1 Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, - - PDF document

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Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements, June 2006 [1] Power Electronics of Piezoelectric Elements Shmuel (Sam) Ben-Yaakov Power Electronics Laboratory Department of Electrical and Computer Engineering Ben-Gurion

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SLIDE 1

1

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [1]

Power Electronics Laboratory Department of Electrical and Computer Engineering Ben-Gurion University of the Negev P.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

  • f 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 devices
  • 3. Drivers
  • 4. Rectifiers
  • 5. PT based CCFL Ballasts
  • The stability issue
  • Envelope Simulation
  • Thermal effects
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SLIDE 2

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

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SLIDE 3

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 Power Electronics 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 devices

The piezoelectric effect

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [9]

where

6 1 values takes q , p 3 1 values takes k , j , i − −

[ ] [

] [ ] [

] [

] [ ] [

] [ ] [

] [

]

k T ik q iq i k kp q E pq p

E T d D E d T s S ⋅ ε + ⋅ = ⋅ − ⋅ =

nt displaceme electric D field electric E companent Stress T companent Strain S

i k q p

= = = =

stress t tan cons at t tan cons ty permittivi t tan cons ric Piezoelect d field electric t tan cons at t tan cons compliance T S s

T ik kp const E q p E pq

= ε = = ∂ ∂ =

=

Compressed notation and matrix arrays:

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SLIDE 4

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 L

Stack of piezoelectric elements

Actuators

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [12]

XY Positioning

200 nm span

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SLIDE 5

5

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [13]

Serial Bimorph Parallel Bimorph

  • Same idea as bi-metal
  • Large deflection, mm range

Bimorph Benders

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [14]

Electrical terminals

p p

x − ∆

Van Bimorphs 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:

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SLIDE 6

6

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [16]

  • Nanomotion Ltd. Israel

piezo ceramic electrode A electrode B electrode C B A common

Elliptic movement

S

1 S2

stator piezo actuator driver 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

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SLIDE 7

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 beam Piezoelectric element Vout

63Ni radioisotope

emitter [12]

Micro-Power Generator

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SLIDE 8

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

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SLIDE 9

9

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [25]

Ski Damping

CEDRAT TECHNOLOGIES & SKI ROSSIGNOL

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [26]

Dampers experiment

http://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

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SLIDE 10

10

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [28]

Piezoelectric Transformers

Vin Vo PT 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 primary part secondary part x x displacement potential VS support point poling

  • High voltage gain

[15-18, 70]

Rosen Type Piezoelectric Transformer

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SLIDE 11

11

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [31]

  • Higher voltage transfer ratio

Vin

A A

Rosen Type Piezoelectric Transformer Multilayer

  • 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 transformers

Advantages

– 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

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SLIDE 12

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) backlight
  • 3. 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 devices

Modeling of Piezoelectric Elements devices

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SLIDE 13

13

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [37]

Electrical-Mechanical Relationships

TechOnLine - Piezoelectric Sidebar 2

Bridging the Mechanical and Electrical Worlds.htm

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [38]

Mechanical-Electrical Analogy

c r m Electronic system Mechanical System m-mass L r-losses R c=1/stiffness C v-velocity i F-force u Cr Lr Rm

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [39]

Electrical Coupling

  • Electrical connection by plated electrodes
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SLIDE 14

14

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [40]

Equivalent Circuit

Lr Rm Cr Vin 1:n Cin

  • The transformer emulates the coupling

between the electrical-mechanical energies

Original Reflected to Primary

Lr Rm Cr Vin 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

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SLIDE 15

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 modes Model

1 nn LSn CSn RSn Cin 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

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SLIDE 16

16

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [46]

Vibrating Van Model

in

C

1 r

C

1 r

L

1 m

R

P.R.B ) j ( Yin ω

2 r

C

3 r

C Van Bimorphs 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 = 100n PW = {1/(2*f req)} PER = {1/f req} V1 = 0 TR = 100n V2 = {Vdc} C2 {C_in} in V3 FREQ = {f req} VAMPL = {ampl} VOFF = 0 R1 {Rm} C1 {Cr} L1 {Lr} 1 2 V1 1Vac 0Vdc PARAMETERS: Lr = 0.00019836 C_in = 39n Cr = 3.5382e-8 f req = 45k ampl = {27.4*1.41} Vdc = 0 Rs = 1u Rm = 155.37

  • Operation near resonance
  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [48]

Ti m e 300us 320us 340us 350us V ( M ) 0V 50V 75V SEL>> I ( V s )

  • 2. 0A

0A

  • 2. 0A

V ( I N ) 0V 50V 100V

Measurement Model Simulation

Voltage Current Voltage Current Drive Drive

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SLIDE 17

17

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [49]

Ti m e 300us 320us 340us 350us I ( V s )

  • 1. 0A

0A

  • 1. 0A

V ( I N )

  • 40V

0V 40V SEL>>

Voltage Current Voltage Current

Measurement Model Simulation

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [50]

  • s

)

  • pt

( L

C R ω = 1

RL P

  • ut
  • C

in

i

RL

( )2

2

1

L

  • s

L ) rms ( in

  • ut

R C R I P 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) Cr Lr Rm Cin Co Energy-Coupling input Energy-Coupling

  • utput

1:n1 1:n2 PT R

L

V

in

V

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SLIDE 18

18

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [52]

Equivalent Circuits of a PT

Cr Lr Rm Cin Co Cr Lr Rm Cin Co Vin Vo ir n ir n Vo 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

  • C

R ′ ′ ′ ′ and

  • f

connection Series

2

  • n

R R = ′

  • 2
  • C

n C = ′

  • C

R ′ ′ and

  • f

connection Parallel

2

  • )

R C ( 1 R R ′ ′ ω + ′ = ′ ′

2

  • 2
  • )

R C ( ) R C ( 1 C C ′ ′ ω ′ ′ ω + ′ = ′ ′

Lr Cin Rm Cr Vin V'o R''

  • C''
  • Lr

Cin C'o Rm Cr R'o Vin V'o [22]

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [54]

Input output voltage transfer ratio

Rosen Type; Cr=37.234pF, Lr=155.3mH, Rm=136.1157 W, n=4.4899, Cin=720.32pF, Co=19.404pF, frs=66.191kHz.

slide-19
SLIDE 19

19

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [55]

Generic Characteristics of PTs

Definitions:

max in V

  • ut

V m 21 k ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ′ =

) r L r C ( 2 in V

  • P

bas P

  • P

*

  • P

= =

100 in P

  • P

× = η

r C r L

  • R
  • C
  • R
  • C

rs Q = ω = m R r C rs 1 m Q ω = r C

  • C

2 n r C

  • C

c = ′ =

[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]

η η= 0.5 ηm (k21)ηm [Q] k21m Po m * Po * (Po)ηm * [k21m ] [η] [Po] * c Qm Qm c + 1 1 1 + 1 2c

Generic Characteristics

[22]

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [57] 0.5 1 1.5 2 2.5 3 10 1 5 10 15 20 25 30

Vout V in m

) )

R o [Ω ] Po Vin

2

mW V 2

10 2 10 3 10 4 10 5 10 6

P o V in

2

V out V in )

)

m

Experimental Results

circles - experimental results; lines - theoretical prediction. [22]

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SLIDE 20

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 & Nonlinearity

Input admittance ,magnitude 150 160 170 180 190 200 210 220 230 240 250 0.5 1 1.5 2 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

20 40 60 80 100 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

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SLIDE 21

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]

Ω 50

  • utput

input R A

A ×

B . R . P , in

Y

Network Analyzer

in

Y

P.R.B . Amp ,

  • ut

V

B . R . P

I Amplifier RF

Ω 50 RShunt RAtten

  • Connection for 50Ω input resistance analyzer

DUT

[2]

Measurements under high power excitation

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SLIDE 22

22

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [64] 150 160 170 180 190 200 210 220 230 240 250 0.5 1 1.5 2 x 10

  • 4 Input admittance magnitude

measured calculated 150 160 170 180 190 200 210 220 230 240 250 20 40 60 80 100 frequency[Hz] Input admittance phase[degrees] measured calculated

Fitting area Fitting area

f1=195[Hz] f2=200.5[Hz]

f > fr

C=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 loaded condition

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [66]

EXPERIMENTAL SETUP

Ω 50

  • utput

input R A

A ×

Network Analyzer

Amplifier RF

Ω 50 Rd1

PT

Rd2 Vout Vin

  • Forward connection
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SLIDE 23

23

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [67]

FORWARD

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ω − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ω + ω − + + = =

f r

  • m

f r

  • r

2 r

  • f

m in

  • R

C n C nR R nL j C nL C nC R nR n 1 V V k

L r Cr Rm Cin Co

+

  • V
  • n

I r

Ir n

Vin Rf T1 T2 Vo L r Cr Rm Cin I r Vin Co

n2

Rf

n2

Vo

n ( ) ( ) ( ) ( ) ( )

f f f f f f

  • ut

in f

k Re k Im tan k Im j k Re V V k = ϕ + = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [68]

BACKWARD

⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ω − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ω + ω − + + = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

r r in m r r in r 2 r in r m in

  • i

R C n C nR R nL j C nL C nC R nR n 1 1 V V k

L r Cr Rm Cin

+

  • V
  • n

I r T2

in

V Co

Ir n

T

1

Rr Vo L r Cr Rm Cin Ir Vin

n

Rr V

  • (

) ( ) ( ) ( ) ( )

r r r r r r

  • ut

in r

k Re k Im tan k Im j k Re V V k = ϕ + = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ =

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [69]

Solving for ϕ

( ) ( ) ( )

  • r

2 r

  • f

m f r

  • m

f r f f f

C nL C nC R nR n R C n C nR R nL k Re k Im tan ω − + + ω − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ω = = ϕ

( ) ( ) ( )

in r 2 r in r m r r in m r r r r r

C nL C nC R nR n 1 R C n C nR R nL k Re k Im tan ω − + + ω − ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ + ω = = ϕ

slide-24
SLIDE 24

24

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [70]

Expanding

( ) ( ) ( )

f r

  • r

3 f

  • r

m f r f r

  • m

r r 2 f

R C C L R C C R R C 1 R C C R C L tan ω − + + ω − + ω = ϕ

( ) ( )

r r in r 3 r in r m r r 2 r r in m r r 2 r

R C C L R C C R R C n 1 1 R C C R C L tan ω − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + ω − + ω = ϕ

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [71]

FITTING ( ) ( ) ( ) ( )

⎩ ⎨ ⎧ = ϕ ω − ω + ϕ ω = ϕ ω − ω + ϕ ω 1 tan b b tan b 1 tan a a tan a

r 3 2 2 r 3 1 f 3 2 2 f 3 1

ai-bi are found by mean square error method

( ) ( ) ( )

f r

  • r

3 f

  • r

m f r f r

  • m

r r 2 f

R C C L R C C R R C 1 R C C R C L tan ω − + + ω − + ω = ϕ

( ) ( )

r r in r 3 r in r m r r 2 r r in m r r 2 r

R C C L R C C R R C n 1 1 R C C R C L tan ω − ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ + + ω − + ω = ϕ

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [72]

Least-Square Fitting

r in r m r r 2 3

R C C R R C n 1 b + + =

r r in r 1

R C C L b =

r r in m r r 2

R C C R C L b + =

f r

  • r

1

R C C L a =

f r

  • m

r r 2

R C C R C L a + =

f

  • r

m f r 3

R C C R R C a + + =

Initial estimation of PT equivalent parameters: Lr(ini),Cr(ini), Rm(ini), Cin(ini), Co(ini), n(ini) ( ) ( ) ( ) ( )

⎩ ⎨ ⎧ = ϕ ω − ω + ϕ ω = ϕ ω − ω + ϕ ω 1 tan b b tan b 1 tan a a tan a

r 3 2 2 r 3 1 f 3 2 2 f 3 1

ai-bi are found by mean square error method

slide-25
SLIDE 25

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 Parameters 0 – 600 KOhm

n Cr Rm Fr

slide-26
SLIDE 26

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]

control

GS

V

S

V

S

V

S

I

d

J

switching

P t t t

Switching losses due to overlap Pd linear with fS !

Switching losses Hard Switching

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [78]

Soft Switching

Real and pseudo

snubber dt dV

D

V

D

I dt dVD

D

V t switching soft " True " switching soft " Pseudo " snubber dt dI

slide-27
SLIDE 27

27

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [79]

Inverter PT Input Matching Network Vo Vin VDS Control IDS

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 AB

VCC

  • VEE

Vin Q1 Q2 VCC Q3 Q4

  • “Charge recovery”

[26, 27, 58]

Class D

  • High Losses
slide-28
SLIDE 28

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 ( LG 1 K H A

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 ( g Im )) f ( LG Re(

1 −

m

Φ

Nyquist criterion can be used to test

for the location of {1+LG(f)} roots.

slide-29
SLIDE 29

29

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [85]

Capacitive Load - Stability Issue

L

C

O

R

f

R

in

R

in

V ] Hz [ f

1

f

2

f

P

f

L O C

, R ] Hz [ f ] Hz [ f

LG

] dB [ A ] DB [ LG dec / dB 20 − dec / dB 40 − dec / dB 60 − combined

1

f

2

f

P

f dec / dB 20 − dec / dB 40 −

] DB [ LG

L O P

C R 2 1 f π =

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [86]

Decoupling Resistor

One possible solution

] dB [ A ] Hz [ f

1

f

2

f

P

f

L O C

, R ] Hz [ f ] Hz [ f

OL

A ] dB [ A ] dB [ A dec / dB 20 − dec / dB 40 − dec / dB 20 − combined

1

f

2

f

P

f

Z

f dec / dB 40 −

Z

f dec / dB 20 − dec / dB 40 −

L

C

O

R

f

R

in

R

in

V

S

R

L S O P

C ) R R ( 2 1 f + π =

L S Z

C R 2 1 f π =

Signal attenuation at f > fP

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [87]

Demo Circuit

slide-30
SLIDE 30

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 Vin Ls Vp 1:n Vin

LLCC LC and PWM

Q1 Q2 Cin VCC D1 D2

  • 1. LC

D3 D4 Q3 Q4 Lr Rm Cr Output filter

  • 2. LCC
  • 3. PWM

[26]

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [89]

Converter topology LC LLCC PWM

] A [ ˆ i ] mH [ L ] A [ ˆ i ] mH [ L ] A [ ˆ i ] mH [ L

Series inductance

S

L

0.01 8.8 0.01 6.37 0.01 0.258 Parallel inductance

P

L

  • 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
slide-31
SLIDE 31

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 Iin

Series inductance (Lseries) that needs to be placed in series with the PRB to achieve ZVS:

C ) f 2 ( 1 L

2 r series

π >

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 frequency Sinusoidal drive Constant frequency operation Variable amplitude Fast 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

slide-32
SLIDE 32

32

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [94]

Lin RL CL C2 Vin

OSCILLATOR + DRIVERS

Lm n2 T1 ZL V n1 n1 Vtap C1 D Q2 VGS2 VD2 2 D1 Q1 VGS1 D1

time

V Ts Ts 2

VD1 V D2 V D2 Vtap VGS1 VGS2 Vtap Vtap time time time time

The Current-Fed Push-Pull Parallel-Resonant Inverter (CFPPRI)

r s

f f =

r s

f f <

r s

f f > 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 in CL ZL RL VD2 Vin D2 C2 C3 Ibias D1 Q1 Q2 VD1 Rin2 n T1 Lr n2 n11 12 n3 R2 Phase comparator LPF

Fin

Rin1 R1 C1

Fβ

D3 Q3 Vin +

  • PWM

Modulator Rf Vref A1 Vtap VGS2 VGS1 COMP1 Vref Q Q T DR2 DR1 FF

phase feedback Soft Switching Controller (SSC) Current feedback Controlled inductor

[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)
slide-33
SLIDE 33

33

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [97]

PT

Control Input Matching Network Iin Vin Vout

Hard switching Soft switching

V

DS

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 Waveforms

  • f the ZVS PT Inverter

) t sin( I ) t ( i

m

ψ − ω =

i(t) Vin D2 D1 Iin Cin Q1 Q2 VDC

Res. tank

VGS1 V

GS2

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]

slide-34
SLIDE 34

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

∆

1.015 1.005 1.01 1.02 1.025 0.05 0.15 0.25 %) 97 = (ηPT 37 . Q = 25 . Q = %) 5 . 90 (ηPT= 13 . Q = %) 5 . 94 (ηPT= ∆r is the normalized charging time k is the normalized

  • peration 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

slide-35
SLIDE 35

35

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [103]

Vin Lp Inverter PT Cb

Vin Lp Inverter PT Cb

A B A - DC on PT B – 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 Q2 Cin Vin D1 D2 CDS1 CDS2 PT VGS2 VGS1 Control LP CB

r C P

C 2 DT ) D 1 ( T L − =

2 DS 1 DS in r

C C C C + + =

cycle duty D −

period T − T 1 . T

C ≈ r

C

  • f

time ing arg ch the

  • 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 PT Lin

  • 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]

slide-36
SLIDE 36

36

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [106]

Input Impedance of the PT

Fr equency 100K H z 150K H z p( I ( L2) ) - p( V ( PTI N A C) ) 0d

  • 100d

100d SEL>> V ( O U TA C) / V ( PTI N A C)

  • 0. 50
  • 1. 00
  • 0. 05
  • Not always capacitive around the operating frequency

inductive

Fr equency

  • 100. 0K

H z

  • 43. 6K

H z p( I ( L4) ) - p( V ( PTTA C) ) 0d 50d 100d V ( out ) / V ( PTTA C)

  • 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 100K H z 120K H z 140K H z 150K H z V ( O U TA C) / V ( I N PU TA C)

  • 1. 0
  • 2. 0

P( - I ( V 6) )

  • 100d

0d 100d SEL>> V ( O U TA C) / V ( PTI N A C)

  • 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 m e

  • 920. 0us
  • 930. 0us
  • 914. 3us
  • 935. 0us

V ( I N PU TTRA N ) 50V

  • 10V

SEL>> V ( PTTRA N S) 0V 25V 50V I ( L4)

  • 40m

A 0A 40m A

Inductor current PT voltage HB commutation

  • Large-signal time-domain (TRAN) simulation
slide-37
SLIDE 37

37

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [109]

Ti m e

  • 672. 00us
  • 674. 00us
  • 676. 00us

V ( I N PU TTRA N ) 0V 20V 40V 52V

Green=1mH Red=1.6mH Blue= 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 PT C1 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 m e

  • 700. 0us
  • 710. 0us
  • 720. 0us
  • 730. 0us

V ( I N PU TTRA N ) 0V 200V V ( PTTRA N S)

  • 200V

0V 200V SEL>> I ( L104)

  • 100m

A 0A 100m A V ( O U TTRA N )

  • 500V

0V 500V

Output voltage Inductor current PT input voltage HB commutation

slide-38
SLIDE 38

38

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [112]

I t t I t t

Q 4 3 D 3 1

> − > − V t t

  • ff

Q t t

in C 1 2

> − − − Advantages:

  • 1. Only one switch
  • 2. Low cost
  • 3. Better EMI suppression

Disadvantage:

  • 1. Small operational range
  • 2. High voltage stress

L Lr Cin C'o Rm Cr R'o Vin V'o D Q VCin ID IQ 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)

Vin VoPT Q1 CDS1 D1 Q2 CDS2 D2 L2 L1 IL1 IL2 Ro PT C VDS1 VDS2 D2 D1 Q2 Q1 Interval

1

  • t

t −

2 1

t t −

3 2

t t −

4 3

t t −

  • n
  • ff
  • ff
  • ff
  • ff
  • ff
  • ff
  • ff
  • ff
  • ff
  • ff
  • n
  • n
  • n
  • n
  • n

Advantages: Nearly sinusoidal waveform Disadvantages: Narrow

  • perational 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

Lin C2 Vin

OSCILLATOR + DRIVERS

Lm n2 T1 PT V n1 n1 Vtap C1 D Q2 VGS2 VD2 2 D1 Q1 VGS1 D1 [28]

slide-39
SLIDE 39

39

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [115]

Resonant Forward-Flyback Inverter

Vin VoPT Ro PT Q C D Lm Llkg2 CIN IME IME – Integrated Magnetic Element Lm – magnetization inductance Llkg2 – 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

slide-40
SLIDE 40

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 Lr Cr VLr Q2

VGS1 VGS2 VDS1 VLr t t t VGS ) D sin( D V V in Lr π − π = 1 2

  • ZVS
  • Voltage gain
  • Squarewave drive

[37, 38]

0.2 0.4 0.6 0.8 1

in

  • V

V Active clamp Asymmetrical D

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [120]

Lo PT

in

V

2

D

1

D

f

L

f

C

L

R PT

in

V

2

D

1

D

f

C

L

R L1 L2

Current Doubler Half Wave

[21, 38, 43]

  • 4. Rectifiers

PT Rectifiers - Inductive Filter

slide-41
SLIDE 41

41

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [121]

PT Rectifiers - Capacitive Filter Voltage Doubler Diode Bridge

CF Vin PT Ro D2 D1 D3 D4 Vin CF PT Ro D1 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

iD1 iD2

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

PT

in

V

L

R

  • C

Rect

n vCo in V in C r L r C m R n ir C Req eq

[39-41]

slide-42
SLIDE 42

42

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [124]

Equivalent Circuit Parameters m PT PT ) 1 ( 2 L eq r m

Q K A sin R R 1 ϕ + ω = ω

Voltage Doubler

⎪ ⎪ ⎩ ⎪ ⎪ ⎨ ⎧ ω ϕ = =

VD eq ) 1 ( VD eq L 2 ) 1 ( VD eq

R tan C R k 8 1 R

) 1 ( pk ) 1 ( Co L rect

k 2 V V k = =

Current Doubler

⎪ ⎪ ⎪ ⎩ ⎪ ⎪ ⎪ ⎨ ⎧ ω ϕ = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ λ π =

CD eq ) 1 ( CD eq L 2 ) 1 ( 2 2 CD eq

R tan C R k 2 1 R

) 1 ( 2 pk ) 1 ( Co L rect

k V V k π λ = =

Rectifier Voltage Transfer Ratio Frequency of the Maximum Output Voltage

[43]

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [125]

10000 0.1 1 10 100 1000 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 R

  • L

[ ]

eq

R /RL

ad

C /Co [C /C ]

ad

  • [R /R ]

eq L

  • 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 eq C eq

2 eq ' eq 2 eq ' eq

n C C n R R = =

) 1 ( 2 ' eq ' ' eq ) 1 ( 2 ' eq ' ' eq

sin C C cos R R ϕ = ϕ =

L r C r R m C in Ir V in

eq

C R eq

[22, 39, 40]

Normalized parameters:

  • KPT=RL/n2Rm – Normalized load factor
  • APT=ωrCon2Rm – Normalized PT factor
  • Qm=1/ωrCrRm – PT mechanical quality factor
slide-43
SLIDE 43

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

101 Current Doubler Voltage Doubler

KPT=RL/n2Rm Overall voltage gain Vo(DC)/Vin(AC)

[43]

0.2 0.4 0.6 0.8

η

100 102 104 KPT Current Doubler Voltage Doubler

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 0.03

10 20 30 40 100 101 102 103 104

∆PT kPT

0.01 0.02 0.03

Qm =1000

APT=0.008 APT=0.008 Current doubler Voltage doubler

KPT=RL/n2Rm APT=ωrCon2Rm Qm=1/ωrCrRm

[43]

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [129]

Boundary Conditions for Choosing the Rectifier type

VD CD

Qm=1000 500 200 50 0.01 0.03 0.05 APT KPT 20 60 100

KPT=RL/n2Rm APT=ωrCon2Rm Qm=1/ωrCrRm

[43]

slide-44
SLIDE 44

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 in High Voltage Application

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [131]

S 2 S 1 L b C 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

V

Lmax

(V )

L fr

[V , V]

L

[R , MOhm] 0 5 10 15 20

L

[39, 40]

slide-45
SLIDE 45

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 ir

The phase of the current iD2 is the

same as one of ir

The trailing edge of the iD2 level

detection wave may be used as Phase Reference Phase Reference D2 D1 Cf RL VCo VL Co Cr Rm Lr Vin ir ir N VCo N

iD2 level detection 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

370uH 10k 4.7k 4.7k D1 D2 CL RL PT Vin Vout p(Vin) p(Id) Phase detector 39k 1n VCO 4.2k 1.5k 3.3k 1k 15v 15v 15v

FF Q Q

IR 2110 driver

0.22u 10.2n 10k 4.7 10k 4.7 CD4046A VLF f High voltage V1 V4 V2 V3 BN 6.6n

[44]

slide-46
SLIDE 46

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

  • s

)

  • pt

( L

C R ω = 1

RL P

  • ut
  • C

in

i

RL

( )2

2

1

L

  • s

L ) rms ( in

  • ut

R C R I P ω + =

Ropt

Piezo Source Load

slide-47
SLIDE 47

47

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [139]

Capacitive Source Problem

  • C

in

i

L

C

in

V

  • ut

i

L

V

L

I

1 B

D

2 B

D

3 B

D

4 B

D

RL

in

V

in

I

  • ut

i

1

t

2

t

3

t

) pk ( in

V

π ω + π ω − π = =

L

  • s

D

  • s

P L

  • ut

R C V C I I i 2 1 4 2 IL

L L

  • s

D

  • s

P L L

R R C V C I ) R ( P ⋅ ⎟ ⎟ ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎜ ⎜ ⎝ ⎛ π ω + π ω − π =

2

2 1 4 2 ) V V ( C R

L D

  • s

)

  • pt

( L

2 1 1 2 + ω ⋅ π = DB2 ‘ DB3 DB1 ‘ DB4

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [140]

What if Co=0 ?

in

i

L

C

in

V

  • ut

i

L

V

L

I

1 B

D

2 B

D

3 B

D

4 B

D

RL

in

V

  • ut

i

IL

π = π ω + π ω − π = =

=

P L

  • s

D

  • s

P L

  • ut

I R C V C I I i

  • C

2 2 1 4 2

L P L L

R I ) R ( P ⋅ ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ π =

2

2 ∞ ≈

)

  • pt

( L

R

in

i

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [141]

Earlier solutions and their limitations

  • C

in

i

RL L

  • s

LC 1 = ω

Disadvantage Large inductance

Passive and active solutions

Emulator

Disadvantages 1.Large in size 2.Difficult to tune 3.High sensitivity 4.External source

slide-48
SLIDE 48

48

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [142]

Proposed Resonant Rectifier Circuit

  • C

in

i

L

C

L

R

in

V

  • ut

i

1

D

2

D

res

L

der

V

c

V 1 sw 2 sw

COMP.

res

i

dt d

L

V

L

I

1 B

D

2 B

D

3 B

D

4 B

D

Capacitive Source Differentiator Comparator Diode Bridge Inductor & Switches

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [143]

Principles of operation

c

V

der

V

res

i

in

V

  • ut

i

1

t

2

t

3

t

4

t

5

t

  • C

in

i

L

C

L

R

in

V

  • ut

i

1

D

2

D res

L

der

V

c

V 1 sw 2 sw

COMP.

res

i

dt d

L

V

L

I

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

  • s

2 D ) pk ( in ) loss ( R

1 e 1 C f ) V V ( P

r r r

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ω α + − ⋅ ⋅ ⋅ − =

ω α π − 2 r r ) ( D ) pk ( in

  • s

D ) loss ( D

1 e 1 ) V V ( C f V 2 P

r r

⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ ω α + + ⋅ − ⋅ ⋅ ⋅ =

ω α π − Q ) pk ( in ) loss .( Comp

I V 2 P ⋅ ≈

s ) pk ( in ) n ( gs s ) pk ( in ) p ( gs ) loss ( Gate

f V Q f V Q P ⋅ ⋅ + ⋅ ⋅ ≈ L D ) loss ( Bridge I V 2 P ⋅ ≈

Bridge losses Gate drive losses Comparator losses Diode losses Resistance losses

slide-49
SLIDE 49

49

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [145]

  • C

ex

V

L

R in

V

1

D

2

D

res

L der

V

S

V +

S

V −

n

M

p

M

sens

R

hys

R

der

C

der

R COMP. c

V

1 S

D

2 S

D

1 S

C

2 S

C

L

C

1 B

D

2 B

D

3 B

D

4 B

D in R L

V

+ − in

i

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 Differentiator

Current source

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [146]

L

R in

V

1

D

2

D

res

L der

V

S

V +

S

V −

n

M

p

M

hys

R

der

C

der

R COMP. c

V

1 S

D

2 S

D

1 S

C

2 S

C

L

C

1 B

D

2 B

D

3 B

D

4 B

D L

V

+ − Actuator Transducer ex

V 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

  • C

in

i

L

C

in

V

  • ut

i

L

V

L

I

1 B

D

2 B

D

3 B

D

4 B

D

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.

  • C

ex

V

L

R in

V

1

D

2

D

res

L der

V

S

V +

S

V −

n

M

p

M

sens

R

hys

R

der

C

der

R

COMP.

c

V

L

C

1 B

D

2 B

D

3 B

D

4 B

D in

R L

V

+ −

1 S

D

2 S

D

1 S

C

2 S

C in

i

External

slide-50
SLIDE 50

50

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [148]

Results

251% 3.16mW 3.51KΩ 3.34V RESONANT RECTIFIER WITH EXTERNAL SUPPLIES VS=±4V 142% 1.79mW 2.75KΩ 2.2V RESONANT RECTIFIER

  • 1.26mW

2.1KΩ 1.6V STANDARD RECTIFIER GAIN (%) COMPARED WITH STANDARD RECTIFIER OUTPUT POWER OPTIMAL LOAD RESISTANCE OUTPUT VOLTAGE (DC) CIRCUIT TOPOLOGY 230% 1.23mW 11.43KΩ 3.75V 118% 0.636mW 5.19KΩ 1.818V

  • 0.537mW

5.89KΩ 1.779V 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)

in in i

V ⋅

in

i

in

V

1

t

2

t

3

t

4

t

5

t

in

V

der

V

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.

slide-51
SLIDE 51

51

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [151]

PT Inverter Vo Vin= 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]

slide-52
SLIDE 52

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 Fast Current Changes Slow Power Changes I(lamp) [Arms] V(lamp) [Vrms] Fast Current Changes A Req1 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]

eq 1

R ) lamp ( V G =

) I ( f R

) rms ( lamp eq =

RiCi match the dynamic response of lamp

2 1

)} lamp ( i { E ≡ ) p ( v E2 ≡

+

  • +
  • rms

Lamp Model R

lamp isq p

Ci Ri E2 E1 G1

Lamp

[83]

SPICE Compatible Fluorescent Lamp Model

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [156]

1 f jf 1 R R f jf s R ) L f ( inc Z

L s eq L

+ − =

eq INC L s INC L

R Z f For R Z f For → ∞ → − → →

  • “Right-Half Complex-Plane” Zero

[83]

Incremental impedance

  • f fluorescent lamps
slide-53
SLIDE 53

53

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [157] Frequency 100Hz 10KHz 1.0MHz db

  • 50
  • 45
  • 40

0o

  • 200
  • 100
  • | 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

  • measured

response

  • simulated

response

I V I V

[83]

Response to modulation

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [159]

Modulation frequency 5kHz Excitation frequency 50kHz

Positive incremental resistance

I V

  • measured

response

  • simulated

response

I V

[83]

Response to a modulation

slide-54
SLIDE 54

54

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [160]

1A

  • 1A

200V

  • 200V
  • measured

response

  • simulated

response

I V I V

[83]

Response to a power step

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [161]

Vlamp Zlamp V ex +

  • Ilamp

Zballast 1 V ex Zballast Zlamp Vlamp Ilamp Ballast Zballast Zlamp V ex

lamp ballast

Z Z 1 LoopGain =

Ballast-Lamp Interaction Feedback Model

[78]

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [162]

Stability Criteria for Carrier Driven Systems What is Z ?

Lamp (Non-Linear Negative Resistance Load) Ls Cs Vin fc s s r c

C L 2π 1 f f = >>

s s r c

C L 2π 1 f f = ≈ Stable Unstable

slide-55
SLIDE 55

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 ex m inc

∆I ∆V f Z =

Ls Cs V ex Iex ∆Iex ∆V ex

  • 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

fr fc fm fm

( ) ( ) ( ) ( )

t 2 sin t 2 sin A 1 t V

c m m ex

f f π π + =

Ls Cs Rs AM Modulated Signal Yinc fm ( )

fm sweep Vex Y of Resonant Network

  • 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

slide-56
SLIDE 56

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 Reactive network 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]

( ) ( ) ( ) ( )

] e t jI t I Re[ t i

t f 2 j 2 1

c

π

+ =

A Primer to Envelope Simulation

Any analog modulated signal (AM, FM

  • r PM) can be described by the following

expression:

The Current in the network excited by u(t):

( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

] e t jU t U Re[ t f 2 sin t U t f 2 cos t U t u

t f 2 j 2 1 c 2 c 1

c

π

− = π + π =

slide-57
SLIDE 57

57

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [169]

( ) ( ) ( ) ( ) ( ) ( )

⎪ ⎩ ⎪ ⎨ ⎧ π + = π − = ] t LI f 2 dt t dI L [ j ] t V [ j t LI f 2 dt t dI L t V

1 c 2 2 2 c 1 1

( ) ( ) ( )

t I t I t i

2 2 2 1

+ =

( ) ( ) ( )

t V t V t v

2 2 2 1

+ =

Phasor Analysis

Inductance

L iL L L I2 I1 I2(t) ωcL I1(t) ωcL Im Re

+

  • +
  • V1

V2

( ) ( ) ( ) ( ) ( ) ( ) ( )

] e ) t LI f 2 j dt t dI jL t tI f 2 dt t dI L Re[( ] e t jV t V Re[

t f 2 j 1 c 2 2 c 1 t f 2 j 2 1

c c

π π

π + + π + = −

( ) ( )

dt t di L t v =

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [170]

Phasor Analysis

Capacitance Resistance

VC C C C V2 V1ωcC V2ωcC Im Re V1 I1 I2 R R R Im Re I1 I2 V1 V2

( ) ( )

dt t dv C t i =

( ) ( )

t Ri t v =

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [171]

Splitting the Network into Two Cross-Coupled Components - Imaginary and Real

Load

Network

Source in

V

( )

t u

  • ut

V

slide-58
SLIDE 58

58

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [172]

imaginary circuit component real circuit component coupling

inre inim

  • utre
  • utim

U

1

U2

2 2 V(outim) V(outre) +

  • ut

V

Real Load Component Imaginary Load Component

Splitting the Network into 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

Load Vout

FM

Vo Vin

Rectifier

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [174]

Example: Piezoelectric Transformer Driven by FM Signal (SPICE)

Vin Excitation

Ro

Load Vout

FM

Rectifier

Co Lr +

  • Cr

Rm 1:n Vo/n Vo I(Lr)/n Ci

Equivalent cirquit of the Piezoelectric Transformer

I(Lr)

slide-59
SLIDE 59

59

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [175]

Example: Piezoelectric Transformer Driven by FM Signal (SPICE)

Vin Excitation

Ro

Load Vout

FM

Co Lr +

  • Cr

Rm 1:n Vo/n Vo I(Lr)/n Ci

Equivalent cirquit of the Piezoelectric Transformer

I(Lr) Req Ceq

Equivalent replacement

  • f rectifier
  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [176]

Example: Piezoelectric Transformer Driven by FM Signal (SPICE)

Vin Excitation

Ro

Load Vout

FM

Co Lr +

  • Cr

Rm 1:n Vo/n Vo I(Lr)/n Ci

Equivalent cirquit of the Piezoelectric Transformer

I(Lr)

( ) ( )

( )

∫

π + π = dt t u k 2 t f 2 cos A t u

m f c c

( )

t f 2 sin A ) t ( u

m m m

π =

  • Harmonic modulating signal

Req Ceq

Equivalent replacement

  • f rectifier
  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [177]

( ) ( ) ( ) ( ) ( ) ( ) ( )

t f 2 sin t f 2 sin sin A t f 2 cos t f 2 sin cos A t u

c m c c m c

π π β − π π β =

Example: Piezoelectric Transformer Driven by FM Signal (SPICE)

Vin Excitation

Ro

Load Vout

FM

Co Lr +

  • Cr

Rm 1:n Vo/n Vo I(Lr)/n Ci

Equivalent cirquit of the Piezoelectric Transformer

I(Lr)

( ) ( ) ( )

t f 2 cos t f 2 cos A t u

m c c

π β − π =

m m f

f A k where = β

Req Ceq

Equivalent replacement

  • f rectifier
slide-60
SLIDE 60

60

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [178] {I(iim)/n} {Co}

  • utre

{Lr} ire 0Vdc {Co} inim {Rm} {V(outim)/n} {-V(outim)* 2*π*fc*Co} {Ro} a inre {Lr} {Cr} {V(outre)* 2*π*fc*Co} d iim 0Vdc c {Ro} {Ac*cos((Am*kf/fm)* sin(6.283186*fm*time))} VinputRE {(V(a)-V(b))*2*π*fc*Cr} {Cr} b {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} {I(ire)/n}

  • utim

Excitation

{-(V(c)-V(d))*2*π*fc*Cr} {Rm} PARAMETERS: Lr = 22.6m Cr = 9.83p Rm = 1.121k n = 0.647 Co = 225p Ro = 20k PARAMETERS: fc = 358k fm = 8k Am = 1 Ac = 1 kf = 1000 sqrt(v(outre)**2+v(outim)**2)

  • ut

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 m e 0s

  • 1. 0m

s

  • 2. 0m

s

  • 3. 0m

s

  • 4. 0m

s

  • 5. 0m

s

  • 6. 0m

s

  • 7. 0m

s 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
  • 1. 0

v( 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

( )

⎩ ⎨ ⎧ = + = U t u A k A U

2 m c a c 1

inre E1 {V(%IN+, %IN-)*ka*Ac} EVALUE

OUT+ OUT- IN+ IN-

V1 {Ac} inim um(t) inre E1 {V(%IN+, %IN-)*ka*Ac} EVALUE

OUT+ OUT- IN+ IN-

V1 {Ac} inim

VAC {Am}

The source is linear and suitable for AC analysis – as is ( ) ( ) ( ) ( )

t f 2 cos t u k 1 A t u

c m a c

π + =

phasor phasor phasor

slide-61
SLIDE 61

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 ( )

( )

( )

( )

⎩ ⎨ ⎧ = = t u k sin A U t u k cos A U

m p c 2 m p c 1

( ) ( )

( )

t u k t f 2 cos A t u

m p c c

+ π =

VAC inre VDC {Ac} PM {Am} inim {kp*Ac} GAIN1

Linear source =Ac

Small signal inre inim {Ac*cos(V(%IN) )} {Ac*sin(V(%IN))} {kp} GAIN1 um(t)

phasor phasor phasor

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [182]

Linear source

VAC {Am} inre {2*Pi*Ac*kf} INTEG1 inim VDC FM {Ac}

Linearization of Sources for Angle Modulation

Frequency Modulation

FM – Nonlinear source ( ) ( )

( ) ( )

∫

+ π = dt t u k t f 2 cos A t u

m f c c

( )

( )

( )

( )

⎪ ⎩ ⎪ ⎨ ⎧ = =

∫ ∫

dt t u k sin A U dt t u k cos A U

m f c 2 m f c 1

=Ac

Small signal

=Ac*kp*∫u(t)dt

Small signal {2*π*kf} INTEG1 {Ac*cos(V(%IN) )} inre {Ac*sin(V(%IN))} inim u(t)

phasor phasor phasor

  • 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

  • 70
  • 80
  • 90
  • 100
  • 110
  • 120

F requency, kH z

  • 360
  • 270
  • 180

0.1 1 10 100 G ain, db P hase, deg

fc=3 6 0kH z fc=35 8 .5 kH z fc=35 7 kH z

slide-62
SLIDE 62

62

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [184]

ZPT Lin Vin Zlamp PT

PTs: ELECERAM Co. Experimental Circuit

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [185]

V ex Zballast Zlamp Vlamp Ilamp Ballast Zballast Zlamp V ex

lamp ballast

Z Z 1 LoopGain =

[78]

Vlamp Zlamp V ex +

  • Ilamp

Zballast 1

Ballast-Lamp Interaction Feedback 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 R9 1k 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*Cin} GVALUE OUT+ OUT- IN+ IN- E6 {V(out_re)/n_e} EVALUE OUT+ OUT- IN+ IN- G3 {I(I_re)/n_e+V(out_im)*6.28*fc*Co } GVALUE C3 {Co} R5 {Ro}

  • ut_re

R7 1u R8 1u OUT+ OUT- IN+ IN- E7 {V(out_im)/n_e} EVALUE OUT+ OUT- IN+ IN- G4 {I(I_im)/n_e-V(out_re)*6.28*fc*Co } GVALUE C4 {Co} R6 {Ro}

  • ut_im

V2 {Am*Ac*Ka} {Ac} 1 2 L1 {Lr} C1 {Cr} R1 {Rm} OUT+ OUT- IN+ IN- E1 {-I(I_im)*6.28*fc*Lr} EVALUE PARAMETERS: Lr = {1.125m*(n_a*n_a)} Cr = {8.5n/(n_a*n_a)} Rm = {.67*(n_a*n_a)} Co = 230n Ro = 1u fm = 5k Cin = 32p n_a = 57 n_e = {57/(n_a*n_a)} fc = 50k Ac = 1 a OUT+ OUT- IN+ IN- G1 {-(V(c)-V(d))*6.28*fc*Cr} GVALUE I_re 0Vdc b a 1 2 L2 {Lr} C2 {Cr} R2 {Rm} OUT+ OUT- IN+ IN- E2 {I(I_re)*6.28*fc*Lr} EVALUE c OUT+ OUT- IN+ IN- G2 {(V(a)-V(b))*6.28*fc*Cr} GVALUE C5 {Cin} I_im 0Vdc d C6 {Cin} OUT+ OUT- IN+ IN- E5 sqrt(V(x_re)**2+V(in_im)**2) EVALUE

  • ut

R4 1k R19 1u in_im OUT+ OUT- IN+ IN- G5 {-(V(in_im))*6.28*fc*Cin} GVALUE x_re in_re in_re

Real Part Imaginary Part Excitation (AM)

PT envelope simulation - Zinc measurement

slide-63
SLIDE 63

63

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [187] Frequency 100Hz 1.0KHz 10KHz P(V(tot_cur)) 0d

  • 200d

180d V(tot_cur) 0V 200uV 400uV fc = 51KHz fc = 52KHz fc = 49KHz fc = 54KHz fc = 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]

( )

rms lamp

I f R =

OUT+ OUT- IN+ IN- E3 I(V3)**2 EVALUE OUT+ OUT- IN+ IN- E9 sqrt(V(p)) EVALUE R3 100 C10 1u IC = p V3 0Vdc rms OUT+ OUT- IN+ IN- G8 V(lamp)/V(Rinc) GVALUE lamp R11 1meg V4 2.5kVdc V5 1Vac 0Vdc OUT+ OUT- IN+ IN- E10 V(rms) ETABLE Rinc

ETABLE

Ilamp 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

1 2 3 4 5 (a) Forced air flow (b) Natural convection

33oC @ 3mA 40oC @ 3mA Rs1 Rs2

slide-64
SLIDE 64

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 Rs

500 550 600 650 700 750 800 0.5 1 1.5 2.5 3.5 4.5 2 3 4 5

[mA] Ilamp [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 10H z 100H z

  • 1. 0K

H z 10K H z 100K H z V ( l am p) / I ( V 3) 200K 400K p( V ( l am p) / I ( V 3) ) 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 93 ZECCFL [dB] (a) 33oC (b) 40oC

slide-65
SLIDE 65

65

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [193]

Stability Criterion

) f ( LG 1 K H A

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 ( g Im )) f ( LG Re(

1 −

m

Φ

lamp ballast

Z Z 1 LoopGain =

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [195]

Possible modes of operation

ZEPT ZECCFL (T) T TOP |Z| , P Nominal P Tmax P

Mode 1: Carrier frequency is far from resonance – stable mode

CCFL PT

Zinc Zinc <

lamp ballast

Z Z 1 LoopGain =

slide-66
SLIDE 66

66

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [196]

Possible modes of operation

Mode 2: Carrier frequency is equal to the resonant frequency – unstable mode

CCFL PT

Zinc Zinc >

Tmax ZEPT ZECCFL (T) T |Z| , P Nominal P P

lamp ballast

Z Z 1 LoopGain =

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [197]

Possible modes of operation

Mode 3: Carrier frequency is near the resonance –

  • scillatory mode

CCFL PT

Zinc Zinc ≈

T TOP |Z| , P Nominal P ZECCFL (T) ZEPT LG < -1 LG > -1 P UNSTABLE STABLE lamp ballast

Z Z 1 LoopGain =

Sustained oscillation

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [198]

  • 8
  • 6
  • 4

2 2 4 6 8

  • 2
  • 1

1 2 3 4 5 6 7

Re(LG) Im(LG) c f = 49 KHz 33oC 40oC

Nyquist Plot

lamp ballast

Z Z 1 LoopGain = Stable

PT-Lamp Envelope Simulation Results

slide-67
SLIDE 67

67

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [199]

Nyquist curves

lamp ballast

Z Z 1 LoopGain = Stable for 40oC but unstable for 33oC

  • 4
  • 6
  • 2

2 4 6

  • 3

2 1 1 2 3

Re(LG) Im(LG) c f = 51 KHz 33oC 40oC

PT-Lamp Envelope Simulation Results

  • Prof. S. Ben-Yaakov, Power Electronics of Piezoelectric Elements,

June 2006 [200]

Simulation & Experimental

Time 4.00ms 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 Remarks

Overview Power Electronics point of view

As market develops, prices will drop and PE

use will expand

Thank You for Your Attention

The support of the Israeli Science Foundation is acknowledged