Unified SPICE Compatible Model (Envelope Simulations)

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Transcript Unified SPICE Compatible Model (Envelope Simulations) 

BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
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 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: [email protected], Website: www.ee.bgu.ac.il/~pel
[1]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Power System
Driven by a modulated signal
uc(t)
ModulatorDriver
um(t)
Reactive
network
u (t)
Load
uout( t )
[2]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Example 1: a Resonant Network
Excited by a Modulated Signal
fc
Vref
PT
FM
Modulator
Rectifier

Controller
Vin Lr Cr Rm 1:n Vo
Ci
+
-
Co
Vo/n I(Lr)/n
Load
[3]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Example 2: Electronic Ballast
I lamp
Power
Electronic
Driver
FM input signal Vlamp
Freq
 +
Vref
Feedback
[4]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
[5]
A Primer to Envelope Simulation
Any analog modulated signal (AM, FM
or PM) can be described by the following
expression:
ut   U1t  cos2fc t   U2 t  sin2fc t  
Re[ U1t   jU2 t e
j2fc t
]
The Current in the network excited by u(t):
it   Re[I1t   jI2 t e
j2fc t
]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Phasor Analysis
[6]
dit 
v t   L
Inductance
dt
dI1t 
j2fc t
Re[ V1t   jV2 t e
]  Re[(L
 2fc tI2 t  
dt
2
it   I12 t   I22 t 
V2
I 2 (t)  c L
+
-
+
-
dI2 t 
jL
 j2fcLI1t )e j2fc t ]
dt
V1
V t   L dI1t   2f LI t 
L
1
c
2
Re

dt
I1

 j[ V2 t ]  j[L dI2 t   2fcLI1t ]
L
iL

dt
L
Im
v t   V12 t   V22 t 
I
I 1 (t)  c L
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Phasor Analysis
Capacitance
VC
V1
C
I1
Re
dv t 
it   C
dt
V2 cC
V1cC
C
Im
I2
Resistance
[7]
Re
R
C
V2
I1
R
V1
V2
Im
I2
R
v t   Rit 
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Splitting the Network
into Two Cross-Coupled Components Imaginary and Real
Source
u t 
Vout
Vin
Network
Load
[8]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Splitting the Network
into Two Cross-Coupled Components Imaginary and Real
Real Load
Component
Imaginary
Load
Component
[9]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
[10]
Simulation Alternatives
Cycle-by-cycle (full simulation)
High and low frequencies
Very long simulation
Only transient
AC transfer function -> point-by-point
Envelope simulation (Large Signal -Previous study)
Only low frequency
Only transient
AC transfer function -> point-by-point
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Example: Piezoelectric Transformer
Driven by FM Signal (SPICE)
Excitation
Vin
FM
Rectifier V
Load
out
Ro
[11]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Example: Piezoelectric Transformer
Driven by FM Signal (SPICE)
Excitation
Vin
FM
Equivalent cirquit of the Piezoelectric
Transformer
Lr
Cr
Rm
Rectifier V
Vo
1:n
Ci
Co
I(Lr)
+
Vo/n
I(Lr)/n
Load
out
Ro
[12]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Example: Piezoelectric Transformer
Driven by FM Signal (SPICE)
Excitation
Vin
FM
Equivalent cirquit of the Piezoelectric Equivalent
replacement
Transformer
of rectifier
Lr
Cr
Rm
Vo
Vout Load
1:n
Ci
Co
I(Lr)
+
Vo/n
I(Lr)/n
C eq
R eq
Ro
[13]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Example: Piezoelectric Transformer
Driven by FM Signal (SPICE)
Excitation
Vin
FM
Equivalent cirquit of the Piezoelectric Equivalent
replacement
Transformer
of rectifier
Lr
Cr
Rm
Vo
Vout Load
1:n
Ci
Co
I(Lr)
+
Vo/n

C eq
R eq
Ro
I(Lr)/n
ut   A c cos 2fc t  2k f  um t dt

um ( t )  Am sin2fmt  - Harmonic modulating signal
[14]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Example: Piezoelectric Transformer
Driven by FM Signal (SPICE)
Excitation
Vin
FM
Equivalent cirquit of the Piezoelectric Equivalent
replacement
Transformer
of rectifier
Lr
Cr
Rm
Vo
Vout Load
1:n
Ci
Co
I(Lr)
+
Vo/n
C eq
R eq
Ro
I(Lr)/n
ut   A c cos2fc t   cos2fmt 
ut   A c cos sin2fmt  cos2fc t  
A c sin sin2fmt  sin2fc t 
k f Am
where  
fm
[15]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
[16]
OrCAD Schematics
for Envelope Simulation
Excitation (Large Signal)
{Ac*cos((Am*kf/fm)*
sin(6.283186*fm*time))}
inre
0Vdc
{Lr}
ire
a b
{Rm}
outre
{-I(iim)*2**fc*Lr} {Cr}
VinputRE
PARAMETERS:
fm = 8k
fc = 358k
Am
=1
Ac = 1
kf = 1000
VinputIM
{-(V(c)-V(d))*2**fc*Cr}
inim
{Ac*sin((Am*kf/fm)*
sin(6.283186*fm*time))}
{Co} {Ro}
PARAMETERS:
{-V(outim)*
Lr = 22.6m
{V(outre)/n} {I(ire)/n}
2**fc*Co}
Cr = 9.83p
Rm = 1.121k
0
n = 0.647
sqrt(v(outre)**2+v(outim)**2)
Co = 225p
out
Ro = 20k
{(V(a)-V(b))*2**fc*Cr} abs_out
0Vdc
{Lr}
{Rm}
iim
outim
c d
{I(ire)*2**fc*Lr}
{Cr}
{Co} {Ro}
{V(outim)/n} {I(iim)/n}
0
{V(outre)*
2**fc*Co}
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
[17]
Results of Full and Envelope
Transient Simulations
1.0V
The
0V
modulating
input signal-1.0V
Envelope
v(input)
1.0
The
Frequency 0
modulated
-1.0
signal
Cycle-by-cycle
v(in)
2.0V
Output
signal
sqrt(v(a)*v(a)+v(b)*v(b))
Envelope
Cycle-by-cycle
0V
SEL>>
-2.0V
0s
1.0ms
2.0ms
v(output)
v(out)
3.0ms
4.0ms
Time
5.0ms
6.0ms
7.0ms
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
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
[18]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Proposed Method – Small Signal
Analysis Using AC–Simulation
Amplitude modulation
ut   A c 1  k aum t  cos2fc t 
U1  A c  k a A cum t 

U2  0
phasor
EVALUE
{V(%IN+, %IN-)*ka*Ac}
inre
IN+ OUT+
um(t)
IN- OUT{Ac}
E1
V1
0
inim
0
EVALUE
{V(%IN+, %IN-)*ka*Ac}
inre
IN+ OUT+
IN- OUT-
The source is linear and suitable
for AC analysis – as is
VAC
{Am}
{Ac}
E1
V1
inim
0
[19]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Linearization of Sources
for Angle Modulation
Phase Modulation
U1  A c cosk pum t 

U2  A c sink pum t 
ut   A c cos2fc t  k pum t 
=Ac
{Ac*cos(V(%IN) )}
inre
phasor
inre
PM
{Ac}
VDC
Small signal
{kp}
um(t)
GAIN1
=Ac*kp*u(t)
inim
Small signal
{Ac*sin(V(%IN))}
PM – Nonlinear source
{kp*Ac}
inim
VAC
{Am}
GAIN1
0
Linear source
[20]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Linearization of Sources
for Angle Modulation
[21]
Frequency Modulation ut   A c cos2fc t  k f  um t dt 




U1  A c cos k f  um t dt


U2  A c sin k f  um t dt
=Ac
{Ac*cos(V(%IN) )}
inre
{2**kf}
Small signal
u(t)
0
INTEG1
=Ac*kp*u(t)dt
inim
Small signal
{Ac*sin(V(%IN))}
FM – Nonlinear source
phasor
inre
FM
VDC
{Ac}
{2*Pi*Ac*kf}
inim
VAC
{Am}
0
INTEG1
0
Linear source
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Results: Piezoelectric Transformer
Driven by FM signal (AC and Point-by-Point)
for Different Carrier Frequencies
-70
Gain, db
-80
-90
-100
fc=360kHz
fc=358.5 kHz
fc=357 kHz
-110
-120
-180
Phase, deg
-270
Frequency, kHz
-360
0.1
1
10
100
[22]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
Results: Piezoelectric Transformer
Driven by FM signal (AC and Point-by-Point)
for Different Carrier Frequencies
-70
Gain, db
-80
-90
-100
fc=360kHz
fc=358.5 kHz
fc=357 kHz
-110
-120
-180
Phase, deg
-270
Frequency, kHz
-360
0.1
1
10
100
[23]
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
[24]
Frequency Response of the Network
(unmodulated input signal)
using DC-sweep
DC-sweep in envelope simulation is equivalent
to frequency sweep in full simulation
The parameter of DC sweep is a carrier
frequency fc
inre
DC
The source for DC sweep:
{Ac}
VDC
inim
0
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
[25]
Example: Frequency Response
of Piezoelectric Transformer
with Different Resistive Loads
3.0V
Output Voltage
Ro=50k
Ro=20k
2.0V
Ro=10k
Ro=5k
1.0V
0V
340
Frequency,kHz
345
350
355
360
365
370
BEN-GURION UNIVERSITY OF THE NEGEV
PESC’03
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.
[26]