Download DC/DC converter, part 1

TSTE25 Power Electronics
Lecture 6
Tomas Jonsson
ISY/EKS
TSTE25/Tomas Jonsson
Outline
 DC power supplies
 DC-DC Converter
 Step-down (buck)
 Step-up (boost)
 Other converter topologies (overview)
 Exercises 7-1, 7-2, 7-7, 7-8
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Basic use of DC-DC converter
 Unregulated DC input, controlled DC output
 Regulated DC may be larger or smaller than the unregulated DC
voltage
 Input to DC-DC converter may vary a lot
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DC Power supplies
 Regulated output
 Defined tolerance of output voltages
 Isolation
 No direct electric connection to supply voltage
 Multiple outputs
 Both positive and negative possible
 Various current and voltage ratings
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Linear power supply
 Bulky transformer
 Low frequency
 Poor efficiency
 30 – 60 %
 Low EMI
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Switch-mode dc power supply schematic
 Small size
 High efficiency
 EMI protection
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Multiple voltages
 Linear control may be applied
if multiple controlled voltages
are required
 High efficiency (70 – 90 %)
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Step down converter principle
 Vd > Vo
 Ts constant, ton and toff changing
 Large ripple on Vd
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DC/DC-converter control
• Pulse width modulation,
PWM,
to control switching
• Switching frequency fs
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PWM waveform, duty cycle
 Switch duty cycle
(duty ratio)
𝐷=
𝑡𝑜𝑛 𝑣𝑐𝑜𝑛𝑡𝑟𝑜𝑙
=
𝑇𝑠
𝑉෠𝑠𝑡
0<𝐷<1
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Step-down (buck) converter
 Add filter to reduce ripple voltage
 Diode added to protect switch
 VL -> infinity if no diode and instantaneous switching!
 Parasitic capacitances Cx would be charged by the inductor current
Cx
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Step-down converter waveforms
 Ts = ton + toff
 Average output voltage
𝑉𝑜 =
𝑡𝑜𝑛
𝑉 = 𝐷 ∙ 𝑉𝑑
𝑇𝑠 𝑑
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Input voltage before low-pass filter
 Voi = Vd when switch on
 When switch off
 Voi = 0 if iL > 0
 Voi = Vo if iL = 0
 LP filter BW(fc) << fs
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Current Conduction modes
 Average iL equals io
 Two current conduction modes (iL)
 Continuous current conduction
 Non-continuous current conduction
 Converter characteristics different depending on mode
 Both modes can be supported by a converter
 Mode applicable is depending on load
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Continuous Conduction mode
 Switch on (diode off)
 Switch off (diode on)
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Continuous conduction mode, cont.
 iL never zero
 Steady state => A = B
𝑡𝑜𝑛 𝑉𝑑 − 𝑉𝑜 = 𝑉𝑜 𝑇𝑠 − 𝑡𝑜𝑛 =>
 Average voi output voltage, average vL zero in
steady state
𝑉𝑑 𝑡𝑜𝑛 + 0 ∙ 𝑡𝑜𝑓𝑓
= 𝑉𝑜
𝑇𝑠
 Ideal conditions: No power loss in converter

𝑃𝑑 = 𝑃𝑜 ⇒ 𝑉𝑑 𝐼𝑑 = 𝑉𝑜 𝐼𝑜
𝐼𝑜 𝑉𝑑 1
=
=
𝐼𝑑 𝑉𝑜 𝐷
 DC transformer with turns ratio equal to D
 id still slanted square wave
𝑉𝑜 𝑡𝑜𝑛
=
=𝐷
𝑉𝑑
𝑇𝑠
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Discontinuous/Continuous Conduction mode
boundary
 iL reach zero at end of period
 Average Io

1
𝑡𝑜𝑛
𝑖𝐿,𝑝𝑒𝑎𝑘 =
𝑉 − 𝑉𝑜
2
2𝐿 𝑑
𝐷𝑇𝑠
𝐼𝐿𝐵 =
𝑉 − 𝑉𝑜
2𝐿 𝑑
𝐷𝑇𝑠
𝑇𝑠 𝑉𝑑
=
𝑉 1−𝐷 <
2𝐿 𝑑
8𝐿
𝐼𝐿𝐵 =

𝐼𝐿𝐵
 For fixed input voltage Vd
 ILB,max at 50% duty cycle
 𝐼𝐿𝐵,𝑚𝑎𝑥 =
𝑇𝑠 𝑉𝑑
8𝐿
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Discontinuous conduction mode
𝐸𝑞𝑢𝑎𝑙 𝑎𝑟𝑒𝑎:
𝑉𝑑 − 𝑉𝑜 𝐷𝑇𝑠 + −𝑉𝑜 Δ1 𝑇𝑠 = 0
voi
𝑉𝑜
𝐷
=
𝑉𝑑
𝐷 + Δ1
𝑉𝑜
𝑖𝐿,𝑝𝑒𝑎𝑘 = Δ1 𝑇𝑠
𝐿
vL,iL
𝐷 + Δ1
𝐼𝑜 = 𝑖𝐿,𝑝𝑒𝑎𝑘
2
𝑉𝑜 𝑇𝑠
𝑉𝑑 𝑇𝑠
𝐼𝑜 =
𝐷 + Δ1 Δ1 =
𝐷Δ1
2𝐿
2𝐿
𝐼𝑜
Δ1 =
4𝐼𝐿𝐵,𝑚𝑎𝑥 𝐷
𝑉𝑜
𝐷2
=
𝑉𝑑 𝐷2 + 1 𝐼 /𝐼
4 𝑜 𝐿𝐵,𝑚𝑎𝑥
vd
vo
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Constant Vd step-down characteristic
 Very low load result in increased output voltage!
𝐼𝐿𝐵,𝑚𝑎𝑥 =
𝑇𝑠 𝑉𝑑
8𝐿
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Discontinuous conduction mode with
constant Vo

𝐼𝐿𝐵,𝑚𝑎𝑥
𝑇𝑠 𝑉𝑜
=
2𝐿
 Control ratio
for constant Vo
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Output voltage ripple
 Assuming:
 ripple current in C
 Average current in R
Δ𝑄 1 1 Δ𝐼𝐿 𝑇𝑠
Δ𝑉𝑜 =
=
𝐶
𝐶2 2 2
𝑉𝑜
∆𝐼𝐿 =
1 − 𝐷 𝑇𝑠
𝐿
Δ𝑉𝑜 1 𝑇𝑠2 1 − 𝐷
=
=
𝑉𝑜
8
𝐿𝐶
π2
=
1−𝐷
2
𝑓𝑐
𝑓𝑠
2
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Step-down (buck) converter summary
•
Output vs input
𝑉𝑜
=𝐷
𝑉𝑑
𝐼𝑜 1
=
𝐼𝑑 𝐷
•
High ripple current
𝐼𝐿𝑝𝑒𝑎𝑘 = 2𝐼𝑜
•
Practical for D not lower
than 0.2
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Lecture 6
Exercises, buck-converter
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7-1
• In a step-down converter, consider all components to be ideal.
Let vo  Vo be held constant at 5 V by controlling the switch duty
ratio D.
• Calculate the minimum inductance L required to keep the
converter operation in a continuous-conduction mode under all
conditions if:
Vd is 10-40 V , Po 5 W, and fs = 50 kHz.
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7-2
•
Consider all components to be ideal. Assume Vo = 5 V, fs = 20 kHz,
L = 1 mH, and C = 470 µF.
•
Calculate Vo (peak-peak) if Vd = 12.6 V, and I0 = 200 mA.
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Lecture 6
Step-up, boost-converter
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Step-up (boost) converter
 Output must be larger than input voltage
 Otherwise is Vd driving Vo directly => Vo = Vd
 Load energy into inductor, then output energy into load while
still consuming energy from source
 C large enough to give low ripple, vo(t)  Vo
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Step-up converter waveform, continuous
conduction mode
 Switch on, diode off
 Switch off, diode on
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Step-up converter, continuous mode
𝑉𝑑 𝑡𝑜𝑛 + 𝑉𝑑 − 𝑉𝑜 𝑡𝑜𝑓𝑓 = 0
𝑇𝑠
1
𝑉𝑜 /𝑉𝑑 =
=
𝑡𝑜𝑓𝑓 1 − 𝐷
Lossless circuit: 𝑉𝑑 𝐼𝑑 = 𝑉𝑜 𝐼𝑜
𝐼𝑜
⇒ = 1−𝐷
𝐼𝑑
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Boundary between continuous and
discontinuous mode
1
1 𝑉𝑑
𝑖𝐿,𝑝𝑒𝑎𝑘 =
𝑡
2
2 𝐿 𝑜𝑛
𝑇𝑠 𝑉𝑜
𝐼𝐿𝐵 =
𝐷 1−𝐷
2𝐿
𝑇𝑠 𝑉𝑜
𝐼𝑜𝐵 =
𝐷 1−𝐷 2
2𝐿
𝑇𝑠 𝑉𝑜
𝐿=
𝐷 1−𝐷 2
2𝐼𝑜𝐵
𝐼𝐿𝐵 =
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Boundary between continuous and
discontinuous mode
𝑉𝑜 𝑐𝑜𝑛𝑠𝑡𝑎𝑛𝑡
𝐼𝐿𝐵 max when D = 0.5
𝑇𝑠 𝑉𝑜
𝐼𝐿𝐵,𝑚𝑎𝑥 =
8𝐿
𝐼𝑜𝐵 max when D = 1/3
2 𝑇𝑠 𝑉𝑜
𝑇𝑠 𝑉𝑜
𝐼𝑜𝐵,𝑚𝑎𝑥 =
= 0.074
27 𝐿
𝐿
𝐼𝐿𝐵 = 4D 1 − 𝐷 𝐼𝐿𝐵,𝑚𝑎𝑥
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𝐼𝑜𝐵 =
𝐷 1 − 𝐷 2 𝐼𝑜𝐵,𝑚𝑎𝑥
4
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Step-up, discontinuous mode
𝑉𝑑 𝐷𝑇𝑠 + 𝑉𝑑 − 𝑉𝑜 Δ1 𝑇𝑠 = 0
𝑉𝑜 Δ1 + 𝐷
=
𝑉𝑑
Δ1
𝐼𝑜
Δ1
=
𝐼𝑑 Δ1 + 𝐷
𝑉𝑑
𝐼𝑑 =
𝐷𝑇 𝐷 + Δ1
2𝐿 𝑠
𝑇𝑠 𝑉𝑑
𝐼𝑜 =
𝐷Δ1
2𝐿
Controller
4 𝑉𝑜 𝑉𝑜
𝐼𝑜
𝐷=
−1
27 𝑉𝑑 𝑉𝑑
𝐼𝑜𝐵,𝑚𝑎𝑥
1/2
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Step up converter characteristics, Vo constant
𝐼𝑜𝐵,𝑚𝑎𝑥 = 0.074
𝑇𝑠 𝑉𝑜
𝐿
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Effects of parasitics
 Losses in L, diode, switch, C
 Limited also by acceptable D ratio
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Output voltage ripple
Δ𝑄 𝐼𝑜 𝐷𝑇𝑠
=
𝐶
𝐶
Δ𝑉𝑜 𝐷𝑇𝑠
𝑇𝑠
=
=𝐷
𝑉𝑜
𝑅𝐶
τ
Δ𝑉𝑜 =
where
τ = 𝑅𝐶time constant
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Lecture 6
Exercises on boost converter
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7-7
• In a step-up converter, consider all components to be
ideal. Let Vd be 8-16 V, Vo = 24 V (regulated), fs = 20
kHz, and C = 470 µF.
• Calculate Lmin that will keep the converter operating
in a continuous-conduction mode if Po  5 W.
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7-8
• In a step-up converter, Vd =12 V, Vo = 24 V,
I0 = 0.5 A, L = 150 µH, C = 470 µF, and fs =20 kHz.
• Calculate Vo (peak-peak).
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Equivalent Circuits in DC-DC Converters
a) Buck, b) Boost, c) Buck-Boost, d) Cúk
Lecture 6
Other converter topologies
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Flyback converter
 Derived from buck-boost
structure
 Second winding gives
electric isolation
 Only flux flow in one direction
 Never negative currents
in the transformer
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Flyback converter circuit states
 Switch on and switch off
 Continuous conduction mode
 Incomplete demagnetization
 Lm size important
 Ideal transformer have
inifinite Lm
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Flyback converter waveforms
 Same control
equation as
for buck-boost
converter
𝑡𝑜𝑛
𝑇𝑠
𝑉𝑜 𝑁2 𝐷
=
𝑉𝑑 𝑁1 1 − 𝐷
𝐷=
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Alternative flyback converter topologies
 Two transistor flyback
 Both turn on and off
simultaneously
 Voltage rating half
compared to single
transistor
 No snubber necessary
because of diodes
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Alternative flyback converter topologies
 Paralleling flyback
converter
 Same frequency of
switching
 Phase-shifting
switches π
 Allow higher power
 Redundancy
 Increased effective
switching frequency
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Forward converter
 Derived from step-down
converter
 Ideal transformer
assumed
 Transformer magnetizing
current not included
 Converter failure if
not taken care of
𝑉𝑜 𝑁2
=
𝐷
𝑉𝑑 𝑁1
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Practical forward converter
 Feed magnetic current
back to source
 Requires a third winding
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Practical forward converter waveforms
 To guarantee
demagnitized
transformer
𝑡𝑚
𝑚𝑎𝑥
=1−𝐷
𝑇𝑠
𝑁3
1 − 𝐷𝑚𝑎𝑥 =
𝐷
𝑁1 𝑚𝑎𝑥
1
𝐷𝑚𝑎𝑥 =
1 + 𝑁3 /𝑁1
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Other forward converter topologies
 Two-switch forward converter
 Commonly used
 Voltage rating half
of single transistor
case
 No snubbers
necessary
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Other forward converter topologies
 Parallelled forward
converter
 Same advantages
as parallelled
flyback
converter
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Push-pull converter
 Derived
from
step-down
converter
 Diodes due to
leakage
inductances
 PWM control
𝑉𝑜
𝑁2
=2 𝐷
𝑉𝑑
𝑁1
0 < 𝐷 < 0.5
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Half-bridge converter
 Derived from
step-down
converter
 Additional
diodes for
switch protection
𝑉𝑜 𝑁2
=
𝐷
𝑉𝑑 𝑁1
0 < 𝐷 < 0.5
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Full-bridge converter
 Derived from
step-down
converter
 Switches carry
half the current
compared to the
half bridge
converter
𝑉𝑜
𝑁2
=2 𝐷
𝑉𝑑
𝑁1
0 < 𝐷 < 0.5
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Current-source dc-dc converter
 Ld and D > 0.5 gives current source input
 One or both switches always on
 Operates like a step-up converter
𝑉𝑜 𝑁2
1
=
𝑉𝑑 𝑁1 2 1 − 𝐷
𝐷 > 0.5
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