Power Elec Notes 07a Intro to Dc-dc Converters

1Introduction to DC/DC Converters© M. T. Thompson, 2008

Power Electronics Notes 07AIntroduction to DC/DC Converters

Portions of these notes excerpted from the CD ROM accompanying Mohan, Undeland and Robbins, Power Electronics Converters, Applications and Design, 3d edition, John Wiley 2003Other notes © Marc Thompson, 2008

Marc T. Thompson, Ph.D.Thompson Consulting, Inc.

9 Jacob Gates RoadHarvard, MA 01451

Phone: (978) 456-7722 Fax: (888) 538-3824

Email: [email protected]: http://www.thompsonrd.com


Summary

• Non-isolated (i.e. no transformer) DC/DC converters• Step down (buck)• Step up (boost)• Buck-boost• Cuk converter• SEPIC

• Full-bridge• Comparison of DC/DC converters


Block Diagram of Typical AC Input, Regulated DC Output System

• Typically, a power supply front end has uncontrolled full-wave diode rectifier, followed by a bus (“hold-up”) capacitor, followed by a DC/DC converter with active feedback control


Offline Flyback Converter

Reference: http://www.st.com/stonline/products/literature/an/7310.pdf


Some Real-World Design Issues that We’ll Get to Later On in the Term


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, the fraction of the total switching cycle that the switch is ON


Frequency Spectrum of Vo

fs= 1/TsVo = Vd D

• The output voltage contains switching harmonics


Adding a Lowpass Filter to the Buck Converter

• The goal of the lowpass filter LC is to pass the DC component, while attenuating the switching components• As frequency increases, XL increases and XC decreases


Adding a Lowpass Filter to the Buck Converter

• The corner frequency must be lower than the switching frequency to attenuate the switching harmonics.

• Corner frequency:

-40 dB/decade


Step-Down (Buck) Converter

• Diode needed to provide current path for output current when switch is OFF


Buck Converter in Continuous Conduction• In periodic steady state, inductor current flows continuously• Waveform here are for buck in continuous conduction mode; note that inductor current never decays to zero• In discontinuous conduction mode, there are 3 states


Buck Converter: PSPICE Circuit

• Circuit shown: fsw = 200 kHz, D = 0.5


Buck Converter: Startup Waveforms• These waveforms are shown for a constant duty cycle of D = 0.5 during startup • Note large overshoot on output voltage and inductor current


Same Circuit --- PSIM Simulation


Same Circuit --- PSIM Simulation


Analysis for DC/DC Converters 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. For instance, output voltage ripple is small compared to the DC value


Inductor Voltage and Current• Remember that in an inductor:

dt

diLv L

L


Buck Converter in Continuous Conduction

V o

DiL

LV cc

v c

+

-

C R

• In continuous conduction, buck converter has 2 states --- switch OPEN and switch CLOSED.• We can solve for output voltage by focusing on inductor Volt-second balance



V o

DiL

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



• The inductor ripple current UP equals ripple DOWN

• We already knew this result by inspection, but this methodology of inductor Volt-second balance can be used to evaluate other more complicated DC/DC converters, such as the boost, buck-boost, etc.

( ) ( )V V DT

L

V D T

LV DV

CC o o

o CC

10


Buck Converter in Continuous Conduction --- Idealized Switching Waveforms

• Idealized because we assume that switches and diodes turn on and off with zero risetime


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 Converter: Capacitor Current Ripple

• Continuous conduction mode


Buck Converter: Output Voltage Ripple

• ESR is assumed to be zero; continuous conduction mode


Buck Converter: 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(


Example 1: Buck Converter 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,


Example 1: Buck in Periodic Steady State

• Analysis shows inductor ripple = 0.38 A-pp, output voltage ripple = 24 mV-pp, confirmed by SPICE


Step-Up (Boost) DC-DC Converter

• Output voltage is greater than the input, with the same polarity


Boost Converter Waveforms in CCM• Continuous conduction mode (CCM)

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 Converter: Discontinuous Conduction

• Occurs at light loads


Boost Converter: Effect of Parasitics• The duty-ratio D is generally limited before the parasitic effects become significant• As D gets big, input current gets very large (think about power balance….); the voltage drop in inductor and switch cause efficiency to suffer


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


Boost Converter --- PSIM Simulation• What is the output voltage?


Boost Converter --- PSIM Simulation• Vo = Vi/(1-D) in continuous conduction

Output voltage during startup


Boost Converter --- PSIM Simulation• Note that inductor current I(RL1) never decays to zero, so we’re in continuous conduction


Example 2: Boost Converter Example• Mohan, Example 7-1• Boost converter on the edge of discontinuous conduction• Vi = 12V, D = 0.75, Vo = 48V, Po = 120W


Example 2: Boost Converter Example

Output voltage ripple

Inductor ripple current


Step-Down/Up (Buck-Boost) Converter

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


Buck-Boost Converter: Waveforms• Continuous conduction mode

Switch closed:

di

dt

V

LL CC

Switch open:

di

dt

v

LL o

Inductor Volt-second balance:

D

DVV

L

TDV

L

DTV

CCo

oCC

1

0)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: 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


Example 3: Buck-Boost Converter: Simulation

• Vo should be -10V after startup transient dies out


Example 3: Buck-Boost Converter: Simulation

• Vo should be -10V in steady-state after startup transients die out



Buck-Boost Converter: Simulation

• The ripple is pretty big (0.5 V pp)• Let’s increase the size of the filter capacitor by 10 --- what will happen?



• With larger C• What has happened?




• Note that ripple is smaller, but startup transient is slower (makes sense); LC is larger



Cuk DC-DC Converter• The output voltage can be higher or lower than the input voltage• Capacitor C1 stores and transfers 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• This circuit is useful for lithium battery powered equipment

D

D

V

V

d

o

1


SEPIC Converter

• Circuits for 2 different switching states

Reference: National Semiconductor, Application Note AN-1484, “Designing a SEPIC Converter”


SEPIC Converter --- Example

• Example from application note

Reference: National Semiconductor, Application Note AN-1484, “Designing a SEPIC Converter”


SEPIC Converter


SEPIC Converter

Output voltage ripple


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

• DC motor drives• DC to AC inverters for UPS


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

Power Elec Notes 07a Intro to Dc-dc Converters

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