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課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
1/38
2009年4月15日
鄒 應 嶼 教 授
國立交通大學 電機與控制工程研究所
DC-DC Converters: Modeling Techniques
LAB808NCTU
Lab808: 電力電子系統與晶片實驗室Power Electronic Systems & Chips, NCTU, TAIWAN
台灣新竹•交通大學•電機與控制工程研究所
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電力電子系統晶片、數位電源、DSP控制、馬達與伺服控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
2/38
DC-DC Converters: Modeling Techniques
1. Modeling of Switching Converters2. State-Space Averaging Technique3. PWM Switch Modeling Technique4. CIECM Modeling Techniques5. Modeling of Current-Mode DC-DC Converters6. Difficulties with Modeling and Control of SPS
2
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
3/38
Modeling of Switching Converters
Power Electronic Systems & Chips Lab., NCTU, Taiwan
電力電子系統與晶片實驗室Power Electronic Systems & Chips Lab.交通大學 • 電機與控制工程研究所
4/38
Modeling of Switching Converters
Why Modeling ? Classification of Modeling Techniques Modeling of Switching Power Converters State-Space Averaging Technique Transfer Functions Small-Signal Equivalent Circuit Model
3
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
5/38
Objective of Modeling
Objective of Modeling
Analysis
Simulation
DesignEfficiency
Output Impedance
Static Characteristics
6/38
Difficulties with Modeling of SPS
Nonsmooth Systems (time and state discontinuity)Nonlinearity due to operating point Concepts of existence, uniqueness, stability not clearly defined for systems with discontinuous right half-plan zero Inherent Nonlinear Dynamic Behavior! Concept of chaotic dynamics relatively new to power electronicsMagneticsNoises and EMI Thermal and Temperature Distribution
4
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
7/38
Working Profile of a Switching Converter
Power-on Power-off
ov
oi
Wat
ts
% C
PU
time
Dell power edge 2400 (web/SQL server)
Static Characteristics of a DC-DC Converter
Buck
Boost
Buck-Boost L C
D
vovi
L
C
D
vovi
vi vo
L
CD
5
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
9/38
Operating Region Operating Point Operating Mode?
IN
OUT
VV
)(max,LB
o
II
0 0.5 1.0 1.5 2.0
0
0.25
0.50
0.75
1.0
DCM
D = 1.0
0.1
0.3
0.5
0.7
0.9
CCMCRM
VIN = constant
(min)
(max)
IN
OUT
VV
(max)
(min)
IN
OUT
VV
(max)OUTI(min)OUTI
10/38
Operating Point Steady-State Trajectory
DCM
D = 1.0
0.1
0.3
0.5
0.7
0.9
CCM
80% 100%60%40%20% 110%90%50%
500 R o
testI
testI2A
5msec 100msec
If the components are not ideal, its parasitic parameters will change its static curves. The illustrated example is obtained with the following parameters: RDS(ON) = 50 mMOSFET reverse diode voltage drop = 0.7VDiode voltage drop = 0.7V Inductor ESR = 25mCapacitor ESR = 2m
Vo/Vi = 1.0
0.25
0.5
0.75
0
1.0
6
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
11/38
Operating Point Small-Signal Perturbations
DCM
D = 1.0
0.1
0.3
0.5
0.7
0.9
CCM
80% 100%60%40%20% 110%90%
Step Load Change1A
0AOutput Voltage
Inductor Current
B
50%
電流負載的步階切換!Vo/Vi = 1.0
0.25
0.5
0.75
0
1.0
12/38
Operating Point Frequency Response
oR
DCM
D = 1.0
0.1
0.3
0.5
0.7
0.9
CCM
80% 100%60%40%20% 110%90%50%
YOP XOP
QX = 0.707
QY = 7.070
QB = 3.535
QA = 1.414
QX = 0.707
QY = 7.07
QB = 3.535 QA = 1.414
7
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
13/38
Operating Region State-Variable Plane
DCM
D = 1.0
0.1
0.3
0.5
0.7
0.9
CCM
80% 100%60%40% 110%90%10% 20%
從工作點
到工作點
的軌跡均在連續導
通工作區內,但是從工作點
到工作點
則有部分會進入不連續導通工作區。
Vo/Vi = 1.0
0.25
0.5
0.75
0
1.0
14/38
Modeling of Switching Power Converters
Modeling of Voltage-Mode DC-DC Converters- Power Stage Modeling State-space average model (Middlebrook and C'uk 1977) Discrete time-domain model (Lee 1979) Equivalent circuit model (Chetty 1981) Unified topological model (Pietkiewicz and Tollik, 1987) PWM switch model (Voperian 1988) Injected-absorbed-current model (Kisovski 1991)
- Error Processor Modeling (Chetty 1982)- Pulsewidth Modulator Modeling Describing function model (Lee 1983) Equivalent circuit model (Bello 1981)
- Larger Signal Modeling (Vicua 1992)
Modeling of Current-Mode DC-DC Converters- Equivalent Circuit Model (Chetty 1981)- y-parameter Model (Middlebrook 1989)
8
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
15/38
Modeling Techniques
State Space Averaging Method[1] R. D. Middlebrook and S. Cuk, “A general unified approach to modeling switching-converter
stages,” IEEE PESC Conf. Rec., pp. 18-34, 1976. [Pioneer Paper][2] S. Cuk and R. D. Middlebrook, “A general unified approach to modeling switching DC-to-DC
converters in discontinuous conduction mode,” IEEE PESC Conf. Rec., pp. 36-57, 1977.
Modeling of Switching Converters in DCM Operation[1] D. Maksimovic and S. Cuk, “A unified analysis of PWM converters in discontinuous modes,” IEEE
Trans. Power Electron., vol. 6, pp. 476–490, May 1991. [2] J. Sun, D. M. Mitchell, M. F. Greuel, P. T. Krein, and R. M. Bass, “Averaged modeling of PWM
converters operating in discontinuous conduction mode,” IEEE Trans. Power Electron., vol. 16, pp. 482-492, July 2001.
R. D. Middlebrook and S. Cuk, “A general unified approach to modeling switching-converter stages,”IEEE PESC Conf. Rec., pp. 18-34, 1976.
16/38
Modeling Techniques ..
PWM Switch Method[1] V. Vorperian, “Simplified Analysis of PWM Converters Using Model of PWM Switch Part I:
Continuous Conduction Mode,” IEEE Trans. on Aero. and Elec. Sys., vol. 26, no. 3, pp. 490-496, May 1990.
[2] V. Vorperian, “Simplified Analysis of PWM Converters Using Model of PWM Switch Part II: Discontinuous Conduction Mode,” IEEE Trans. on Aero. and Electron. Sys., vol. 26, no. 3, pp. 497-505, May 1990.
Fast Analytical Techniques for Electrical and Electronic Circuits,V. Vorperian, Cambridge Press, 2004. Vatche Vorperian, (1984) Analysis of resonant converters. Dissertation (Ph.D.), California Institute of Technology, Advised by S. Cuk.
1. Introduction2. Transfer functions3. The extra element theorem4. The N-extra element theorem5. Electronic negative feedback6. High-frequency and microwave circuits7. Passive filters8. PWM switching dc-to-dc converters
9
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
17/38
Modeling Techniques ..
Discrete Time-Domain Method[1] F. C. Lee, R. P. Iwens, Y. Yu, and J. E. Triner, “Generalized computer-aided discrete time-domain
modeling and analysis of DC-DC converters,” IEEE Trans. IECI, vol. 26, pp. 58-69, May 1979.
Equivalent Circuit Method[1] P.R.K. Chetty, Switch-Mode Power Supply Design, TAB BOOKS, Inc., 1986.
Modeling of Current-Programmed Converter[1] R. D. Middlebrook, “Modeling current programmed buck and boost converters,” IEEE Trans. on
Power Electronics, vol. 4, pp. 36-52, January 1989. [2] Teuvo Suntio, “Analysis and modeling of peak-current-mode-controlled buck converter in DICM,”
IEEE Trans. on Ind. Electron., vol. 48, no. 1, pp. 127-135, Feb. 2001.
Unified Topological Method[1] Pietkiewicz, A. and D. Tollik, “Unified topological modeling method of switching dc-dc converters
in duty-ratio programmed mode,” IEEE Trans. on Power Electron., vol. 2, no. 3, pp. 218-226, July 1987.
Injected-Absorbed-Current Method[1] Kislovski, A. S., R. Redl, and N. O. Sokal, Dynamic Analysis of Switching-Mode DC/DC
Converters, Van Nostrand Reinhold, 1991.
18/38
Modeling Techniques ..
Small-Signal z-Domain Analysis[1] D. M.Van de Sype, K. De Gusseme, F.M.L.L. DeBelie, A. P. Van den Bossche, and J. A. Melkebeek,
“Small-signal z -domain analysis of digitally controlled converters,” IEEE Transactions on Power Electronics, vol. 21, no. 2, pp. 470- 478, March 2006.
[2] D. M.Van de Sype, K. De Gusseme, A. P. Van den Bossche, and J. A. Melkebeek, “Experimental verification of the z-domain model for digitally controlled converters,” IEEE Power Electronics Specialists Conference, vol., no., pp.2164-2170, 16-16 June 2005.
[3] Yu-Cheng Lin; Dan Chen; Yen-Tang Wang; Wei-Hsu Chang; “A novel loop gain correction method for digitally controlled DC-DC power converters,” IEEE Energy Conversion Congress and Exposition(ECCE) pp.3530-3535, 20-24 Sept. 2009.
Digital Current-Mode Control [1]Y. S. Jung, “Small-signal model-based design of digital current-mode control,” IEE Proceedings -
Electric Power Applications, vol.152, no.4, pp. 871- 877, 8 July 2005. [2] S. Chattopadhyay and S. Das, “A digital current-mode control technique for DC–DC converters,”
IEEE Transactions on Power Electronics, vol.21, no.6, pp.1718-1726, Nov. 2006.
10
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
Control of DC-DC Converters
voltagereference
Pulse-widthmodulator
gate driver
cv)(tcompensator
sGc
refv
+–
tδ
tsTsdT
tv
t
H. P. Forghani-Zadeh and G.A. Rincon-Mora, "Current-sensing techniques for DC-DC converters," The IEEE 45th Midwest Symposium on Circuits and Systems (MWSCAS), Aug. 2002.
J. T. Mossoba and P. T. Krein, "Design and control of sensorless current mode DC-DC converters," IEEE APEC Conf. Rec., 2003.
Timothy Hegarty , Voltage-mode control and compensation - Intricacies for buck regulators, EDN 2008.
Brian Lynch, Current-mode vs. voltage-mode control in synchronous buck converters, TI.
Lloyd Dixon, Average Current Mode Control of Switching Power Supplies, 1990.
Ray Ridley, 30 Years of current-mode control, 2008.
Robert Mammano, SPS Topology -voltage Mode versus current-mode, DN-62 slua119. Lloyd Dixon, Control loop cookbook,
TI-Unitrode slup113a.
BUCK Converter Control Cookbook, Zach Zhang, Alpha & Omega Semiconductor, Inc. PIC-003.
20/38
Modeling and Control of DC-DC Converters
Output voltage feedback only!
PWMModulator
LoopCompensator
v o
digital signal processor analog signal processor
vR
d
load
LR di~
Buck Converter Boost Converter
Buck/Boost Converter C,uk Converter
vi vo
L
CD
L
C
D
vovi
L C
D
v ovi
L1
C2D
C1
vi vo
Switching power converters
oi
Define the Operating Point!
Define the Load Disturbance
vgosZ
sv~
sV
Define the Line
Disturbance
Define the Source Output Impedance!
11
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
Small-Signal Modeling of a Buck Converter
IN
OUT
VV
)(max,LB
o
II
0 0.5 1.0 1.5 2.0
0
0.25
0.50
0.75
1.0
DCM
D = 1.0
0.1
0.3
0.5
0.7
0.9
CCMCRM
Averaged Switch Modeling of Boundary Conduction Mode DC-to-DC ConvertersJ, Chen, R. Erickson, and D. Maksimovic, IECON 2001.
VIN = constant
V. Vorperian, "Simplified Analysis of PWM Converters Using Model of PWM Switch Part II: Discontinuous Conduction Mode," IEEE Trans. on Aero. and Electron. Sys., vol. 26, no. 3, pp. 497-505, May 1990.
V. Vorperian, "Simplified Analysis of PWM Converters Using Model of PWM Switch Part I: Continuous Conduction Mode," IEEE Trans. on Aero. and Elec. Sys., vol. 26, no. 3, pp. 490-496, May 1990.
22/38
Modeling of Switching Converters in DCM Operation
IN
OUT
VV
)(max,LB
o
II
0 0.5 1.0 1.5 2.0
0
0.25
0.50
0.75
1.0
DCM
D = 1.0
0.1
0.3
0.5
0.7
0.9
CCMCRM
VIN = constant
V. Vorperian, "Simplified Analysis of PWM Converters Using Model of PWM Switch Part II: Discontinuous Conduction Mode," IEEE Trans. on Aero. and Electron. Sys., vol. 26, no. 3, pp. 497-505, May 1990.
J. Sun, D. M. Mitchell, M. F. Greuel, P. T. Krein, and R. M. Bass, “Averaged modeling of PWM converters operating in discontinuous conduction mode,”IEEE Trans. Power Electron., vol. 16, pp. 482-492, July 2001.
D. Maksimovic and S. Cuk, “A unified analysis of PWM converters in discontinuous modes,” IEEE Trans. Power Electron., vol. 6, pp. 476–490, May 1991.
12
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
Systematic View of DC-DC ConvertersEfficiency
Output Impedance
Selection of Switching Frequency and PWM Strategies
Frequency Responses
Time Responses
Current Injection Testing
24/38
PWM DC-DC Power Conversion and Regulation
CLOCK RAMP
Zi
vref
vo
vx
D
vi
T
TOND T
TON
vpvx
Z f
13
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
25/38
Signal Composition of a PWM DC-DC Converters
comparator
D
d
V c
v c v c
V g
v g vg
igI g
i g
clock ramp
analogamplifier
reference
load
Vv v
modulator-power-stagesubsystem
Ii i
26/38
Frequency Spectrum
f 2f 3f fs - f fs
outputspectrum
bandpassfilter
frequency
fs + f 2fs 3fs
14
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
27/38
AC and DC Quantities in a PWM Switching DC-DC Converter
I ii i vd ioioIo
vovoVo
C
L
Z f
vref
vc
V vI i
CLOCK RAMP
vd
Vc
vc vc
io
vo
Z i
LoadINPUToR
Analysis of Dynamic Responses
28/38
Small-Signal Modeling of a Switching Power Converter
iIi iIi ˆ
RLC
L
error processor
Zi
Z f
v ref
v c
v V vi I i
duty cyclemodulator
power stage
d D d
open
oOo iIi ˆ v V vo O o
AveragedPower Stage
vi
oîd
vo
v o
The concerned transfer functions under small perturbations can be measured under an open loop condition.
15
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
29/38
Definition of
v to( )
t
V I VO O I, ,
ioo viv ˆ,ˆ,ˆi to( )
v ti( )
small signal perturbation
t
TtD on
D
d(t)
d t( )
t
IOO VIV ,, Ttd xˆ
power switch gating waveform
xt
Tont
d
30/38
BuckBoost
Buck/Boost
Small-Signal Modeling of Voltage-Mode DC-DC Converters
Power Stage
PulseModulator
ErrorProcessor
vr
vo
vc
io
d
vi
16
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
31/38
Modeling of Single-Loop DC-DC Converters
vo
vc
i od
vi
;
;
vv
vi
vd
o
i
o
o
o
K PWM A(s)
( , , )v f v i do i o
vi
io
d vc
vo
Zp
Gd
-A(s)
Gv
KPWM
32/38
Small Signal Transfer Functions
G s vvv
o
i d io
( )
,
0 0
: Open-loop input-to-output
G vdd
o
v ii o
,0 0
cvdkˆˆ
PWM
: Open-loop output impedance
: Control to output transfer function
: PWM modulator gain
Z vip
o
o d vi
, 0 0
A s vv
c
o
( )
K
VpPWM
1: Compensator gain: PWM dc gain
17
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
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Closed-Loop Transfer Functions
Gv,CL (Closed-loop Audio Susceptibility)
v G v G do v i d
d AK vo PWM
vv
GG K A
GT
o
i
v
d
v
1 1PWM
Zp,CL (Closed-loop Output Impedance)
v Z i G do p o d
d AK vo PWMvi
ZT
o
o
p1
Loop Gain: PWMT A s K Gd ( )
vo
vc
i od
vi
;
;
vv
vi
vd
o
i
o
o
o
K PWM A(s)
( , , )v f v i do i o
vi
io
d vc
vo
Zp
Gd
-A(s)
Gv
KPWM
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Modeling of PWM DC-DC Converters
A dc-to-dc switching regulator incorporating a three-port duty ratio programmed modulator-power-stage subsystem whose transfer functions are defined in terms of ratios of small-signal ac quantities (hats) superimposed upon large-signal dc quantities (capitals).
The spectrum of the output signal contains the switching frequency, the control frequency, their respective harmonics, and sidebands.
The modeling objective is to find, as function of frequency, the loop gain and the closed properties of the regulator.
The essential prerequisite is to find the transfer function of the three-port subsystem of the modulator-power-stage.
18
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
35/38
Concerned Transfer Functions
Control-to-output transfer function Line-to-output transfer function (audio susceptibility) Reference-to-output transfer function Input impedance Output impedance
A voltage sourcing power supply should have a low (zero) output impedance, while a current sourcing power supply should have a high (infinite) output impedance.
Modeling of DC-DC Converters
voltagereference
Pulse-widthmodulator
cv)(t sGc
refv
+–vH
tδ
tsTsdT
tv
t
Complex Behavior of Switching Power Converters, Chi Kong Tse, CRC Press, 2004.
Dynamic Analysis of Switching-Mode DC/DC Converters, Andre'S. Kislovski, Richard Redl and Nathan O. Sokal, Van Nostrand Reinhold, New York, USA, 1991
SMPS Simulation with SPICE 3, Steven M. Sandler, McGraw-Hill Professional, Dec. 1, 1996.
Computer-Aided Analysis and Design of Switch-Mode Power Supplies, Yim-ShuLee, Marcel Dekker, Inc., Feb. 23, 1993.
Switch-Mode Power Supplies -SPICE Simulations and Practical Designs, Christophe Basso, McGraw-Hill, Feb. 1, 2008. Fast Analytical Techniques for Electrical and Electronic Circuits,
V. Vorperian, Cambridge Press, 2004.
Teuvo Suntio, Dynamic Profile of Switched-Mode Converter: Modeling, Analysis and Control,John Wiley, May 2009.
Mikko Hankaniemi, Dynamical Profile of Switched-Mode Converter – Fact or Fiction?, PhD Thesis, Tampere University of Technology, 2007.
19
課程講義:【電力電子】 DC-DC Converter - Modeling Techniques交通大學 808-電力電子實驗室 April 15, 2009
台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電源系統與晶片、數位電源、馬達控制驅動晶片、DSP/FPGA控制
http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronic Systems & Chips Lab., NCTU, Taiwan
37/38
PWM Switch Modeling of DC-DC Converters
Advances in Averaged Switch Modeling and SimulationDragan Maksimovic and Robert EricksonColorado Power Electronics Center (CoPEC)IEEE PESC1999 Seminar
The “PWM Switch” in mode transitioning SPICE modelsPCIM Germany 2005.Christophe Basso – On-Semi Application Manager
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Questions inspire effective learning!
Any Questions ???
Power Electronic Systems & Chips Lab., NCTU, Taiwan
電力電子系統與晶片實驗室Power Electronic Systems & Chips Lab.交通大學 • 電機與控制工程研究所
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