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Power electronics Slobodan Cuk came to Caltech in 1974 and obtained his PhD degree in Power Electronics in 1976. From 1977 until December, 1999 he was at the California Institute of Technology where he conducted research and taught courses in Power Electronics and Fundamentals of Energy Processing. During his 23 years at Caltech, more than 35 students obtained Ph.D. degree in Power Electronics under his guidance. From 2000 until present, Dr. Cuk continued his research contributions through TESLAco, the company he founded. Dr. Cuk is Fellow of IEEE and is the inventor of numerous switching converter circuits such as the Cuk converter, the TESLAconverter and many others.
Dr. Cuk is also the originator of the State-Space Averaging Method and more recently new switching methods: Hybrid Switching and Storageless Switching methods, which resulted in a number of ultra efficient, very compact and low cost switching converters for solar inverters, AC-DC battery chargers, data center power supplies and many other Power Electronics applications.
USC Power ResearchWorkshop:
Power Electronics
Dr. Slobodan Ćuk
November 18, 2011
1
2
PCSC ’70 and PCSC’71
Power Conditioning Specialists
PPESC’72
Power Processing and Electronics
PESC’73
Power Electronics Specialists
PCSC ’70 and PCSC’71
Power Conditioning Specialists
PPESC’72
Power Processing and Electronics
PESC’73
Power Electronics Specialists
What is in the name:What is in the name:
3
Sept. 2010: celebration of 100 years of Electrical
Engineering at Caltech
1910-1956: High Voltage Laboratory of Prof.
Sorensen
1970- 1999 Power Electronics Laboratory (Profs.
Middlebrook and Cuk)
Sept. 2010: celebration of 100 years of Electrical
Engineering at Caltech
1910-1956: High Voltage Laboratory of Prof.
Sorensen
1970- 1999 Power Electronics Laboratory (Profs.
Middlebrook and Cuk)
Electrical Engineering at Caltech Electrical Engineering at Caltech
4
Started in 1970 by Prof. Middlebrook
as second in nation after Duke 1968Both academic courses and research
program on a PhD level
PCSC’71 at Jet Propulsion Laboratory
PESC’73 at Caltech
Started in 1970 by Prof. Middlebrook
as second in nation after Duke 1968Both academic courses and research
program on a PhD level
PCSC’71 at Jet Propulsion Laboratory
PESC’73 at Caltech
Power Electronics at Caltech :Power Electronics at Caltech :
5
From 1970 – 1999
36 PhD students
1998: 11 PhD in Electrical Engineering out of
which 5 in Power Electronics
Prof. Middlebrook retired in 1998
Prof. Cuk semi-retired in 1999
From 1970 – 1999
36 PhD students
1998: 11 PhD in Electrical Engineering out of
which 5 in Power Electronics
Prof. Middlebrook retired in 1998
Prof. Cuk semi-retired in 1999
Power Electronics Group ( PEG) Power Electronics Group ( PEG)
6
NASA ( subcontract from TRW)
NOSC ( Naval Ocean System Center
(San Diego )
ONR- Office of Naval Research
IBM
Other companies
NASA ( subcontract from TRW)
NOSC ( Naval Ocean System Center
(San Diego )
ONR- Office of Naval Research
IBM
Other companies
First Sponsors 1974 and on First Sponsors 1974 and on
Boost Converter
CVg
+
-
Vg/(1-D)
R
CR
S
L
S
tTON T
OFF
TS
1973: Prof. Middlebrook sent me an
article with boost converter
7
8
Power Electronics-Emerging from Limbo1973 keynote by W.E. Newell, Westinghouse
Power Electronics-Emerging from Limbo1973 keynote by W.E. Newell, Westinghouse
9
State-space AveragingState-space Averaging
35 Years Anniversary 35 Years Anniversary
*Slobodan Ćuk; “MODELING, ANALYSIS, AND
DESIGN OF SWITCHING CONVERTERS”
Ph.D. Thesis, Caltech, November 1976
*R.D.Middlebrook and Slobodan Ćuk; “A general
Unified Approach to Modeling Switching-
Converter Power Stages, IEEE PESC, 1976
10
State-space AveragingState-space Averaging
35 Years Anniversary 35 Years Anniversary
*Slobodan Ćuk; “MODELING, ANALYSIS, AND
DESIGN OF SWITCHING CONVERTERS”
Ph.D. Thesis, Caltech, November 1976
*R.D.Middlebrook and Slobodan Ćuk; “A general
Unified Approach to Modeling Switching-
Converter Power Stages, IEEE PESC, 1976
11
1. Flux Balance on All Inductors
2. Charge Balance on All Capacitors
The State-space Averaging Uses Different Criteria
t
iC(t)
0
DTS
−
+
(1-D)TS
t
vL1(t)
0
DTS
(1-D)TS
−
+
−
+CR
V/Vg=D/(1-D)
RVg
C−+
L2
S
L1
1-DD
Ćuk Converter*
*US Patents: 4,184,197; 4,257,087; 4,274,133*US Patents: 4,184,197; 4,257,087; 4,274,133
t
vL2(t)
0
DTS
(1-D)TS
−
+
L1: Flux Balance L2: Flux Balance
C: Charge Balance
12
Flux Balance on L1
vL1 = DVg + (1-D)(Vg-VC)
Flux Balance on L1
vL1 = DVg + (1-D)(Vg-VC)
Flux Balance on L2
vL2 = D(VC-V) + (1-D)(-V)
Flux Balance on L2
vL2 = D(VC-V) + (1-D)(-V)
Charge Balance on Cr
iC = D(-I2) + (1-D)(I1)
Charge Balance on Cr
iC = D(-I2) + (1-D)(I1)t
iC(t)
0
DTS
−
+
(1-D)TS
I1
I2
t
vL1(t)
0
DTS
+
−
(1-D)TS
Vg
Vg-V
C
t
vL2(t)
0
DTS
+
−
(1-D)TS
V
VC-V
DC Solution: VL1 = 0; IC = 0; VL2 = 0 DC Solution: VL1 = 0; IC = 0; VL2 = 0
13
State-space Formulation of Flux and Charge Balances
vL1 = Vg
iC = -I2vL2 = VC-V
D ××××
State-space Averaging DC Model:
1. Multiply equations for ON-time by D2. Multiply equations for OFF-time by (1-D)3. Add together and set VL1=0, IC=0, VL2=0
1. Multiply equations for ON-time by D2. Multiply equations for OFF-time by (1-D)3. Add together and set VL1=0, IC=0, VL2=0
−
+C RV
g
C−+
L2
L1
−+ +−
−
+C RV
g
C−+
L2
L1
−+ +−
vL1 = Vg-VC
iC = I1vL2 = -V
ON-time Interval: OFF-time Interval:
{ (1-D) ××××{
Dynamic (Small Signal AC) Response
v V v x X x
d D d d D d
g g g= + = +
= + = −
$ ; $
$ ; ' ' $
$& $ $ $x Ax bvg
A A X b b Vgd= + + −
+ −
1 2 1 2
Steady-State
AX bVg++++ ==== 0
A DA D A==== ++++1 2'
b Db D b==== ++++1 2'
14
15
S C A M P
SwitchingConverterAnalysis andMeasurement
Program
SwitchingConverterAnalysis andMeasurement
Program
16
Coupled-Inductor Isolated Ćuk Converter
17
Manu Driven Graphics on First IBM-PC
From Paper at APEC Conference
18
Frequency Response – Loop Gain
19
Power Electronics Group exhibit at 1983 conference in San Diego
Power Electronics Group exhibit at 1983 conference in San Diego
20
Can your SCAMP program do this:
Enter desired frequency plot then
Draw the converter topology?
Can your SCAMP program do this:
Enter desired frequency plot then
Draw the converter topology?
Question asked:Question asked:
21
Can you enter desired DC voltage
gain such as V/Vg = D x D and:
DRAW ALL SUCH CONVERTERS:
Both known converters and
NEW (!!!) converter topologies?
Can you enter desired DC voltage
gain such as V/Vg = D x D and:
DRAW ALL SUCH CONVERTERS:
Both known converters and
NEW (!!!) converter topologies?
Related question:Related question:
CONFIDENTIALCONFIDENTIAL
22
S1
S2
S'1
S'2
L2
L1
C1
C2 RV
g
Computer Generated Converters*Computer Generated Converters*
*Dragan Maksimovic, “Synthesis of PWM and Quasi-resonant DC-to-DC Power Converters”, Ph.D. Thesis, January 12, 1989,
Caltech, Pasadena
*Dragan Maksimovic, “Synthesis of PWM and Quasi-resonant DC-to-DC Power Converters”, Ph.D. Thesis, January 12, 1989,
Caltech, Pasadena
If Solution to:
AX + bVg = 0exists, than:
Valid DC-DC Converters:
2 Inductors
1 Capacitor
2 States: ON&OFF
1 million possibilities} Only 30 Working
(Ćuk converter was there too !)
Only 30 Working(Ćuk converter was there too !)
AN EXAMPLE: (243, 146.2)
0
R
2
C1
C2
L1
1
Vg
L2
3
R
2
0
1
3L2
C2
L1
C1V
g
V C C L Lg 1 2 1 2
V C C L Lg 1 2 1 2
0
1
2
3
1
1
0
0
1
0
1
0
0
1
0
1
1
0
0
1
0
1
1
0
1 1
1
−−−− −−−−
−−−−
−−−−
−−−−
++++
↑↑↑↑ ↑↑↑↑
T E
H1 2444 3444
0
1
2
3
1
1
0
0
1
0
1
0
1
0
0
1
1
0
0
1
0
0
1
1
2 2
2
−−−− −−−− −−−− −−−−
−−−−
↑↑↑↑ ↑↑↑↑
T E
H1 2444 3444
23
Enumeration via Incidence Matrices
NEW CONVERTER
TL
2
C1
L1
C2
D2
D1
D3
M (D) = D2
( 243, 146.2 )
24
One Transistor, Three Diodes
Dr. Ćuk’s Power Technics 1988 cover Dr. Ćuk’s Power Technics 1988 cover
1988
ηηηη=83%
fs=500kHz
Ploss=20.5W
ββββ=20.5%
25
26
Power Electronics 117 class of 1998:TESLA temple prank
Power Electronics 117 class of 1998:TESLA temple prank
27
TESLAconverter
NCT converter
Hybrid Switching Method
Storageless Switching Method
Bridgeless PFC converters
Single-stage converters
Solar inverters
TESLAconverter
NCT converter
Hybrid Switching Method
Storageless Switching Method
Bridgeless PFC converters
Single-stage converters
Solar inverters
TESLAco years: 1999- presentTESLAco years: 1999- present
28
Isolated Full-bridge Buck Converter
Total of 8 Switches
C+
−R
S1
S2
S3
S4
D1 D
2
D3
D4
1:1
Vg
L
T
DVg
Two magnetic components
Square-wave Switching:
No 3 switches allowedEight needed for isolationNo capacitors
Hybrid-Switching Method:
3 switches onlyResonant capacitorResonant inductor
29
What about converters with 3 switches
30
CRS1
S2
2. A Resonant Capacitor
3. A Resonant InductorLr
1. Three Switches
Cr
31
“Birth ” of Hybrid-Switching Methodand Related Converter Topologies
“Birth ” of Hybrid-Switching Methodand Related Converter Topologies
#1#2 #4
#5#6
#7
#8#9#3
AC-DC
Converter Comparison
32
33
Conventional Three Power Processing Stage ApproachConventional Three Power Processing Stage Approach
C
LB
+
−R
S1
S2
S3
S4
D1 D
2
D3 D
4
n:1
vac
DB1
DB2
DB3
DB4
Cf
Lf
SB
+
−CB
DB
L48V400V
Polarity Inverting
DC-DC Converter
34
Boost Converter
CVg
+
-
Vg/(1-D)
R
CR
S
L
S
tTON T
OFF
TS
Problem
How to make a polarity inverting boost
converter 35
Polarity Inverting 3 Switch Boost Converter*
Vr=Vg/(1-D)
CSVg
L
-
+
LrI
L IC V
R
+ -Vr
I
CR2
CR1
Cr
Vg
L IL I
C
+ -Vr
CR2
Cr
S
S C-
+
LrI
C
R
+ -Vr
ICR1
Resonant
Discharge
Cr
*US Patent No. 7,778,046
OFF-time Interval (1-D)TS
V=Vg/(1-D)
V=Vr
36
Boost Converter
37
Positive and Negative Half-cycle of Input VoltagePositive and Negative Half-cycle of Input Voltage
Source Polarity Controls Conduction Interval of Two Diodes:
Full-Bridge Eliminated
Source Polarity Controls Conduction Interval of Two Diodes:
Full-Bridge Eliminated
S CVg
L
+
-
Lr
CR1
IL I
rCR
2 V
R
+ -VCr
IA
G
+
-
+
-
iS
D D
D'
Cr
S CVg
L
+
-
Lr
CR1
IL I
rCR
2 V
R
- +VCr
IA
G
-
+
-
+
iS
D D'
D
Cr
V=Vg/(1-D)
VCr=0
VCr=V
True Bridgeless
PFC Converter
38
39
True Bridgeless PFC Converter*True Bridgeless PFC Converter*
Cr
S C
L
+
-
Lr
CR1
iAC I
rCR
2 V
R
- +VCr
I
-
+
iS
vAC D
Input Voltage110V
THD=1.7%PF=0.999
*US and foreign patents pending*US and foreign patents pending
40
One Implementation of the Controlling SwitchOne Implementation of the Controlling Switch
Cr
C
L
+
-CR
1
IL I
rCR
2 V
R
+ -VCr
I
vAC
A
DS1
S2
Lr
ION
VOFF
I
III
DS1
S2
41
t
S
tTON T
OFF
vi, i
i
ii
vi
TS
Index "i" =1, 2, 3
Input Current Modulation for Each Phase at High Switching Frequency
Input Current Modulation for Each Phase at High Switching Frequency
42
Voltage and Current Waveforms in Ćuk-rectifierwith Integrated Magnetics Implemented
Voltage and Current Waveforms in Ćuk-rectifierwith Integrated Magnetics Implemented
Input Voltage110V
Input Voltage220V
THD=1.7%PF=0.999
THD=2.0%PF=0.991
43
Efficiency and Power Loss of Ćuk-rectifierEfficiency and Power Loss of Ćuk-rectifier
90%
91%
92%
93%
94%
95%
96%
97%
98%
99%
80 100 120 140 160 180 200 220 240
Input Voltage [V]
Effic
ienc
y
0.0
2.0
4.0
6.0
8.0
10.0
12.0
80 100 120 140 160 180 200 220 240
Input Voltage [V]
Pow
er L
oss
Demo #1:
400W Bridgeless
PFC converter 44
45
46
True Isolated
Bridgeless
PFC Converter 47
48
CR2
+
−CR
1S C
V
R
IM
Cr1
L
NP
NS
PFC IC Controler
iAC
Lr
Cr2
vAC
vAC, i
AC
iAC
vAC
t
S
tTON T
OFF
TS
True Bridgeless PFC Converter with Isolation*True Bridgeless PFC Converter with Isolation*
*US and foreign patents pending*US and foreign patents pending
49
H
BS
+BS
-BS
2BS
True AC TransformerTrue AC Transformer
No Air-gapNo Energy StorageAutomatic ResetScalable to High Power
50
ComparisonComparison
Power Processing Single-stage Three-stage
Type of Converter Isolated Bridgeless PFC Bridge-Boost PFC-Full-
bridge
Switching Method HYBRID Square-wave
Number of switches 3 14
Switch-voltage Stress Low High
Lossless-switching YES NO
Control Simple Complex
Magnetics pieces 1 4
Power Losses 3% 10%
Efficiency >97% 88% to 90%
Size Small Big
Weight Light Heavy
Cost Low High
Three-PhaseAC-DC
Converter Comparison
51
52
v0
+VH
L1
i0
Q1 Q
2Q
3
Q4
Q5 Q
6
C
L3
L2
v240
Present Approach: Two StagesPresent Approach: Two Stages
Three-phase properties prematurely
lost after rectification and PFC control
First Stage: Rectification and PFC
Efficiency = 98%
First Stage: Rectification and PFC
Efficiency = 98%
53
C C+
−R
n:1
L V+VH
S1 S
2
S3 S
4
D1 D
2
D3 D
4
Second Stage: Isolated DC-to-DC converter Second Stage: Isolated DC-to-DC converter
Second Stage: DC Isolation
Efficiency = 95%
Second Stage: DC Isolation
Efficiency = 95%
Power processed sequentially in Two stages so
Low Total Efficiency of 92%
New Single-stage
Three-phase Rectifier
54
55
56
57
v1
Isolated Bridgeless PFC
Phase 1
+V
v2
v3
R
i01 i
0
i02
i03
i1
i2
i3
nCIsolated Bridgeless PFC
Phase 2
Isolated Bridgeless PFC
Phase 3
New Direct Three-Phase to DC Conversion with PFC and Isolation in a Single Stage
New Direct Three-Phase to DC Conversion with PFC and Isolation in a Single Stage
Power processed in parallel and not in series
Each Phase Efficiency 98%; TOTAL Efficiency 98%Each Phase Efficiency 98%; TOTAL Efficiency 98%
98%
98%
98%
58
CR2
+
−CR
1S C
V
R
Cr1
L
NP
NS
Islolated
Bridgeless PFC IC
ii
vi
Lr
Cr2
AC-DC Converter for Each Phase with PFC and Isolation*AC-DC Converter for Each Phase with PFC and Isolation*
Three Switches OnlyThree Switches Only
*US Patent No. 7,778,046*US Patent No. 7,778,046
59
v1 v
2
v3
R
i1
i2
i3
nBridgeless
3-phase Isolated
PFC Converter
C
3-phase Isolated
Bridgeless PFC IC
Three-Phase Ćuk-rectifier with PFC IC Control
Three-Phase Ćuk-rectifier with PFC IC Control
60
0
0.25
0.5
0.75
1
1.25
1.5
1.75
0 60 120 180 240 300 360
po1, p
o2, p
o3, P
P
po3
po1
po2
Sum of Instantaneous Output Powers of Three Phases is Constant
Sum of Instantaneous Output Powers of Three Phases is Constant
61
0
0.25
0.5
0.75
1
1.25
1.5
1.75
0 60 120 180 240 300 360
io1,io2,io3,I
I
io3
io1
io2
Sum of Instantaneous Output Currents of Each Phase is Constant
Sum of Instantaneous Output Currents of Each Phase is Constant
62
t0
v(t)
V
t0
i01+ i
02+ i
03I
i0(t)
V = constant
P = constantI = constant
Constant Output Power and Constant Output Voltage Lead to Constant Output Current
Constant Output Power and Constant Output Voltage Lead to Constant Output Current
63
“Birth ” of Storageless Switching Methodand Related Converter Topologies
“Birth ” of Storageless Switching Methodand Related Converter Topologies
#1#2 #4
#5#6
#7
#8#9#3
Demo #2:
200W DC-DC converter
48V to 24V
64
Power Stage of 200W Storageless Converter Power Stage of 200W Storageless Converter
CONFIDENTIALCONFIDENTIAL
65
Bi-directional Specifications
Switching Frequency: 50kHz
Input Voltage: 48V
Output Voltage: 24V
Output Current: 4A
Power: 200W
Volume : 0.2in3
Power Density: 1kW/in3
No Heat SinkNo Heat SinkNo Heat SinkNo Heat Sink
No Forced Air CoolingNo Forced Air CoolingNo Forced Air CoolingNo Forced Air Cooling
CONFIDENTIALCONFIDENTIAL
66
67
CONFIDENTIALCONFIDENTIAL
200W, 48V/24V Storageless Ćuk-buck Converter200W, 48V/24V Storageless Ćuk-buck Converter
Efficiency of 200W Storageless Converter Efficiency of 200W Storageless Converter
Efficiency vs Output Power
97.0%
97.5%
98.0%
98.5%
99.0%
99.5%
100.0%
0 25 50 75 100 125 150 175 200
Output Power (W)
Efficiency
CONFIDENTIALCONFIDENTIAL
68
69
Power Stage of 750W, 48V Prototype*Power Stage of 750W, 48V Prototype*
Efficiency over 99%Efficiency over 99%
*US and foreign patents pending*US and foreign patents pending
Storageless Buck ConverterStorageless Buck Converter
70
Efficiency of 750W, 100V to 48V ConverterEfficiency of 750W, 100V to 48V Converter
98.0%
98.5%
99.0%
99.5%
100.0%
2 3 4 5 6 7 8 9 10 11 12 13 14 15
Iout (A)
Eff
icie
nc
y
71
Isolated Storageless Converter*Isolated Storageless Converter*
*US and foreign patents pending*US and foreign patents pending
72
360V to 24V Efficiency
75.00%
80.00%
85.00%
90.00%
95.00%
100.00%
0.00 50.00 100.00 150.00 200.00 250.00 300.00 350.00
Output Power (W)
Eff
360V to 24V Efficiency
Efficiency of Isolated Storageless Converter Efficiency of Isolated Storageless Converter
98.2% efficiency
73
Green Dream Power Technology™Green Dream Power Technology™
v1 v
2
v3
R
i1
i2
i3
n 3-phase Isolated
Bridgeless PFC
C
3-phase Isolated
Bridgeless PFC IC
3 switch-
buck
non-isolated
3 switch
POL
48V 12V 1V
Efficiency 98% 99% 97%
Switchingmethod Hybrid Storageless POL
74
Applications SummaryApplications Summary
- Computer servers
Battery chargers for electric cars and bycycles
- Desktop computers
- AC Adapters, projectors, etc.
-Solar photovoltaic conversion
-LED lighting
VRM (12V to 1V regulators)
75
Applications SummaryApplications Summary
-Wide range of power
-From cell hones and under a one 1 Watt to 100kW for electric drive for motors, etc.
76
July 10, 2010 : Memorial for Professor Middlebrook July 10, 2010 : Memorial for Professor Middlebrook
77
July 10, 2010 : Power Electronics Group Members and their relatives
July 10, 2010 : Power Electronics Group Members and their relatives
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