power electronics of piezoelectric elements - bgupel/presentation/gordon/pz_3_slides.pdf · 2 prof....
TRANSCRIPT
1
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [1]
Power Electronics LaboratoryDepartment of Electrical and Computer Engineering
Ben-Gurion University of the NegevP.O. Box 653, Beer-Sheva 84105, ISRAEL
Phone: +972-8-646-1561; Fax: +972-8-647-2949;Email: sby@ee. bgu.ac.il; Website: www.ee.bgu.ac.il/~pel
Gordon Seminar, Tel-Aviv University, June 2006
Shmuel (Sam) Ben-Yaakov
Power Electronics of Piezoelectric Elements
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [2]
1. Introduction• Piezoelectricity• Brief overview of Piezoelectric devices
• Actuators• Vibrating vans• Motors • Micro-PowerGenerators/Dampers• Transformers• Miscellaneous
OUTLINE
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [3]
OUTLINE (Cont.)
2. Models of Piezoelectric devices3. Drivers4. Rectifiers5. PT based CCFL Ballasts
• The stability issue• Envelope Simulation• Thermal effects
2
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [4]
Piezoelectricity
Discovery-1880 by Pierre and Jacques Curie– Sonar transducer– Pickup and microphone– High frequency quartz resonators
1. Introduction
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [5]
Piezoelectricity (Cont.)1940- Piezoelectric Ceramics
e.g. lead-zirconate-titanate (PZT), lead-titanate (PbTiO2), lead-zirconate (PbZrO3), and barium-titanate (BaTiO3)Plastic Piezo material, PVDF (Polyvinylidene fluoride)
–Powerful “sonars”–Systems of piezo-ignition –Ceramic tone-transducers, Buzzers, Speakers –Piezoelectric motors an actuators –Piezoelectric transformers–“Exotic” devices: damper, power sources…
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [6]
Range of Applications
TechOnLine –Applications for Piezoelectric Ceramics.htm
3
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [7]
This seminar relates to modern piezoelectric devices with particular emphasis on piezoelectric transformers.
Overview of Piezoelectric devices and associated electronics from the PowerElectronics point of view.
OBJECTIVE
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [8]
V
V
• Mechanical electrical interaction• Electrical field Mechanical Stress
Piezoelectric material
Electrode
1. Brief overview of piezoelectric devicesThe piezoelectric effect
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [9]
where
61valuestakesq,p31valuestakesk,j,i
−−[ ] [ ] [ ] [ ] [ ]
[ ] [ ] [ ] [ ] [ ]kTikqiqi
kkpqEpqp
ETdD
EdTsS
⋅ε+⋅=
⋅−⋅=
ntdisplacemeelectricDfieldelectricE
companentStressT
companentStrainS
i
k
q
p
==
=
=
stressttanconsatttanconstypermittivi
ttanconsricPiezoelectd
fieldelectricttanconsatttanconscomplianceTS
s
Tik
kp
constEq
pEpq
=ε
=
=∂
∂=
=
Compressed notation and matrix arrays:
4
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [10]
Constants – IEEE Standard
table_piezo_nomenklature_01.jpg table_piezo_nomenklature_02.jpg
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [11]
Features and Applications:
• Small deflection (µm range)• Static and dynamic applications• Light deflection • Positioning, no friction or backlash • Valve control
L
LStack of piezoelectric elements
Actuators
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [12]
XY Positioning
200 nm span
5
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [13]
Serial BimorphParallel Bimorph
•Same idea as bi-metal•Large deflection, mm range
Bimorph Benders
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [14]
Electricalterminals
ppx −∆
VanBimorphs Piezoelectric element
Base
Vibrating Van
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [15]
Bi-Morph Actuators and Vibrating Vans
• Large deflection • Light Choppers• Remote operation• Valve control • Fan
Features and Applications:
6
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [16]
• Nanomotion Ltd. Israel
piezo ceramicelectrode A
electrode B
electrode C B
A
common
Ellipticmovement
S1 S2
stator
piezo actuatordriver
VAC
stage
Piezoelectric motors
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [17]
Operation Demo
Nano_motor.avi
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [18]
Nanomotion’s NanoLens
7
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [19]
Features and Applications:
• Linear motion• Circular motion• Sub-micron motion and positioning• Small size• Vacuum compatible• Camera lenses• HD drive• Microelectronics manipulators
Piezoelectric Motors
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [20]
MASS
Mechanical Vibration
Micro-Power Generators (Mechanical to Electrical energy harvesting)
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [21]
Silicon beamPiezoelectric
element
Vout
63Ni radioisotopeemitter
[12]
Micro-Power Generator
8
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [22]
MIT’s Piezo Tennis Shoe
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [23]
Shaking table
Piezoelectric element
Beam
Vin
Dampers
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [24]
Sports Active Damping Patent
9
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [25]
Ski DampingCEDRAT TECHNOLOGIES & SKI ROSSIGNOL
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [26]
Dampers experimenthttp://live.pege.org/2005-material/oscillation-damping.htm
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [27]
Features and Applications:
• Active suspension• Skis• Motorcycles• Remote energy sources• Tennis shoes• Structures
Micro-Power Generators and Dampers
10
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [28]
Piezoelectric Transformers
Vin VoPT RL
Vin
Vo
[15]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [29]
Transformer examples
P
P
T
Vin
Vout
• Radial mode[16]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [30]
VP
VS
primarypart
secondarypart
x
xdisplacement
potentialVS
supportpoint
poling
• High voltage gain
[15-18, 70]
Rosen Type Piezoelectric Transformer
11
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [31]
• Higher voltage transfer ratio
Vin
A
A
Rosen Type Piezoelectric TransformerMultilayer
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [32]
Step Down
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [33]
Characteristics of Piezo transformersAdvantages– Potentially low costs– Compact size– High efficiency – Ability to work at high frequency– Good insulation capability– No windings, i.e. no magnetic fields
Disadvantages– Resonant device (frequency and load dependent)– Low Power– Cost
12
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [34]
1. Fluorescent lamp driver for laptop backlight (commercial)
2. Fluorescent lamp driver for LCD monitor (TV) backlight3. Ionizer (commercial)4. Fluorescent lamp ballast (high power) 5. Cell phone battery charger 6. Laptop battery charger 7. Isolated gate driver
The main reason for commercial holdup: price
Piezoelectric Transformer Applications
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [35]
• Welders • Ultrasonic Cleaners• Humidifiers• Nebulizers• Massage and skin scrubbers• Ozonator (high voltage)
Miscellaneous devices and applications
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [36]
Purpose: •Analytical derivations•Simulation
Approach:• Mechanical-Electrical analogy• Equivalent circuit (based on Mason’s Model)
2. Models of piezoelectric devicesModeling of Piezoelectric Elements
devices
13
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [37]
Electrical-Mechanical Relationships
TechOnLine - Piezoelectric Sidebar 2Bridging the Mechanical and Electrical Worlds.htm
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [38]
Mechanical-Electrical Analogyc
rm
Electronicsystem
MechanicalSystemm-mass L
r-losses R
c=1/stiffness C
v-velocity i
F-force u
CrLrRm
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [39]
Electrical Coupling
• Electrical connection by plated electrodes
14
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [40]
Equivalent Circuit
LrRm CrVin
1:n
Cin
• The transformer emulates the coupling between the electrical-mechanical energies
Original
Reflected to PrimaryLrRm CrVin
Cin
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [41]
Resonant modes
Longitudal
Shear
Flexural
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [42]
Standing-Waves Wavelengths
displacement
Z
λ/2(a)
Half wavelength
15
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [43]
λ(b)
displacement
Full wavelength
Standing-Waves Wavelengths
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [44]
Many resonant modesModel
1 nn
LSn CSn RSnCin
1 n2
LS2 CS2 RS2
1 n1
LS1 CS1 RS1
Vin
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [45]
• Usually operated below resonance• Mass includes the work piece • For practical actuators ZCm<< Rm• Cm in the µF range• Highly capacitive
L
L
Actuators
16
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [46]
Vibrating Van Model
inC
1rC
1rL
1mR
P.R.B
)j(Yin ω 2rC 3rC
VanBimorphs Piezoelectric element
Base
• Low frequency • Operation at resonance for maximum
displacement
[2]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [47]
Piezoelectric Motor Model m
R2
Rs
Vs
0Vdc
V4
TD = 0
TF = 100nPW = 1/(2*f req)PER = 1/f req
V1 = 0
TR = 100n
V2 = Vdc
C2
C_in
in
V3
FREQ = f reqVAMPL = amplVOFF = 0
R1
Rm
C1
Cr
L1
Lr
1
2
V11Vac0Vdc
PARAMETERS:Lr = 0.00019836C_in = 39nCr = 3.5382e-8f req = 45kampl = 27.4*1.41Vdc = 0Rs = 1uRm = 155.37
0
• Operation near resonance
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [48]
Ti me
300us 320us 340us 350usV( M)
0V
50V75V
SEL>>
I ( Vs )- 2. 0A
0A
2. 0AV( I N)
0V
50V
100V
Measurement
ModelSimulation
Voltage
Current
Voltage
Current
Drive
Drive
17
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [49]
Ti me
300us 320us 340us 350usI ( Vs )
- 1. 0A
0A
1. 0AV( I N)
- 40V
0V
40V
SEL>>
Voltage
Current
Voltage
Current
Measurement
ModelSimulation
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [50]
os)opt(L C
Rω
=1
RL
PoutoCini RL
( )22
1 Los
L)rms(inout
RC
RIP
ω+=
Ropt
Piezo Source Load
[82]
Basic Generator/Damper Model
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [51]
Piezoelectric Transformer (PT) Model (for One Resonant Mode, Close to Resonant Frequency)
CrLr RmCin Co
Energy-Couplinginput
Energy-Couplingoutput
1:n1 1:n2
PT RL
Vin
Vo
18
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [52]
Equivalent Circuits of a PTCrLr RmCin Co
CrLr RmCin CoVin Vo
ir
nir
nVo
1:n
A
B
• Model B is preferred for simulation[22]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [53]
Reflecting the output side to the primary
oo CR ′′′′ andofconnectionSeries
2o
o nRR =′
o2
o CnC =′
oo CR ′′ andofconnectionParallel
2oo
oo )RC(1
RR′′ω+
′=′′
2oo
2oo
oo )RC()RC(1CC
′′ω′′ω+′=′′
Lr
Cin
Rm Cr
Vin V'o
R''o
C''o
Lr
Cin C'o
Rm Cr R'oVin V'o
[22]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [54]
Input output voltage transfer ratioRosen Type; Cr=37.234pF, Lr=155.3mH, Rm=136.1157 W,
n=4.4899, Cin=720.32pF, Co=19.404pF, frs=66.191kHz.
19
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [55]
Generic Characteristics of PTsDefinitions:
maxinVoutV
m21k ⎟⎟⎠
⎞⎜⎜⎝
⎛ ′=
)rLrC(2inV
oP
basPoP*
oP ==
100inPoP×=η
rCrLoRoC
oRoCrsQ =ω=
mRrCrs
1mQ
ω=
rCoC2n
rCoCc =′
=[22]
- output capacitance times the stiffness of the ceramic
- maximum value of output to input voltage ratio
- output power per unit system
- efficiency
- normalized load
- mechanical quality factor
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [56]
ηη= 0.5
ηm
(k21)ηm
[Q]
k21m
Po m*
Po*
(Po)ηm*
[k21m]
[η][Po]*
cQm
Qmc + 1
1
1 + 12c
Generic Characteristics
[22]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [57]
0
0.5
1
1.5
2
2.5
3
10 10
5
10
15
20
25
30
VoutV in m
))
R o [Ω ]
PoVin
2mWV 2
10 2 10 3 10 4 10 5 10 6
P oV in
2
V outV in )
)
mm
Experimental Results
circles - experimental results; lines - theoretical prediction. [22]
20
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [58]
Model Parameters Extraction• Measurements (Network Analyzer)• Fitting
[2, 15]
Problems• Model is drive-level dependent• Model is load dependent• Model is non-linear• Some have a low Q
Most published parameters are based on low voltage measurements for one load
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [59]
Drive Dependence & NonlinearityInput admittance ,magnitude
150 160 170 180 190 200 210 220 230 240 2500
0.51
1.52
2.5
Input admittance ,phase [degrees]
3x 10-4
Vin=5(Vrms)Vin=25(Vrms)
150 160 170 180 190 200 210 220 230 240 250-20
020406080
100
frequency [Hz]
Vin=5(Vrms)Vin=25(Vrms)
non-linear region
[2]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [60]
Red- V0=500V, green – 400V, blue – 100Vrms
Vo/Vin
Rosen type single layer
Model dependence on output voltage
21
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [61]
Rosentype Multilayer. ELECERAM Ltd.
Model dependence on load
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [62]
Rosen type single layer
Fitting range
Simulation/Experimental agreement
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [63]
Ω50output input
RA
A×
B.R.P,inY
Network Analyzer
inY
P.R.B
.Amp,outV
B.R.PI
AmplifierRF
Ω50
RShunt
RAtten
• Connection for 50Ω input resistance analyzer
DUT
[2]
Measurements under high power excitation
22
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [64]
150 160 170 180 190 200 210 220 230 240 2500
0.5
1
1.5
2 x 10-4 Input admittance magnitude
measuredcalculated
150 160 170 180 190 200 210 220 230 240 2500
20
4060
80100
frequency[Hz]
Input admittance phase[degrees]
measuredcalculated
Fitting area
Fitting area
f1=195[Hz]f2=200.5[Hz]
f > frC=67.8nF Lr=84.551H Cr=8.6184nF Rm=6508Ω
[2]
Results of Least square fitting
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [65]
Transformer Model- Parameter fitting
• Can follow the impedance measurements procedure by shorting the output
• Shorting the output may lead to erroneous results
• Proposed method: Fitting under nominal voltage/power conditions by a Forward-Backward method – under loadedcondition
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [66]
EXPERIMENTAL SETUP
Ω50output input
RA
A×
Network Analyzer
AmplifierRF
Ω50
Rd1
PT
Rd2
VoutVin
• Forward connection
23
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [67]
FORWARD
⎥⎦
⎤⎢⎣
⎡
ω−⎟⎟
⎠
⎞⎜⎜⎝
⎛+ω+ω−++
==
from
f
ror
2
r
o
f
min
oo
RCnCnR
RnLjCnL
CnC
RnRn
1VV
k
L r Cr Rm
Cin Co+-Vo
n
I r
IrnVin Rf
T1 T2
Vo
L r Cr Rm
Cin
I r
Vin Con2 Rf
n2
Von
( ) ( )
( ) ( )( )f
ff
fffout
inf
kRekIm
tan
kImjkReVVk
=ϕ
+=⎟⎟⎠
⎞⎜⎜⎝
⎛=
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [68]
BACKWARD
⎥⎦
⎤⎢⎣
⎡
ω−⎟⎟
⎠
⎞⎜⎜⎝
⎛+ω+ω−++
=⎟⎟⎠
⎞⎜⎜⎝
⎛=
rrinm
r
rinr
2
r
in
r
min
oi
RCnCnR
RnLjCnL
CnC
RnR
n1
1VV
k
L r Cr Rm
Cin+-Vo
n
I rT2
inVCoIrn
T1
RrVo
L r Cr Rm
Cin
I r
Vinn
RrVo
( ) ( )
( ) ( )( )r
rr
rrrout
inr
kRekImtan
kImjkReVVk
=ϕ
+=⎟⎟⎠
⎞⎜⎜⎝
⎛=
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [69]
Solving for ϕ
( ) ( )( )
or2
r
o
f
m
from
f
r
f
ff
CnLC
nCR
nRn
RCnCnR
RnL
kRekIm
tanω−++
ω−⎟⎟
⎠
⎞⎜⎜⎝
⎛+ω
==ϕ
( ) ( )( )
inr2
r
in
r
m
rrinm
r
r
r
rr
CnLC
nCR
nRn1
RCnCnR
RnL
kRekImtan
ω−++
ω−⎟⎟
⎠
⎞⎜⎜⎝
⎛+ω
==ϕ
24
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [70]
Expanding
( ) ( )( ) fror
3formfr
fromrr2
fRCCLRCCRRC
1RCCRCLtan
ω−++ω
−+ω=ϕ
( ) ( )
rrinr3
rinrmrr2
rrinmrr2
rRCCLRCCRRC
n1
1RCCRCLtan
ω−⎟⎠⎞
⎜⎝⎛ ++ω
−+ω=ϕ
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [71]
FITTING
( ) ( )( ) ( )⎩
⎨⎧
=ϕω−ω+ϕω=ϕω−ω+ϕω
1tanbbtanb1tanaatana
r32
2r3
1
f32
2f3
1 ai-bi are found by mean square error method
( ) ( )( ) fror
3formfr
fromrr2
fRCCLRCCRRC
1RCCRCLtan
ω−++ω
−+ω=ϕ
( ) ( )
rrinr3
rinrmrr2
rrinmrr2
rRCCLRCCRRC
n1
1RCCRCLtanω−⎟
⎠⎞
⎜⎝⎛ ++ω
−+ω=ϕ
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [72]
Least-Square Fitting
rinrmrr23 RCCRRCn1b ++=
rrinr1 RCCLb =
rrinmrr2 RCCRCLb +=
fror1 RCCLa =
fromrr2 RCCRCLa +=
formfr3 RCCRRCa ++=
Initial estimation of PT equivalent parameters:Lr(ini),Cr(ini), Rm(ini), Cin(ini), Co(ini), n(ini)
( ) ( )( ) ( )⎩
⎨⎧
=ϕω−ω+ϕω=ϕω−ω+ϕω
1tanbbtanb1tanaatana
r32
2r3
1
f32
2f3
1 ai-bi are found by mean square error method
25
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [73]
Calculations and Experimental Results
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [74]
Phase
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [75]
Load Dependence of Parameters0 – 600 KOhm
nCr
Rm Fr
26
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [76]
DRIVERS
Main Issue:
• High input capacitance • Need for nearly sinusoidal drive• Fast response
3. Drivers
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [77]
controlGSV
SV SVSI
dJswitchingP
t
t
t
Switching losses due to overlap Pd linear with fS !
Switching lossesHard Switching
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [78]
Soft Switching Real and pseudo
snubberdtdV
DVDI
dtdVD
DV
t
switchingsoft"True"
switchingsoft"Pseudo"
snubberdtdI
27
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [79]
Inverter
PTInputMatchingNetwork
Vo
Vin
VDS
ControlIDS
VDS
IDS
Hard switching
Achieving ZVS of the inverter switches
VDS IDS
Soft switching
[23, 24]
Input Matching Network
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [80]
Main problem:Extremely high input capacitance
Requirements:• DC to low frequency• High accuracy• Low frequency ripple• Voltage range: 100V-1000V• Charge recovery method
Actuators Drivers
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [81]
Class ABVCC
-VEE
Vin
Q1
Q2VCC
Q3
Q4
• “Charge recovery”
[26, 27, 58]
Class D
• High Losses
28
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [82]
Commercial Amplifier
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [83]
Stability Criterion
)f(LG1KHA 1
CL +=
The system is unstable if 1+LG(f) has roots in the right half of the complex plane.
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [84]
Nyquist
))f(LG(gIm
))f(LGRe(1−
mΦ
Nyquist criterion can be used to test for the location of 1+LG(f) roots.
29
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [85]
Capacitive Load - Stability Issue
LCOR
fRinR
inV]Hz[f
1f 2f
Pf
LO C,R]Hz[f
]Hz[f
LG
]dB[A
]DB[LG dec/dB20−
dec/dB40−
dec/dB60−
combined
1f 2fPf
dec/dB20−
dec/dB40−
]DB[LG
LOP CR2
1fπ
=
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [86]
Decoupling ResistorOne possible solution
]dB[A
]Hz[f1f 2f
Pf
LO C,R]Hz[f
]Hz[f
OLA
]dB[A
]dB[A dec/dB20−dec/dB40−
dec/dB20−combined
1f 2fPf
Zf
dec/dB40−
Zf
dec/dB20−
dec/dB40−
LCOR
fR
inR
inV SR
LSOP C)RR(2
1f+π
=
LSZ CR2
1fπ
=
Signal attenuation at f > fP
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [87]
Demo Circuit
30
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [88]
High Power Vibrating Devices Drivers(welders, atomizers, etc.)
• Resonant drivers• Class D
Ls Cs Vp
1:n
VinLs
Vp
1:n
Vin
LLCC
LC and PWM
Q1
Q2
CinVCC
D1
D2
1. LC
D3
D4
Q3
Q4
LrRm Cr
Outputfilter
2. LCC3. PWM
[26]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [89]
Converter topology
LC LLCC PWM
]A[i ]mH[L ]A[i ]mH[L ]A[i ]mH[LSeries
inductance SL 0.01 8.8 0.01 6.37 0.01 0.258
Parallel inductance PL - - 0.0029 6.37 - -
PWM: Most compact but higher losses due to hard switching at 250kHz
(After [26])
Operating frequency ~ 20kHz
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [90]
Vibrating Van Drivers
Requirements:
• Low frequency• Low power• Constant frequency• Locking to resonant frequency
31
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [91]
Vin
Iin
Squarewave Sinusoidal Trapezoidal
Vin
Iin
[2]
Vin
Iin
Vin
Iin
Vin
IinSeries inductance (Lseries) that needs to be placed in series with the PRB to achieve ZVS:
C)f2(1L 2r
seriesπ
>
For commercial PRB, Lseries>10H !
Vibrating Van Drive
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [92]
Motors Drivers
Requirements:Relatively high frequencySinusoidal driveConstant frequency operationVariable amplitudeFast response
[6, 7, 13, 14, 46]
At operating point:
ZCm<< Rm Very high reactive current
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [93]
• Soft switching• Requires high Q• Sensitivity to capacitance variations• High circulating current • High switch current
[3, 4]
Resonant inverter
32
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [94]
LinRLCLC2
Vin
OSCILLATOR + DRIVERS
Lmn2
T1 ZL
V
n1
n1
VtapC1
DQ2
VGS2
VD2
2D1
Q1VGS1
D1
time
V
Ts
Ts 2
VD1VD2 VD2
Vtap
VGS1
VGS2
Vtap
Vtap
time
time
time
time
The Current-Fed Push-Pull Parallel-Resonant Inverter (CFPPRI)
rs ff =
rs ff <
rs ff >
Frequency deviation will cause:
Efficiency reduction.
Output signal distortion.
ZVS
Boost period
Hard switching
[3]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [95]
Self-Adjusting CFPPRI
L inCL
ZL
RL
VD2
V in
D2
C2
C3
Ibias
D1
Q1 Q2
VD1
R in2
n
T1
Lrn2
n11
12
n3R2
Phasecomparator
LPFFin Rin1R1C1
Fβ
D3
Q3Vin
+-
PWMModulator
R f
Vref
A1
Vtap
VGS2VGS1
COMP1
Vref
Q QTDR2DR1
FF
phas
e fe
edba
ck
Soft Switching Controller (SSC)
Current feedback
Controlledinductor
[28]• Reactive power locked in resonant tank
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [96]
Transformers Drivers
Requirements:
• Relatively high frequency• Near Sinusoidal waveform • Soft switching• Gain• Power range (DC-DC, Ballast)• Ignition voltage (Ballast)
33
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [97]
PTControl InputMatchingNetwork
Iin
Vin Vout
Hard switching Soft switching
VDS
IDS
VDS IDS
[29]
Half-Bridge Inverter Topology
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [98]
Inductor-less Half Bridge drive
PT
• Simplest and most elegant
[30-32]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [99]
Steady-State Current and Voltage Waveformsof the ZVS PT Inverter
)tsin(I)t(i m ψ−ω=
i(t)
VinD2
D1
Iin
Cin
Q1
Q2
VDC
Res.tank
VGS1
VGS2
Im and ψ are the current peak and the initial phase
VGS2 VGS1
Vin
iin
i(t)
VGS
t
t
t
t
t0 t1 t2 t3 t4 t5
t0-t1 – charging time
t0-t2 – dead time
t2-t3 – Q1-ON
t3-t4 – discharging time
t3-t5 – dead time
[32]
34
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [100]
Normalized load factor Q and frequency range
k
∆κ
∆κ∆κ
r∆
1.0151.005 1.01 1.02 1.025
0.05
0.15
0.25%)97=(ηPT
37.0Q =
25.0Q =
%)5.90(ηPT=13.0Q =
%)5.94(ηPT=
∆r is the normalized charging time
k is the normalized operation frequency
Q is the normalized load factor
∆k is the frequency range for soft switching
Limitations:Qmax at ∆r=0.25
Qmin at ∆PD=10%
0.13<Q<0.37 [32]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [101]
f=120kHz, RL=130Ω (Q=0.15)
tr
[32]
Experimental voltage curves
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [102]
Advantages:•Simple •Low cost
Disadvantages:•Small operational range•Non optimal operation•Not applicable to all transformers•Trapezoidal waveform• No voltage gain
[29-32]
Inductor-less Half Bridge drive
35
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [103]
Vin LpInverter PTCb
Vin
LpInverter PT
Cb
A B
A - DC on PTB – Only AC on PT
Voltage on Cb = ½ Vin [21, 29, 50]
Parallel Inductor
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [104]
Q1
Q2Cin
Vin
D1
D2
CDS1
CDS2
PT
VGS2
VGS1
ControlLP
CB
r
CP C2
DT)D1(TL −=
2DS1DSinr CCCC ++=
cycledutyD −
periodT−T1.0TC ≈
rCoftimeingargchthe
• Advantages: ZVS, lower EMI, constant voltage• Disadvantages: Non sinusoidal waveform, higher
conduction losses, no voltage gain
• Trading switching losses with conduction losses[21, 29]
Voltage-Fed Half Bridge Inverter with a Parallel Matching Inductor LP
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [105]
Series Inductor
PTLin
• Simple method for obtaining soft switching• May attenuate or boost PT input voltage• May change overall frequency response• Best dealt by simulation • A coupling capacitor will eliminate DC on PT
[25, 29, 48, 50, 62, 63, 69, 74]
36
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [106]
Input Impedance of the PT
Fr equency
100KHz 150KHzp( I ( L2) ) - p( V( PTI NAC) )
0d
- 100d
100d
SEL>>
V( OUTAC) / V( PTI NAC)
0. 50
1. 00
0. 05
• Not always capacitive around the operating frequency
inductive Fr equency
100. 0KHz43. 6KHzp( I ( L4) ) - p( V( PTTAC) )
0d
50d
100dV( out ) / V( PTTAC)
0
2. 5
5. 0
7. 0
SEL>>
Vout/Vin
Phase
PT “A” PT “B”
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [107]
Fr equency
100KHz 120KHz 140KHz 150KHzV( OUTAC) / V( I NPUTAC)
0
1. 0
2. 0
P( - I ( V6) )- 100d
0d
100d
SEL>>
V( OUTAC) / V( PTI NAC)0
1. 0
2. 0
• Examination by small signal (AC) simulation
Overall Vout/Vin
PT response
Phase of series inductor current
1mH 1.6mH
2.4mH
PT Operating Region
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [108]
Ti me
920. 0us 930. 0us914. 3us 935. 0usV( I NPUTTRAN)
50V
- 10VSEL>>
V( PTTRANS)0V
25V
50VI ( L4)
- 40mA
0A
40mA
Inductor current
PT voltage
HB commutation
• Large-signal time-domain (TRAN) simulation
37
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [109]
Ti me
672. 00us 674. 00us 676. 00usV( I NPUTTRAN)
0V
20V
40V
52V
Green=1mHRed=1.6mHBlue= 2.4mH
• HB commutation
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [110]
Diode Clamped Resonant Snubber
Q1
Q2
Lr
Cin
VCC
DQ1
DQ2
PTC1
C2
D1
D2 Cex
• Forces soft commutation [39, 44]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [111]
Lin=10m; Cex=1n
Single layer, RosenType, ELS-60 Eleceram Co.
Ti me
700. 0us 710. 0us 720. 0us 730. 0usV( I NPUTTRAN)
0V
200VV( PTTRANS)
- 200V
0V
200V
SEL>>
I ( L104)- 100mA
0A
100mAV( OUTTRAN)
- 500V
0V
500V
Output voltage
Inductor current
PT input voltage
HB commutation
38
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [112]
0Itt0Itt
Q43
D31
>−
>−0Vtt
offQtt
inC10
20
>−
−−
Advantages:1. Only one switch2. Low cost3. Better EMI suppression
Disadvantage:1. Small operational range2. High voltage stress
L Lr
Cin C'o
Rm
Cr R'oVin V'oDQ
VCin
IDIQ
IIN PT
Control
[33-35, 54]
Class E Inverter
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [113]
Dual inductor Current-Fed Push-Pull Inverter (PPRI)
VinVoPT
Q1CDS1
D1 Q2
CDS2D2
L2L1IL1 IL2
RoPTCVDS1
VDS2
D2D1Q2Q1Interval
1o tt −
21 tt −
32 tt −
43 tt −
on off off off
off
off
off off
off off
off
on
on
on on
on
Advantages: Nearly sinusoidal waveformDisadvantages: Narrow operational range, no voltage gain
[36]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [114]
Single Inductor PPRI
• Extra voltage gain by transformer• Good for fixed power level
LinC2
Vin
OSCILLATOR + DRIVERS
Lmn2
T1
PT
V
n1
n1
VtapC1
D
Q2VGS2
VD2
2D1
Q1VGS1
D1
[28]
39
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [115]
Resonant Forward-Flyback Inverter
Vin VoPTRo
PT
QC D
Lm
Llkg2
CIN
IME
IME – Integrated Magnetic ElementLm – magnetization inductanceLlkg2 – leakage inductance reflected to the secondary
[47]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [116]
Resonant forward-flyback self-oscillating inverter(magnetic element on pot core P14/8) and Rosen type PT (PXE43 48 x 8 x 2.2 mm)
[47]
A Piezoelectric Cold Cathode Fluorescent Lamp Driver Operating from a 5 Volt Bus
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [117]
[47]
Experimental Results
40
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [118]
Power Control
• Frequency shift• PWM
• Resonant converters• Asymmetrical (half bridge) • Low frequency PWM (ON-OFF)
• PFM Combined PWM and PFM [37, 66]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [119]
Half Bridge Driver with Active-Clamp
VinDC
PT
Q1
LS
LrCr
VLrQ2
VGS1 VGS2
VDS1
VLr
t
t
t
VGS
)Dsin(D
VV inLr π
−π=
12
• ZVS• Voltage gain• Squarewave drive [37, 38]
0 0.2 0.4 0.6 0.8 1
in
oVV
Active clamp
Asymmetrical
D
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [120]
Lo
PTinV 2D
1D fL
fC LR
PTinV
2D1D fC
LR
L1
L2
Current Doubler
Half Wave
[21, 38, 43]
4. RectifiersPT Rectifiers - Inductive Filter
41
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [121]
PT Rectifiers - Capacitive Filter
VoltageDoubler
DiodeBridge
CF
Vin
PTRo
D2
D1
D3
D4
VinCF
PTRoD1
D2
[19, 30, 31, 39, 40, 62, 73]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [122]
Voltage Doubler Current Doubler
VCo
ir
iD iD1iD2
ϑ
ϑ
ϑ
θ
VCo
ir
iD
ϑ
ϑ
ϑ
iD1 iD2
λ
• Voltage and current may not be in phase• Equivalent AC load is not resistive [39, 40, 43]
The PT Voltage and the Current Waveforms
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [123]
Analytical Method
PTinV LRoC Rect
n
vCoinV inC
rL rC mR
nir
C Reqeq
[39-41]
42
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [124]
Equivalent Circuit Parameters
mPTPT
)1(2
L
eqrm QKA
sin
R
R1
ϕ+ω=ω
Voltage Doubler
⎪⎪⎩
⎪⎪⎨
⎧
ω
ϕ=
=
VDeq
)1(VDeq
L2
)1(VDeq
R
tanC
Rk81R
)1(pk)1(Co
Lrect k
2V
Vk ==
Current Doubler
⎪⎪⎪
⎩
⎪⎪⎪
⎨
⎧
ω
ϕ=
⎟⎟⎠
⎞⎜⎜⎝
⎛
λπ
=
CDeq
)1(CDeq
L2
)1(
22CDeq
R
tanC
Rk21R
)1(2pk)1(Co
Lrect
kVV
kπ
λ==
Rectifier Voltage Transfer Ratio
Frequency of the Maximum Output Voltage
[43]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [125]
100000.1 1 10 100 10000
0.5
1
1.5
2
2.5
3
3.5
4
0.12
0.13
0.14
0.15
0.16
0.17
0.18
0.19
0.2
ω C Ro L[ ]
eqR /RL
adC /Co
[C
/C ]
ado
[R
/R ]
eqL
• Equivalent AC load for voltage doubler[40]
Cad =Ceq-Co
Example
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [126]
Equivalent Circuit of a PT AC/DC Converter Referred to the Primary
L r C r R m
C in
Ir
V in R eqC eq
2eq
'eq
2eq
'eq
nCC
nRR
=
=
)1(2
'eq''
eq
)1(2'
eq''eq
sin
CC
cosRR
ϕ=
ϕ=
Lr Cr R m
Cin
Ir
V ineqC
Req
[22, 39, 40]
Normalized parameters:• KPT=RL/n2Rm – Normalized load factor• APT=ωrCon2Rm – Normalized PT factor• Qm=1/ωrCrRm – PT mechanical quality factor
43
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [127]
Voltage Transfer Ratio(Same specific PT)
10-2
10-1
100
100 102 104 KPT
ko
101CurrentDoubler
VoltageDoubler
KPT=RL/n2Rm
Overall voltage gain Vo(DC)/Vin(AC)
[43]
0.2
0.4
0.6
0.8
η
100 102 104 KPT
CurrentDoubler
VoltageDoubler
Efficiency
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [128]
Power Handling Capability(Output power/PT dissipated power)
0.01
0.02
0.0310
20
30
40
100 101 102 103 104
∆PT
kPT
0.01
0.02
0.03
Qm =1000
APT=0.008
APT=0.008Currentdoubler
Voltagedoubler
KPT=RL/n2Rm
APT=ωrCon2Rm
Qm=1/ωrCrRm
[43]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [129]
Boundary Conditionsfor Choosing the Rectifier type
VD
CD
Qm=1000500200
50
0.01 0.03 0.05APT
KPT
20
60
100
KPT=RL/n2Rm
APT=ωrCon2Rm
Qm=1/ωrCrRm
[43]
44
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [130]
Applications• Ionizers• Ozone generation• Sparkers
• High gain• Good insulation
[39, 40]
Piezoelectric Transformers inHigh Voltage Application
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [131]
S 2
S 1 L bC f
D 3
D 1
D 2
PZT
C s e
R L
D 4
C 1
C 2
+
Inverter
C
[39, 40, 61]
HV DC Output
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [132]
.
2000
3000
4000
5000
6000
1000
0
VLmax
(V )L fr
[V ,
V]
L
[R , MOhm]0 5 10 15 20
L[39, 40]
45
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [133]
1.004
1.008
1.012
1.000
1.016
1 10 100 1000 10000[RL, kOhm]
[ω∗]
• Need for frequency tracking[40, 45]
Frequency of Maximum Output
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [134]
The Proposed Frequency Tracking Method
Current iD2 in part of cycle θ is proportional to irThe phase of the current iD2 is the same as one of irThe trailing edge of the iD2 level detection wave may be used as Phase Reference
Phase Reference
D2
D1
Cf RL
VCo VL
Co
Cr RmLrVin
ir irN
VCoN
iD2 leveldetection
iD2
ir
θ ϑ
ϑ
ϑ
[44, 46]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [135]
Experimental Setup for Resonant Frequency Tracking
370uH10k
4.7k 4.7k
D1
D2CL RL
PTVin Vout
p(Vin) p(Id)
Phasedetector
39k
1n
VCO
4.2k
1.5k3.3k
1k15v
15v 15v
FFQ
QIR2110driver
0.22u
10.2n
10k4.7
10k4.7
CD4046A
VLF
f
Highvoltage
V1V4 V2
V3
BN
6.6n
[44]
46
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [136]
The System With PLL Control
[44]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [137]
for Micro-Power Generators and Dampers
[82]
Resonant Rectifier
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [138]
Vibrating Piezo - Electrical Model
os)opt(L C
Rω
=1
RL
PoutoCini RL
( )22
1 Los
L)rms(inout
RC
RIP
ω+=
Ropt
Piezo Source Load
47
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [139]
Capacitive Source Problem
oCini LC
inVouti
LVLI
1BD 2BD
3BD 4BD
RL
inV
inI
outi
1t 2t 3t
)pk(inV
πω+
πω−
π==Los
DosP
Lout RC
VCI
Ii 21
42
IL
LLos
DosP
LL RRC
VCI
)R(P ⋅⎟⎟⎟⎟
⎠
⎞
⎜⎜⎜⎜
⎝
⎛
πω
+
πω−
π=
2
21
42
)VV(C
R
L
Dos
)opt(L 21
12 +ω⋅
π=
DB2 ‘ DB3 DB1 ‘ DB4
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [140]
What if Co=0 ?
ini LC
inVouti
LVLI
1BD 2BD
3BD 4BD
RL
inV
outiIL
π=
πω+
πω−
π==
=
P
Los
DosP
LoutI
RC
VCI
Ii
oC
221
42
0
LP
LL RI)R(P ⋅⎟⎠⎞
⎜⎝⎛π
=22
∞≈)opt(LR
ini
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [141]
Earlier solutions and their limitations
oCini RLL
os LC
1=ω
Disadvantage
Large inductance
Passive and active solutions
EmulatorDisadvantages
1.Large in size
2.Difficult to tune
3.High sensitivity
4.External source
48
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [142]
Proposed Resonant Rectifier Circuit
oCini LC LR
inVouti
1D 2D
resL
derV
cV
1sw 2sw
COMP.
resi
dtd
LVLI
1BD 2BD
3BD 4BD
Capacitive Source
Differentiator
Comparator
Diode Bridge
Inductor & Switches
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [143]
Principles of operation
cV
derV
resi
inV
outi
1t 2t 3t 4t 5t
oCini LC LR
inVouti
1D 2D
resL
derV
cV
1sw 2sw
COMP.
resi
dtd
LVLI
Why the commutation was not completed during t3~t4 ?
1. Co Voltage droped during t2~t3.
2. Power loss during t3~t4.
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [144]
Losses Calculation
2
r
r
)(2
os2
D)pk(in)loss(R
1
e1Cf)VV(Pr
r
r
⎟⎟⎠
⎞⎜⎜⎝
⎛ωα
+
−⋅⋅⋅−=
ωα
π−
2
r
r
)(
D)pk(inosD)loss(D
1
e1)VV(CfV2Pr
r
⎟⎟⎠
⎞⎜⎜⎝
⎛ωα
+
+⋅−⋅⋅⋅=
ωα
π−
Q)pk(in)loss.(Comp IV2P ⋅≈
s)pk(in)n(gss)pk(in)p(gs)loss(Gate fVQfVQP ⋅⋅+⋅⋅≈
LD)loss(Bridge IV2P ⋅≈Bridge losses
Gate drive losses
Comparator losses
Diode losses
Resistance losses
49
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [145]
oCexV LR
inV
1D 2D
resL
derV
SV+
SV−
nM pMsensR
hysRderC
derR
COMP. cV
1SD2SD
1SC2SC
LC1BD 2BD
3BD 4BD
inR
LV
+
−
ini
Experiment with dummy current source
• Schottky diodes 1N5817
• Ultra low power IC(MAX921, Maxim, USA)
• MOSFET (VP0104, VN0104)
200V floating source
Rin=100KΩ
Rsens=1KΩ
Co=330nF
Lres=1mH
CL=1µF
fs=185Hz
DifferentiatorCurrent source
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [146]
LR
inV
1D 2D
resL
derV
SV+
SV−
nM pM
hysRderC
derR
COMP. cV
1SD2SD
1SC2SC
LC1BD 2BD
3BD 4BD
LV
+
−
Actuator Transducer
exV
Longitudinally piezoelectric bimorph van element
RBL-1-006 model, Piezo Systems, Inc, USA
Experiment with Piezoelectric Generator
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [147]
Experimental Circuits
oCini LC
inVouti
LVLI
1BD 2BD
3BD 4BD
RL
2.Proposed rectifier.
3.Proposed rectifier with external supplies.
a. Higher VS reduces Rds(on).b. Supplies the (small) power
consumption of the comparator circuitry.
1.Reference circuit.
oCexV LR
inV
1D 2D
resL
derV
SV+
SV−
nM pMsensR
hysRderC
derR
COMP. cV
LC1BD 2BD
3BD 4BD
inR
LV
+
−
1SD2SD
1SC2SC
ini
External
50
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [148]
Results
251%3.16mW3.51KΩ3.34VRESONANT RECTIFIER WITH EXTERNAL SUPPLIES VS=±4V
142%1.79mW2.75KΩ2.2VRESONANT RECTIFIER
-1.26mW2.1KΩ1.6VSTANDARD RECTIFIER
GAIN (%) COMPARED WITH STANDARD
RECTIFIER
OUTPUT POWER
OPTIMAL LOAD
RESISTANCE
OUTPUT VOLTAGE (DC)CIRCUIT TOPOLOGY
230%1.23mW11.43KΩ3.75V
118%0.636mW5.19KΩ1.818V
-0.537mW5.89KΩ1.779V
RESONANT RECTIFIER WITH EXTERNAL SUPPLIES VS=±4V
RESONANT RECTIFIER
STANDARD RECTIFIER
GAIN (%) COMPARED WITH STANDARD
RECTIFIER
OUTPUT POWER
OPTIMAL LOAD
RESISTANCE
OUTPUT VOLTAGE (DC)CIRCUIT TOPOLOGY
Dummy current source
Piezoelectric Generator
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [149]
Experiment Waveforms(with external PS)
inin iV ⋅
ini
inV
1t 2t 3t 4t 5t
inV
derV
5V/div
2mA/div
2V/div
2V/div
Input Voltage
Input Current
Input Voltage
Instantaneous input power
Derivative Signal
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [150]
The Resonant Rectifier
The operation of the new rectifier is based on self commutation of capacitor voltage
A considerable portion of the losses are due to forward voltage drop of the bridge diodes.
The resonant rectifier exhibits a substantial improvement compared to the conventional rectifier.
Additional improvement could be achieved by replacing the diode bridge by a synchronous rectification scheme.
51
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [151]
PTInverter VoVin= 5V Lamp
[31, 47-58]
PT Based CCFL Ballasts
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [152]
Peak voltage
[47]
Cold cathode Fluorescent lamp (CCFL)Drivers
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [153]
Requirements:• Power handling capability• High ignition voltage ~1000V• Sufficient energy to pass the peak voltage• High operating voltage ~ 600V
The Issue of Dynamic Stability
Lamp Current
Lamp Voltage[49, 50, 78]
52
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [154]
Dynamic changes of V-I characteristics of a fluorescent lamp operating at high frequency
P1
P2
B
FastCurrent
ChangesSlow Power
Changes
I(lamp) [Arms]
V(lamp) [Vrms] FastCurrent
Changes
AReq1
Req2
Vs
Static V-A line
• Linear approximation of V-I curve [78, 83]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [155]
eq1 R
)lamp(VG =
)I(fR )rms(lampeq =
RiCi match the dynamic response of lamp
21 )lamp(iE ≡
)p(vE2 ≡
+-
+-
rms
Lamp Model
R
lamp isq p
Ci
Ri
E2E1G1
Lamp
[83]
SPICE Compatible Fluorescent Lamp Model
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [156]
1fjf
1R
Rfjf
sR)Lf(incZ
0
Ls
eq
0
L
+
−=
eqINCL
sINCLRZfForRZ0fFor
→∞→−→→
• “Right-Half Complex-Plane” Zero [83]
Incremental impedance of fluorescent lamps
53
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [157]
Frequency100Hz 10KHz 1.0MHz
db
-50
-45
-40
0o
-200o
-100o
| Yinc |
Phase
Negative incremental resistance at low modulating frequency [83]
Incremental Admittance of Experimental Lamp Obtained by Simulation
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [158]
Modulation frequency 200Hz
Negative incremental resistance
Excitation frequency 50kHz
measuredresponse
simulatedresponse
I
V
I
V
[83]
Response to modulation
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [159]
Modulation frequency 5kHzExcitation frequency 50kHz
Positive incremental resistance
IV
measuredresponse
simulatedresponse
IV
[83]
Response to a modulation
54
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [160]
1A
-1A
200V
-200V
measuredresponse
simulatedresponse
I
V
I
V
[83]
Response to a power step
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [161]
Vlamp
Zlamp
Vex +-
IlampZballast
1
Vex
Zballast
Zlamp
VlampIlampBallast
Zballast Zlamp
Vex
lampballast
ZZ
1LoopGain =
Ballast-Lamp InteractionFeedback Model
[78]
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [162]
Stability Criteria for Carrier Driven SystemsWhat is Z ?
Lamp(Non-Linear
NegativeResistance
Load)
LsCs
Vin fc
ssrc CL2π
1ff =>>
ssrc CL2π
1ff =≈
Stable
Unstable
55
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [163]
For the Lamp-Ballast system:The relevant impedance is the INCREMENTAL IMPEDANCE under the specific carrier excitation
( )ex
exminc ∆I
∆VfZ =
LsCs
Vex
Iex∆ Iex
∆Vex
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [164]
How does an incremental impedance (Zinc) behave ?Example & Intuitive Observation
• Yinc(fm) will have a peak when fm = |fr – fc| • Envelope analysis
f r fc
fm fm
( ) ( )( ) ( )t2sint2sinA1tV cmmex ff ππ+=
LsCs
Rs
AM ModulatedSignal
Yinc fm( )
fm sweep
Vex
Y ofResonantNetwork
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [165]
• Fast large signal simulation(as compared to TRAN simulation)
• Very fast small signal simulation(as compared to TRAN simulation)
• Large (TRAN) and Small Signal (AC) compatible
• Can be implemented on any modern circuit simulator
For details see [77-79] and Appendix A
SPICE Compatible Envelope Simulation
56
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [166]
[77-79]
Envelope Simulation Primer
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [167]
Power System Driven by a Modulated Signal
Modulator-Driver
Reactivenetwork Load
uc(t)
um(t) )t(uout)t(u
The need for Envelope Simulation
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [168]
( ) ( ) ( )( ) ]etjItIRe[ti tf2j21
cπ+=
A Primer to Envelope Simulation
Any analog modulated signal (AM, FM or PM) can be described by the following expression:
The Current in the network excited by u(t):
( ) ( ) ( ) ( ) ( )( ) ( )( ) ]etjUtURe[
tf2sintUtf2costUtutf2j
21
c2c1
cπ−
=π+π=
57
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [169]
( ) ( ) ( )
( ) ( ) ( )⎪⎩
⎪⎨
⎧
π+=
π−=
]tLIf2dt
tdIL[j]tV[j
tLIf2dt
tdILtV
1c2
2
2c1
1
( ) ( ) ( )tItIti 22
21 +=
( ) ( ) ( )tVtVtv 22
21 +=
Phasor Analysis
Inductance
LiL
L
LI2
I1
I2(t)ωcL
I1(t)ωcLIm
Re
+ -
+-
V1
V2
( ) ( )( ) ( ) ( )
( ) ( ) ]e)tLIf2jdt
tdIjL
ttIf2dt
tdILRe[(]etjVtVRe[
tf2j1c
2
2c1tf2j
21
c
c
π
π
π+
+π+=−
( ) ( )dt
tdiLtv =
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [170]
Phasor Analysis
Capacitance
Resistance
VC C
C
CV2
V1ωcCV2ωcC
Im
Re
V1I1
I2
RR
RIm
Re I1
I2
V1
V2
( ) ( )dt
tdvCti =
( ) ( )tRitv =
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [171]
Splitting the Networkinto Two Cross-Coupled Components -
Imaginary and Real
LoadNetworkSource inV
( )tu
outV
58
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [172]
imaginary circuitcomponent
real circuitcomponent
coupling
inre
inim
outre
outim
U1
U2
22 V(outim)V(outre) + outV
Real Load Component
Imaginary Load Component
Splitting the Networkinto Two Cross-Coupled Components -
Imaginary and Real
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [173]
Example: Piezoelectric Transformer Driven by FM Signal (SPICE)
Vin
Excitation
Ro
LoadVoutFMVoVin
Rectifier
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [174]
Example: Piezoelectric Transformer Driven by FM Signal (SPICE)
Vin
Excitation
Ro
LoadVoutFMRectifier
Co
Lr
+-
Cr Rm1:n
Vo/n
Vo
I(Lr)/n
Ci
Equivalent cirquit of the PiezoelectricTransformer
I(Lr)
59
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [175]
Example: Piezoelectric Transformer Driven by FM Signal (SPICE)
Vin
Excitation
Ro
LoadVoutFMCo
Lr
+-
Cr Rm1:n
Vo/n
Vo
I(Lr)/n
Ci
Equivalent cirquit of the PiezoelectricTransformer
I(Lr) ReqCeq
Equivalentreplacementof rectifier
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [176]
Example: Piezoelectric Transformer Driven by FM Signal (SPICE)
Vin
Excitation
Ro
LoadVoutFMCo
Lr
+-
Cr Rm1:n
Vo/n
Vo
I(Lr)/n
Ci
Equivalent cirquit of the PiezoelectricTransformer
I(Lr)
( ) ( )( )∫π+π= dttuk2tf2cosAtu mfcc
( )tf2sinA)t(u mmm π= - Harmonic modulating signal
ReqCeq
Equivalentreplacementof rectifier
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [177]
( ) ( )( ) ( )( )( ) ( )tf2sintf2sinsinA
tf2costf2sincosAtu
cmc
cmcππβ
−ππβ=
Example: Piezoelectric Transformer Driven by FM Signal (SPICE)
Vin
Excitation
Ro
LoadVoutFMCo
Lr
+-
Cr Rm1:n
Vo/n
Vo
I(Lr)/n
Ci
Equivalent cirquit of the PiezoelectricTransformer
I(Lr)
( ) ( )( )tf2costf2cosAtu mcc πβ−π=m
mffAkwhere =β
ReqCeq
Equivalentreplacementof rectifier
60
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [178]
I(iim)/n
Co
outre
Lr
ire0Vdc
Co
inim
Rm
V(outim)/n
-V(outim)*2*π*fc*Co
Ro
ainre Lr
Cr
V(outre)*2*π*fc*Co
diim0Vdc
c
Ro
Ac*cos((Am*kf/fm)*sin(6.283186*fm*time))
VinputRE
(V(a)-V(b))*2*π*fc*Cr
Crb
Ac*sin((Am*kf/fm)*sin(6.283186*fm*time))
VinputIM
-I(iim)*2*π*fc*Lr
I(ire)*2*π*fc*Lr
V(outre)/n
0
I(ire)/n
outim
Excitation
-(V(c)-V(d))*2*π*fc*Cr
Rm
0
PARAMETERS:Lr = 22.6mCr = 9.83pRm = 1.121kn = 0.647Co = 225pRo = 20k
PARAMETERS:fc = 358k fm = 8k
Am = 1Ac = 1kf = 1000 sqrt(v(outre)**2+v(outim)**2)
out
abs_out
OrCAD Schematics for Envelope Simulation
(Large Signal)
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [179]
Results of Full and Envelope Transient Simulations
The modulating input signal
The Frequency modulated signal
Output signal
Ti me0s 1. 0ms 2. 0ms 3. 0ms 4. 0ms 5. 0ms 6. 0ms 7. 0ms
v( out ) v( out put )
- 2. 0V
0V
2. 0V
SEL>>
v( i n) s qr t ( v( a ) *v( a ) +v( b) *v( b) )- 1. 0
0
1. 0v( i nput )
- 1. 0V
0V
1. 0V
Cycle-by-cycle
Cycle-by-cycle
Envelope
Envelope
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [180]
Small Signal (AC) Envelope Simulation
Amplitude modulation
( )⎩⎨⎧
=
+=
0UtuAkAU
2
mcac1
inre
E1
V(%IN+, %IN-)*ka*AcEVALUE
OUT+OUT-
IN+IN-
V1Ac
inim
um(t)
0 0
inre
0
E1
V(%IN+, %IN-)*ka*AcEVALUE
OUT+OUT-
IN+IN-
V1Ac
inim
VAC
Am
The source is linear and suitable for AC analysis – as is
( ) ( )( ) ( )tf2costuk1Atu cmac π+=
phasorphasorphasor
61
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [181]
=Ac*kp*u(t)
Small signal
Linearization of Sources for Angle Modulation
Phase Modulation
PM – Nonlinear source
( )( )( )( )⎩
⎨⎧
=
=
tuksinAU
tukcosAU
mpc2
mpc1
( ) ( )( )tuktf2cosAtu mpcc +π=
VAC
inre
0
VDCAcPM
Am
inimkp*Ac
GAIN1
Linear source
=Ac
Small signalinre
inim
Ac*cos(V(%IN) )
Ac*sin(V(%IN))
kp
GAIN1um(t)
phasorphasorphasor
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [182]
Linear source
VACAm
inre
2*Pi*Ac*kf
INTEG1
inim
0
VDC
0
FM
Ac
Linearization of Sources for Angle Modulation
Frequency Modulation
FM – Nonlinear source
( ) ( )( )( )∫+π= dttuktf2cosAtu mfcc
( )( )( )( )⎪⎩
⎪⎨⎧
=
=
∫∫
dttuksinAU
dttukcosAU
mfc2
mfc1
=Ac
Small signal
=Ac*kp*∫u(t)dt
Small signal
0
2*π*kf
INTEG1
Ac*cos(V(%IN) )inre
Ac*sin(V(%IN))
inim
u(t)
phasorphasorphasor
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [183]
Results: Piezoelectric Transformer Driven by FM signal (AC and Point-by-Point)
for Different Carrier Frequencies
-7 0
-8 0
-9 0
-1 00
-1 10
-1 20
F re qu en cy , kH z-3 60
-2 70
-1 80
0 .1 1 10 1 00
G a in , d b
P h a se , d e g
fc= 3 6 0 kH zfc = 3 5 8 .5 kH zfc = 3 5 7 kH z
62
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [184]
ZPT
LinVin
Zlamp
PT
PTs: ELECERAM Co.
Experimental Circuit
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [185]
Vex
Zballast
Zlamp
VlampIlampBallast
Zballast Zlamp
Vex
lampballast
ZZ
1LoopGain =
[78]
Vlamp
Zlamp
Vex +-
IlampZballast
1
Ballast-Lamp InteractionFeedback Model
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [186]
OUT+OUT-
IN+IN-
E8
sqrt(i(V12)**2+i(V11)**2)EVALUE
tot_cur
R91k
0
0
OUT+OUT-
IN+IN-
E4
Ac*(1+.05*Ka*Am*sin(6.28*fm*time))
EVALUE
V11
0Vdc
V12
0Vdc
OUT+OUT-
IN+IN-
G6
(V(in_re))*6.28*fc*CinGVALUE
OUT+OUT-
IN+IN-
E6
V(out_re)/n_eEVALUE OUT+
OUT-IN+IN-
G3
I(I_re)/n_e+V(out_im)*6.28*fc*Co
GVALUE
C3Co
R5Ro
out_re
R7
1u
R8
1u
OUT+OUT-
IN+IN-
E7
V(out_im)/n_eEVALUE OUT+
OUT-IN+IN-
G4
I(I_im)/n_e-V(out_re)*6.28*fc*Co
GVALUE
C4Co
R6Ro
out_im
0
V2
Am*Ac*KaAc
0
1 2L1
Lr
C1
Cr
R1
RmOUT+OUT-
IN+IN-
E1
-I(I_im)*6.28*fc*LrEVALUE
PARAMETERS:
Lr = 1.125m*(n_a*n_a)Cr = 8.5n/(n_a*n_a)Rm = .67*(n_a*n_a)
Co = 230nRo = 1ufm = 5k
Cin = 32pn_a = 57
n_e = 57/(n_a*n_a)
fc = 50kAc = 1
a
OUT+OUT-
IN+IN-
G1
-(V(c)-V(d))*6.28*fc*CrGVALUE
0
0
I_re
0Vdc
0
ba
1 2L2
Lr
C2
Cr
R2
RmOUT+OUT-
IN+IN-
E2
I(I_re)*6.28*fc*LrEVALUE
c
OUT+OUT-
IN+IN-
G2
(V(a)-V(b))*6.28*fc*CrGVALUE
C5Cin
0
0
I_im
0Vdc
d
0
C6Cin
OUT+OUT-
IN+IN-
E5
sqrt(V(x_re)**2+V(in_im)**2)EVALUE
out
R41k
0
R19
1u
in_im
OUT+OUT-
IN+IN-
G5
-(V(in_im))*6.28*fc*CinGVALUE
x_re
in_re
in_re
Real Part
Imaginary Part
Excitation (AM)
PT envelope simulation - Zinc measurement
63
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [187]
Frequency
100Hz 1.0KHz 10KHzP(V(tot_cur))
0d
-200d
180dV(tot_cur)
0V
200uV
400uV
fc = 51KHz
fc = 52KHz
fc = 49KHz
fc = 54KHzfc = 53KHz
fc = 50KHz
PT incremental output admittance for several carrier signals, above and below resonance
PT resonance at 51.5 KHz
Magnitude
Phase
PT Envelope Simulation Results
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [188]
( )rmslamp IfR =
OUT+OUT-
IN+IN-
E3
I(V3)**2EVALUE
OUT+OUT-
IN+IN-
E9
sqrt(V(p))EVALUE
R3
100
C101u
IC =
p
0
V3
0Vdc
rms
OUT+OUT-
IN+IN-
G8
V(lamp)/V(Rinc)
GVALUE
lampR11
1meg
V42.5kVdc
0
V51Vac0Vdc
OUT+OUT-
IN+IN-
E10
V(rms)ETABLE
0
Rinc
ETABLEIlamp
Rlamp
Lamp Model(Orcad 10.3)
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [189]
Thermal dependence of the CCFL
500
520
540
560
580
600
620
640
660
680
700
[mA]Ilamp
[V]Vlamp
0 1 2 3 4 5
(a) Forced air flow
(b) Natural convection
33oC @ 3mA
40oC @ 3mA
Rs1
Rs2
64
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [190]
Static Incremental Resistance (Rs)
Forced air flow (mes)
Natural convection (sim)
Natural convection (mes)
Forced air flow (sim)
Natural convection Rs
Forced air flow Rs500
550
600
650
700
750
800
0 0.5 1 1.5 2.5 3.5 4.52 3 4 5[mA]I lamp
[V]Vlamp
-15
-20
-25
-30
-35
-40
-45[KΩ]R s
Rs
V-I
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [191]
Fr equency
10Hz 100Hz 1. 0KHz 10KHz 100KHzV( l amp) / I ( V3)
0
200K
400Kp( V( l amp) / I ( V3) )
0d
90d
180d
SEL>>
Magnitude
Phase
CCFL incremental impedance for lamp currents
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [192]
Thermal effects on the CCFL’s Zinc
110
120
130
140
150
160
170
180
0.1 1 10
ϕ ZECCFL [deg]
Modulating frequency, fm [KHz]
(a) 33oC
(b) 40oC
86
87
88
89
90
91
92
93ZECCFL [dB]
(a) 33oC
(b) 40oC
65
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [193]
Stability Criterion
)f(LG1KHA 1
CL +=
The system is unstable if 1+LG(f) has roots in the right half of the complex plane.Nyquist criterion is a test for location of 1+LG(f) roots.
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [194]
Nyquist
))f(LG(gIm
))f(LGRe(1−
mΦ
lampballast
ZZ
1LoopGain =
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [195]
Possible modes of operation
ZEPT
ZECCFL (T)
TTOP
|Z| , PNominal P
Tmax
P
Mode 1: Carrier frequency is far from resonance –stable mode CCFLPT ZincZinc <
lampballast
ZZ
1LoopGain =
66
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [196]
Possible modes of operationMode 2: Carrier frequency is equal to the resonant
frequency – unstable mode
CCFLPT ZincZinc >
Tmax
ZEPT
ZECCFL (T)
T
|Z| , P
Nominal P
P
lampballast
ZZ
1LoopGain =
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [197]
Possible modes of operationMode 3: Carrier frequency is near the resonance –
oscillatory mode CCFLPT ZincZinc ≈
TTOP
|Z| , P
Nominal P
ZECCFL (T)ZEPT
LG < -1 LG > -1
P
UNSTABLESTABLE
lampballast
ZZ
1LoopGain =
Sustained oscillation
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [198]
-
- 8
- 6
- 4
2
0
2
4
6
8
-2 -1 0 1 2 3 4 5 6 7Re(LG)
Im(LG)
cf = 49 KHz
33oC
40oC
Nyquist Plot lampballast
ZZ
1LoopGain =
Stable
PT-Lamp Envelope Simulation Results
67
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [199]
Nyquist curves lampballast
ZZ
1LoopGain =
Stable for 40oC but unstable for 33oC
-
4
-
6
-
2
0
2
4
6
- - -3 2 1 0 1 2 3Re(LG)
Im(LG)
cf = 51 KHz33oC40oC
PT-Lamp Envelope Simulation Results
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [200]
Simulation & Experimental
Time4.00ms 4.25ms 4.50ms 4.75ms 4.95ms
Ilamp
0A
-6mA
6mA
0V
-1.2KV
1.2KV
Vlamp
Vlamp
Ilamp
Cycle-by-cycle(TRAN) Simulation
Experimental
Sustained Oscillations in PT-Lamp System
Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [201]
Concluding RemarksOverviewPower Electronics point of viewAs market develops, prices will drop and PE
use will expand
Thank You for Your Attention
The support of theIsraeli Science Foundation
is acknowledged