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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
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-1
Summary
• Non-isolated (i.e. no transformer) DC/DC converters
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-2
Block Diagram of Typical AC Input,
Regulated DC Output System
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-3
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
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-4
Step-Down (Buck) DC-DC Converter
• Add LC filter to reduce
switching ripple
• Flyback diode also
needed
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-5
Buck Converter: Waveforms
• Steady state; inductor current flows continuously
• Waveform below for buck in continuous conduction mode
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-6
Buck Converter: SPICE Circuit
• Circuit shown: fsw = 200 kHz, D = 0.5
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-7
Buck Converter: Startup Waveforms
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-8
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
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-9
Buck Converter in Continuous Conduction
• In continuous conduction, buck converter has 2 states --switch OPEN and switch CLOSED
iL
D
L
Vcc
Vo
+
R
C
vc
-
Switch closed (for time DT)
iL
Vcc
iL
L
Vo
+
C
L
Vo
+
R
vc
vc
-
-
di L VCC  v o

dt
L
Power Electronics
Switch open (for time (1-D)T)
di L
vo

dt
L
Chapter 7 Introduction to DC/DC Converters
7-10
Buck Converter in Continuous Conduction
• The inductor ripple current UP equals ripple DOWN
(VCC  Vo ) DT Vo (1  D)T

0
L
L
Vo  DVCC
• 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
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-11
Buck Converter: Waveforms at the Boundary
of Cont./Discont. Conduction
• ILB = critical current below which inductor current becomes
discontinuous
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-12
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
Vo

Vd
D2
0.25 I o
D2 
I LB ,max
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-13
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
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-14
Buck: Limits of Cont./Discont. Conduction
• In regulated power supply, Vd may fluctuate but Vo is kept
constant by control of D
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-15
Buck Conv.: Output Voltage Ripple
• ESR is assumed to be zero; continuous conduction mode
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-16
Buck Conv.: Output Voltage Ripple
• ESR is assumed to be zero
iL, pp 
Vo (1  D )T Vo (1  D )

L
f sw L
 1  T  iL, pp  Vo (1  D)
 
Q    
8 f sw2 L
 2  2  2 
vo , pp 
Q Vo (1  D )

C
8 f sw2 LC
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-17
Buck Conv.: Calculations
• Shown for SPICE example with fsw = 200 kHz, D = 0.5, L =
33 µH, C = 10 µF, Io = 1A
iL, pp 
vo , pp
Vo (1  D )
(5)(1  0.5)

 0.38 A
5
6
f sw L
( 2  10 )( 33  10 )
Q Vo (1  D )
(5)(1  0.5)



 24 mV
2
5 2
6
6
C
8 f sw LC
8( 2  10 ) (33  10 )(10  10 )
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-18
Buck: SPICE Result in Periodic Steady State
• Analysis shows inductor ripple = 0.38 A-pp, output voltage
ripple = 24 mV-pp, confirmed by SPICE
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-19
Pulse-Width Modulation (PWM) in DC-DC
Converters
vcontrol
D
Vˆst
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-20
Step-Up (Boost) DC-DC Converter
• Output voltage must be greater than the input
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-21
Boost Converter Waveforms
• Continuous current conduction mode
Switch closed:
di L VCC

dt
L
Switch open:
di L VCC  v o

dt
L
Inductor Volt-second balance:
VCC DT (VCC  Vo )(1  D)T

0
L
L
V
Vo  CC
1 D
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-22
Boost: Limits of Cont./Discont. Conduction
• The output voltage is held constant
• For low load current, current conduction becomes
discontinuous
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-23
Boost Converter: Discont. Conduction
• Occurs at light loads
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-24
Boost: Limits of Cont./Discont. Conduction
• The output voltage is held constant
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-25
Boost Converter: Effect of Parasitics
• The duty-ratio D is generally limited before the parasitic
effects become significant
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-26
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
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-27
Step-Down/Up (Buck-Boost) Converter
• The output voltage can be higher or lower than the input
voltage
• Note output phase inversion
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-28
Buck-Boost Converter: Waveforms
• Continuation conduction mode
Switch closed:
di L VCC

dt
L
Switch open:
di L v o

dt
L
Inductor Volt-second balance:
VCC DT Vo (1  D)T

0
L
L
DVCC
Vo  
1 D
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-29
Buck-Boost: Limits of Cont./Discont. Conduction
• The output voltage is held constant
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-30
Buck-Boost: Discontinuous Conduction
• This occurs at light loads
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-31
Buck-Boost Converter: Limits of
Cont./Discont. Conduction
• The output voltage is held constant
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-32
Buck-Boost Converter: Effect of Parasitics
• The duty-ratio is limited to avoid these parasitic effects
from becoming significant
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-33
Buck-boost Converter: Output Voltage Ripple
• ESR is assumed to be zero
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-34
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
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-35
Cuk DC-DC Converter: Waveforms
• The capacitor
voltage is assumed
constant (very large)
• Note phase inversion
at the output
Vo
D

Vd
1 D
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-36
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
Vo
D

Vd 1  D
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-37
Converter for DC-Motor Drives
• Four quadrant operation is possible
• For:
• DC motor drives
• DC to AC inverters for UPS
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-38
Converter Waveforms
• Bi-polar voltage switching
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-39
Converter Waveforms
• Uni-polar voltage switching
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-40
Output Ripple in Converters for DC-Motor
Drives
• Bi-polar and uni-polar voltage switching
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-41
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
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-42
Equivalent Circuits in DC-DC Converters
• Replacing inductors and capacitors by current and voltage
sources, respectively
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-43
Reversing the Power Flow in DC-DC Conv.
• For power flow from right to left, the input current
direction should also reverse
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-44
Real-World Issue: Capacitor ESR
• Real-world capacitors have equivalent series resistance (ESR)
• This ESR may have dominant effect on output ripple
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-45
Effects of Capacitor ESR
• Without ESR, output ripple is 24 mV-pp
• ESR has increased ripple to approximately 30 mV-pp
Power Electronics
Chapter 7 Introduction to DC/DC Converters
7-46