simon lineykin and sam ben-yaakov*

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


Power System Driven by a modulated signal

Modulator-Driver

Reactivenetwork

Load

uc(t)

um(t) )t(uout)t(u


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


Example 2: Electronic Ballast

ElectronicDriver

Feedback -+

Vref

Freq

Power

FM input signal Vlamp

I lamp


]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


]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


Phasor Analysis

Capacitance

Resistance

VCC

C

CV2

V1cCV2cC

Im

Re

V1I1

I2

R

R

RIm

Re I1

I2

V1

V2

tRitv


Splitting the Network into Two Cross-Coupled Components -

Imaginary and Real

LoadNetwork

SourceinV

tu

outV


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


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


Example: Piezoelectric Transformer Driven by FM Signal (SPICE)

Vin

Excitation

Ro

LoadVoutFMVoVin

Rectifier



Vin

Excitation

Ro

LoadVoutFMRectifier

Co

Lr

+-

Cr Rm

1:n

Vo/n

Vo

I(Lr)/n

Ci

Equivalent cirquit of the PiezoelectricTransformer

I(Lr)



Vin

Excitation

Ro

LoadVoutFMCo

Lr

+-

Cr Rm

1:n

Vo/n

Vo

I(Lr)/n

Ci


I(Lr) ReqCeq

Equivalentreplacementof rectifier



Vin

Excitation

Ro

LoadVoutFMCo

Lr

+-

Cr Rm

1:n

Vo/n

Vo

I(Lr)/n

Ci


I(Lr)

dttuk2tf2cosAtu mfcc

tf2sinA)t(u mmm - Harmonic modulating signal

ReqCeq



tf2sintf2sinsinA

tf2costf2sincosAtu

cmc

cmc


Vin

Excitation

Ro

LoadVoutFMCo

Lr

+-

Cr Rm

1:n

Vo/n

Vo

I(Lr)/n

Ci


I(Lr)

tf2costf2cosAtu mcc m

mf

fAk

where

ReqCeq



OrCAD Schematics for Envelope Simulation

(Large Signal)


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


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


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


=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)



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)



Results: Piezoelectric Transformer Driven by FM signal (AC and Point-by-Point)

for Different Carrier Frequencies


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}


Example: Frequency Response of Piezoelectric Transformer with Different Resistive Loads


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.

simon lineykin and sam ben-yaakov*

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