7-1 Power Electronics Chapter 7 Introduction to DC/DC Converters 7. Introduction to DC/DC Converters Marc T. Thompson, Ph.D. Adjunct Associate Professor

Power Electronics Chapter 7 Introduction to DC/DC Converters 7-1

7. Introduction to DC/DC Converters

Marc T. Thompson, Ph.D.Adjunct Associate Professor of Electrical Engineering

Worcester Polytechnic Institute

Thompson Consulting, Inc.9 Jacob Gates Road Harvard, MA 01451

Phone: (978) 456-7722 Email: [email protected]

Website: http://members.aol.com/marctt/index.htm

Portions of these notes excerpted from the CD ROM accompanying Mohan, Undeland and Robbins, Power Electronics Converters, Applications and Design, 3d edition, John Wiley 2003


Summary• Non-isolated (i.e. no transformer) DC/DC converters


Block Diagram of Typical AC Input, Regulated DC Output System


Stepping Down a DC Voltage

• In this example, the average value of the output voltage = DVin where D is the DUTY CYCLE in PWM (pulse-width modulation) control• D = ton/Ts


Step-Down (Buck) DC-DC Converter

• Add LC filter to reduce switching ripple• Flyback diode also needed


Buck Converter: Waveforms• Steady state; inductor current flows continuously• Waveform below for buck in continuous conduction mode


Buck Converter: SPICE Circuit• Circuit shown: fsw = 200 kHz, D = 0.5


Buck Converter: Startup Waveforms


Analysis for DC/DC Converter in Continuous Conduction and Steady State• In steady state, the inductor current returns to the same value every switching cycle, or every T seconds• Therefore, the inductor ripple current UP equals ripple DOWN• Several assumptions to simplify analysis:

• Periodic steady state --- all startup transients have died out• Small ripple --- ripple is small compared to average values


Buck Converter in Continuous Conduction

V o

D

iL

LV cc

v c

+

-

C R

V o

iL

LV cc

v c

+

-

C R

V o

iL

L

v c

+

-

Switch closed (for time DT) Switch open (for time (1-D)T)

di

dt

V v

LL CC o

di

dt

v

LL o

• In continuous conduction, buck converter has 2 states --- switch OPEN and switch CLOSED


Buck Converter in Continuous Conduction• The inductor ripple current UP equals ripple DOWN

• We already knew this result from first principles, but this methodology of inductor Volt-second balance can be used to evaluate other more complicated DC/DC converters

( ) ( )V V DT

L

V D T

LV DV

CC o o

o CC

10


Buck Converter: Waveforms at the Boundary of Cont./Discont. Conduction

• ILB = critical current below which inductor current becomes discontinuous


Buck Converter: Discontinuous Conduction Mode• Steady state; inductor current discontinuous (i.e. it goes zero for a time)• Note that output voltage depends on load current

max,

2

2

25.0

LB

od

o

I

ID

D

V

V


Buck: Limits of Discontinuous Conduction

• The duty-ratio of 0.5 has the highest value of the critical current• For low output current, buck goes discontinuous


Buck: Limits of Cont./Discont. Conduction

• In regulated power supply, Vd may fluctuate but Vo is kept constant by control of D


Buck Conv.: Output Voltage Ripple• ESR is assumed to be zero; continuous conduction mode


Buck Conv.: Output Voltage Ripple

• ESR is assumed to be zero

Lf

DV

L

TDVi

sw

ooppL

)1()1(,

Lf

DViTQ

sw

oppL

2

,

8

)1(

222

1

LCf

DV

C

Qv

sw

oppo 2, 8

)1(


Buck Conv.: Calculations

• Shown for SPICE example with fsw = 200 kHz, D = 0.5, L = 33 µH, C = 10 µF, Io = 1A

ALf

DVi

sw

oppL 38.0

)1033)(102(

)5.01)(5()1(65,

mVLCf

DV

C

Qv

sw

oppo 24

)1010)(1033()102(8

)5.01)(5(

8

)1(66252,


Buck: SPICE Result in Periodic Steady State• Analysis shows inductor ripple = 0.38 A-pp, output voltage ripple = 24 mV-pp, confirmed by SPICE


Pulse-Width Modulation (PWM) in DC-DC Converters

st

control

V

vD

ˆ


Step-Up (Boost) DC-DC Converter

• Output voltage must be greater than the input


Boost Converter Waveforms• Continuous current conduction mode

Switch closed:

di

dt

V

LL CC

Switch open:

di

dt

V v

LL CC o

Inductor Volt-second balance:V DT

L

V V D T

L

VV

D

CC CC o

oCC

( )( )10

1


Boost: Limits of Cont./Discont. Conduction• The output voltage is held constant• For low load current, current conduction becomes discontinuous


Boost Converter: Discont. Conduction• Occurs at light loads


Boost: Limits of Cont./Discont. Conduction

• The output voltage is held constant


Boost Converter: Effect of Parasitics• The duty-ratio D is generally limited before the parasitic effects become significant


Boost Converter Output Ripple• ESR is assumed to be zero• Assume that all the ripple component of diode current flows through capacitor; DC component flows through resistor


Step-Down/Up (Buck-Boost) Converter

• The output voltage can be higher or lower than the input voltage• Note output phase inversion


Buck-Boost Converter: Waveforms• Continuation conduction mode

Switch closed:

di

dt

V

LL CC

Switch open:

di

dt

v

LL o

Inductor Volt-second balance:

V DT

L

V D T

L

VDV

D

CC o

oCC

( )10

1


Buck-Boost: Limits of Cont./Discont. Conduction• The output voltage is held constant


Buck-Boost: Discontinuous Conduction• This occurs at light loads


Buck-Boost Converter: Limits of Cont./Discont. Conduction

• The output voltage is held constant


Buck-Boost Converter: Effect of Parasitics

• The duty-ratio is limited to avoid these parasitic effects from becoming significant


Buck-boost Converter: Output Voltage Ripple• ESR is assumed to be zero


Cuk DC-DC Converter• The output voltage can be higher or lower than the input voltage• Capacitor C1 is primary means of storing and transferring energy from input to output• When switch is ON, C1 discharges through the switch and transfers energy to the output• When switch is OFF, capacitor C1 is charged through the diode by energy from the input and L1


Cuk DC-DC Converter: Waveforms

• The capacitor voltage is assumed constant (very large)• Note phase inversion at the output

D

D

V

V

d

o

1


SEPIC Converter• Single-ended primary inductance converter (SEPIC)• Can buck or boost the voltage• Note that output is similar to buck-boost, but without a phase inversion

D

D

V

V

d

o

1


Converter for DC-Motor Drives• Four quadrant operation is possible• For:

• DC motor drives• DC to AC inverters for UPS


Converter Waveforms• Bi-polar voltage switching


Converter Waveforms• Uni-polar voltage switching


Output Ripple in Converters for DC-Motor Drives

• Bi-polar and uni-polar voltage switching


Switch Utilization in DC-DC Converters

• It varies significantly in various converters• PT = VTIT where VT and IT are peak switch voltage and current• In direct converters (buck and boost) switch utilization is good; in indirect converter (buck-boost and Cuk) switch utilization is poor


Equivalent Circuits in DC-DC Converters• Replacing inductors and capacitors by current and voltage sources, respectively


Reversing the Power Flow in DC-DC Conv.

• For power flow from right to left, the input current direction should also reverse


Real-World Issue: Capacitor ESR• Real-world capacitors have equivalent series resistance (ESR)• This ESR may have dominant effect on output ripple


Effects of Capacitor ESR• Without ESR, output ripple is 24 mV-pp• ESR has increased ripple to approximately 30 mV-pp

Documents

7-1 Power Electronics Chapter 7 Introduction to DC/DC Converters 7. Introduction to DC/DC Converters Marc T. Thompson, Ph.D. Adjunct Associate Professor