Power Elec Notes 07a Intro to Dc-dc Converters
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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: marctt@thompsonrd.comWeb: http://www.thompsonrd.com
2Introduction to DC/DC Converters© M. T. Thompson, 2008
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
3Introduction to DC/DC Converters© M. T. Thompson, 2008
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
4Introduction to DC/DC Converters© M. T. Thompson, 2008
Offline Flyback Converter
Reference: http://www.st.com/stonline/products/literature/an/7310.pdf
5Introduction to DC/DC Converters© M. T. Thompson, 2008
Some Real-World Design Issues that We’ll Get to Later On in the Term
6Introduction to DC/DC Converters© M. T. Thompson, 2008
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
7Introduction to DC/DC Converters© M. T. Thompson, 2008
Frequency Spectrum of Vo
fs= 1/TsVo = Vd D
• The output voltage contains switching harmonics
8Introduction to DC/DC Converters© M. T. Thompson, 2008
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
9Introduction to DC/DC Converters© M. T. Thompson, 2008
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
10Introduction to DC/DC Converters© M. T. Thompson, 2008
Step-Down (Buck) Converter
• Diode needed to provide current path for output current when switch is OFF
11Introduction to DC/DC Converters© M. T. Thompson, 2008
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
12Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck Converter: PSPICE Circuit
• Circuit shown: fsw = 200 kHz, D = 0.5
13Introduction to DC/DC Converters© M. T. Thompson, 2008
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
14Introduction to DC/DC Converters© M. T. Thompson, 2008
Same Circuit --- PSIM Simulation
15Introduction to DC/DC Converters© M. T. Thompson, 2008
Same Circuit --- PSIM Simulation
16Introduction to DC/DC Converters© M. T. Thompson, 2008
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
17Introduction to DC/DC Converters© M. T. Thompson, 2008
Inductor Voltage and Current• Remember that in an inductor:
dt
diLv L
L
18Introduction to DC/DC Converters© M. T. Thompson, 2008
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
19Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck Converter in Continuous Conduction
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
20Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck Converter in Continuous Conduction
• 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
21Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck Converter in Continuous Conduction --- Idealized Switching Waveforms
• Idealized because we assume that switches and diodes turn on and off with zero risetime
22Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck Converter: Waveforms at the Boundary of Cont./Discont. Conduction
• ILB = critical current below which inductor current becomes discontinuous
23Introduction to DC/DC Converters© M. T. Thompson, 2008
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
24Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck Converter: Capacitor Current Ripple
• Continuous conduction mode
25Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck Converter: Output Voltage Ripple
• ESR is assumed to be zero; continuous conduction mode
26Introduction to DC/DC Converters© M. T. Thompson, 2008
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(
27Introduction to DC/DC Converters© M. T. Thompson, 2008
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,
28Introduction to DC/DC Converters© M. T. Thompson, 2008
Example 1: Buck in Periodic Steady State
• Analysis shows inductor ripple = 0.38 A-pp, output voltage ripple = 24 mV-pp, confirmed by SPICE
29Introduction to DC/DC Converters© M. T. Thompson, 2008
Step-Up (Boost) DC-DC Converter
• Output voltage is greater than the input, with the same polarity
30Introduction to DC/DC Converters© M. T. Thompson, 2008
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
31Introduction to DC/DC Converters© M. T. Thompson, 2008
Boost Converter: Discontinuous Conduction
• Occurs at light loads
32Introduction to DC/DC Converters© M. T. Thompson, 2008
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
33Introduction to DC/DC Converters© M. T. Thompson, 2008
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
34Introduction to DC/DC Converters© M. T. Thompson, 2008
Boost Converter --- PSIM Simulation• What is the output voltage?
35Introduction to DC/DC Converters© M. T. Thompson, 2008
Boost Converter --- PSIM Simulation• Vo = Vi/(1-D) in continuous conduction
Output voltage during startup
36Introduction to DC/DC Converters© M. T. Thompson, 2008
Boost Converter --- PSIM Simulation• Note that inductor current I(RL1) never decays to zero, so we’re in continuous conduction
37Introduction to DC/DC Converters© M. T. Thompson, 2008
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
38Introduction to DC/DC Converters© M. T. Thompson, 2008
Example 2: Boost Converter Example
Output voltage ripple
Inductor ripple current
39Introduction to DC/DC Converters© M. T. Thompson, 2008
Step-Down/Up (Buck-Boost) Converter
• The output voltage can be higher or lower than the input voltage
40Introduction to DC/DC Converters© M. T. Thompson, 2008
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(
41Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck-Boost: Limits of Cont./Discont. Conduction
• The output voltage is held constant
42Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck-Boost: Discontinuous Conduction• This occurs at light loads
43Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck-Boost Converter: Effect of Parasitics
• The duty-ratio is limited to avoid these parasitic effects from becoming significant
44Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck-Boost Converter: Output Voltage Ripple
• ESR is assumed to be zero
45Introduction to DC/DC Converters© M. T. Thompson, 2008
Example 3: Buck-Boost Converter: Simulation
• Vo should be -10V after startup transient dies out
46Introduction to DC/DC Converters© M. T. Thompson, 2008
Example 3: Buck-Boost Converter: Simulation
• Vo should be -10V in steady-state after startup transients die out
Output voltage during startup
47Introduction to DC/DC Converters© M. T. Thompson, 2008
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?
48Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck-Boost Converter: Simulation
• With larger C• What has happened?
Output voltage during startup
49Introduction to DC/DC Converters© M. T. Thompson, 2008
Buck-Boost Converter: Simulation
• Note that ripple is smaller, but startup transient is slower (makes sense); LC is larger
Output voltage during startup
50Introduction to DC/DC Converters© M. T. Thompson, 2008
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
51Introduction to DC/DC Converters© M. T. Thompson, 2008
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
52Introduction to DC/DC Converters© M. T. Thompson, 2008
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
53Introduction to DC/DC Converters© M. T. Thompson, 2008
SEPIC Converter
• Circuits for 2 different switching states
Reference: National Semiconductor, Application Note AN-1484, “Designing a SEPIC Converter”
54Introduction to DC/DC Converters© M. T. Thompson, 2008
SEPIC Converter --- Example
• Example from application note
Reference: National Semiconductor, Application Note AN-1484, “Designing a SEPIC Converter”
55Introduction to DC/DC Converters© M. T. Thompson, 2008
SEPIC Converter
56Introduction to DC/DC Converters© M. T. Thompson, 2008
SEPIC Converter
Output voltage ripple
57Introduction to DC/DC Converters© M. T. Thompson, 2008
Converter for DC-Motor Drives• Four quadrant operation is possible• For:
• DC motor drives• DC to AC inverters for UPS
58Introduction to DC/DC Converters© M. T. Thompson, 2008
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
59Introduction to DC/DC Converters© M. T. Thompson, 2008
Equivalent Circuits in DC-DC Converters• Replacing inductors and capacitors by current and voltage sources, respectively
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