King saud University
College of Engineering
Electrical Engineering Department
Implementation of Boost Converter
Applied for DC Motor Drive
By:
Ali Mohammad Al-Eshwy
Supervised By:
Dr. Ali M. Eltamaly
December٢٠٠٥
Table of Contents
Table of Contents
Abstract
i
iii
Chapter 1: Review of Power Electronics and DC-Motor
1-1 Introduction of Power Electronics
1
1-2 Introduction of DC Motor
2
1-2-1 History of DC Motor Drives
2
1-2-2 Basic DC Machine Construction
3
1-3 Project Objectives
1-4 Project Organization
5
6
Chapter 2: Analysis of DC-DC Converters
2-1 Introduction
7
2-2 Control of DC-DC Converters
7
2-3 Step Down DC-DC Converter (Buck converter)
9
2-3-1 Continuous Conduction Mode in Buck Converter
12
2-3-2 Discontinuous Conduction Mode with Constant Vd
14
2-3-3 Output Voltage Ripples
2-4 Step up DC-DC Converter (Boost converter)
2-4-1 Continuous Conduction Mode
2-4-2 Boundary between Continuous and Discontinuous Conduction
2-4-3 Discontinuous Conduction Mode
2-4-4 Output Voltage Ripple for Continuous Conduction Mode
16
2
24
23
24
26
Chapter 3: Project Specifications
3-1 Introduction
27
3-2 Control Circuit Components
3-2-1 DC Power Supply
28
28
3-2-2 Voltage Controlled Saw-tooth Oscillator and Comparator
3-2-3 Comparator.
3-3 Power Circuit.
31
33
36
Chapter 4: Conclusion
4-1 Conclusions
References
39
40
Abstract
This project discusses convert AC to DC or DC to DC by power supply unit.
A power supply unit’s main purpose is to convert or condition the power from these
two sources so that it is suitable for used on other electronic devices.
Chapter١
REVIEW OF POWER ELECTRONICS AND DC MOTORS
1-1 Introduction of SWITCHED-MODE POWER SUPPLIES:
All semiconductor electronics devices need a power supply in order to operate and not
only do they need a power supply, different devices required different supply voltages
to operate. These devices utilize DC voltage instead of AC voltages. There are only
two ways of obtaining DC power supply, the first methods is to convert AC mains
power into DC power supply via a AC to DC converter and the second method is via
stored DC power supply such as batteries and other power storage medium. However,
in most case the power obtained by the above means are not suitable for direct used
by the electronic devices and hence a power supply unit is required. A power supply
unit’s main purpose is to convert or condition the power from these two sources so
that it's suitable for used on other electronic devices. Fig.1.1 shows the power supply
unit concept in simple form.
Fig.1.1 Power supply unit.
A power supply must be able to perform several major functions:
•
Convert if necessary from AC main to DC voltage suitable for any particular
electronic devices or systems also termed as loads.
•
When the source supplies are already in DC, the power supply units are then
required to stabilize or filter the voltage to reduce any sort of noise or ripple as
within the designed specification that is termed as line regulation.
•
In some cases, the power supply unit provides electrical isolation for the input
source and the output loads.
•
The output voltage should stay constant irrespective of the input source voltage,
temperature variation and load current over a specified range.
Features listed below are desirable in a power supply unit.
•
The output should be able to vary according to needs.
•
Current protection features should be included, such as over-current protection
and short circuit protection.
•
The power supply unit should be able to operate within a wide temperature
range.
•
Thermal protection should also be included to protect the supply unit from
thermal runaway effects.
•
The power supply unit should cause little or minimal noise to equipment that
are operated near or around the supply unit.
•
Efficiency, size, weight and economical advantages should be optimized.
1-2 Introduction of DC Motor
1-2-1 History of DC Motor Drives
During the last century, industry has boomed and the DC motor has been an
integral part of the electrical industry’s history. Most power at the beginning of the
century was constant voltage direct current because of its easy of use and it only
requires two transmission buses, unlike the three-phase transmission of today.
Last century DC drives were typically constant speed, due to the limited of
knowledge of commutation. This caused problems with commutator sparking and
reduced life of brushes. The variation of speed was only possible through adjustment
in field flux of the most durable motors. However with improvements in commutation
then came improvements in speed control.
In the 1890’s a more successful method of speed control was introduced, the WardLeonard method. The system utilized a motor generator set to vary the power supplied
to the DC machine by varying the generator excitation. This consequentially varied
the voltage and then provided continuous control of the motor of a wide range. This
system was the first to provide better performance in machine speed control.
Meanwhile, the development of AC systems continued to become more attractive due
to their durability. They also exhibited no problem with commutation as current was
passed to the machine via a set of slip rings located on the rotor.
In the late 1940’s, electronic control gas filled rectifiers brought a significant
change to the speed control industry. They provided advantages of electronic control
by possessing faster response, increased accuracy and allowed the first automatic
closed loop system to operate. This began the move of electronic drives, a movement,
which is still increasing accuracy, response and controllability of motors.
As the decades rolled on the use and new innovation of solid state electronic devices
took over, with the introduction of the thyristor. The thyristor was a semi-controlled
device, which allowed greater control, rugged systems.
Today the electronic drives are increasing smaller and able to handle larger currents
and voltages. In addition, with the introduction of micro-controller drives the limits
seem endless. The direction into the new millennium is uncertain but all the same
assured for the use of electronic drives. Perhaps the next step will be into cheaper
electric cars.
1-2-2 Basic DC Machine Construction
The processes, which take place within DC motors, and generators, are the same, and
as a result, the same machine can perform both functions. To produce a rotational
torque from a motor, an arrangement of conductors is required to generate magnetic
fields that interact to cause a resultant force or torque. The DC machine consists of
three essential items: the stator, the rotor and the commutator (not shown) illustrated
in Fig.1.2.
Fig.1.2 Cross-section of a 4-pole with inter poles DC machines.
The stator, so called because it is stationary, consists of salient poles that carry the
main field coils, commonly called the field windings. These coils are connected in
series to ensure that each coil carries the same current and the same magneto-motive
force (mmf). The current through each conductor must be equal, as the magnitude is a
function of current.
ξ
=
N
∗
I
(1.1)
Where ξ = magneto-motive force (mmf),
I = the current in the coil (A),
N = the number of turns in the coil.
The main flux path is shown in the diagram above by the broken lines. The stator
yoke, pole shoes and rotor are constructed from ferromagnetic materials to enhance
the flux of the machine. The pole shoes are used to increase the output of the machine
by placing more armature windings, on the rotor, under strong influence from a
magnetic field. With the rotation of the armature, there will be eddy currents present
in the pole shoe material. Therefore, laminated steel sections are used to reduce eddy
current loss.
The armature, or rotor, named so because it rotates, caries the armature windings that
under the influence from the field windings. This interaction between the armature
windings and the field windings causes rotational torque to be produced. The rotor
should possess a uniform small air gap (typically 0.05cm to 0.25cm) between the pole
shoes and the armature to reduce losses due to the reluctance torque, TR. The
reluctance can be described simply as the unwillingness of the magnetic circuit to be
at a point other than equilibrium (un-aligned with the poles).
This reluctance torque is the force required overcoming the reluctance of the armature
when it is not aligned with the pole faces (at minimum reluctance). It reduces the
maximum possible output and efficiency of the motor.
The commutator converts the direct current of the supply voltage to an alternating
current to develop a unidirectional torque within the rotor. The commutator is a series
of small copper conducting segments around the rotor shaft, and a stationary set of
brushes. This is shown below in Fig.1.3.
Fig.1.3 4-pole commutator arrangement.
1-3 Project Objectives
The primary objective of this Project was to analyze basic DC to DC converter
circuits namely buck converter and boost converter circuits. Apply the simulation for
analysis circuit using the simulation package Psim.
Initially design specifications were defined for boost converter circuits. Then
designed by developing a detailed step-by-step design procedure. Different tests are
performed for obtaining practical values for currents, voltages as well as ripple’s
involved a digital oscilloscope is used. The practical values are then compared with
the values obtained in the simulation.
As a secondary objective a lab manual for testing of these circuits where prepared for
the use in future laboratory experiments.
1-4 Project Organization
The Project is partitioned into 4 chapters, the first of which is an introduction to the
power electronics and DC Motors.
The background is discussed in Chapter 2. It explores the various DC-DC converters
and their characteristics and operational modes. The section highlights several types
of DC-DC configurations and methods of operations.
Chapter 3 outlines a broader project specification and introduces the system as a
series of interconnected devices. It is the collective operation of these devices, which
provides the overall solution. This chapter investigates the design of the DC-DC
converter required within the project sub-systems. It is a complete overview of the
design assumptions and component manufacture.
Chapter 4 is the final and concluding section within this composition. The various
advantages and disadvantages related to this project design are profiled within this
chapter. Future refinements are also proposed, to alleviate current problems
discovered with this approach. The project achievements are highlighted and the level
of completion revealed.
Chapter 2
ANALYSIS OF DC-DC CONVERTERS
2-1 Introduction
There are literally hundreds of different circuit configurations for switch mode
converters. However, one can classify most of them into two basic categories:
. Step-down or buck converters.
. Step-up or boost converters.
Many of the other topologies that are in the literature are combinations of these two
basic topologies.
The basic layout of a SMPC system is shown in Fig.2.1 below. The input to the
converter is usually the mains. Since this is AC the first step is to convert this to DC
via a rectifier. Notice that one can also feed DC, from a battery, directly in at the
output point of the rectifier. The unregulated DC is usually filtered with a capacitor,
before feeding the DC-DC converter electronics. The output of this stage then feeds
the load.
Fig.2.1 Block diagram of structure of typical DC-DC Converter.
2-2 Control Of DC-DC converters
In DC-DC converter, the average DC output voltage must be controlled to equal level,
though the input voltage and the output load fluctuate. Switch mode
DC-DC
converters utilize one or more switches to transform DC from one level to another in a
DC-DC converter with a given input voltage, the average output voltage is controlled
by controlling the switch on and off durations ( ton and toff ). One of the methods for
controlling the output voltage employs switching at a constant frequency (hence, a
constant switching time period is shown in (2.1)
Ts
=
t on
+
t off
(2.1)
and adjusting the on duration of the switch to control the average output voltage. In
this method, called pulse-width modulation (PWM) switching the switch duty ratio D,
which is defined as the ratio of the on duration to the switching time period, is varied.
Variation in the switching frequency makes it difficult to filter the ripple Components
in the input and the output wave forms of the converter.
Fig.2.2 Wave form in saw tooth based PWM modulator.
Fig.2.3 Simple PWM generator signal.
In the PWM switching frequency, the switch control signal, which controls the state
(on or off) of the switch, is generated by comparing a signal-level control voltage
v control
with a repetitive wave form as shown in Fig.2.2 and Fig.2.3
The control voltage signal generally is obtained by amplifying the error, or the
difference between the actual output voltage and it desired value. The frequency of
the recitative waveform with a constant peak, which is shown to be a saw tooth,
establishes the switching frequency. This frequency is kept constant in a PWM
control and is chosen to be in a few kilohertz to a few hundred kilohertz range. When
the amplified error signal, which varies very slowly with time relative to the switching
frequency, is greater than the saw tooth waveform, the switch control signal becomes
high, causing the switch to turn on. Other wise, the switch is off. In terms of vcontrol
and the peak off the saw tooth waveform? In previous figure the switch duty can be
expressed as
D = t on / T s
=
v control / V st
(2.2)
The DC-DC converters can work in two modes of operation: (1) continuous current
conduction and (2) discontinuous current conduction
In practice, a converter may operate in both modes, which have significantly deferent
characteristic. Therefore, a converter and its control should be designed based on both
modes of operation.
2-3 Step Down DC-DC Converter (Buck Converter)
The step-down or buck converter is distinguished by the fact that the output voltage is
always less than the input voltage. This means, that regardless of the switching
strategy, it is impossible to get the output at a higher voltage than the input. The
distinguishing circuit feature of the buck converter is that one cannot get any current
to flow in the circuit when the power device is turned on, if the output voltage is
greater than or equal to the input voltage. Fig.2.4 shows a basic circuit for a buck
converter. Before analyzing the circuit, let us look at it heuristically to determine its
basic operation. When the switch SW closes, current will flow to the resistive load via
the inductor L. The capacitor C will charge up during this process. Note that there is a
transient involved in the inductor current building up and the voltage being
established on the capacitor. When the switch is opened the current through the
inductor cannot stop instantly (if it does then the voltage across the inductor will
become very large and the circuit will most probably be destroyed). The diode in the
circuit will become forward biased, allowing the current in the inductor to continue
flowing in the same direction (towards the load). During this phase of operation the
energy that was stored in the field of the inductor during the switch on time is being
transferred to the load. If the switch remains open for a long time the inductor current
gradually decreases to zero, and at the same time the current drawn from the capacitor
increases. If the switch is closed before the inductor current decreases to zero, then the
current begins to increase again.
Remark 2.1 Note that the maximum current that can flow through the inductor if the
switch is left closed is Vd / RL .
Remark 2.2 If the inductor current goes to zero then the converter is said to be
operating in discontinuous mode. If it does not go to zero, then the converter is
operating in continuous current mode. Generally speaking, it is desirable to operate
the converter in one mode or the other, without a change of mode. Changes in mode
can result in difficulties in controlling the output voltage of the converter. A change of
mode can occur depending on load changes.
Remark 2.3 If the filter were not present in Fig.2.4 then the output voltage would
exactly mirror the input voltage – i.e. if the switch is opened and closed then the
output would be a square wave voltage. The filter has to be designed so that the cut
frequency is significantly below the switching frequency. If this is the case then the
filter will reject most of the AC components present at the Vod, so that the output
voltage will essentially be a DC value equal to the average value of the voltage Vod.
Remark 2.4 One of the distinguishing features of this type of circuit is that when the
switch is closed the input is connected to the output, but when the switch is open the
input is disconnected from the output.
Another distinguishing feature of the buck converter is that the inductor is not placed
across the input voltage when the switch is closed. The inductor has a voltage
imposed across it that is usually somewhat lower than the input voltage.
This means that the inductor does not store all the energy being supplied by the input.
Remark 2.5 If multiple output voltages are required then the buck converter as
depicted here is not the topology to use. Other converters, such as the forward
converter, that are related to the buck converter can be used.
Remark 2.6 Since the switch is at the input to the converter, and then the input
current is discontinuous. Therefore, the input filter to this circuit is more complicated
compared to other converter types.
Practical Issue 2.1 Driving the gate of a buck converter can be a problem. If we
assume that the switching element is a n-channel MOSFET (as it would be)
Fig.2.4 A basic buck or Step down DC-DC converter.
A buck converter or step- down switch mode power supply can also called a switch
mode regulator.
Popularity of a switch mode regulator is due to its fairly high efficiency and
compact size and a switch mode regulator is used in place of a linear voltage regulator
at relatively high output, because linear voltage regulators are inefficient. Since the
power devices used in linear regulators have to dissipate a fairly large amount of
power, they have to be adequately cooled, by mounting them on heat sinks and the
heat is transferred from the heat sinks to the surrounding air either by natural
convection or by forced-air cooling. Heat sinks and provision for cooling makes the
regulator bulky and large. In applications where size and efficiency are critical, linear
voltage regulators cannot be used.
A switch mode regulator overcomes the drawbacks of linear regulators. Switched
power supplies are more efficient and they tend to have an efficiency of 80% or more.
They can be packaged in a fraction of the size of linear regulators. Unlike linear
regulators, switched power supplies can step up or step down the input voltage. A
simplified diagram of a step down DC-DC converter is shown in Fig.2.5 The output
voltage is shown in Fig.2.6 This average output voltage depends on the duty ratio, D
where D =
t on
.
TS
Fig.2.5 Simplified circuit diagram of a step down DC-DC converter.
vo
Vd
Vo
ton
toff
Ts
Fig.2.6 The output voltage of step down converter.
Fig.2.7 shows buck converter, in this circuit we assume that the switch is ideal and
the output capacitor is assumed to be very large. When the switch S is turned on at
t = 0,
the diode will be reverse biased and the supply is connected to the load,
vo = Vdc and it will supply the load and inductor with energy. When the switch S is
turned off, the diode will be forward bias and the inductor current will flow through
the diode, transferring some of its stored energy to the load. The output voltage from
buck converter is shown in Fig.2.8
Id
L
Vo
iL
Vd
R
Fig.2.7 circuit diagram of buck converter.
vL
Vd -Vo
A
-Vo
ton
B
toff
Ts
Fig.2.8 The output voltage from buck converter.
2-3-1 Continuous Conduction Mode In Buck Converter
t
For the circuit in Fig.2.7,the output voltage equals the input voltage when the switch
is “ON” and it is zero when the switch is “OFF”. By varying the duration for which
the switch is ON and OFF, it can be seen that the average output voltage can be
varied, but the output voltage is not pure DC. The output voltage contains an average
voltage with a square-voltage superimposed on it, as shown in Fig.2.8. Usually the
desired outcome is a DC voltage without any noticeable ripple content. When the
switch is on for a time duration ton, the switch conducts the inductor current and the
diode become reverse biased. This results in a positive voltage v L
= Vd − Vo across
the inductor in Fig.2.7. This voltage causes a linear increase in the inductor current
iL . When the switch is turned OFF, because of inductive energy storage, iL
continues to flow. This current now flows through the diode, and
vL = −Vo in
Fig.2.7. In steady state operation, the integral of the inductor voltage
vL over one
time period must be zero. Then,
TS
t on
TS
o
o
t on
∫ vL dt = ∫ vL dt + ∫ vL dt = 0
(2.3)
In Fig.2.7 the forgoing equation implies that the areas A and B must be equal.
Therefore;
(Vd − VO ) ton = VO (TS − ton )
(2.4)
Then,
VO ton
=
=D
Vd TS
(2.5)
Neglecting power losses associated with all the circuit elements, the input power Pd
equals the output power PO:
Pd = PO
(2.6)
Vd I d = VO I O
(2.7)
I O Vd 1
=
=
I d VO D
(2.8)
At the edge of the continuous conduction mode, Fig.2.9 shows the waveforms for
vL and iL . Being at the boundary between the continuous and discontinuous mode,
by definition, the inductor current iL goes to zero at the end of OFF period. At this
boundary, the average inductor current, where the subscript B refers to the boundary
is:
I LB =
t
DTS
1
I L, peak = on (Vd − VO ) =
(Vd − VO ) = I OB
2
2L
2L
(2.9)
iL,peak
iL
I LB = I OB
vL
Vd -Vo
-Vo
ton
toff
Ts
Fig.2.9 Inductor voltage and current at the boundary of continuous-discontinuous
conduction mode
2-3-2 Discontinuous Conduction Mode with Constant Vd
In an application such as DC motor speed control, Vdc essentially constant and VO is
controlled by adjusting the converter duty ratio D. Since VO = DVd , the average
inductor current at the edge of the continuous conduction mode from equation (2.9)
I LB =
TS Vd
D(1 − D)
2L
(2.10)
Using this equation, we find that the output current required for a continuous
conduction mode is maximum at D
I LB , max =
= 0.5 .
TS Vd
8L
(2.11)
From equation (4.10) and (4.11)
I LB = 4 I LB ,max D(1 − D)
(2.12)
Next, the voltage ratio
Vo / Vd will be calculated in the discontinuous mode. Let
us assume that initially the converter is operating at the edge of continuous
conduction mode as in Fig.2.9, for given values of T, L, Vd and D. If these parameters
are kept constant and the output load power is decreased (i.e., the load resistance goes
up), then the average inductor current will decrease. As is shown in Fig.2.10, this
dictates a higher value of VO than before and results in discontinuous inductor current.
iL,peak
iL
I L = IO
vL
Vd -Vo
-Vo
ton
∆1Ts ∆ 2Ts
Ts
Fig.2.10 Inductor voltage and current at discontinuous conduction mode.
During the interval ∆ 2Ts where the inductor current is zero, the power to the load
resistance is supplied by filter capacitor alone. The inductor voltage
vL during this
interval is zero. Again, equating the integral of the inductor voltage over one time
period to zero yields:
(Vd − VO ) D TS + (−VO ) ∆1 TS = 0
(2.13)
Then,
VO
D
=
Vd D + ∆1
(2.14)
Where
D + ∆1 < 1.0 . From Fig.2.10
I L, peak =
VO
∆1TS
L
(2.15)
Therefore, I O
= I L, peak
D + ∆1
2
(2.16)
=
VO TS
( D + ∆1 ) ∆1
2L
(2.17)
=
Vd TS
D∆1
2L
(2.18)
= 4 I LB , max D ∆1
(2.19)
Then
∆1 =
IO
4 I LB , max D
(2.20)
From equations (2.14) and (2.20)
VO
=
Vd
D2
1 I

D2 +  O
I LB , max 
4
(2.21)
2-3-3 Discontinuous Conduction Mode with Constant Output Voltage
In applications such as regulated DC power supplies,
Vd may fluctuate but Vo is
kept constant by adjusting the duty ratio D.
SinceVd
= VO / D , the average inductor current at the edge of the continuous
conduction mode from (4.46) is:
I LB =
TS VO
(1 − D)
2L
(2.22)
Equation (2.22) shows that if
occurs at
D=0
Vo is kept constant, the maximum value of I LB
I LB ,max =
TS VO
2L
(2.23)
I LB = (1 − D) I LB ,max
(2.24)
From equation (4.12),
∆1 = D
Vd
−D
VO
(2.25)
Substitute from equation (2.25) into (2.17). Then,
IO =

VO TS 2 Vd  Vd

− 1
D
2L
VO  VO

(2.26)
But from equation (2.23) substitute into (2.26)
I O = I LB , max D 2

Vd  Vd

− 1
VO  VO

(2.27)
V
Then, D = O
Vd
1/ 2

I I
*  O LB ,max 
 (1 − VO Vd ) 
(2.28)
4.5.2.4 Output Voltage Ripples
In the previous analysis, the output capacitor is assumed to be so large as to yield
vO (t ) = VO . However, the ripple in the output voltage with a practical value of
capacitor can be calculating by considering the waveform shown in Fig.2.11 in
continuous conduction mode of operation and Fig.2.12 in discontinuous conduction
mode of operation.
I LB = I OB
vL
Vd -Vo
-Vo
ton
toff
Ts
iL,peak
iL
∆Q
I LB = I OB
Ts / 2
∆VO
VO
Fig.2.11 Output waveforms of buck converter in continuous conduction mode.
In case continuous conduction mode, assume that all of the ripple component in iL
flows through the capacitor and its average component flows through the load
resistor, the shaded area in Fig.2.11 represents an additional charge to the capacitor,
the peak to peak voltage ripple ∆VO can be written as:
∆Q 1 1 ∆I L TS
=
C C2 2 2
∆VO =
(2.29)
From Fig.2.11 during tOFF
∆I L =
VO
(1 − D)TS
L
(2.30)
Therefore, substituting from equation (2.29) into the previous equation gives:
∆VO =
TS VO
(1 − D)TS
8C L
(2.31)
f 
∆VO 1 TS2 (1 − D) π 2
(1 − D) C 
=
=
VO
LC
8
2
 fS 
2
(2.32)
Where switching frequency f S = 1 TS and f C =
1
2π LC
A similar analysis can be performed for the discontinuous conduction mode as
following:Fig.2.12 shows the inductor current in discontinuous conduction mode.
iL,peak
iL
I L = IO
vL
Vd -Vo
-Vo
∆1Ts ∆ 2Ts
ton
Ts
iL,peak
iL
∆Q
I L = IO
t 2 − t1
t2
t1
∆VO
VO
Fig.2.12 Output waveforms of buck converter in discontinuous conduction mode.
di V
=
dt L
(2.33)
Then
Vd − VO
t1 = I O
L
(2.34)
Then, t1
=
L IO
Vd − VO
(2.35)
Where t1 is defined in Fig.2.12
It is clear from Fig.2.12 that:
iL , peak =
DTS
(Vd − VO )
L
(2.36)
But t 2 = DTS +
L (i L , peak − I O )
VO
(2.37)
From (4.72) and (4.74) we get:
t 2 − t1 =
L (i L, peak − I O )
− L IO
+ DTS +
Vd − VO
VO
(2.38)
Then:
 DT

DTS (Vd − VO )VO − L I OVO + L (Vd − VO ) S (Vd − VO ) − I O 
 (2.3
 L
t 2 − t1 =
VO (Vd − VO )
9)
Then;
∆Q 1 1
(iL, peak − I O )(t 2 − t1 )
=
C
C2
1  DTS

=
−
−
(
V
V
)
I
d
O
O
 (t 2 − t1 )
2 C  L

∆VO =
(2.40)
Then;
∆VO =
[DTS (Vd − VO ) − L I O ]DTS (Vd − VO )VO − L I OVO + L (Vd − VO ) DTS (Vd − VO ) − I O 
2 LC VO (Vd − VO )
 L

(2.41)
2-4 Step Up DC-DC converter (Boost converter)
As the name implies, the boost or step-up converter has an output voltage that is
always greater than the input voltage. The boost converter also has the added
advantage that the output can isolated from the input (using transformer isolation).
Fig.2.13 shows a conceptual diagram of a non-isolated boost converter. The basic
operation mechanism is that when the switch is closed the load is isolated from the
input by the diode, and current builds up in the inductor. This current build is
effectively storing energy in the field of the inductor. When the switch is opened, the
current in the inductor wishes to continue to flow in the same direction and with the
same magnitude. Therefore the diode will turn on and the current will immediately
flow into the filter capacitor and any connected load.
Remark 2.7 If the voltage on the capacitor is larger than the supply voltage, the
inductor will produce whatever voltage is required so that Vd + VL = Vo. This is
required in order for the current to continue to low in the inductor. One can see that
because the polarity of VL shown in Fig.2.13 always has to reverse for this situation,
then the output voltage must always be greater than the input voltage (except under
initial start-up conditions).
Remark 2.8 The main feature of the boost converter is that current can flow through
the switch regardless of the relationship between the input and output voltages. This
usually occurs because the input to the circuit is disconnected from the output when
the switch is closed. It is this feature that one must look boost distinguishing for when
one is trying to ascertain what category a particular topology falls into. When the
switch is opened, the input is connected to the output because the diode switches on.
Another distinguishing feature is that when the switch is closed the input voltage is
placed across the inductor (so that it stores all the energy being supplied by the input),
and when the switch is opened the inductor is placed in series with the load. and this
stored energy is transferred to the load.
Remark 2.9 In a boost converter the inductor fulfills an energy storage function,
whereas in the buck converter the inductor forms a filtering function. Therefore, one
can view the boost converter as not having a filter capacitor. This distinction is not
very clear for the non-isolated converter, but when we look at isolated converters in
the next chapter, we shall see that there is a clear distinction.
Remark 2.10 There is a maximum power that is practical to build for converters that
rely on the energy storage principle. This is especially true for low input voltages. As
we shall see in the next chapter, a related converter is the fly back converter, which
operates using the same principle, and hence suffers from the same power limitations.
In order to cater for high power output with an energy storage converter, one needs to
have a very small energy storage inductor (since E =
1 2
Li , and therefore the current
2
contributes most significantly to the stored energy). It turns out that for powers much
above 50W when the input voltage is low, the inductance becomes very small and is
comparable with the parasitic of the circuit. Therefore, the circuit becomes very
difficult to manufacture.
Fig.2.13 shows a step up converter. Its main application is in regulated DC power
supplies and the regenerative braking of DC motors. As the name implies, the output
voltage is always greater than the input voltage. When the switch is ON, the diode is
reverse biased, thus isolating the output stage. The input supplies energy to the
inductor. When the switch is OFF, the output stage receives energy from the inductor
as well as from the input. In steady state analysis presented here, the output filter
capacitor is assumed to be very large to ensure a constant output voltage vo (t ) = VO .
IT + VL -
Io
Vo
Vd
RL
Fig.2.13 Step up DC-DC converter.
2-4-1 Continuous Conduction Mode
Fig.2.14 shows the steady state waveform for this mode of condition where the
inductor current flows continuously [ iL (t ) > 0 ].
vL
Vd
ton
Ts
toff
Vd -Vo
iL
IL
ton
Ts
toff
Fig.2.14 The steady state waveform for this mode of condition.
Since in steady state the time integral of the inductor voltage over one time period
must be zero,
Vd t on + (Vd − VO ) t off = 0
(2.42)
Dividing both sides by TS and rearranging terms yield;
VO TS
1
=
=
Vd Toff 1 − D
(2.43)
Assuming a lossless circuit,
Pd = PO ,
∴ Vd I d = VO I O
(2.44)
And
IO
= (1 − D)
Id
(2.43)
2-4-2 Boundary between Continuous and Discontinuous Conduction
Fig.2.15 shows the waveforms at the edge of continuous conduction. By definition,
in the mode iL goes to zero at the end of the OFF interval. The average value of the
inductor current at the boundary is:
I LB =
T V
1
1 Vd
I L, peal =
t on = S O D(1 − D)
2
2 L
2L
(2.44)
Fig.2.15 The waveforms of step-up DC-DC converter at the edge of continuous
conduction.
Recognizing that in a step up converter the inductor current and the input current
are the same ( id
= iL ) and using equation (2.45) and (2.46), we find that the average
output current at the edge of continuous conduction is:
I OB =
TS VO
D(1 − D) 2
2L
(2.45)
From equation (2.46) I LB reaches a maximum value at D
I LB ,max =
= 0.5 :
TS VO
8L
(2.46)
Also, I OB has its maximum at D=1/3=0.3333.
I OB ,max =
T V
2 TS VO
= 0.074 S O
27 L
L
(2.47)
In terms of their maximum values, I LB and I OB can be expressed as:
I LB = 4 D(1 − D) I LB ,max
(2.48)
I OB =
27
D(1 − D) 2 I OB ,max
4
(2.49)
2-4-3 Discontinuous Conduction Mode
Fig.2.16 show the inductor current in discontinuous conduction mode. The
inductor voltage over one time period is zero,
Vd DTS + (Vd − VO ) ∆1TS = 0
(2.50)
VO
∆ +D
= 1
Vd
∆1
(2.51)
And
IO
∆1
=
Id
∆1 + D
(2.52)
Fig.2.16 Step up converter waveforms at discontinuous conduction mode.
From Fig.2.16, the average input current, which is also equal to the inductor
current, is
Id =
Vd
DTS ( D + ∆1 )
2L
(2.53)
From equation (2.54) yields;
T V 
I O =  S d  D∆1
 2L 
(2.54)
In practice, since
VO is held constant and D varies in response to the variation
inVd , it is more useful to obtain the required duty ratio D as a function of load
current for various values of
VO / Vd . By using (4.90), (4.93) and (4.86), we
determine that:
 4 VO  VO  I O 

− 1
D=

I
 27 Vd  Vd
 OB, max 
1/ 2
(2.55)
2-4-4 Output Voltage Ripple for Continuous Conduction Mode
The peak-to-peak ripple in the output voltage can be calculated by considering the
waveform shown in Fig.4.17 for a continuous mode of operation. Assuming that all
the ripple current component of the diode current iD flows through the capacitor and
its average value flows through the load resistor, the shaded area in Fig.2.17
represents charge ∆Q. Therefore, the peak-to-peak voltage ripple is given by:
∆VO =
∆Q I O DTS VO DTS
=
=
C
C
RC
(2.56)
∆VO DTS
T
=
= D S (Where τ =RC time constant)
τ
VO
RC
(2.57)
Fig.2.17 Step-up converter output voltage ripple in continuous conduction mode of
boost converter.
Chapter3
Project Specifications
3-1 Introduction
With a full working background of DC motor characteristic operation achieved in
Chapter 1, the project specification can then be developed. The aim of this chapter is
to express the system as a series of interconnected systems that interact to provide a
collective response.
The expression of the project as sub-system blocks constitutes a significant portion of
this text where each subsequent block is examined in proceeding chapters. By
dividing the project into these sub system blocks the design can become a simpler
project with each block relying on set assumptions and design goals. The goal of this
approach is to design a system that can be altered with ease and can more importantly
be tested on a per entity basis. This testing concept allows each system to have a
greater reliability due to the high reliability of surrounding components. Thus
prerequisite for each sub system module is justified. The system can be simplified for
design purposes by breaking down the system into a series of sub-systems connected
together in a network configuration. Consider the block representation of the system
below.
Fig.3.1 Block diagram of the structure of a typical DC-DC converter.
The system of a DC speed controller was separated into several components, which
rely on each component around them for operation. This may be related to an object
oriented design approach taken in software design.
The project was divided into sub-sequent parts, control circuit components and
power circuit components.
Each of these component parts is related together to represent the entire system.
This approach was also useful in regards to testing the various features of the system
where the functionality of each block could be completed separately.
These sub-systems are the subject of analysis, design and implementation throughout
the remainder of the chapters comprising this project composition.
3-2 Control Circuit Components
The control circuit components consist of the following parts:
3-2-1 DC Power Supply
The most critical system with regard to the entire system is the power supply. If the
power supply is not operational then the entire circuit is not operational. It could be
said that the power supply is the stomach of the system and without energy the system
would not operate. It is used to supply power to the integrated circuits (ICs) and for
the analog circuits.
This division of the system supplies +15 V, -15 V, and 0 V to the entire system to
operate all the integrated circuitry of the micro-controller unit. The following are
some details of the power supply components:
Transformer Connection
To convert the AC mains voltage to a useable voltage to then be filtered a
transformer is required to step down the voltage rectifier bridge. for input to a The
transformer connections to supply the regulators are as shown in Fig.3.2.
Fig.3.2 Transformer which we use it .
The transformer selected for this section was 240 V 30 VA tapped secondary
transformer. The secondary taps selected to be used from the transformers were 0 V,
15 V, and 30 V, which were arranged to provide +15 V, 0 V and –15 V to the system.
A 500 mA fuse was used with this transformer to provide a protection and safety
device.
Rectifier Circuit
The voltage output from the transformer is given as shown in Fig.3.3 But when the
transformation through the rectifier bridge occurs, the output DC voltage is obtained
from the following equation:
Vdc1 =
2 Vm
π
=
2 * 24 * 2
π
= 15.2V
(3.1)
Fig.3.3 Transformer and rectifier connection.
Fig.3.4 The output voltage for the previous connection.
The initial stage of this project was to prototype a Power Supply Module. LM7815
and LM7915 are used to supply +15 Volts and –15 Volts respectively. The expected
total power consumption required by the circuits is approximately 10 Watts. All
capacitors should be the highest quality, especially the output capacitor. The input
capacitor is an easier-to-get size capacitor of 100 microfarads; I included the output
capacitor of 10 microfarads to help eliminate any distortion when it is supplying the
analog circuits.
The component required:
1- 10 W transformer 220/ 12-0-12.
2- LM7812.
3-LM7912.
4-Two units of 100uF capacitors.
5- Two units of 10uF capacitors.
6- 10W bridge diode or four separate diodes.
In
0.1A Fuse
24
+
10uF
0
+
+15
+
100uF
220V
out
7815
100uF
10uF
0
+
24
In
7915
out
Fig.3.5 Schematic diagram of the Power Supply Module.
Physical Construction of Power Supply
As explained previously the boards were first tested on prototype breadboard
before implementation was carried out in the form of printed circuit boards. The entire
circuit is illustrated in. The fully constructed power supply is shown below.
3-2-2 Voltage Controlled Saw-tooth Oscillator and Comparator
The voltage controlled oscillator (VCO) is an oscillator whose frequency can be
changed by a variable DC control voltage. One way to build a voltage controlled sawtooth oscillator is with an op-amp integrator that uses a switching device (PUT) in
parallel with the feedback capacitor to terminate each ramp at a prescribed level and
effectively "rest" the circuit. Fig.3.6 shows the implementation of this circuit.
The PUT is a programmable unijunction transistor with an anode, a cathode and a
gate terminal. The gate is always biased positively with respect to the cathode. When
the anode voltage exceeds the gate voltage by approximately 0.7 V, the PUT turns on
and acts as forward biased diode, when the anode voltage falls below this level, the
PUT turns off. Also, the current must be above the holding value to maintain
conduction. The frequency of the saw-tooth oscillator can be obtained from the
following equation:
fs =
(R2 )Vcc
R1 + R2
(3.2)
*
1  1 


Ri C  VP − 1 
-15
Where VP =
R4
(Vcc ) + 0.7
R3 + R4
(3.3)
Then, V P =
10
(15) + 0.7 = 10.075 V
6 + 10
(3.4)
Then the minimum switching frequency can be obtained when the input resistance is
at its maximum value as following:
f s _ min =
(6)*15 *
6+6
1
100 * 10 * 10 * 10 −9
3
 1 

 = 1042 Hz
 8 .2 − 1 
(3.5)
The maximum value can be obtained from the performance of the circuit. The
sawtooth signal has to be compared using voltage comparator (see Fig.3.6) with
variable control signal by us 100 k potentiometer. The output from comparator
depends on the following logic.
If Vcontrol > Vsawtooth the output voltage will be +15V and
If Vcontrol < Vsawtooth the output voltage will be -15V
So, if we need the output voltage to be zero when Vcontrol < Vsawtooth we can use
diode at the output signal as shown in Fig.3.6 . Therefore, with the diode connected at
the output, The output from comparator depends on the following logic.
If Vcontrol > Vsawtooth the output voltage will be +15V and,
If Vcontrol < Vsawtooth the output voltage will be 0V.
+15V
2n6027
10k
R3
6k
R4
2
3
-15V
6k
R1
1
10nF
+15V
100k
2
6k
R2
Ri
741
3
+15V
7
2
6
4
+15V
-15V
‫ﻟﻠﺘﺤﻜﻢ ﰱ ﺍﻟﺘﺮﺩﺩ‬
0.5kHz to 10kHz
3
Pot., 100k
1 kΩ
7
741
100 Ω
6
4
-15V
‫ﻟﻠﺘﺤﻜﻢ ﰱ‬
Duty
Fig.3.6 Voltage controlled Saw-tooth Oscillator and comparator circuit
Fig.3.7 Sawtooth wave.
3-2-3 Comparator
Comparator is the second op-amp in control circuit, it compare between the
sawtooth wave and a DC voltage at specified level we make control on the DC
voltage by an potentiometer 100 kilo ohms it can make the output DC voltage from
10V to 15V the applied DC voltage at the 3rd terminal of the 741 IC (positive input).
The negative input is the sawtooth wave it is applied at the 2nd terminal of the 741
IC as we see in the Fig.3.6.
The output of the comparator is +15 voltage when the control voltage (DC voltage)
is greater than the sawtooth wave it be -15 when the control voltage is less than the
sawtooth wave as we see in the middle waveform of Fig.3.9.
At the output of the comparator we connect a suitable diode to remove –Ve
component at the output of the comparator to make it +Ve only.
Resistance connected between the output and the MOSFET gate to protect the gate
of the MOSFET and make it surly open or closed.
+15V
‫ﺧﺮج ﺳﻦ اﻟﻤﻨﺸﺎر‬
2
+12V
Pot., 100k
7
324N
4
3
10 kΩ
6
-15V
1 kΩ
‫ﻟﻠﺘﺤﻜﻢ ﻓﻰ‬
Duty
Fig.3.8 The comparator circuit.
Fig.3.9 The output of voltage of the comparator circuit.
Table 3-1 Voltage controlled Saw-tooth circuit components.
Components
Item number
Quantity
PUT
2n6027
1
OP-amp
741
2
diode
Any
1
Ceramic Capacitor
10nF
1
Potentiometer
100 k
2
Resistors
6k
3
Resistors
10k
2
Resistor
1k
1
Table 3-2 power supply for the controlling circuit.
Components
Item number
Quantity
10 W transformer
220/ 12-0-12
2
regulator
LM7812
1
regulator
LM7912
1
Ceramic Capacitor
10uF
4
bridge diode
10 w
1
3-3 Power Circuit
Power circuits feed the DC motor with a voltage between 10V and 80V as a variable
DC voltage. The DC Motor speed is proportional with the applied voltage on it. So we
design our power supply to vary the input voltage of the DC motor to change its
speed. Power Circuit (see Fug.3.10) is consisting of the following components:
Power Transformer
We choose a suitable step down transformer with the following specification:
Primary voltage is 220V sinusoidal AC
Secondary voltage is 12V sinusoidal AC
It has VA equal 25 VA
Fig 3.10 The power circuit of boost converter.
Bridge or 4 suitable diodes
The bridge has the following specification:
It can operate with the full load current(10A) without over heated. The output of the
bridge can be obtained by the following equation:
Vdc =
1
π
V
π∫
m
sin ωt dωt =
0
2 Vm
π
==
2 *12 * 2
π
= 10.8V
(3-7)
Inductance
The main question is how we can get a coil which inductance of it is 12mh?
As we know inductance is depends on the:
Number of turns in the coil, the radius of the coil and on the type of material around
which the coil is wound (core).
So there are important electrical specifications to consider when searching for
inductors, chokes, and coils include inductance range, inductance tolerance,
maximum DC resistance, and operating current range
For that we make our inductance with the following specifications.
Ferromagnetic core, Diameter of the wire is suitable for the full load current and
then varied the number of turn to make the inductance equal 12mH.
Switch(MOSFET or IGBT)
MOSFET plays a significant role in controlling the applied voltage on the DC
Motor. Its Gate triggered by the out put of the controlling circuit. We can recognize
that the MOSFET is used on these design in place of IGBT switch.
Smoothing capacitor
We use this capacitance to make the output nearing the pure DC voltage. We
choose this capacitance suitable and can be withstand with the applied voltage (80 V).
Table 3-3 power circuit component
Components
Item number
Quantity
10 W transformer
220/ 12-0-12
1
Inductance
12mh
1
MOSFET
Irpfpc50
1
Ceramic Capacitor
330uF(100V)
1
Chapter 4
Conclusion
4-1 Conclusions
There are several advantages to this specific approach of speed control of DC
motors incorporating the use of input DC voltage control. However, there are also
some limitations within the design. These factors are discussed in the following items:
•
The flexibility of the system where the whole construct can be changed or
added-on so as to improve the future design.
•
The structure can be seen to be simply plug and play as the whole project
requires only a main supply and connection to the DC motor. This represents a
much improved and user friendly structure.
•
There also exists flexibility within the magnetic design where the inductance
may be changed or the power handling can be increased if necessary.
•
The design also offers lowered ratings of components required for the power
circuit as the field winding is considered an individual output. Therefore, it
also involves a very essential cost savings.
Experimental results