PE_ENEL37_3

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1

ENEL371S2

Power Electronics 1Lecture 3 Buck Converter

Continuous Conduction

Department of ECE

University of Canterbury2012

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Single-Switch

Switching Cell

Read Chapter 7, Mohan etc.

CONCEPT

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Single Switch ConversionAny semiconductor p - n junction powerswitch device (e.g. Diode, Thyristor, MOSFET,

IGBT etc.) is one way switch , i.e. current canflow in one direction. It cant feed energy backto power supply (as shown in Energy Recovery ).

Diode IGBT

To charge and discharge theenergy storage devices(inductor, capacitor) byswitching, a controllable powerswitch needs a diode toprovide freewheeling path

GeneralControllable

Switch

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Single Switch Configuration

BOOST

Diode One-way Freewheeling channelfor current

Inductor Energy Storage or Filtering

Switch Power Switching RegulationSwitch+Diode = 1 Pole 2 Throw Switch

The Same 3 Components but Different Combinations

BUCK

Conversion Conversion

BUCK-BOOST

Conversion

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One-Pole-Two-Throw Switch1P2D Switch

Buck Converter

Buck-Boost Converter

Discontinuous Input Source Current

Boost Converter

Continuous Input Source Current

iLInputChargingCurrent

OutputDischarging

Current

Source

Output

12

InputChargingCurrent

OutputDischarging

Current

iL

Source

Output

1P2D Switch

1 2

+

+

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Basic Switching Cells

P-cell N-cell

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Steady State


CONCEPT

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Power Processing - Revisit

Power electronic conversion actually is to manipulate theenergy in energy storage devices by switching the powerswitches to control the power flow.

A power converters is mainly constituted by PowerSwitches and Energy Storage Devices (inductors,capacitors, transformers).

Switching strategy PWM constant switching frequencyvariable duty ratio switching method

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Steady-State InductorFor an energy storage inductor in DC-DCconverters, steady state means that energy rise

is equal to energy fall in the inductor over oneswitching period.

0

2

0

0

( 0

12

1( ) 0 )

L L

T L L

L L

L

L

L L

L

T

i t T i t E

v t dt

i t

E Li

di L v

v t d

i

t

T

t

t

d L

RULES

Average voltage per

switching period = 0

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Steady-State CapacitorFor an energy storage capacitor in DC-DCconverters, steady state means that energy rise

is equal to energy fall in the capacitor over oneswitching period.

0

2

0

0

( 0

12

1( ) 0 )

C C

C T C

C C

C

C

C C

C

T

v t T v t E

i t dt

v t

E Cv

dvC i

i t d

v

t

T

t

t

d C

RULESAverage current perswitching period = 0

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Steady-State Conversion

Control input to the switch (i.e. duty ratio)keeps constant

Input voltage constant

Voltage increase and voltage decrease inoutput voltage over one switching periodare equal

For a steady-state PWM DC-DCconverter, steady state switchingmeans that

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Continuous and DiscontinuousConduction


CONCEPT

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Continuous and Discontinuous

i L

t

i L(min)

i L(max)

i L(min)

Continuous Conduction

i L

t

AverageValue

i L(min)

i L(max)

i L(min)

Current Conduction State

of Inductor ( EnergyStorage Device ) inswitching cell play an

important role in DC-DC

converter circuit analysis

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DC-DC ConvertersPWM Conversion

Voltage Regulator


CONCEPT

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PWM Conversion for DC Motor

With addition low pass filter, PWM voltage vo can be usedto drive DC motor directly ( if coil inductance is largeenough ), DC motor coils act as low pass filter to get low-ripple (constant) dc current in coils. Here DC-DCconverters is not voltage regulator.

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DC-DC Voltage Regulator

A DC-DC voltage regulator is designed toautomatically maintain a constant DC voltage level:output a low-ripple (constant) DC voltage to load

s o

Constant DCVoltage2nd Order LC filter

PWMVoltage

DC-DC Buck Converter (Voltage Regulator)

DC-DC voltageregulators willinvestigated inthis course.

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Buck Converters(Voltage Regulator)

Continuous Conduction Mode (CCM)


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Basic Requirements

Three things we need to calculate1. Output/Input voltage ratio2. Inductor current ripple3. Load (Capacitor) voltage ripple

Things we need to know

1. Draw the inductor current waveform2. Draw the inductor voltage waveform3. Draw three circuit states (ON/OFF/IDLE)

For the steady-state analysis of all single-switch DC-DC voltage regulators

TechniqueSpecifications forVoltage Regulators

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Assumptions

To simplify the analysis, for steady-state buckvoltage regulator, it is reasonable to assume1. vC is reasonably ripple free (~1% ripple) and i R is

ripple-free too

2. Since average capacitor current ic is zero, averagevalues of inductor current i L and resistor current i Rare equal

C o Rv v i R

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Buck Converter (Regulators)

1. Step-down Ratio

Output voltage is lessthan the input voltage

2. Inductor Current Ripple

3. Capacitor (Output) Voltage Ripple

:

on on

s on off

duty ratio

t t k

T t t

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Circuit States in CCM

vd

-

+

voR C

L

vC

i L

v L

i L

Switch OFF, Diode ON

charging

discharging

Inductor voltage

Inductor current

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Step-Down Voltage Ratio

0

0

( ) 0

) 0

1

(

0

s s

s

kT T

d o okT

d

T

o s o

L

oo d

d

s

v v dt v t dt

v v kT v k T

o

v t

vv kv k

vr

dt

0

( ) 0sT

Lv t dt

In Steady State, for the inductor L

RULES Inductor voltage

L L

div L

dt

Switch

ON

SwitchOFF

SwitchON

SwitchOFF

Inductor current

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Inductor Current Ripple

1Charge :

1Discharg : 1

s

s

s

L L L L

kT d o

L d o so

T o

L o sk

s

T

L I i i

v vi v v dt kT

L L

vi v dt k T

L

i t T i t

L

L s Li t T i t In Steady State, for the inductor L

RULES Inductor voltage

SwitchON

SwitchOFF

charging discharging

L L

div L

dt

L I

1 1

1 1

d d L s

s

o os

s

o d

v v I k k T k k

L f L

v vk T k L

v k

L

v

f

Inductor current

1s

s f T

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Inductor Current Ripple

1 1

1 1

d d

L ss

o os

s

v v I k k T k k L f L

v vk T k

L f L

1

1 1

1L

o R R L

o R L

s

L s

s

L

s

v i R and i I

v i R I k k f L f

R k I

I f

L

R

f L L

I

k

Absolute value Relative value

Obviously, to increase switching frequency andinductor value, the inductor current ripple can bereduced; low duty ratio and light load will increaseinductor current ripple.

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Class Quiz

25

L

L

L

L

IL

max min 2? L L L

I I I I I

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Capacitor Voltage Ripple

1 1

2

1

2 2

1

8

C C C C

S C

L

L

S

Q

T I

dvi C v

QvC C

i dt C

f

t C

I

C

d

2

2 2

18

1 18

1

8

d C

s

o C

s

d L o

s

s

d

vv k k

v I k k and v k

f LC

v vk k

f LC

v

f LC

f L

: 1 / s sswitching frequency f T

Inductor voltage

Inductor current

capacitor voltageC ov v

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Capacitor Voltage Ripple

2

2

2

21

2

1 18 8

C c

C s

d C C

s s

v vv k k k

f LC f

v f v f

LC

k

1LC filter cutoff frequency :

2c f

LC

2

22

2

18

1 128

d C

s

C cC

ss

vv k k

f LC

v f k k v f f LC

Absolute value Relative value

Obviously, to increase switching frequency cansignificantly reduce the capacitor voltage ripple;high duty ratio and narrow LC bandwidth will

reduce capacitor voltage ripple too.

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Lecture 3 - Summary

Concepts single-switch switchingcells, steady-state, continuous anddiscontinuous conduction, voltage

regulatorBuck Voltage Regulator step-

down ratio; inductor current ripple,capacitor/output voltage ripple

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Homework #3

Download homework #3 questions forLecture 3 fromLearn/ENEL371/Term3/Lecture3

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Contact Information :

Dr. Keliang Zhou

Office: Electrical A512

Email: [email protected]

Phone: 3642240 Ext.6240

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PE_ENEL37_3