dc dc converters
DESCRIPTION
Descripción de los circuitos convertidores DC-DCTRANSCRIPT
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POWER ELECTRONICSPOWER ELECTRONICS
DCDC --DC CONVERTERSDC CONVERTERS
Dr. Adel GastliEmail: [email protected]
http://adel.gastli.net
Dr. Adel Gastli DC-DC Converters 2
Learning ObjectivesLearning ObjectivesTo learn the switching technique fordc-dc conversion and types of dc-dc
convertersTo study the operation of dc-dcconvertersTo understand the performanceparameters of dc-dc converters.To learn the techniques of analysisand design of dc-dc converters
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Dr. Adel Gastli DC-DC Converters 3
CONTENTSCONTENTSCONTENTS1. Introduction
2. Buck Converter 3. Boost Converter 4. Buck-Boost Converter5. Čuk Converter
6. Two Quadrant Converters7. Full Bridge Converter 8. Summary
Dr. Adel Gastli DC-DC Converters 4
INTRODUCTIONINTRODUCTION
Step-down (Buck) converter : where theoutput voltage of the converter is lower
than the input voltage.Step-up (Boost) converter : where theoutput voltage is higher than the inputvoltage.Step-down/step-up (Buck-Boost)converter .
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Dr. Adel Gastli DC-DC Converters 5
BUCK CONVERTERBUCK CONVERTER• Voltage step-down and current step-up
converter.
V o
I s
V s
I ot on T
t on T
ON OFF ON
1- Continuous conduction mode (CCM)
+-V s D I oV o
S +
-
I s
Mode 1Mode 2
Typical converter topology and waveformsTypical converter topology and waveforms
Dr. Adel Gastli DC-DC Converters 6
V o
I s
V s
I ot on T
t on T
ON OFF ON
son
sa kV T t
V V ==
f t T t
V V
k onon
s
a ===Duty ratio (0-1)
orturn ratio of equivalent
transformer t on
T
V s
aV
),( f t F V ona =Constant frequency operation
Variable frequency operation
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Dr. Adel Gastli DC-DC Converters 7
),( sona f t F V =
t on is the on pulse width.
Controlling t on is known as PWM control
f s
is the switching frequency.
PWM control is more popular PWM control is more popular
Is a linear function
Dr. Adel Gastli DC-DC Converters 8
s
kT
rms V k dt vT
V == ∫0
200
1 Rms value ofoutput voltage
RV k dt RvT idt vT P skT kT
i
2
0
2
00 0 11 === ∫∫
Inputpower
k R
RkV V
I V
R s
s
a
si ===
/
Effective inputresistance seen fromthe source
RkV
RV
I saa == V s
+- Ri
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Dr. Adel Gastli DC-DC Converters 9
• Neglecting power losses in the circuitelements:
aa s s I V I V =
k V V
I I
a
s
s
a 1== sa I I ≥
StepStep --upup
action inaction incurrentcurrent
Dr. Adel Gastli DC-DC Converters 10
ExampleExample
mst
k k V k V T t
V
on
s son
a
0834.02.0417.0
417.0125
512
=×=
==⇒====
?;5;12
)(5===
=ona s t V V V V
frequency switching kHz
ms f
T 2.0511 ===Solution
(Study also example 5.1)
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Dr. Adel Gastli DC-DC Converters 11
Low Current RippleLow Current Ripple
a s V V dt di
L −=0
aV dt di
L −=0
⎥⎦
⎤⎢⎣
⎡ += ∫∫ T
t L
t
Laon
on
dt idt iT
I 0
1 ( )ona t T LV
I −=Δ
V 1
I s
V s
I 0min
t on T
ON OFF ON
Δ I
Continuous conduction
Peak-to-peakripple current
+-V s D
I o
V a
S + _
I s
Mode 1
Mode 2
LV 1
I 0max
Dr. Adel Gastli DC-DC Converters 12
( ) ( )k Tk LV
k T LV
I sa −=−=Δ 11
Independent of the magnitude of load currentIt’s a function of t on and T, and L
I o
t on T
Δ I I omax
I omin
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Dr. Adel Gastli DC-DC Converters 13
Low Voltage RippleLow Voltage Ripple
Assumptions:• voltage ripple ΔVo is a smallpercentage of dc voltage Vo
• ripple current through inductorflows into filter capacitor and notR .
V s+- D
I o
V o
S
I s L
C R
V 1
(Page 187)
V 1
V o
V s
i L
kT T
ON OFF ON
Δ I
0V Δ
ic Δ I
io
charge discharge
Dr. Adel Gastli DC-DC Converters 14
4 I
I C
Δ=
The average capacitor charge current, whichflows into for t on /2 + t off /2=T/2 is
The capacitor charge ΔQc is
82 IT T
I Q C c
Δ==Δ
The capacitor voltage variation is ΔV0
C IT
C QV V c
c 80Δ=Δ=Δ=Δ
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Dr. Adel Gastli DC-DC Converters 15
C IT
C Q
V c
80
Δ=Δ=Δ
)1(2
)1(8
222
0
0 k f f k
LC T
V V C −⎥
⎦⎤⎢
⎣⎡=−=Δ π
Independent of load resistance R andload current Io
Low value of f C/f will provide low voltage
ripple.
( )k L
T V I −=Δ 10
Remember
LC f
T f
C π 2
1
1
=
=
20 8)1(
LCf k k V
V V sc
−=Δ=Δ
Dr. Adel Gastli DC-DC Converters 16
The condition for criticalcontinuous inductor currentand capacitor voltage issatisfied when:
2
I I L
Δ=
( ) RkV
I I k L
T V I s
a LC
22210 ===−=Δ
f Rk
LC 2)1( −
=Criticalinductance
V 1
v0
V s
I L
kT T
ON OFF ON
Δ I
0V Δ
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Dr. Adel Gastli DC-DC Converters 17
If V C is the average capacitorvoltage, the ripple voltageΔVC =2V a :
aC
a V f LC k V
28)1(2 =
−
216)1(
Lf k
C C
−=
Critical
capacitor
V 1
V a
V s
I L
kT T
ON OFF ON
Δ I
0V Δ
Dr. Adel Gastli DC-DC Converters 18
Example : Finding the values of LCfilter for the Buck Converter
Vs=12V. The required average output voltageis V a=5V at R=500 Ω and the peak-to-peakoutput ripple voltage is 20mV. The switchingfrequency is 25kHz. If the peak-to-peak ripplecurrent of inductor is limited to 0.8A,determine:
a) Duty cycle, k
b) Filter inductance, L
c) Filter capacitor, Cd) Critical values of L and C .
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Dr. Adel Gastli DC-DC Converters 19
Solution
V5,kHz25,A8.0mV,20,V12 ===Δ=Δ= aC s V f I V V
a) %67.414167.012
5 ==== s
a
V
V k
b) ( )
( ) ( )
μ H83.1458.0250004167.015
1
1
0
0
=×−
=−Δ=⇒
−=Δ
k I f V
L
k L
T V I
Dr. Adel Gastli DC-DC Converters 20
c)
d) mH83.5500250002
)4167.01(2
1 =××−=−= R
f k
LC
F
V f I
C
C IT V
μ 200
1020102588.0
8
8
330
0
=××××
=ΔΔ=⇒
Δ=Δ
−
( ) μ F4.0
250001083.516)4167.01(
161
232 =××× −=−= − Lf k C C
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Dr. Adel Gastli DC-DC Converters 21
Switch StressSwitch Stress
Peak voltage stress on the switch:
Peak current stress through the switch:
fL
V I I I I s
aa sw 82
1maxmax
+=Δ+=
s s sw V V V V =−= min1max
V s+-
D
I o
V o
S
I s L
C R
V 1
k=0.5
Dr. Adel Gastli DC-DC Converters 22
2- Discontinuous conduction mode (DCM)
21 τ τ LV
LV V
I aa s =−=Δ
321
1
1 k k
V V
s
a
−=
+=
τ τ τ
T T
k T
k =++== 3213
31 and , τ τ τ
τ τ
)1(1
)1( 33
32 k k k
k L
T V k k L
T V LV I saa −−−=−−==Δ τ
τ1 τ2 τ3
T 0
Δ I i0
t on
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Dr. Adel Gastli DC-DC Converters 23
)1(21
21
21
3
3
21
k I
T T
I
T I I a
−Δ=
−Δ=
+Δ=
τ
τ τ
)1(2 3 k k k LT V
I sa −−=
τ1 τ2 τ3
T 0
Δ I i0 a I
Dr. Adel Gastli DC-DC Converters 24
ExampleExample
A dc-dc converter converts a source of 48V to12V. The converter components are R =10 Ω,L=5mH, and f =40kHz. Plot the output voltage andcurrent waveforms and determine:
1. The mode of operation.2. The amount of current ripple.3. The filter capacitor value if the voltage ripple is
to be less than 1% of the output voltage.
4. The inductor for which the converter would justenter in the discontinuous conduction mode.
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Dr. Adel Gastli DC-DC Converters 25
1- mode of operation
CCM2 2.11012
A;0225.0)1(22
;
⇒
Δ>>===
=−==
I A
V I
k k LT V Δ I
V V
k
a
a
s s
s
a
2- current ripple
A045.0)1( =−=Δ k L
T V I a
3- filter capacitor for V0/V0=1%
kHz f f
V V
cc 079.2)25.01(000,402
01.022
0
0 =⇒−⎥⎦
⎤⎢⎣
⎡==Δ π
Dr. Adel Gastli DC-DC Converters 26
F L f
C c
μ π
17.14
122 ==⇒=
LC f C
π 21
4- Critical filter inductance for DCM
mH k k I T V L DCM a
sC 094.0)1(
2 =−=⇒
(Study also example 5.5 )
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Dr. Adel Gastli DC-DC Converters 27
Features of a buck converter Features of a buck converter
• It requires only onetransistor
• Is simple• Has high efficiency
(greater than 90%)• di/dt of the load current
is limited by inductor
• Input current is normallydiscontinuous and asmoothing input filter isrequired.
• It provides one polarity ofoutput voltage andunidirectional outputcurrent.
• It requires a protectioncircuit in case of possibleshort circuit across thediode path.
Advantages Limitations
Dr. Adel Gastli DC-DC Converters 28
BOOST CONVERTERBOOST CONVERTER• Voltage step-up and current step-down
converter.
1- Continuous conduction mode (CCM)
Typical converter circuit and waveformsTypical converter circuit and waveforms
+-V s D
io
V o
S +
-
i s
Mode 1Mode 2
L
C
V L
io
V s
i s
t on T
ON OFF ON
Δ I
Continuous conduction
(V s-V o )
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Dr. Adel Gastli DC-DC Converters 29
s L V
dt di
L =
)( 0V V dt di
L s L −=
+-V s D
io
V o
S +
-
i s
Mode 1
Mode 2
L
( )( ) 00 =−−+ on son s t T V V t V
Average voltage across inductor is 0
k V V
T t
k s s
on
−==
11
; 0
00 I V I V s s = k V V
I I s
s−== 1
0
0
Dr. Adel Gastli DC-DC Converters 30
k V V
s −=
110
Forward voltage transfer ratio Vo /Vs
can be ideally infinity for k=1, however,the parasitic capacitance across openswitch would bring it down.
NOTE:NOTE:
1 k
Vo/V s
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Dr. Adel Gastli DC-DC Converters 31
s L V
dt di
L =
)( 0V V dt
di L s
L −=
+-V s D
io
V o
S +
-
i s
Mode 1
Mode 2
L
Low Current RippleLow Current Ripple
k fLV
t LV
I son
s L ==Δ
1
T f =
Dr. Adel Gastli DC-DC Converters 32
Low Voltage RippleLow Voltage RippleAssumptions:
voltage ripple ΔVo is asmall percentage of dcvoltage Vo
ripple current throughdiode flows into filtercapacitor and not R .
+-V s D
io
V o
S
i s L
C R
V 1
fC k RV fC k I
C t I
C Q
V onc
00
00
==
=Δ=Δ f
kf V V C =Δ0
0
RC f C
1=Low value of f C/f will provide low
voltage ripple.
V 0 ΔV 0
t on T
Capacitordischargesthrough theload
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Dr. Adel Gastli DC-DC Converters 33
Switch StressSwitch Stress
Peak voltage stress on the switch:
Peak current stress through the switch:
fL
V I I I I s
L sw
22
10max0max +=Δ+=
0max V V sw =
k=1
Dr. Adel Gastli DC-DC Converters 34
2- Discontinuous conduction mode (DCM)
τ1 τ2 τ3
T s0
Δ I i s ( ) 0201 =−+ τ τ V V V s s
3
3
2
210
11
k k k
V V
s −−−=+=τ
τ τ
T T
k T
k =++== 3213
31 and , τ τ τ
τ τ
k LT V
I s=Δ
Average voltage across inductor is 0
( )32
0 1221
k k k LT V
T I I s
−−=Δ= τ
Load current average value
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Dr. Adel Gastli DC-DC Converters 35
3- Condition for continuous inductor current
a L I I
I =Δ=2
Average inductor current
RV I k
fLV I I a
aC
s L ===Δ=
22 Rk V k
fLV s
C
s
)1(2 −=
f Rk k
LC 2)1( −
=
I a Δ I
Limit forContinuousconduction
Dr. Adel Gastli DC-DC Converters 36
4- Condition for continuous capacitorvoltage
20
0V
V Δ=Average capacitor voltage
R I fC
k I V
C 0
00 2
==
fRk C C 2=
V 0 ΔV 0
Limit forContinuousconduction
(Study example 5.6 )
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Dr. Adel Gastli DC-DC Converters 37
BUCKBUCK --BOOST CONVERTERSBOOST CONVERTERS• Voltage step-up and step-down converter.
+-
io
V o
S i s
Li L
RC
v L
i L
i s
i0
V s
-V 0t on T
Δ I
Dr. Adel Gastli DC-DC Converters 38
( )( ) 00 =−−+= onon s L t T V t V V
k k
V V
s −=1
0
k k
I I
s−= 10
Voltage step-up action: k>0.5
Voltage step-down action: k<0.5
1- Continuous conduction mode (CCM)
v L
i L
i s
i0
V s
-V 0t on T
Δ I
k fLV t
LV I s
on s
L ==Δ+-
io
V o
S i s
Li L RC
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Dr. Adel Gastli DC-DC Converters 39
Switch StressSwitch Stress
Peak voltage stress on the switch:
Peak current stress through the switch:
fL
V
I I I I s
L sw 22
10max0max +=Δ+=
0max V V V s sw +=
Dr. Adel Gastli DC-DC Converters 40
3- Condition for continuous inductor current
2 I
I I a L
Δ==Average inductor current
R
V I
fL
kV I I a
aC
s L ===Δ=
22 Rk
kV k
fL
V s
C
s
)1(2 −=
f Rk
LC 2)1( −=
I a Δ I
Limit for
Continuousconduction
fLk V s
2= (Eq. 5.85)
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Dr. Adel Gastli DC-DC Converters 41
4- Condition for continuous capacitorvoltage
20
0V
V Δ=Average capacitor voltage
R I fC
k I V a
C
a ==20
fRk
C C 2=
V 0 ΔV 0
Limit forContinuousconduction
(Study example 5.7 )
fC k I V ac
22=Δ=
(Eq. 5.87)
Dr. Adel Gastli DC-DC Converters 42
Notice that only the buckconverter shows a linearrelationship between the
control (duty ratio) andoutput voltage.
The buck-boost canreduce or increase thevoltage ratio with unit
gain for a duty ratio of50%.
Comparison of Voltage ratioComparison of Voltage ratio3
2
1
00 10.2 0.4 0.6 0.8
Duty Ratio
V o
l t a g e
R a
t i o
Boost
Buck
Buck-Boost
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Dr. Adel Gastli DC-DC Converters 43
ČČ UK CONVERTERSUK CONVERTERS• Voltage step-up and step-down converter. Dual
of buck-boost converter.
+-
io
V oS
i s
L1 R
V s
L2C C o
D
io
V oS
i s
I s I o
+ -
V C
DV s
Dr. Adel Gastli DC-DC Converters 44
io
V oS
i s
I s I o
+ -
V C
DV s
Mode 1
io
V oS
i s
I s I o
+ -
V C
DV s
Mode 2
0V V V
sC +=
( ) 00 =−− onon s t T V t V
k k
V V
s −=
10
01 = LV V L1
V L2
i s ,io
Δ I
V s
V C -V o=V sV s-V C =-V o
-V o
Mode 1 Mode 2
Analysis is similar to that of abuck-boost converter.
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Dr. Adel Gastli DC-DC Converters 45
TWOTWO --QUADRANT CONVERTERSQUADRANT CONVERTERS
Enables the return of energy back to thesource when the load does not need it.(i.e. dynamic breaking of a dc motor)
+-
io
V o
S 1
i s L
+ _ RC
V s S 2
Two-quadrant buck converter topology
ExampleExample : Buck Topology: Buck Topology
Dr. Adel Gastli DC-DC Converters 46
+-
io
V o
S 1i s
L
+ _
V s S 2
D1
D2
Mode -1
+-
io
V o
S 1i s
L
+ _
V s S 2
D1
D2
Mode +1
+-
io
V o
S 1
i s L
+ _
V s S 2
D1
D2
Mode -2
+-
io
V o
S 1
i s L
+ _
V s S 2
D1
D2
Mode +2
CCM onlyCCM only
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Dr. Adel Gastli DC-DC Converters 47
+-
io
V o
S 1
i s L
+ _ R
C V s S 2
v1
S 1 and S 2 can not be bothON at the same time.
Average value of output current can be positive ornegative depending on the switching sequence of
S 1 and S 2.
τ T0
0
0
is
io
v1
I1
I2
I0
D1S1 D2
S2
Dr. Adel Gastli DC-DC Converters 48
FULLFULL --BRIDGE CONVERTERBRIDGE CONVERTERIt is known as the four quadrant dc-dc converter.
Output voltage and current can have positive ornegative polarities and power flows in both directions.
Always operates in the CCM.
Full bridge converter topology
ExampleExample : Buck Topology: Buck Topology
+- io V 0
i s
+ -V sS 4
S 1
S 3
S 2 L
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Dr. Adel Gastli DC-DC Converters 49
Bipolar switchingBipolar switching
• Switches are turned ON-OFF exclusively inpairs.• S 1-S 3 forms one pair and S 2-S 4 forms another
pair.• When S 1-S 3 is ON S 2-S 4 is OFF and vice versa.
• This switching sequence is also referred asPWM switching, and produces a bipolar voltagewaveform as shall be seen shortly.
+-
io V 0
i s
+ -V s
S 4
S 1
S 3
S 2 L
D1
D4
D2
D3
Dr. Adel Gastli DC-DC Converters 50
Mode 1 Mode 2 Mode 3 Mode 4
ton0 T s
iL
vL 0V V s −
0V V s −−
S 1, S 3
S 2, S 4
t
S 1, S 3D1, D 3
ON
D2, D 4
I0
+-
io V 0
i s
+ -V s
S 4
S 1
S 3
S 2 L
D1
D4
D2
D3
Mode 4
+-
io V 0
i s
+ -V s
S 4
S 1
S 3
S 2 L D1
D4
D2
D3
Mode 1
+-
io V 0
i s
+ -V s
S 4
S 1
S 3
S 2 L
D1
D4
D2
D3
Mode 2
+-
io V 0
i s
+ -V s
S 4
S 1
S 3
S 2 L
D1
D4
D2
D3
Mode 3
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Dr. Adel Gastli DC-DC Converters 51
( ) ( )( ) ( )120 000 −=⇒=−−−+− k V V t T V V t V V son son s
The average inductor voltage is zero
120 −= k V V
s [ ] ]10[for110 →=→−= k V V
s
T t
k on= (t on is ON time of S 1)
)1(200 k k
fLV t
LV V I s
on s −=−=Δ
The output current peak-to-peak ripple is
Does not dependon load resistance
Ripple frequency is f=1/T.
SUMMARYSUMMARYBuck, boost and buck-boost combinationconverters have been analyzed in continuous anddiscontinuous current conduction modes.
Voltage step-down converter is also a currentstep-up converter and conversely, Voltage step-upconverter is also a current step-down converter.
Single-switch, two-switch and four-switchtopologies have been analyzed.
Analysis consisted of deriving controlcharacteristics and component stress calculations.