Chapter3 DC-DC Converters 2016

EE2025: Pow er Ele ctronics Chapter 3: DC-DC Converters

MCH5001: Power Electroni cs – Jan. 2013 – SK Panda

Learn in g Obj ect ives and Out co mes •

Learning Obje ctive s: 

Understand about basic principles of operation of linear and switched-mode DC-DC Converters.



Understand the classifications of DC-DC Converters.  Understand the principles of operation of non-isolated DC-DC converters such as buck, boost and buck-boost types.  Understand the basic principles of operation of isolated DC-DC converter such as forward converter.  Applications of DC-DC Converters.

•

Learni ng out com e 

You should be able to design a suitable DC-DC convert for any given application.

EE2025: Power Electronics –

August. 201 6 – SK Panda

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Introduction • DC-DC converters are widely used in applications such as regulated dc power supplies and dc motor drives. • Input to these converters is unregulated dc voltag mainly obtained by rectification of single or three phase AC supply voltages at line (supply) frequency. Alternatively, it could be from a DC source such as battery or PV panel. • DC-DC converters can be considered as an equivalent of transformer in DC circuits either to step-up or step-down DC voltage levels. EE2025: Power Electronics –


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Battery

Diode bridge 1AC I/P

rectifier

Unregulated dc Filter

Unregulated dc

Regul ated & variable dc

DC-DC Converter

Load

control voltage

Figure 3.1 A DC-DC converter system

• The main function of the dc-dc converter is to: convert unregulated dc voltage into a regulated (controlled) dc output voltage which can be maintained constant at the desired value irrespective of the supply voltage or load variation. EE2025: Power Electronics –


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Figure 3.2 An AC-DC converter system



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Figure 3.3 A DC-DC converter system EE2025: Power Electronics –


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• The dc-dc converter can be either a linear regulator type or of switching converter type.

+

v CE

-

RL

Vs

ic + Vo -

Vs

RL

ic + V -

Figure 3.4 A basic linear DC-DC converter system

• The main drawback of linear regulator is inefficiency – an alternative is to use switching converter that is highly efficient. EE2025: Power Electronics –


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Figure 3.5 A bas DC-DC switchin converter system



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Linear Power Supplies

Figure 3.6

• Very poor efficiency and large weight and size. EE2025: Power Electronics –


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Swi tc hi ng DC Pow er Sup pl y

Figure 3.7

• High efficiency and small weight and size EE2025: Power Electronics –


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Swi tc hi ng DC Pow er Sup pl y: Mul ti pl e Out pu ts

Figure 3.8

• In most applications, several dc voltages are required, possibly electrically isolated from each other. EE2025: Power Electronics –


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Classi fication of DC-DC Conv erters • Non -is ol ated dc -dc co nv ert ers  

Buck (Step-down) Boost (step-up)



Buck-Boost (Step-down/up)

• Iso lated dc -dc co nv erters 

Flyback



Forward



Half- and Full-Bridge



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•

Alternatively, depending on the direction of the output current and polarity of the output voltage the DC/DC converter (choppers) can also be classified as:  

Class- A (single -qua dra nt, Q-I) Class- B (single -qua dra nt, Q-II)



Class- C (two- qua dra nts, Q-I & Q-II)



Class- D (two- qua dra nts, Q-I & Q-IV)



Class- E (four -qua dra nts )

in the current-voltage two dimensional plane.



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o

o

o

o

o

o

o

o

o

o

Figure 3.9 Classification of choppers by quadrants of operation EE2025: Power Electronics –


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• Class A: Both vO and iO are positive, giving rise to single- quadrant operation in quadrant-1. Also called as step-down chopper as the output voltage is always less than the input voltage. • Class B: vO > 0 and iO < 0 . This is also a single quadrant chopper but operates in the secondquadrant. Since pO = vO  iO  0 power flow is always from the load to the source. As the power flow is from the lower load voltage vO to a higher voltage Vs, this chopper is also referred to as stepup chopper.



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• Class C: vO > 0 and the load current iO can either be positive or negative. This is known as a twoquadrant chopper and operates in quadrants I and II. • Class D: This iO > 0also anda vOtwo-quadrant can either bechopper positive bu or negative. operates in quadrants I and IV. • Class E: This is a four-quadrant chopper and both vO and iO can have either polarities. Such chopper finds application in DC motor drive.



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• We will mainly focus our attention on step-down, step-up, and two-quadrant converters in this course. Moreover, we will analyze the converters for steadystate operation. • The switches are treated as ideal and inductors and capacitors as loss-less elements. • Input to the converter is a diode bridge rectified AC line voltage with a filter capacitor to provide low ripple dc voltage. • Output stage consists of a small filter and supplie to a resistor in case of switched-mode-power-supply (SMPS) or a voltage source in series with a motor winding (E-R-L) in case of dc motor drive (DC Drive). EE2025: Power Electronics –


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• A dc-dc converter can be considered as dc equivalent to an AC transformer with a continuously variable turns ratio. Just like a transformer it can be used either to step-down or step-up a dc voltage level.



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Control of DC-DC Converters

Figure 3.10 Switch-mode dc-dc conversion



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• For a fixed input voltage, Vd the output voltage, V0 can be controlled either by controlling the on period, ton or the off period, toff .

 ton  Vo   Vd  D  Vd (3.1)  Ts  • The output voltage, V0 is controlled by

pulse-

width modulation (PWM) switching at a constant frequency , fs and varying the on duration, ton of the switch i.e. the duty cycle, D. EE2025: Power Electronics –


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D

ton Ts



vcontrol 

(3.2)

V st

Fig. 3.11 Pulse-width modulator: (a) block diagram and (b) comparator signal EE2025: Power Electronics –


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Figure 3.12 Pulse-Width Modulation with constant switching frequency EE2025: Power Electronics –


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• VO can also be controlled by pulse-frequency modulation (PFM) in which the ton period is kept constant and the switching frequency fs is varied. • The disadvantage of the PFM method is that a low output voltage, the switching frequency is low and results in discontinuous (DCM) operation as well as increases the ripples in output current Alternatively, at higher frequencies the switching losses become significant.



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vo

t on1 t off1

t on1

Ts1

t off2

time

time

Ts2

t on1

t off3 Ts3



Figure 3.13 Pulse-Frequency time Modulation: with variable switching frequency C hap. 3

• The

PWM

method

with

constant

switching

frequency has the advantage of low ripple current and hence require smaller filter components. This method is widely used. • DC-DC converters can have two different modes of operations: continuous conduction mode (CCM and discontinuous conduction mode (DCM) operation. However, in this course we will discuss mainly CCM of operation.



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Swit chi ng p owe r-pol e as t he bui ldi ng b loc k of dc- dc con verte rs A

vL iL

Vin

t

0 DTs

vL

B

Ts

iL t

0 q

(a )

(b )

Figure Switching power-pole as the building block of dc-dc converters.

In DC Steady State: A

vL iL Vin

t

0 DTs

vL

B

Ts

iL t

0 q

(a )

(b )

Waveform repeats with the Time-Period Ts:

iL(t )  i tL(T s ) MCH5001: Power Electroni cs – Jan. 2013 – SK Panda

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In Steady State:

v0 (t )



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In Steady State, the average voltage across an inductor over a cycle is zero:

vL  L iL ( Ts )



diL

dt diL i T i  L (0)  0 L( s)

iL (0)

1

Ts

v  L

L

 dt  0

0

VL 

1 Ts

Ts



v dt L  0

0

A

vL iL

Vin

t

0 DTs

vL

B

Ts

iL t

0 q

(a)

(b)

 T  DT 1 VL   vd L vd  s

0  Ts   area A





s

L

DTs

   

area B

   0  

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Concept Quiz-1 A switching power-pole is operating in dc steady st ate at a dut y-rati o of 0.5. The average vo lt age at t he cu rr ent -po rt is 12 V. What i s t he average vol tage acros s t he outp ut l oad resistor ? A. 6 V B. 0 V C. 12 V



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In Steady State, the average current through a capacitor is zero:

dvC

iC  C

dt

vC ( Ts )



) dvC vC T s ( Cv

(0)  0

vC (0)

1

Ts

i  C

C

 dt  0

0

IC  MCH5001: Power Electroni cs – Jan. 2013 – SK Panda

1 Ts

Ts

i

C

 dt  0

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Out pu t Vol tage Ripp les L

L

L L

s

o off

on s

o

o o

Figure 3.19 Output voltage ripple in a step-down converter EE2025: Power Electronics –


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Clicker Quiz#2 In a st ep-dow n (Buc k) conv erter, the out put vo lt age is 12 V (dc ) th e ou tp ut po wer is 60 W. Calc ul ate the a vera ge va lu e of th e in du ct or current. A. 12 A B. 5A C. 60 A EE2025: Power Electronics –


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Con tr ol of dc -dc Con vert ers

Figure 3.14 Switch-mode dc-dc conversion EE2025: Power Electronics –


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Step-do wn (Buc k) Con verter •

Referring to Fig.3.14 the average output voltage, V0 is: Ts 1 ton  1 V0  v0 (t ) dt   Vd dt  0 dt   [Vd ton ]  DVd (3.3 Ts 0 Ts  o  Ts t on

1

•

Ts











Now substituting eqn.3.1 in eqn.3.2 we have    v  V  control  VO    Vd   d vcontrol  kvcontrol  Vst   Vst    V  where k   d   constant . V   st 



(3.4)

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• By varying the duty cycle D of the switch th average output voltage, V0 can be controlled. • V0 varies linearly with the control voltage vcontrol as in the case of linear amplifier. • Two main drawbacks of this simple circuit Fig. 3.14: 

in practice loads are inductive in nature rather than resistive – stored inductive energy will destroy the switch  output voltage v0(t) fluctuates between 0 and Vd - might not be acceptable in many applications.

• The problem of stored inductive energy is overcome by using a freewheeling diode as shown in Fig. 3.15. • The output voltage fluctuations are reduced b using a low pass filter consisting of an inductor and a capacitor C as shown in Fig. 3.15. EE2025: Power Electronics –


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Figure 3.15 Step down dc-dc converter



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•

When the switch is on the diode is reverse biased and the source provides energy not only to the load but also to the inductor. • During the interval when the switch is off the inductor current continues to flow through the freewheeli diode and in the process transfers some of its energy to the load. • For steady-state analysis it can be assumed that th capacitor is large enough to make v0(t) = V0. • Average inductor current, IL is equal to the average 0 because the average capacit output Ic over a Icycle current, current, is zero (Why?).



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Con ti nu ou s Con du ct io n Mod e (CCM

Figure 3.16: Step down dc-dc converter circuit states: (a) switch on and (b) switch off EE2025: Power Electronics –


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• During the interval when the switch is on the voltage across the inductor vL = Vd  V0 refer Fig.3.16. • This causes the inductor current to rise linearly with time, (why?) vL  L

•

v v   iL (t )    L  dt  L t (3.5) dt L L

diL

When the switch is off the stored energy in the inductor causes the inductor current to continue to flow but now through the freewheeling diode and hence vL = V0.



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•

In steady-state the average voltage across an inductor over a cycle is zero.



Ts

0

vL dt 



t on

0

(Vd  V0 )dt 



Ts

t on

 V0 dt  0

0  (Vd  V0 )ton  V0 (Ts  ton )

V0 (Ts  ton )  (Vd  V0 )ton V0Ts  Vd ton 

• •

V0 Vd



ton Ts

 D  V0  DVd

(3.6)

Thus, the average output voltage V0 varies linearly with duty cycle D for a given input voltage Vd. V0 does not depend on any circuit parameters.



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• Neglecting power losses in the circuit elements we have Pin  Pout  Vd  I d  V0  I 0 

I0 I d

•



Vd V



1

D

(3.7)

0

Under continuous conduction mode (CCM) operation, the step-down converter is equivalent to a dc transformer where the turns ratio of the equivalent transformer can be continuously controlled in the ra nge of 0 to 1 electronically by controlling the duty cycle D of the switch.



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Boundary between CCM and DCM

Figure 3.17 Current at the boundary of continuous-discontinuous mode of conduction

• Boundary between CCM and DCM of operation that when the inductor current, iL goes to zero at the end of the off period as shown above. EE2025: Power Electronics –


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vL  L

diL dt

 Vd  V0  L

I L t on

 I L 

Vd  V0 L

t on

(3.8

• Average of the inductor current iLB, at the boundary

is: t 1 1 I LB  12 I L   (Vd  V0 ) on   (Vd  V0 ) DTs  I OB (3.9) L  2L 2

• •

During the converter operation if I0 < ILB then iL becomes discontinuous. It is possible to derive the expression for Imax and Imin by using eqn.3.8, we have V  V0 V  DVd V (1  D ) iL  pk  iL  d t on  d t on  d t on (3.10..) L



L

L

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

VO (1  D ) D

L

ton 

VO

(1  D )

 ton     Ts 

L

ton 

VO (1  D ) fs L

(3.10)



I L (max)  I O  I  V  V (1 D ) 2 R 2 fs L I L (min)  I O 

• For

L

O

I L

VO

2



R

O



VO (1  D )

(3.11)

2 fs L

the load current to be discontinuous

the

necessary condition is that V V (1  D ) (1  D ) R I L (min)  0  O  O (3.12)  Lmin  R



2 fs L

2 fs

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•

For a given switching frequency, fs, eqn.3.12 gives the minimum inductance, Lmin required for maintaining the continuous current mode (CCM) of operation in the converter.



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Dis co nt in uo us Con du ct io n Mod e(DCM) •

During operation if IL drops below ILB (eqn.3.9) due to decrease in load power then iL goes into DCM.

Figure 3.18 (a) Discontinuous mode of conduction of step-down converter EE2025: Power Electronics –


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Figure 3.18(b) Step-down converter characteristics keeping Vd constant.


Chap3 -

Out pu t Vol tage Ripp les iC

IL /2

0 iL 0

IL

Ts /2

IL = Io t off

t

t on Ts vo

Vo Vo t

Figure 3.19 Output voltage ripple in a step-down converter EE2025: Power Electronics –


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•

Earlier in our analysis, we had assumed that v0( = V0 . However, in practical cases this cannot be achieved as C   .

•

From Fig.3.19 when iL > I0 the capacitor is getting charged and when discharged.

V  0



Q C



iL < I0 the capacitor is getting

1  1 Ts I L 

(3.13)

C  2 2 2 

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• Substituting the value of IL from eqn.3.8 in eqn.3.13 we have,

V0 

Ts V0 8C L

(1  D )Ts 

V0



V

1 Ts

2

8 LC

0

V0 V0



1 Ts

2

8 LC

where f s 

(1  D ) 

1

Ts



2

1

1

2 4 2 LC f s2

and f c 

(1  D )

(1  D ) 

(1  D ) 

2

8 LCf s 

2

2

(3.13a

 fc    fs 

(1  D )

1 2 LC



•

0 and Given a certain V0 , the value of C can be determined using V eqn. (3.13a). • Also the ripples can be minimized by making fc << fs



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Examp le 1 A chopper as shown below is switching at a frequency of fs = 1 kHz with a duty cycle of 50 %.

Figure.3.20



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a) Determine the average load current. b) Determine the peak-to-peak ripple current as an absolute value as well as a percentage of the average value. c) If the chopping frequency is increased by 4 times i.e. fs = 4 kHz, determine how the ripple current is affected. d) Instead of increasing the frequency by four times if the inductance is increased by 4 times i.e. L 40 mH, what will be the percentage ripple current.



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SOLUTION

The parameters of the step-down regulator are: Vd  100 V f, skHz 1 D ,



 50% , L  mH 10, R

5



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(c) For fs = 4 kHz we have

Thus, by increasing the frequency by four times the ripple in load current is reduced by a factor of 4. (d) For L = 40 mH and fs = 1 kHz, we have

Thus, by increasing the inductance by four times, the ripple in load current can also be reduced by a factor of 4. EE2025: Power Electronics –


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•

From the above calculations it can be seen tha the ripple current in the load can be reduced by two different means: (a) by increasing the switching frequency and (b) by increasing the

inductance. • Out of the two different schemes, the first scheme is preferred because it is much easier to increase the switching frequency with advanced powe semiconductor devices rather than using a bulky inductor.



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Applications: Step-down Chopper Feeding a DC Motor Load

Figure 3.21 Class-A chopper feeding DC Motor load EE2025: Power Electronics –


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VS va

t on

t off

Ea

ig ia

is iD T

T

Figure 3.22 Class-A chopper feeding DC Motor load (c) discontinuousmode of conduction and (b) continuous mode of conduction. EE2025: Power Electronics –


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Va  Vs  Ea  I a Ra  Ia 

Vs  Ea

m 

Ra Vs k e



 Tem  keI a  Ra 2

ke 

Tem

Figure 3.23 (a): Torque-speed characteristics of dc motor by armature voltage control



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Step-up (Boost) Converter L

o L

d

o

Figure 3.23 Step-up dc-dc converter

• Its main application is in regulated dc power supplies and regenerative braking of dc motor drive. • In this converter the output voltage is higher than the input voltage. EE2025: Power Electronics –


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Cont inu ous C ond uct io n Mode

Figure 3.24 Continuous conduction mode: (a) switch-on and (b) switch-off EE2025: Power Electronics –


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• For steady-state analysis it is assumed that the capacitor C to be large enough to make v0(t)  V0. • The average voltage across the inductor over a cycle is zero. Vd ton  (Vd  V0 )toff  0  Vd (ton  toff )  V0toff Vd Ts  V0toff  V0 (Ts  DTs ) VO Vd

•



Ts toff



1 1 D

 VO  Vd (3.14) 1 D From eqn.3.14 it can seen that for 0 < D < 1 , Vd < V 0 < .



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•

Assuming a lossless circuit we have: Pin  Pout  Vd  I d  V0  I 0 

•

I0 Id



Vd V0

 (1  D ) (3.15)

From the outputwe power and assuming the converter to be loss-less, have, 2

 Vd    2 2 VO V 1 D  d PO     Vd  ( I d  I L ) 2 (1  D ) R R R IL 



Vd (1  D ) R 2

(3.16)

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• During the period when the switch is closed we have

vL  Vd  L

diL



Vd

dt L V V DT iL  d DTs  d s (3.17) L L

•

dt

or

diL

The maximum and minimum inductor currents are given by I Vd V DT I  L   d s I L (max) L 2 (1  D ) 2 R 2L I Vd Vd DTs  I L (min)  I L  L  (3.18) 2 2 (1  D ) R 2L



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Boundary between CCM and DCM

Figure 3.25 Step-up dc-dc converter at the boundary of continuous conduction



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• The boundary between the continuous discontinuous current is determined by

I L (min)  0 



•

Vd (1  D ) R 2

Vd (1  D ) 2 R



Vd DTs 2L



Vd DTs



Vd D

and

2L 2 Lf s

(3.19)

Therefore, the minimum combination of inductan and switching frequency for continuous current in the boost converter is D (1  D ) 2 R 2 1  D (1  D ) 2 R 2 fs

( Lf s ) min 

 Lmin EE2025: Power Electronics –


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Effect s o f Parasi tic Element s ideal case

Vo / Vd

. pra cti cal case Figure 3.26 Effect o parasitic element on voltage conversion ratio

0

1

D

 In our analysis we had assumed that the circuit is lossless. In practical circuits inductor and capacitor are not lossless.

 The ratio VO/Vd drops as shown above rather than approaching  as D  1. EE2025: Power Electronics –


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Out pu t Volt age Rip pl es .

iD iD Q

• average iD flows through load • ripple of iD flows through C

Q vo

ID = Io

ton

Figure 3.27 Stepup converter output voltage ripple

toff

vo Vo

ripple voltage VO is given by  The output Q 1 V DT T V DT  V0 

C



C

I 0 DTs 

0

R C

s



0

V0



s

RC

D

s

(3.21)



where  = RC is the time constant of the circuit. EE2025: Power Electronics –


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Boost converter: voltage transfer ratio

Vo Vin

1 1 D 1

IL

0

DCM


I L , crit

CCM

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Con cept Qui z • In a Boost conv erte r op erating in a cont inuo uscond ucti on mode, inc reasin g the duty-ra tio decr eases the ou tpu t vo lt age to t he inp ut vol tage ra tio . A. False B. True



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Class-B C ho pper f eeding a DC Motor Load D

A

s

A

F

A sw

S

g

A A

Figure 3.28 Class-B chopper feeding DC Motor load



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ig 0 t on

0

t

ia iD

i sw

Vs va 0

t

Figure 3.29 (a) Class-B chopper feeding DC Motor load (b) waveforms

0 is



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m 

 'V s

k e



Ra

ke 

2

Tem (3.24)

Figure 3.29(b) : Torque-speed characteristics of dc motor by armature voltage control EE2025: Power Electronics –


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Clic ker Qui z A Boost dc-dc converter is operating in dc steady state under the following conditions:

Vin  5V ,

V  12 V , P  30W , and f  200 kHz . The value of the inductor is selected such as that under o

o

s

these operating conditions, the peak-to-peak ripple What is the value of the inductance L in A. 3.65

H

B. 7.29

H

C. 14.58

H

iL  2 A .

?

H



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Bu ck -Bo os t Con vert er id + sw Vd + vL -

iL

C

-

R io

Vo +

Figure 3.30 Buck-Boost Converter EE2025: Power Electronics –


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• The main application of the Buck-Boost converter is in regulated DC power supplies. The output voltage would have a negative polarity and also the magnitude can be made higher or lower than the input voltage. • Such a converter can be made by cascade connection of a step-down and a step-up converter as shown in Fig.3.30.



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• In steady-state the output to input voltage conversion ratio can be obtained by the product of the conversion ratios of the two individua converters (assuming the duty cycle of the switches in both the converters remain the same)

VO Vd

 D

1

1 D

(3.22)

• When the switch is closed the input source provides energy to the inductor and the diode is reversed biased as shown in the equivalent circuit Fig.3.31(a). • When the switch is opened energy stored in the inductor is transferred to the load. During this period no energy is provided by the input source. EE2025: Power Electronics –


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Vd

+

vL

Vd

0

+ vL

iL

t

RL

-

-

- Vo

-

C +

Vo +

+

iL IL = Id + Io 0

t t

Vd

= DT on

s

t off

=

(1-D)Ts

-

iL

vL +

C

RL

Vo +

Ts Figure 3.31 Buck-Boost Converter iL > 0, (a) switch-on and (b) switch-off



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•

For steady-state analysis assumptions have been made:

the

following

1. The inductor current is continuous. 2. The capacitor is large enough to assume vO(t) = VO. 3. The switch is closed for time DTs and open for time (1  D)Ts. 4. The components are ideal.

•

When the switch is closed we have vL  Vd  L diL or diL  Vd  iL  Vd DTs dt dt L L



(3.23

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•

When the switch is opened, current through the inductor cannot change instantaneously and therefore would cause the diode to be forward biased and current flows through the load resistor

and capacitor. • Average inductor voltage over a cycle is zero resulting Ts

V

L

dt  Vd DTs  (VO )(1  D )Ts  0 

0

IO Id




1 D

D

assuming PO  Pd


VO Vd



D 1 D (3.24)

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•

Note that the output voltage has than that of the source.

•

The output voltage of the buck-boost converter can be more than or less than the supply voltage depending on the duty ratio of the switch.

•

The source is never connected directly to the load. Energy is stored in the inductor when the switch is closed and transferred to the load when the switch is open. Therefore, the buck-boost converter is also referred to as the indirect converter.



opposite polarity

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• Average source current Id is related to the average inductor current IL by

I d  DI L

•

(3.25)

Assuming lossless converter, power supplied by the source is equal to the power absorbed by the load i.e.

PO  IL  EE2025: Power Electronics –

VO

2

 Vd  I d  Vd  DI L

R VO

2

Vd DR

2



Vd D 2 Vd DR (1  D )


2



Vd D R (1  D )

2

(3.26) C hap. 3

•

The maximum and minimum inductor currents are given by

I L (max)  I L 

I L



Vd D



R (1 D ) Vd D

2

I L (min)  I L 



I L 2

 R (1  D )

2

2



Vd DTs



2L Vd DTs 2L

(3.27)

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Boundary between CCM & DCM L

d

L on

s

s

off

LB

s o

Figure 3.32 Buck-Boost Converter: boundary between CCM and DCM

 For continuous conduction the inductor current must remain positive. The boundary between continuous and discontinuous mode of conduction can b determined by making IL(min) = 0. EE2025: Power Electronics –


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I L (min)  0 

Vd D R (1  D ) 2



Vd DTs 2L



Vd D R (1  D ) 2



Vd DTs 2L

(3.28

• Therefore, the minimum combination o inductance and switching frequency for continuous current in the buck-boost converter is ( Lf s ) min 

(1  D ) 2 R 2 2

Lmin  (1  D ) R (3.29) 2 fs EE2025: Power Electronics –


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Out pu t Vol tage Rippl es D

D

o

on

o

Figure 3.33 Outpu voltage ripples in a buckboost Converter

off o o

 V0 

Q


C



1 V DTs V DT T I 0 DTs  0  0  s  D s (3.30 ) C R C V0 RC 


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Concept Quiz In a Buck-Boost converter operating in a continuousconduction mode, increasing the duty-ratio beyond a value of 0.5 increases the output voltage to the input voltage ratio. A.False B.True


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Class-C, Two-quadrant Chopper feeding a DC Motor Load s

A g1

1

2

A A

A S

A 2

A

g2 A 1

Figure 3.34 Class-C, two-quadrant chopper feeding a DC Motor load. EE2025: Power Electronics –


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• Va = DV, where D is the duty cycle of switch S1. • Ia = ( Va – Ea)/Ra, if Va > Ea then Ia > 0 and converter operates in buck mode. • Ia = ( Va – Ea)/Ra, if Va < Ea then Ia < 0 and converter operates in boost mode. •Note that output current ia is always continuous , unlike the single-quadrant choppers.



C hap. 3

i g1 2T

t

i g2

va Ia

ia

is

D2

S1 D1 S2 D2

S1 D1 S2D2

S1 D1 S2

Figure 3.35 Class-C, two-quadrant chopper feeding a DC Motor load: (b) waveforms under motoring mode of operation. EE2025: Power Electronics –


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i g1 2T

t

i g2

va

Ia

ia

is

D2

S1D 1 S2

D2 S1 D1

S2 D2

S1D1

S2

Figure 3.35 Class-C, two-quadrant chopper feeding a DC Motor load: (c) waveforms under braking mode of operation. EE2025: Power Electronics –


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Clic ker Qui z In a buck‐boost converter, Vin

 5V , V0  12V , f s  200Hz and the peak‐peak ripple in the inductor

current is 3A. It is operating at the border of CCM and DCM. Calculate the value L of the inductor. A. 2.94 B. 11.76 C. 5.88

H H H



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Isolated Converter • The basic disadvantage of conventional DC-DC converter is the lack of isolation between the input and output. • One way provide isolation is to use transformer on the ac to side. • Transformer operating at line-frequency (50/60 Hz) requires large space and is expensive. • An efficient way to provide isolation is to provide a transformer on the dc-side where the switching frequency is much higher enabling the transformer to be small. • Moreover, the transformer turns-ratio provides an added extra flexibility in input-output voltage relationship. EE2025: Power Electronics –


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C hap . 3, Sl

Why Iso lati on is Requ ir ed • Safety : It is necessary for the low-voltage DC output to be isolated from the utility supply to avoid shock hazard. • Different Reference igh-side power semiconductor devicesPotential: gate driveHsignal needs to be referenced to the “source” terminal of the IGBT. • Voltage matching: Multiple outputs can be generated with additional winding on the transformer.



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Class-C, Two-quadrant Chopper feeding a DC Motor Load s

A g1

1

2

A A

A S

A 2

A

g2 A 1

Figure 3.34 Class-C, two-quadrant chopper feeding a DC Motor load. EE2025: Power Electronics –


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Swi tc hi ng DC Pow er Sup pl y: Mul ti pl e Out pu ts

Figure 3.8

• In most applications, several dc voltages are required, possibly electrically isolated from each other. EE2025: Power Electronics –


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Flyba ck Conve rte r s

1

D

D m 1

Lm

s

c

R

2

2 sw

Fig. 3.39: Flyback converter EE2025: Power Electronics –


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Fig. 3.39 (b) circuit for switch on and (c) circuit for switch off. EE2025: Power Electronics –


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•

Assumptions: 

Transformer is considered lossless and has negligible leakage.



Output capacitor is large making Vo constant.



Circuit is operating under steady-state condition.



The switch is closed for a period of DTs and open for a period of (1-D)Ts.



The switch and diode are ideal.

•

Circuit operation is similar to buck-boost converter: 

Energy is stored in Lm when switch is closed an transferred to the load when switch is opened.



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Analysis for the switch in closed position •

On the source side of the transformer:

 v

1

diLm

 V

s

iLm 

L

closed





dt

m

Vs DTs Lm

diLm dt



iLm t



iLm DTs



Vs Lm

(3.31)

• On the load-side of the transformer:

v2   N 2 v1   N 2 Vs (3.32) vD  Vo   N 2 Vs  0 (3.33  N1   N1   N1  i2  0  i1  0 EE2025: Power Electronics –


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Analysis for the switch in open position •

On the source side of the transformer:

 N1   N1  v    V  (3.34) v  o 1 2  N 2   N 2   N1  di Lm Lm  v1  Vo   dt  N2  di Lm i Lm i Lm  Vo N 1    dt t (1  D )Ts Lm N 2  Vo (1  D)Ts N 1 i Lm open  (3.35) Lm



N2

C hap. 3

•

Since the net change of current in the inductor over one cycle must be zero, we have

i Lmclosed  i Lmopen  0 Vs DTs Lm



Vo (1  D )Ts N 1 Lm

N2

0

 D  N 2  Vo  V s    (3.36)  1  D  N 1  • Output to input voltage relationship is similar to that of buck-boost converter but with additional term of the transformer turns-ratio (N2/N1). EE2025: Power Electronics –


C hap. 3

•

During the switch open position:

N1

N1

iD  i2  i1 N  iLm N 2 2

 N1   vsw  Vs  v1  Vs  Vo   N2  iO 

Vo

,

R



ic  iD  iO  iLm

    (3.37)  N1 Vo    N2

R 

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i Lm 0

i s DTs

0

(1-D)Ts

t

t

iD

Fig. 3.40 Flyback converter voltage and current waveforms

0

t

ic 0

t

Vo

 R

v1 N   Vo  1   N2  EE2025: Power Electronics –


0

VS t

C hap. 3

• Assuming ideal converter operation: Ps  Po  Vs  I s  Is 

I Lm DTs

Vo2

(3.38)

R

 I Lm D

(3.39)

Ts Vs I Lm D  

Vo2 R

 I Lm 

Vo2 Vs DR

(3.40) 2

I Lm 

 EE2025: Power Electronics –

Vo2 Vs DR Vo

  D  N 2    Vs   1  D  N 1     Vs DR

N    2  (1  D ) R  N 1 


 N2     2 (1  D) R  N 1  Vs D

2

(3.41) C hap. 3

iLm ,max  I Lm 

iLm ,min

iLm 2



2

 N 2  Vs DTs     (3.42) 2 (1  D ) R  N1  2 Lm Vs D

2

 N 2  Vs DTs  I Lm      (3.43) 2 (1  D ) 2 R  N1  2 Lm iLm

Vs D

• At the boundary between CCM and DCM

iLm ,min  0  ( Lm ,min ) 


 N 2  Vs DTs     2 (1  D ) R  N1  2 Lm Vs D

(1  D ) 2 R  N 2  2


2

2f

   N1 

(3.44)

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• The output stage of the flyback converter is the same as the buck-boost converter and therefore the output ripple voltage:

Vo Vo





D RCf

(3.45)

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Summary • DC-DC converters can be considered as dc equivalent to an AC transformer with a continuously variable turns ratio by electronic means and are widely used in switching power supplies, battery-based systems and DC motor drives. • A switched mode dc-dc converter is much more efficient than a linear regulator because of the reduced losses across the semiconductor switch. • The buck, boost and buck-boost converters are single-quadrant converters i.e. power flow takes place only from the source to the load. EE2025: Power Electronics –


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• Buck converter allows output voltage to be varied and can be made either less than or equal to the input voltage. • Boost converter allows output voltage to be varied and be made either greater than or equal to the inputcan voltage. • The Class-C chopper is a two-quadrant converter and allows power flow in both directions and is typically used for DC motor drive application.



C hap. 3

References 1. Ned

Mohan,

Course" , John Chapte r 3.

" Power Wiley

Electronics &

Sons.

A

Firs

Inc., 201

2. D. W. Hart, “ Introduction to power electronics Prenti ce Hall , 1997, Chapt ers 6 and 7.



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Chapter3 DC-DC Converters 2016

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