Electronic Power Conversion
DC-DC switch mode converters
Challenge the future
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7. DC-DC switch mode converters
DC-DC switch mode converters
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•  Basic DC-DC converters
•  Step-down converter (neerchopper)
•  Step-up converter (opchopper)
Applications
•  DC-motor drives
•  SMPS
•  Derived circuits
•  Step-down/step-up converter (flyback)
•  (Ćuk-converter)
•  Full-bridge converter (volle brug omzetter)
DC-DC switch mode converters
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Control of dc-dc converters
•  Output voltage has to be kept constant even though input voltage
and output load may fluctuate
•  Controlled by switch on and off durations
Switch
control
signal
Ts
t on
1
1
Vo = ∫ vo (t )dt = (ton ⋅Vd + toff ⋅0) = Vd
Ts 0
Ts
Ts
DC-DC switch mode converters
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vst
vcont
Control of dc-dc converters
ton vcontrol
=
TS
Vˆst
ton
Ts
ton
D=
TS
DC-DC switch mode converters
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Step-down (Buck) converter
1
V0 =
Ts
Ts
1
v
(
t
)
dt
=
∫0 0
Ts
Ts
⎛ DTs
⎞
⎜ ∫ vd (t )dt + ∫ 0 dt ⎟
⎜ 0
⎟
DT
⎝
⎠
ton
=
Vd = D Vd
Ts
V0 = k vcontrol
Features of basic circuit:
•  switch stress when load is inductive
•  fluctuating output voltage
DC-DC switch mode converters
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Features of basic circuit:
•  switch stress when load is inductive è diode
•  fluctuating output voltage è filter used
DC-DC switch mode converters
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Continuous conduction mode
0 < t < ton
vL = Vd − Vo
ton < t < Ts
vL = Vo
t
t
1
iL (t ) = iL (0) + ∫ vL (t )dt =
L0
1
iL (t ) = iL (ton ) + ∫ vL (t )dt =
L ton
Vd −V o
= i L ( 0) +
t
L
= iL (ton ) +
−V o
(t − ton )
L
DC-DC switch mode converters
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0 < t < ton
ton < t < Ts
vL = Vd − Vo
vL = −Vo
iL (t ) = iL (0) +
Vd −V o
t
L
−V o
iL (t ) = iL (ton ) +
(t − ton )
L
DC-DC switch mode converters
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0 < t < ton
ton < t < Ts
vL = Vd − Vo
vL = −Vo
vL,av = 0
è
(Vd − V0 ) ton = V0 (Ts − Ton )
(Vd − Vo ) ⋅ ton + (−Vo ) ⋅ toff = 0
Ts
Vo = D ⋅Vd
Pout = Pin
Vd I d = V0 I 0
I 0 Vd 1
= =
I d V0 D
DC-DC switch mode converters
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Continuous and discontinuous mode
R → Io
Boundary between continuous and discontinuous mode
DC-DC switch mode converters
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Boundary continuous- discontinuous
On boundary B:
mode
t
1
I LB = iL, peak
2
(b)
V0
=D
Vd
I OB =
so
on
(Vd − V0 )
2L
(a)
DTs
=
(Vd − V0 )
2L
Eliminate either Vo or Vd from (a) and (b) depending on what is constant.
Assume Vd constant:
Boundary:
Ts Vd
I OB =
D(1 - D)
2L
DC-DC switch mode converters
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Discontinuous conduction mode
CCM:
?
DCM
VL ,av = 0
Δ1 ?
I 0 = iL, peak
è
V0 = DVd
V0 = f (Vd , D, I 0 )
(Vd − V0 ) DTs − V0 Δ1Ts = 0
V0
D
=
Vd D + Δ1
è
There is a relationship between Δ1 and I0:
D + Δ1
2
Eliminate Δ1
from (1) & (4) è
(2) with
V0
=
Vd
V ΔT
I L, peak = o 1 s (3) è
L
2
D
2L
2
+
I0
D
TsVd
or
I0 =
V0
=
Vd
(1)
Vo Δ1Ts (D + Δ1 )
(4)
L
2
D
2
D +
2
1
( I 0 / I LB,max )
4
DC-DC switch mode converters
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V0
=
Vd
2
D
2L
2
+
I0
D
TsVd
or
V0
=
Vd
D
2
D +
2
1
I 0 / I LB ,max )
(
4
where:
Ts Vd
I LB ,max =
8L
DC-DC switch mode converters
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D(Vd, Io) for Vo constant
Boundary:
TsV0
I LB =
(1 − D)
2L
(5)
I LB ,max =
TsV0
2L
1/ 2
(1) - (4) still hold
V0 ⎛ I 0 /I LB ,max ⎞
D=
⎜
⎟
Vd ⎝ 1 − V0 / Vd ⎠
DC-DC switch mode converters
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Output voltage ripple and capacitor
current (Down conv.) ΔV = ΔQ
0
C
1
1
=
⋅ '' base ⋅ height ''
C
2
Δ IL =
2.Height:
V0
(1 − D) Ts
L
1 1 Ts V0
Δ
V
=
⋅ ⋅ ⋅
(1 − D) Ts
0
è
C 2 2 2L
⎛ fc ⎞
Δ V0 Ts (1 − D) π
=
=
(1 − D) ⎜ ⎟
V0
8LC
2
⎝ fs ⎠
2
or:
2
2
with:
fc =
1
2π LC
•  Only valid for continuous conduction mode (CCM)
DC-DC switch mode converters
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Step-up (or boost) converter
VL ,av = 0 è
Vd D Ts + (Vd − V0 ) ( 1 − D)Ts = 0
V0
1
=
Vd 1 − D
DC-DC switch mode converters
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Boost converter in DCM
same procedure as down converter
CCM:
V0 =
Vd
1− D
?
DCM:
From the time waveforms:
VL ,av = 0
è
Vd D Ts + (Vd − V0 ) Δ1Ts = 0
è
V0 = f (Vd , D, I d )
V0 Δ1 + D
=
Vd
Δ1
(1)
IˆL = f (Vd , D)
(2)
I 0,av = f ( IˆL , D , Δ1 )
(3)
Eliminate
IˆL , D and Δ1 from (1), (2) and (3)
DC-DC switch mode converters
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Vo= constant
Solution not important, however here is the plot:
DC-DC switch mode converters
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Boost converter - output voltage
ripple and capacitor currents
ΔVo =
ΔQ I o DTs Vo DTs
=
=
C
C
R C
DC-DC switch mode converters
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Buck-boost converter
VL ,av = 0
Vd D Ts + ( −V0 ) ( 1 − D)Ts = 0
V0
D
=
Vd 1 − D
and
I0 1 − D
=
Id
D
DC-DC switch mode converters
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Discontinuous conduction mode (DCM)
Method: find several relations:
VL,av = 0
è
IˆL = f (Vd , D)
Vd D Ts + ( −V0 ) Δ1Ts = 0
è
V0 D
=
Vd Δ1
(1)
(2)
I 0,av = f ( IˆL , D , Δ1 ) (3)
Eliminate
IˆL , D and Δ1 from (1), (2) and (3)
DC-DC switch mode converters
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Voltage ripple and capacitor current
Calculate voltage ripple
ΔVo = ?
DC-DC switch mode converters
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Full-bridge dc-dc converter
•  Either + or - switch is on so output voltage is solely determined by status
of the switch-gate signal (not by the current polarity)
•  Current polarity determines whether T or D is conducting
•  Applications:
•  4-quadrant dc motor drives
•  dc-ac sine wave conversion (Chapter 8)
DC-DC switch mode converters
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Dc-dc converter
Dc motor drives
Source: STMicroelectronics
http://www.st.com/web/en/catalog/apps/SE413/AS214/AC899
DC-DC switch mode converters
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VAN = Vd DTA+
DTA− = 1 − DTA+
è
VBN = Vd D T B+
Two PWM control switching strategies
•  PWM bipolar switching: simultaneous synchronized operation of the
phase legs
•  PWM unipolar switching: independent operation of the phase legs
DC-DC switch mode converters
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Bipolar voltage switching
•  single control signal vcontrol
vcontrol > vtri
TA+, TB-
vcontrol < vtri
TA-, TB+
VBN = (1 − D1 )Vd
VAN = D1 Vd
V0 = VAN − VBN = (2D1 − 1) Vd
vcontrol
V0 =
Vd = k vcontrol
ˆ
Vtri
with
k=
Vd
Vˆtri
4 quadrant operation:
All combinations of polarities of
(average) current and voltage possible
DC-DC switch mode converters
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Unipolar voltage switching
•  double control signal +vcontrol and -vcontrol
vcontrol > vtri TA+
− vcontrol > vtri TB+
V0 = VAN − VBN = (2D1 − 1) Vd
vcontrol
Vd = k vcontrol
ˆ
Vtri
V
k = d = constant
with
Vˆtri
V0 =
Comparison unipolar/bipolar:
•  ripple in i0 at 2fs
•  smaller ripple current for the same L
•  slightly more complex control; 2 control
signals required
DC-DC switch mode converters
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Summary
Considered circuits
Assumptions for analysis:
•  all components ideal (no voltage
drop on switches, infinitely fast)
•  output capacitor voltage assumed
to be constant è voltage source
•  output inductor current assumed to
be constant è current source
Phase arm:
•  uni- and bipolar switching
•  control signal uniquely determines vAN(t) and vBN(t)
•  current depends on VAB(t) and load
•  1, 2 and 4 quadrant operation
For all these circuits:
L-side voltage always smaller than C-side voltage
DC-DC switch mode converters
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Comparison of dc-converters
•  switch utilization
•  transformer core utilization
•  size of passives
Switch Utilisation Ratio
P0
SUR =
PT
with PT = VˆT ⋅ IˆT
and
P0 = V0 ⋅ I 0
Problem:
VˆT
Sketch
V0
and
IˆT
I0
as a function of D
for: - step down converter
-  step-up converter
-  buck-boost converter
Assume for simplicity L to be
infinitely large (flat current waveform)
DC-DC switch mode converters
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Figure 1 shows a boost converter used in the Toyota Prius hybrid electric vehicle for stepping up the ba:ery voltage from 150-­‐250 V to 500 V. The converter’s switching frequency is fs= 20kHz. (5) Calculate the criJcal (maximum) inductance value of the output filter inductor to ensure that the converter operates in the disconJnuous conducJon mode for the given input voltage range and the load current up to Io= 10A. (5)Given the inductance value obtained in 1.1 calculate the duty cycle range to keep the output voltage Vo constant (500V) for the given range of the input voltage and the nominal current of Inom= 4A. (10)Calculate the required capacitance value of the output filter capacitor to ensure that at the nominal input voltage (Vinnom = 200V) the peak-­‐to-­‐peak output voltage ripple is less than 2% of the nominal output voltage (Vo). DC-DC switch mode converters
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Vd = 250 V. Switching frequency is 30 kHz. The bridge is connected to a speed controlled dc machine. The armature inductance La = 0,2 mH. The armature resistance is negligible. (a) The bridge is controlled to provide an average output voltage, Vo = 200 V. Find the duty raJos D1 and D2 and the ripple frequency of the two control principles. Sketch vo(t) for the two control principles. At a given speed, the back-­‐emf Ea = 200 V. Unipolar PWM is used. (b) The armature current, Ia, is 1 A, find the maximum and the minimum instantaneous armature current. Sketch the armature current, ia(t). Indicate which of the power semiconductors are conducJng. Also sketch id(t). (c) As in Problem (b), with Ia = 20A. 32
(d) As in Problem (b), except bipolar PWM is used. DC-DC switch mode converters
Image credits
•  All uncredited diagrams are from the book “Power Electronics:
Converters, Applications, and Design” by N. Mohan, T.M.
Undeland and W.P. Robbins.
•  All other uncredited images are from research done at the EWI
faculty.
DC-DC switch mode converters
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