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.

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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

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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



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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 

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(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

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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

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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.

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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

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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