1Copyright 2003Jan Verspecht bvba
Large-Signal Network Analysis“Going beyond S-parameters”
Dr. Jan Verspecht
“Jan Verspecht bvba” URL:
http://www.janverspecht.com
This presentation contains several slides which are used with the permission of Agilent Technologies, Inc.
2Copyright 2003Jan Verspecht bvba
• Part I– Introduction– Instrumentation and Calibration
• Break– Coffee and Cookies
• Part II– Applications– Conclusions
Outline
3Copyright 2003Jan Verspecht bvba
• Introduction
• Signal Representations
• Instrumentation Hardware
• Calibration Aspects
Part I - Outline
4Copyright 2003Jan Verspecht bvba
Large-Signal Network Analysis?
• Put a D.U.T. (“network”) in realistic large-
signal operating conditions
• Completely and accurately characterize the
D.U.T. behavior
• Analyze the D.U.T. behavior using the
measured data
Copyright 1998Agilent Technologies, Inc. – Used with Permission
5Copyright 2003Jan Verspecht bvba
• Introduction
• Signal Representations
• Instrumentation Hardware
• Calibration Aspects
Part I - Outline
6Copyright 2003Jan Verspecht bvba
Signal Representations
)(1 tV
)(1 tI
D.U.T.
)(1 fB
)(1 fA
TUNER
)(2 fA
)(2 fB
)(2 tV
)(2 tI
TUNER
• Representation Domain
– Frequency (f)
– Time (t)
– Envelope (f,t)
• Set of Physical Quantities
– Traveling Waves (A, B)
– Voltage/Current (V, I)
• LSNA is capable of periodic and periodically modulated signals
Copyright 1998Agilent Technologies, Inc. – Used with Permission
7Copyright 2003Jan Verspecht bvba
Traveling Waves versus Current/Voltage
50cZTypically
2
IZVA c
2
IZVB c
BAV
cZ
BAI
Copyright 1998Agilent Technologies, Inc. – Used with Permission
A
BV
I
DUT DUT
8Copyright 2003Jan Verspecht bvba
• 2-port DUT under periodic excitation• E.g. transistor excited by a 1 GHz tone with an
arbitrary output termination• All current and voltage waveforms are represented
by a fundamental and harmonics
• Spectral components Xh = complex Fourier Series coefficients of the waveforms
Signal Class: CW Signals
Freq. (GHz)1 2 3 4DC
Copyright 1998Agilent Technologies, Inc. – Used with Permission
9Copyright 2003Jan Verspecht bvba
CW: Time and Frequency Domain
H
h
tfhjh eXtx
0
2Re)(
1
0
2)(2f
tfhjh dtetxfX
frequencylfundamentaperiodf /1
Copyright 1998Agilent Technologies, Inc. – Used with Permission
10Copyright 2003Jan Verspecht bvba
Time Domain V/I Representation
Time (ns)
Time (ns)
Copyright 1998Agilent Technologies, Inc. – Used with Permission
11Copyright 2003Jan Verspecht bvba
• Periodically modulated version of the previous case• e.g. transistor excited by a modulated 1 GHz tone (modulation period = 10 kHz)
• Spectral components Xhm
Signal Class: Modulated Signals
Freq. (GHz)1 2 3DC10 kHz
Copyright 1998Agilent Technologies, Inc. – Used with Permission
12Copyright 2003Jan Verspecht bvba
Modulation: Time and Frequency Domain
H
h
M
Mm
tfmfhjhm
MCeXtx0
)(2Re)(
T
T
tfmfhj
Thm dtetx
TX MC )(2)(
1lim
frequency modulationfrequencycarrier
M
C
ff
Copyright 1998Agilent Technologies, Inc. – Used with Permission
13Copyright 2003Jan Verspecht bvba
Modulation: Envelope Domain
H
h
tfhjh
cetXtx0
2)(Re)(
M
Mm
tfmjhmh
MeXtX 2)(
Copyright 1998Agilent Technologies, Inc. – Used with Permission
14Copyright 2003Jan Verspecht bvba
Modulation: Time and Envelope Domain
Time (normalized)
B2 (Volt)
Fundamental envelope
3rd harmonicenvelope
Copyright 1998Agilent Technologies, Inc. – Used with Permission
15Copyright 2003Jan Verspecht bvba
Modulation: Frequency Domain
Fund @ 1.9 GHz 2nd @ 3.8 GHz 3rd @ 5.7 GHz
Incidentsignal (a1)
Transmittedsignal (b2)
Reflectedsignal (b1)
IF freq (MHz) IF freq (MHz) IF freq (MHz)
dBm
dBm
dBm
Copyright 1998Agilent Technologies, Inc. – Used with Permission
16Copyright 2003Jan Verspecht bvba
Modulation: 2D Time Domain
tS
(normalized)
tF
(normalized)
B2
(Volt)
),()( 2 tftfxtx McD
H
h
M
Mm
tmthjhmSFD
SFeXttx0
)(22 Re),(
Copyright 1998Agilent Technologies, Inc. – Used with Permission
17Copyright 2003Jan Verspecht bvba
• Introduction
• Signal Representations
• Instrumentation Hardware
• Calibration Aspects
Part I - Outline
18Copyright 2003Jan Verspecht bvba
Hardware: Historical Overview
• 1988 Markku Sipila & al.: 2 channel scope with one coupler at the input (14 GHz)
• 1989 Kompa & Van Raay: 2 channel scope with VNA test-set + receiverLott: VNA test set + receiver (26.5 GHz)
• 1992 Kompa & Van Raay: test-set with MTA (40 GHz)Verspecht & al.: 4 couplers with a 4 channel oscilloscope (20 GHz)
• 1994 Demmler, Tasker, Leckey, Wei, Tkachenko:test-set with MTA (40 GHz)Verspecht & al.: 4 couplers with 2 synchronized MTA’s
• 1996 Verspecht & al.: NNMS, 4 couplers, 4 channel converter, 4 ADC’s• 1998 Nebus & al.: VNA test set + receiver with loadpull and pulsed
capability• 2003 Maury Microwave, Inc.: commercial introduction (LSNA)
Copyright 1998Agilent Technologies, Inc. – Used with Permission
19Copyright 2003Jan Verspecht bvba
Architecture of the LSNA prototype
TUNER
Attenuators
...
10MHz A-to-D
Computer
RF-IF converter
RF bandwidth: 600MHz - 50GHzmax RF power: 10 WattIF bandwidth: 8 MHz
Needs periodic modulation(4 kHz typical)
Copyright 1998Agilent Technologies, Inc. – Used with Permission
20Copyright 2003Jan Verspecht bvba
RF-IF converter: Simplified Schematic
LP
LP
LP
LP
1
2
3
4
1
2
3
4
RF (50 GHz) IF (4 MHz)
fLO (20 MHz)
Copyright 1998Agilent Technologies, Inc. – Used with Permission
21Copyright 2003Jan Verspecht bvba
Harmonic Sampling - Signal Class: CW
Freq. (GHz)1 2 3
50 fLO 100 fLO 150 fLO
Freq. (MHz)1 2 3
RF
IF
fLO=19.98 MHz = (1GHz-1MHz)/50
Copyright 1998Agilent Technologies, Inc. – Used with Permission
22Copyright 2003Jan Verspecht bvba
• Introduction
• Signal Representations
• Instrumentation Hardware
• Calibration Aspects
Part I - Outline
23Copyright 2003Jan Verspecht bvba
Calibration: Historical Overview
• 1988 VNA-like characterization of the test-set
power calibration with a power meter
assumption of an ideal-phase receiver
• 1989 phase calibration by the “golden diode” approach (Urs Lott)
• 1994 harmonic phase calibration with a characterized SRD, traceable to
a nose-to-nose calibrated sampling oscilloscope (Verspecht)
• 2000 IF calibration (Verspecht)
• 2000 NIST investigates “phase reference generator” approach (DeGroot)
• 2001 calibrated electro-optical sampling (D.F. Williams, P. Hale @ NIST)
(provides better harmonic phase accuracy than nose-to-nose)
Copyright 1998Agilent Technologies, Inc. – Used with Permission
24Copyright 2003Jan Verspecht bvba
Raw Quantities versus DUT Quantities
TUNER
Attenuators
...
10MHz A-to-D
RF-IF converter
1Dhma
1Dhmb
2Dhma
2Dhmb
DUT quantities
Raw quantities1R
hma 1Rhmb
Computer2R
hma 2Rhmb
Copyright 1998Agilent Technologies, Inc. – Used with Permission
25Copyright 2003Jan Verspecht bvba
The Error Model
24
23
12
11
2
2
1
1
00
00
00
001
Rhm
Rhm
Rhm
Rhm
hh
hh
hh
h
jh
Dhm
Dhm
Dhm
Dhm
bC
aC
bC
aC
eK
b
a
b
a
h
RF amplitude error
RF phase error
RF relative error
IF error
Raw quantities
DUT quantities
Copyright 1998Agilent Technologies, Inc. – Used with Permission
26Copyright 2003Jan Verspecht bvba
RF Calibration
1. Coaxial SOLT calibration
On wafer LRRM calibration
2. HF amplitude calibration with power meter
3. HF harmonic phase calibration with a SRD diode (characterized by a nose-to-nose calibrated sampling oscilloscope)
OR
Combined with
Copyright 1998Agilent Technologies, Inc. – Used with Permission
27Copyright 2003Jan Verspecht bvba
Coaxial Amplitude and Phase Calibration
Amplitude
Harmonic Phase
Copyright 1998Agilent Technologies, Inc. – Used with Permission
28Copyright 2003Jan Verspecht bvba
On Wafer Amplitude & Phase Calibration
Coaxial LOS
LRRM
Copyright 1998Agilent Technologies, Inc. – Used with Permission
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Calibration Traceability
Relative Cal Power Cal
National Standards (NIST)
Precision Airline Calorimetry
Harmonic Phase
Nose-to-Nose Standard
Electro-Optical Sampler
30Copyright 2003Jan Verspecht bvba
Characterization of the Harmonic Phase Reference
Generator
Sampling oscilloscopeHarmonic Phase Reference generator
Copyright 1998Agilent Technologies, Inc. – Used with Permission
31Copyright 2003Jan Verspecht bvba
Sampling Oscilloscope Characterization:
Nose-to-Nose Calibration Procedure
Copyright 1998Agilent Technologies, Inc. – Used with Permission
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Nose-to-Nose Measurement
Copyright 1998Agilent Technologies, Inc. – Used with Permission
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3 Oscilloscopes are Needed
1
2
1
3
3
2
Copyright 1998Agilent Technologies, Inc. – Used with Permission
34Copyright 2003Jan Verspecht bvba
Electro-Optic Sampling* (D. Williams et al.,
NIST)
* The schematic that is shown is “U.S. Government work not subject to copyright.”D.F. Williams, P.D. Hale, T.S. Clement, and J.M. Morgan, "Calibrating electro-optic sampling systems,“Int. Microwave Symposium Digest, Phoenix, AZ, pp. 1527-1530, May 20-25, 2001.
35Copyright 2003Jan Verspecht bvba
• Part I– Introduction– Instrumentation and Calibration
• Break– Coffee and Cookies
• Part II– Applications– Conclusions
Outline
36Copyright 2003Jan Verspecht bvba
• Part I– Introduction– Instrumentation and Calibration
• Break– Coffee and Cookies
• Part II– Applications– Conclusions
Outline
37Copyright 2003Jan Verspecht bvba
• Waveform Measurements
• Physical Models
• State-Space Models
• Scattering Functions
• Conclusions
Part II - Outline
38Copyright 2003Jan Verspecht bvba
Breakdown Current
Time (ns)
(transistor provided by David Root, Agilent Technologies - MWTC)
Copyright 1998Agilent Technologies, Inc. – Used with Permission
39Copyright 2003Jan Verspecht bvba
Forward Gate Current
Time (ns)
Copyright 1998Agilent Technologies, Inc. – Used with Permission
40Copyright 2003Jan Verspecht bvba
Resistive Mixer Schematic
HEMT transistor(no drain bias applied)
(transistor provided by Dominique Schreurs, IMEC & KUL-TELEMIC)
Copyright 1998Agilent Technologies, Inc. – Used with Permission
41Copyright 2003Jan Verspecht bvba
Resistive Mixer: Time Domain Waveforms
Copyright 1998Agilent Technologies, Inc. – Used with Permission
42Copyright 2003Jan Verspecht bvba
High-Speed Digital Signal Integrity
Calibrated Eye Measurement On Wafer (@10GB/sec)
Oscilloscope Data
Copyright 2002Agilent Technologies, Inc. – Used with Permission
(courtesy of Jonathan Scott, Agilent Technologies)
43Copyright 2003Jan Verspecht bvba
Loadpull and Waveform Engineering
MesFET Class F
Z(f0)=130+j73 Z(2f0)=1-j2.8 Z(3f0)=20-j97
PAE=84%
PAE50%
Data courtesy of IRCOM / Limoges (France)
HARMONICTUNER
LSNA
44Copyright 2003Jan Verspecht bvba
• Waveform Measurements
• Physical Models
• State-Space Models
• Scattering Functions
• Conclusions
Part II - Outline
45Copyright 2003Jan Verspecht bvba
Physical Models
• Represent transistor behavior
• Use electrical circuit schematics
• Contain linear and nonlinear elements such as current sources, capacitors, resistors
• E.g. BSIM3, Chalmers, Materka, Curtice,…
46Copyright 2003Jan Verspecht bvba
Physical Model Improvement
generators apply waveforms measured by an LSNA
“Swept power measurements under mismatched conditions”
Chalmers model to optimizeGaAs pseudomorphic HEMTgate l=0.2 um w=100 um
Parameter Boundaries
(courtesy of Dr. Dominique Schreurs, IMEC & KUL-TELEMIC)
Copyright 1998Agilent Technologies, Inc. – Used with Permission
47Copyright 2003Jan Verspecht bvba
Before OPTIMIZATION
Time domain waveforms Frequency domain
gate drain
voltage
current
gate drain
Voltage - Current State Space
Using the Built-in Optimizer
Copyright 1998Agilent Technologies, Inc. – Used with Permission
48Copyright 2003Jan Verspecht bvba
After OPTIMIZATION
Time domain waveforms Frequency domain
gate drain
voltage
current
gate drain
Voltage - Current State Space
Verification of the Optimized Model
Copyright 1998Agilent Technologies, Inc. – Used with Permission
49Copyright 2003Jan Verspecht bvba
• Waveform Measurements
• Physical Models
• State-Space Models
• Scattering Functions
• Conclusions
Part II - Outline
50Copyright 2003Jan Verspecht bvba
State Space Function Model
Fit with e.g. artificial neural network or spline(David Root, John Wood, Dominique Schreurs)
...),,,,(
...),,,,(
1212122
1212111
dtdI
dtdV
dtdV
VVFI
dtdI
dtdV
dtdV
VVFI
51Copyright 2003Jan Verspecht bvba
Experiment Design: Crucial to Explore Component
Behavior
1V
1I
2V
2I
4.2 GHz 4.8 GHz
Copyright 1998Agilent Technologies, Inc. – Used with Permission
52Copyright 2003Jan Verspecht bvba
State Space Coverage throughProper Experiment Design
Copyright 1998Agilent Technologies, Inc. – Used with Permission
53Copyright 2003Jan Verspecht bvba
• Waveform Measurements
• Physical Models
• State-Space Models
• Scattering Functions
• Conclusions
Part II - Outline
54Copyright 2003Jan Verspecht bvba
When to use Scattering Functions?
Scattering functions are• Black-box frequency domain models,• Directly derived from large-signal measurements.
Scattering functions are used
• With new less understood technology
• When there is a difficult de-embedding problem
• When there are multiple transistors in the circuit
• When the component has distributed characteristics
55Copyright 2003Jan Verspecht bvba
Theoretical Concepts
Scattering Functions
for
Nonlinear Behavioral Modeling
in the
Frequency Domain
Quantities are Waves
Functional Relationship
Input and Output are Discrete Tone Signals
56Copyright 2003Jan Verspecht bvba
Quantities are Traveling Voltage Waves
2
2
ZIV
ZIV
B
A
I
V
Z
Z
Default value of Z = 50 Ohm (classic S-parameters)
Copyright 1998Agilent Technologies, Inc. – Used with Permission
57Copyright 2003Jan Verspecht bvba
Scattering Functions Describe:
• Compression characteristic
• Spectral regrowth
• AM-PM
• PAE
• Harmonic Distortion
• Fundamental loadpull behavior
• Harmonic loadpull behavior
• Time domain voltage & current
• Influence of bias can be included
Copyright 1998Agilent Technologies, Inc. – Used with Permission
58Copyright 2003Jan Verspecht bvba
Notation - Graphical Illustration
kA1
kB1
kA2
kB2
,...),,...,,( 2221121111 AAAAFB kk ,...),,...,,( 2221121122 AAAAFB kk
Copyright 1998Agilent Technologies, Inc. – Used with Permission
59Copyright 2003Jan Verspecht bvba
Phase Normalization
• “Phase normalized” quantities are used
• Defines unambiguous phase for harmonics
• Large-signal A11 is the phase reference(most useful for many applications)
60Copyright 2003Jan Verspecht bvba
Phase Normalization: Mathematics
• We define a reference phasor:)( 11AjeP
• We define phase normalized quantities:k
mkNmk PAA k
mkNmk PBB
• Special case:
1111 AAN
61Copyright 2003Jan Verspecht bvba
Harmonic Superposition Principle
• In general superposition cannot be used to describe the functional relationship between the spectral components
)()( AFAFAAF
• The superposition principle can be used for relatively small components (e.g. harmonics)
62Copyright 2003Jan Verspecht bvba
Harmonic Superposition: Illustration
1A
2B
Copyright 1998Agilent Technologies, Inc. – Used with Permission
63Copyright 2003Jan Verspecht bvba
Basic Mathematical Equation
• A11 assumed to be the only large-signal component
• Superposition assumed to be valid for other Anh
• The notation A* means the complex conjugate of A
• S and S’ are called the scattering functions
• Note that S’mk11 = 0
*)()( 1111Nnh
N
nhmknh
Nnh
N
nhmknh
Nmk AASAASB
64Copyright 2003Jan Verspecht bvba
Applications:Compression and AM-PM conversion
NNN AASB 1111211121 )(
11
21112111 )(
A
BAS
• Only considering B21 and A11 results in
• This can be rewritten as
• S2111(|A11|) represents the compression and AM-PM conversion characteristic
65Copyright 2003Jan Verspecht bvba
Large-Signal Input Match
NNN AASB 1111111111 )(
11
11111111 )(
A
BAS
• Only considering B11 and A11 results in
• This can be rewritten as
• S1111(|A11|) represents the large-signal input reflection coefficient
66Copyright 2003Jan Verspecht bvba
Hot S22
*)()()( 21112121211121211111211121NNNNNNN AASAASAASB
• Considering B21, A21 and A11 results in
• Multiplying both sides with P results in
• The combination of S2121 and S’2121 are a scientifically sound format for “Hot S22”
*)()()( 212
112121211121211111211121 APASAASAASB N
67Copyright 2003Jan Verspecht bvba
Measurement Example
-60
-40
-20
0
20
40
-25 -20 -15 -10 -5 0 5 10
Sca
tteri
ng
fu
nct
ion
s (d
B)
|A11| (dBm)
S2111
S’2121
S2121
• Note that the amplitude of S’2121 becomes arbitrary small for |A11| going to zero
Copyright 1998Agilent Technologies, Inc. – Used with Permission
68Copyright 2003Jan Verspecht bvba
Harmonic Distortion Analysis
• Only considering A11 and B2k one can calculate the harmonic distortion as a function of |A11|
21111231123
1111221122
1111211121
)(
)(
)(
PAASB
PAASB
AASB
69Copyright 2003Jan Verspecht bvba
Harmonic Loadpull Behavior
Nhh
Nh
Nh
N
hhk
Nh
N
hhk
Nk
BA
AASAASB
22
21122211222*)()(
hB2
hA2
h11A
• Solve the set of equations (linear in the real and imaginary parts of A2h and B2h)
70Copyright 2003Jan Verspecht bvba
New Stability Circles for Multiplier Design
DCDC
2200
DCDC
0000
2200
0 1.0
1.0
-1.0
10.0
10.0
-10.0
5.0
5.0
-5.0
2.0
2.0
-2.0
3.0
3.0
-3.0
4.0
4.0
-4.0
0.2
0.2
-0.2
0.4
0.4
-0.4
0.6
0.6
-0.6
0.8
0.8
-0.8
stability_circleSwp Max
2GHz
Swp Min2GHz
SCIR1
due_porte
SCIR2
due_porte
S[1,1]
carichi
S[2,2]
carichi
Stability is not ensuredStability is not ensured
Research performed byProf. Giorgio Leuzzi(Universita dell’Aquila, Italy)
71Copyright 2003Jan Verspecht bvba
Practical Measurement:Experiment Design Concept
Im
Re
*)()()( 21112121211121211111211121NNNNNNN AASAASAASB
• Simple example: S2111, S2121 and S’2121
Re
Im
• Perform 3 independent experiments
Input A21 Output B21
72Copyright 2003Jan Verspecht bvba
Typical Measurement Setup
TUNER
Large-Signal Network Analyzer
11A
11AAmk
matchZ
diplexer
infundamental
harmonics
Copyright 1998Agilent Technologies, Inc. – Used with Permission
Agilent Technologies, Inc. - Patent Pending
73Copyright 2003Jan Verspecht bvba
- 0.3 - 0.2 - 0.1 0 0.1 0.2 0.3
- 0.3
- 0.2
- 0.1
0
0.1
0.2
0.3
- 0.6 - 0.4 - 0.2 0
0
0.2
0.4
0.6
0.8
Measurement Example
Input A21 (Vp) Output B21 (Vp)
ImIm
Re Re
Copyright 1998Agilent Technologies, Inc. – Used with Permission
74Copyright 2003Jan Verspecht bvba
Link to Harmonic Balance Simulators
Copyright 1998Agilent Technologies, Inc. – Used with Permission
75Copyright 2003Jan Verspecht bvba
Simulated Model versus Measurements
Power Transistor WaveformsGateVoltage
GateCurrent
DrainVoltage
DrainCurrent
Copyright 1998Agilent Technologies, Inc. – Used with Permission
76Copyright 2003Jan Verspecht bvba
Scattering Functions with Modulation1.9 GHz RFIC (CDMA)
Incident signal (a1)
Transmitted signal (b2)
(Volt)
(Volt)
Normalized Time
Normalized Time
Copyright 1998Agilent Technologies, Inc. – Used with Permission
77Copyright 2003Jan Verspecht bvba
----- fund----- 2nd harm----- 3rd harm
Input power (dBm)
Output power(dBm)
Dynamic Harmonic Distortion:Transmitted Signal
Copyright 1998Agilent Technologies, Inc. – Used with Permission
78Copyright 2003Jan Verspecht bvba
Dynamic Harmonic Distortion:Reflected Signal
Output power(dBm)
Input power (dBm)
Copyright 1998Agilent Technologies, Inc. – Used with Permission
----- fund----- 2nd harm----- 3rd harm
79Copyright 2003Jan Verspecht bvba
Emulate CDMA Statistics using many Periodic Pseudo-Random Sequences
Frequency Offset from Carrier (Hz)
Amplitude(dBm)
Transmitted Signal
Copyright 1998Agilent Technologies, Inc. – Used with Permission
80Copyright 2003Jan Verspecht bvba
Apply Fitting Technique• For our example we use a piece wise polynomial
(3rd order)
)(11 Va )(11 Va
)(V )(V21I 21Q
Copyright 1998Agilent Technologies, Inc. – Used with Permission
81Copyright 2003Jan Verspecht bvba
Model Verification - Spectral Regrowth
-----model-----measured Frequency Offset from Carrier (MHz)
Amplitude(dBm)
Output signal
Copyright 1998Agilent Technologies, Inc. – Used with Permission
82Copyright 2003Jan Verspecht bvba
• Waveform Measurements
• Physical Models
• State-Space Models
• Black-Box Frequency Domain Models
• Conclusions
Part II - Outline
83Copyright 2003Jan Verspecht bvba
Conclusions
• The dream of accurate and complete large-signal characterization of components under realistic operating conditions is made real
• The only limit to the scope of applications is the imagination of the R&D people who have access to this measurement capability
Copyright 1998Agilent Technologies, Inc. – Used with Permission
84Copyright 2003Jan Verspecht bvba
“Jan Verspecht bvba” Coordinates
• URL: http://www.janverspecht.com
• email: [email protected]
• fax: 32-52-31.27.85
• phone: 32-479-85.59.39
• address: Jan Verspecht bvbaGertrudeveld 15B-1840 LonderzeelBelgium
85Copyright 2003Jan Verspecht bvba
86Copyright 2003Jan Verspecht bvba