Quadrant SEPIC Chopper
at input side A and voltage source is now connected to output B side shown in Figure
3.43.
Figure 3.43: Four Quadrant SEPIC Chopper with differentially connected R-L load at
input side.
Typical waveforms of Four Quadrant SEPIC Chopper connected R-L load of circuit of
Figure 3.43 are shown in Figure 3.44. Figure 3.44 shows that the value of Output Voltage
amplitude and current are alternating.
98
Figure 3.44: Load Current and voltage at B side in forward and reverse direction operation of circuit of Figure 3.40 with
(R=50ohm, L=100mh)
99
From the above investigation it is evident that the 4Q SEPIC dc-dc converter works as a
dc-dc converter and with R-L or R-L-emf load it clearly demonstrate 4-Quadrant
operation (For positive output voltage the load current may be either positive or negative,
and for negative output voltage the load current may be either negative or positive). Also
the reversible operation of the proposed circuit is clearly demonstrate by the fact that the
circuit works in four quadrants even if the source and load position are interchanged.
3.3.4 Typical Result of Modulation index variation of 4-Q SEPIC DC-DC Converter
The modulation index variation of control pulse of the switch of 4-Q SEPIC DC-DC
Converter of Figure 3.43 has been carried out for M=.10 to .90.The control pulse of
Gate1, 11 and Gate2, 22 are opposite PWM pulse. The value of output current and power
has been obtained from 4-Q SEPIC DC-DC Converter of the circuit of Figure 3.43 as
tabulated in Table 3.8 and graphically shown in Figure 3.45 and 3.46
100
Table 3.8:
Value of Output Power and Voltage with changing Modulation Index of Four Quadrant
SEPIC Chopper of Figure 3.43
Output
Power(W)
Modu
lation
index
Input
Voltage(
V)
Input
Power(W)
Voltage
Gain
Output
Voltage(V)
0.1
4.42
0.978
24
5.5
0.187
0.1778
0.2
9.91
4.91
24
10.7
0.41
0.4589
0.3
16.04
12.84
24
20.5
0.66
0.6263
0.4
22.64
25.64
24
36.16
0.94
0.7091
0.5
29.15
44.02
24
56.67
1.21
0.7768
0.6
35.95
64.44
24
86.7
1.49
0.7433
0.7
41.66
87.05
24
119
1.73
0.7315
0.8
45.02
99.6
24
144
1.87
0.6917
0.9
46.6
108.1
24
156
1.94
0.6929
Efficiency
101
Figure 3.45 Characteristics Curve of Voltage Gain Vs Modulation Index of the Four
quadrant SEPIC Chopper for the circuit Figure 3.43.
The simulation result tabulated in Table 3.8 and graphically shown in Figure 3.45
indicate,
i) Voltage gain of the converter increases with modulation index increases.
ii) Voltage gain less than 1 for modulation index<.50 and higher than 1 for modulation
index >.50
Above two results i) and ii) are expected for DC-DC SEPIC Converter
102
Figure 3.46 Characteristics Curve of Efficiency Vs Modulation Index for Four quadrant
SEPIC Chopper for the circuit Figure 3.43
The simulation result tabulated in Table 3.8 and graphically shown in Figure 3.46
indicate, the variation of the efficiency with modulation index.
Efficiency of the converter increases with modulation index and peaks 76% when
Modulation index is .49. After approximate .5 modulation index the efficiency of the 4Q
SEPIC converter operating as a PWM inverter (dc-ac) decreases.
103
Chapter-Four
Conclusion
4.1 Summary Conclusions and Achievements
In power engineering and drives, DC-DC conversion technique is a major subject. DCDC conversion technology has continued to develop for the last six decades. The
multiple-quadrant chopper is a higher step in DC/DC conversion. Ability of multiple
quadrant DC-DC converter at step down and step up output voltage is one such
conversion process.
High frequency switching DC-DC converters are part of electronic equipment to provide
regulated dc of desired voltage. These converters have advantages over their counterpart
the linear power supplies. They have high efficiency, light weight, wide voltage control
range and cost less.
In this thesis, a four Quadrant DC-DC SEPIC converter has been developed. First various
basic topologies of DC-DC converters have been studied. From the study one quadrant
SEPIC dc-dc converter is chosen to develop the four quadrant chopper. One quadrant
SEPIC dc-dc converter is similar to a buck-boost converter, but it has advantages of
having non-inverted output and ability to run in continuous input current mode of
operation.
Investigation has been made with modifying single quadrant dc-dc SEPIC converter
circuit to develop a two quadrant SEPIC DC-DC converter. This has introduced a dc-dc
SEPIC converter with two switches. Two quadrant dc-dc SEPIC converter have been
investigated with variable duty cycle operation for verifying the buck-boost gain
characteristics of the voltage. The circuit has also been investigated with input/output dc
sources connected for two quadrant operation as the duty cycle is varied from 0 to near
one.
104
The converter showed buck-boost voltage gain characteristics and maximum efficiency
of 81 percent as the duty cycle of the converter has been changed. The results has been as
expected of two quadrant SEPIC dc-dc converter and was suitable for adopted the
topology for the development of 4-Quadrant SEPIC dc-dc Converter.
Two 2Q dc-dc SEPIC converter have been differentially connected to introduce a four
quadrant dc-dc converter with four switches. A positive DC voltage source has been
connected at the output side. Four gate pulse were produced to switch four switches of
the 4 Quadrant SEPIC converter. From the simulation result, by varying duty cycle of the
pulse positive and negative output current for (+ve) EMF has been found. This ensured
the quadrant-I and the quadrant-II operation. Again by varying duty cycle of the pulse,
positive and negative output current for (-ve) EMF of the input which ensured quadrantIII and quadrant-IV operation.
Another investigation was also made by using sine PWM gate pulse on proposed four
quadrant SEPIC dc-dc converter. An R-L load was connected to the output of the
converter. From simulation it was found that output voltage and current of the load are ac
which also proved that proposed converter was working as DC-AC converter. In practice,
DC-AC inverters are examples of four quadrant DC-DC converters. Inverters have (+)ve
and (-)ve voltage across load and the current of the load may changed from +ve to –ve for
either +ve or –ve voltage across the load.
105
4.2 Suggestion on future works
The contributions of this thesis indicate the opportunities of extending this work in future
to meet other goals. Some of these may be,
1. Only spice simulation is performed in this study. The proposed new FOUR
QUADRANT SWITCH MODE DC-DC CONVERTER may be implemented
practically to investigate its actual potential. Such practical implementation would
give an insight regarding the cost effectiveness of the proposed scheme compared
to the existing schemes for the similar purpose.
2. The PWM module has been used to generate gating signals for switching the
proposed converter switches at varying duty cycles. Investigation can be made to
improve the quality of the gating signals at different duty cycle.
3. Regulation of the output voltage was not studied in this thesis. Investigation can
be extended to regulate the output voltage.
4. Investigation can be extended to use this dc-dc converter in battery charging
system, particularly for Electrical Vehicle Boost battery charging system.
106
References:
[1] B.K. Bose, “Energy, Environment, and advances in power electronics”, IEEE Trans.
On Power Electronics, vol. 15, no. 4, July 2000.
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Electronics, vol. 7, no1, 1992.
[3] B.K. Bose, Ed., “ Modern Power Electronics Proc”, IEEE, vol. 80,no.8 August 1992.
[4] M. H. Rashid, “Power Electronics Circuits, Devices, Applications and Design”,
Prentice Hall
Englewood Cliffs, 4th Edition, 2004.
[5] N Mohan, T.M Undeland and W.P Robbins, “Power Electronic Converters,
Application and Design”, John Wiley and Sons, New York 1995.
[6]Venkat, “Switch Mode Power Supply”, University of Technology, Sydney,
Australia,March1,2001,availabl at http://www.ee.uts.edu.au /~venkat/
pe_html/pe07_nc8.htm.
[7] F.L.Luo, “Double Output Luo Converter An Advantage of Voltage Lift Technique”
IEE Proc..Electric Power Applications 147,pp.469-485, November 2000.
[8] F.L. Luo , H.Ye and M.H. Rashid, “Two quadrant DC/DC ZVS Quasi-Resonant
Luo-converter”, Proceeding of IEE IPEMC 2000 Beijing , China August 2000.
[9] F.L. Luo, H. Ye and M.H. Rashid, “Four quadrant operation Luo-converters”
Proceeding of IEE PESC 2000 Ireland june 2000.
[10] C.A. Canesin and Barbi, “Novel Zero-Current-Switching PWM converters” IEEE
Transactions on Industrial Electronic, vol.44,372-381,1997.
[11] Mazharul Islam,
“Four Quadrant Buck Boost Converter” M.Sc. thesis , EEE,
BUET, 2012.
107
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[13] S. Ĉuk and R. D. Middlebrook, “A general unified approach to modeling switching
DC-to-DC converters in discontinuous conduction mode”, in IEEE Power Electronics
Specialists Conference Record, 1977, 36–57.
[14] R. G. Hoft, “Semiconductor Power Electronics”, Van Nostrand Reinhold, New
York, 1986, chap. 5
[15] N. Mohan, T. M. Undeland, and W. P. Robbins, “Power Electronics: Converters,
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Upper Saddle River, NJ, 2001, chap. 6.
[17]TESLAco, Ĉukonverter Technology, 1996, 23 February 2001, available at
http://www.teslaco.com/inverter.htm.
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Vol. 1 and 2, TESLAco,Pasadena, CA, 1981.
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switching converters”, presented at IEEE Int. Semiconductor Power Converter
Conference, 1977.
[20] G. W. Weste and R. D. Middlebrook, “Low-frequency characterization of switched
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[23] D. J. Shortt and F. C. Lee, “Extensions of the discrete-average models for converter
power stages”, in PESC Record, 1983, 23–37; IEEE Trans. Aerospace Electron. Syst.,
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[24] D. J. Shortt and F. C Lee , “An improved switching converter model using discrete
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Electron. Syst., AES-19(2), 1983.
[25] V. Bello, “Computer-aided analysis of switching regulators using SPICE2”, in IEEE
Power Electronics Specialists Conference Record, 1980, 3–11.
[26] Sanjaya,Maniktala, “Switching Power Supply Design & Optimization”, McGrawHill, New York 2005.
[27] SEPIC Equations and Component Ratings, Maxim Integrated Products. Appnote
1051, 2005.
109
TABLE OF CONTENT
Page No.
xi
List of Tables
List of Figures
xii
Abbreviations
vi
Acknowledgement
vii
Abstract
Vii
Chapter One: Introduction
1
1.1
Introduction
1
1.2
1.3
1.4
Overview of DC Choppers
Specific aims and possible outcomes
Thesis Outline
Chapter Two: DC-DC Converter
2.1 Choppers
2.2 Buck Converters
2
9
10
11
11
12
2.3
2.2.1 Ideal Buck Circuit
2.2.2 Continuous-Conduction Mode
2.2.3 Discontinuous-Conduction Mode
Boost Converters
12
15
16
18
2.4
2.3.1 Ideal Boost Circuit
2.3.2 Continuous Conduction Mode
2.3.3 Discontinuous-Conduction Mode
Ĉuk Converter
18
19
21
22
2.5
2.4.1 Non isolated Operation
Buck–Boost Converter
23
25
2.5.1
2.5.2
27
34
2.6
2.7
Continuous-Conduction Mode
Discontinuous-Conduction Mode
Two-Quadrant Choppers
Four-Quadrant Choppers
Chapter Three: Four Quadrant SEPIC Converter
3.1 One Quadrant SEPIC converter
37
40
41
41
3.1.1
Simulation Results of One Quadrant SEPIC DC-DC
Converter
46
3.1.2
Typical Result of Duty cycle variation of 1-Q SEPIC
50
ix
DC-DC converter
3.2
3.3
Two Quadrant SEPIC converter
55
3.2.1
Simulation Result of two Quadrant SEPIC DC-DC
Converter
59
3.2.2
Typical Result of Duty cycle variation of 2-Q SEPIC
DC-DC converter
61
Four Quadrant SEPIC converter
68
3.3.1
Simulation Result of 4-Q SEPIC Converter switched by
rectangular wave signal
71
3.3.2
Typical Result of Duty cycle variation of 4-Q SEPIC
DC-DC Converter
91
3.3.3
Simulation Result of Four Quadrant SEPIC Converter
switched by sine PWM wave
95
3.3.4
Typical Result of Modulation index variation of 4-Q
SEPIC DC-DC Converter
100
Chapter Four : Conclusion
104
4.1
Conclusions, summary and achievements
104
4.2
Suggestion on future works
106
References:
107
x
LIST OF TABLES
Table 3.1:
The Value of Voltage with changing Duty Cycle for One
50
quadrant Chopper of The Circuit of Figure 3.4
Table 3.2:
The Value of Power with changing Duty Cycle for One
51
quadrant Chopper of The Circuit of Figure 3.4
Table 3.3:
The Value of Power with changing Duty Cycle for Two
61
quadrant Chopper of Circuit of The Figure 3.10(a)
Table 3.4:
Efficiency with changing Duty Cycle for Two quadrant
64
Chopper of Circuit of The Figure 3.10(a) (Forward
operation)
Table 3.5:
Efficiency with changing Duty Cycle for Two quadrant
66
Chopper of Circuit of The Figure 3.10(a) (Reverse
operation)
Table 3.6:
The value output current changing with Duty Cycle for four
91
quadrant Chopper of The Circuit of Figure 3.20
Table 3.7:
The value output current changing with Duty Cycle for four
93
quadrant Chopper of The Circuit of Figure 3.30
Table 3.8:
Value of Output Power and Voltage with changing
101
Modulation Index of The Four Quadrant SEPIC Chopper of
Figure 3.43
xi
LIST OF FIGURES
Figure 1.1:
Basic DC-DC converter.
3
Figure 1.2:
DC-DC converter voltage waveforms
3
Figure 1.3:
Pulse width modulation concept
4
Figure 1.4:
Block Diagram of SMPS.
7
Figure 1.5:
Switch mode (non dissipative) power conversion circuit
8
Figure 1.6:
Typical switch mode power conversion circuit
8
Figure 2.1:
Ideal buck converter
13
Figure 2.2:
Buck converter with LC filter.
13
Figure 2.3:
Rise and fall of load current in buck converter
14
Figure 2.4:
Buck converter with practical switch
14
Figure 2.5:
Buck converter switch states: (a) switch in position 1; (b)
15
switch in position
Figure 2.6:
Inductor voltage and current for continuous mode of buck
15
converter
Figure 2.7:
Inductor current at boundary point for discontinuous mode
17
of buck converter
Figure 2.8:
Basic boost converter
19
Figure 2.9:
Basic boost converter switch states: (a) switch closed; (b)
19
switch open
xii
Figure 2.10:
Inductor voltage and current waveforms for continuous
20
mode of boost converter
Figure 2.11:
Inductor current at boundary point for discontinuous mode
21
of boost converter
Figure 2.12:
Non-isolated Ĉuk converter
23
Figure 2.13:
Ĉuk converter switch states: (a) switch open; (b) switch
23
closed
Figure 2.14:
Inductor 1, voltage and current waveforms for Ĉuk
24
converter
Figure 2.15:
Inductor 2, voltage and current waveforms for Ĉuk converter
25
Figure 2.16:
Buck–boost converter
26
Figure 2.17:
Typical current waveforms in a buck–boost converter
27
Figure 2.18:
Topology 1 for the buck–boost converter
28
Figure 2.19:
Mode 2 for the buck–boost converter
28
Figure 2.20:
Continuous inductor current
30
Figure 2.21:
Inductor current perturbation
31
Figure 2.22:
Average circuit model of the buck–boost converter
33
Figure 2.23:
The small signal circuit model
33
Figure 2.24:
Discontinuous inductor current
33
Figure 2.25:
Topology 3 for the buck–boost converter (discontinuous
34
inductor current)
Figure 2.26:
General form of discontinuous inductor current
Figure 2.27:
Buck–boost
converter
small
signal
model
35
for
the
36
discontinuous mode
Figure 2.28:
A current reversible chopper
37
xiii
Figure 2.29:
Output current of a two-quadrant chopper
38
Figure 2.30:
(vo, ave. /vin, ave.) -io, ave. characteristic of a two-quadrant
39
converter
Figure 2.31:
A full-bridge four-quadrant chopper
39
Figure 2.32:
Four-quadrant operation of a full-bridge chopper
40
Figure 3.1:
Schematic Circuit diagram of SEPIC converter.
41
Figure 3.2:
With S1 closed current increases through L1 (green) and C1
43
discharges increasing current in L2 (red
Figure 3.3:
With S1 open current through L1 (green) and current
44
through L2 (red) produce current through the load
Figure 3.4:
One Quadrant SEPIC Chopper
46
Figure 3.5:
Gate Signal of the one quadrant SEPIC dc-dc converter.
47
Figure 3.6:
Load Current and voltage are positive of circuit of Figure
48
3.4 for gate signal at DC level 3V (Quadrant-I).
Figure 3.7:
Load Current and voltage are positive of circuit of Figure
49
3.4 for gate signal at DC level 6V (Quadrant-I)
Figure 3.8:
Characteristics Curve Gain Vs Duty Cycle for One quadrant
52
Chopper for the Data Table 3.1
Figure 3.9:
Characteristics Curve Efficiency Vs Duty Cycle for One
53
quadrant Chopper for the Data Table 3.2
Figure3.10(a):
Two Quadrant SEPIC Chopper
55
Figure3.10(b):
Two Quadrant SEPIC converter in forward direction (left to
56
right).
Figure3.10(c):
Two Quadrant SEPIC converter in Reverse direction (right
57
to left)
xiv
Figure3.10(d):
Two quadrant SEPIC converter in Reverse direction (right
57
to left) as combination of a Buck-Boost (right box part) and
lift circuit (left box part)
Figure 3.11:
Gate pulse of switches of Circuit of Figure 3.10(a)
58
Figure 3.12:
Current is Positive at B side for Positive output of circuit of
59
figure 3.10(a) for gate signal at DC level 5V(Quadrant-I)
Figure 3.13:
Current is Negative at B side for Positive Voltage of circuit
60
of figure 3.10(a) for gate signal at DC level 2V (QuadrantII)
Figure 3.14:
Characteristics Curve of Power at A side Vs Duty Cycle for
62
Two quadrant Chopper for the Data Table 3.3
Figure 3.15:
Characteristics Curve of Power at B side Vs Duty Cycle for
63
Two quadrant Chopper for the Data Table 3.3
Figure 3.16:
Characteristics Curve of Efficiency Vs Duty Cycle for Two
65
quadrant Chopper for the Data Table 3.4
Figure 3.17:
Characteristics Curve of Efficiency Vs Duty Cycle for Two
67
quadrant Chopper for the Data Table 3.5
Figure 3.18:
Four Quadrant SEPIC Chopper
68
Figure 3.19:
Typical Gate pulses of four quadrant SEPIC dc dc
69
Converter
Figure 3.20:
Four quadrant SEPIC Chopper with output positive DC
71
voltage.
Figure 3.21:
Current at B side of Four Quadrant SEPIC Chopper of
72
circuit of Figure 3.20 for pulse width .02ms
Figure 3.22:
Current at B side of Four Quadrant SEPIC Chopper of
73
circuit of Figure 3.20 for pulse width .04ms.
Figure 3.23:
Current at B side of Four Quadrant SEPIC Chopper of
74
xv
circuit of figure 3.20 for pulse width .06ms.
Figure 3.24:
Current at B side of Four Quadrant SEPIC Chopper of
75
circuit of Figure 3.20 for pulse width .08ms
Figure 3.25:
Current at B side of Four Quadrant SEPIC Chopper of
76
circuit of figure 3.20 for pulse width .10ms
Figure 3.26:
Current at B side of Four Quadrant SEPIC Chopper of
77
circuit of figure 3.20 for pulse width .12ms
Figure 3.27:
Current at B side of Four Quadrant SEPIC Chopper of
78
circuit of Figure 3.20 for pulse width .14ms.
Figure 3.28:
Current at B side of Four Quadrant SEPIC Chopper of
79
circuit of Figure 3.20 for pulse width .16ms.
Figure 3.29:
Current at B side of Four Quadrant SEPIC Chopper of
80
circuit of Figure 3.20 for pulse width .18ms
Figure 3.30:
Four Quadrant SEPIC Chopper with output negative DC
81
voltage.
Figure 3.31:
Current at B side of Four Quadrant SEPIC Chopper of
82
circuit of Figure 3.30 for pulse width .02ms
Figure 3.32:
Current at B side of Four Quadrant SEPIC Chopper of
83
circuit of Figure 3.30 for pulse width .04ms
Figure 3.33:
Current at B side of Four Quadrant SEPIC Chopper of
84
circuit of Figure 3.30 for pulse width .06ms
Figure 3.34:
Current at B side of Four Quadrant SEPIC Chopper of
85
circuit of Figure 3.30 for pulse width .08ms
Figure 3.35:
Current at B side of Four Quadrant SEPIC Chopper of
86
circuit of Figure 3.30 for pulse width .10ms
xvi
Figure 3.36:
Current at B side of Four Quadrant SEPIC Chopper of
87
circuit of Figure 3.30 for pulse width .12ms
Figure 3.37:
Current at B side of Four Quadrant SEPIC Chopper of
88
circuit of Figure 3.30 for pulse width .14ms
Figure 3.38:
Current at B side of Four Quadrant SEPIC Chopper of
89
circuit of Figure 3.30 for pulse width .16ms
Figure 3.39:
Current at B side of Four Quadrant SEPIC Chopper of
90
circuit of Figure 3.30 for pulse width .18ms
Figure 3.40:
Four Quadrant SEPIC Chopper with differentially
95
connected R-L load
Figure 3.41:
Typical PWM gate pulses of Four Quadrant SEPIC DC-DC
96
converter
Figure 3.42:
Load Current and voltage at B side in forward and reverse
97
direction operation of circuit of Figure 3.40 with
(R=50ohm,L=100mh)
Figure 3.43:
Four Quadrant SEPIC Chopper with differentially
98
connected R-L load at input side
Figure 3.44:
Load Current and voltage at B side in forward and reverse
99
direction operation of circuit of Figure 3.40 with
(R=50ohm,L=100mh)
Figure 3.45:
Characteristics Curve of Voltage Gain Vs Modulation Index
102
for Four quadrant SEPIC Chopper for the circuit Figure
3.43
Figure 3.46:
Characteristics Curve of Efficiency Vs Modulation Index
103
for Four quadrant SEPIC Chopper for the circuit Figure
3.43
xvii