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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [1]
A Unified SPICE Compatible Model for Large and Small Signal
Envelope Simulation of Linear Circuits
Excited by Modulated Signals Simon Lineykin and Sam Ben-Yaakov*
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: +972-8-647-2949Email: [email protected], Website: www.ee.bgu.ac.il/~pel
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [2]
Power System Driven by a modulated signal
Modulator-Driver
Reactivenetwork
Load
uc(t)
um(t) )t(uout)t(u
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [3]
Example 1: a Resonant Network Excited by a Modulated Signal
FM
Vref PT
RectifierModulator
Controller
Load
fc
Co
Lr
+-
Cr Rm 1:n
Vo/n
Vo
I(Lr)/n
Ci
Vin
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [4]
Example 2: Electronic Ballast
ElectronicDriver
Feedback -+
Vref
Freq
Power
FM input signal Vlamp
I lamp
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [5]
]etjItIRe[ti tf2j21
c
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
c
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [6]
]tLIf2dt
tdIL[j]tV[j
tLIf2dt
tdILtV
1c2
2
2c1
1
tItIti 22
21
tVtVtv 22
21
Phasor Analysis
Inductance
LiL
L
L
I2
I1
I2(t) cL
I1(t) cLIm
Re
+ -
+-
V1
V2
]e)tLIf2jdt
tdIjL
ttIf2dt
tdILRe[(]etjVtVRe[
tf2j1c
2
2c1tf2j
21
c
c
dt
tdiLtv
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [7]
Phasor Analysis
Capacitance
Resistance
VCC
C
CV2
V1cCV2cC
Im
Re
V1I1
I2
R
R
RIm
Re I1
I2
V1
V2
tRitv
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [8]
Splitting the Network into Two Cross-Coupled Components -
Imaginary and Real
LoadNetwork
SourceinV
tu
outV
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [9]
imaginary circuitcomponent
real circuitcomponent
coupling
inre
inim
outre
outim
U1
U2
22V(outim)V(outre) + outV
Real Load Component
Imaginary Load Component
Splitting the Network into Two Cross-Coupled Components -
Imaginary and Real
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [10]
Simulation Alternatives
Cycle-by-cycle (full simulation)High and low frequenciesVery long simulationOnly transientAC transfer function -> point-by-point
Envelope simulation (Large Signal -Previous study)Only low frequency Only transientAC transfer function -> point-by-point
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [11]
Example: Piezoelectric Transformer Driven by FM Signal (SPICE)
Vin
Excitation
Ro
LoadVoutFMVoVin
Rectifier
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [12]
Example: Piezoelectric Transformer Driven by FM Signal (SPICE)
Vin
Excitation
Ro
LoadVoutFMRectifier
Co
Lr
+-
Cr Rm
1:n
Vo/n
Vo
I(Lr)/n
Ci
Equivalent cirquit of the PiezoelectricTransformer
I(Lr)
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [13]
Example: Piezoelectric Transformer Driven by FM Signal (SPICE)
Vin
Excitation
Ro
LoadVoutFMCo
Lr
+-
Cr Rm
1:n
Vo/n
Vo
I(Lr)/n
Ci
Equivalent cirquit of the PiezoelectricTransformer
I(Lr) ReqCeq
Equivalentreplacementof rectifier
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [14]
Example: Piezoelectric Transformer Driven by FM Signal (SPICE)
Vin
Excitation
Ro
LoadVoutFMCo
Lr
+-
Cr Rm
1:n
Vo/n
Vo
I(Lr)/n
Ci
Equivalent cirquit of the PiezoelectricTransformer
I(Lr)
dttuk2tf2cosAtu mfcc
tf2sinA)t(u mmm - Harmonic modulating signal
ReqCeq
Equivalentreplacementof rectifier
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [15]
tf2sintf2sinsinA
tf2costf2sincosAtu
cmc
cmc
Example: Piezoelectric Transformer Driven by FM Signal (SPICE)
Vin
Excitation
Ro
LoadVoutFMCo
Lr
+-
Cr Rm
1:n
Vo/n
Vo
I(Lr)/n
Ci
Equivalent cirquit of the PiezoelectricTransformer
I(Lr)
tf2costf2cosAtu mcc m
mf
fAk
where
ReqCeq
Equivalentreplacementof rectifier
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [16]
OrCAD Schematics for Envelope Simulation
(Large Signal)
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [17]
Results of Full and Envelope Transient Simulations
The modulating input signal
The Frequency modulated signal
Output signal
Time0s 1.0ms 2.0ms 3.0ms 4.0ms 5.0ms 6.0ms 7.0ms
v(out) v(output)
-2.0V
0V
2.0V
SEL>>
v(in) sqrt(v(a)*v(a)+v(b)*v(b))-1.0
0
1.0v(input)
-1.0V
0V
1.0V
Cycle-by-cycle
Cycle-by-cycle
Envelope
Envelope
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [18]
Objectives of this Study
To extend the envelope simulation method to AC analysis
A method that would not need an analytical derivation
Same model compatible with DC, AC, and Transient analysis types
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [19]
Proposed Method – Small Signal Analysis Using AC–Simulation
Amplitude modulation
0U
tuAkAU
2
mcac1
inre
E1
{V(%IN+, %IN-)*ka*Ac}EVALUE
OUT+OUT-
IN+IN-
V1
{Ac}
inim
um(t)
0 0
inre
0
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
tf2costuk1Atu cmac
phasorphasorphasorphasor
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [20]
=Ac*kp*u(t)
Small signal
Linearization of Sources for Angle Modulation
Phase Modulation
PM – Nonlinear source
tuksinAU
tukcosAU
mpc2
mpc1
tuktf2cosAtu mpcc
VAC
inre
0
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)
phasorphasorphasorphasor
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [21]
Linear source
VAC{Am}
inre
{2*Pi*Ac*kf}
INTEG1
inim
0
VDC
0
FM
{Ac}
Linearization of Sources for Angle Modulation
Frequency Modulation
FM – Nonlinear source
dttuktf2cosAtu mfcc
dttuksinAU
dttukcosAU
mfc2
mfc1
=Ac
Small signal
=Ac*kp*u(t)dt
Small signal
0
{2**kf}
INTEG1
{Ac*cos(V(%IN) )}inre
{Ac*sin(V(%IN))}
inim
u(t)
phasorphasorphasorphasor
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [22]
Results: Piezoelectric Transformer Driven by FM signal (AC and Point-by-Point)
for Different Carrier Frequencies
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [23]
Results: Piezoelectric Transformer Driven by FM signal (AC and Point-by-Point)
for Different Carrier Frequencies
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [24]
Frequency Response of the Network (unmodulated input signal)
using DC-sweepDC-sweep in envelope simulation is equivalent to frequency sweep in full simulation
The parameter of DC sweep is a carrier frequency fc
The source for DC sweep:inre
inim
0
VDC
DC
{Ac}
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [25]
Example: Frequency Response of Piezoelectric Transformer with Different Resistive Loads
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BEN-GURION UNIVERSITY OF THE NEGEV PESC’03 [26]
Conclusions
Envelope simulation method was extended to cover all simulation types: Transient, AC, DC.
Method is suitable for any linear circuit.
Method is also suitable for nonlinear circuits that can be linearized for small signal.