Download "Modnum" Scilab toolbox for the communication systems User's Guide

"Modnum"
Scilab toolbox
for the communication systems
User’s
Guide
Draft Version
IRCOM Group
Alan Layec
February 8, 2006
CONTENTS
1
Contents
I Scicos Diagrams
3
1 Chaotic dynamical systems
5
Continous time systems
1.1
Lorentz’s system . . . . . . . . . . . . . . . . . . . .
1.2
Discrete Van Der Pol’s system (trapezoidal méthode)
1.3
Discrete forced Van Der Pol’s system (Euler method)
1.4
Duffing-Van Der Pol’s system . . . . . . . . . . . . .
1.5
Rössler’s system . . . . . . . . . . . . . . . . . . . .
1.6
Duffing’s oscillator . . . . . . . . . . . . . . . . . .
1.7
Chua’s system . . . . . . . . . . . . . . . . . . . . .
1.8
Sub-system of Chua’s circuit . . . . . . . . . . . . .
1.9
Master-slave synchronization of Chua’s circuit . . . .
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5
5
7
8
10
11
13
14
17
19
Discrete time systems
1.10 2D bifurcation of the logistic map . . . . . . . . . . . .
1.11 3D bifurcation of the logistic map . . . . . . . . . . . .
1.12 Henon’s system . . . . . . . . . . . . . . . . . . . . .
1.13 Chaotic first order Delta-Sigma modulator . . . . . . .
1.14 Frey’s chaotic encoder . . . . . . . . . . . . . . . . . .
1.15 Second order Infinite Impulse Response filter . . . . . .
1.16 Master-slave synchronization of second order IIR filter .
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21
21
22
24
25
26
28
30
2 Oscillators and Phase Locked Loop systems
32
Open loop models of oscillators
2.1
Continous Voltage Controled Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
Discrete Voltage Controled Oscillator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
32
32
34
Integer N Frequency synthesizers
2.3
Simple scicos diagram of an integer-N frequency synthesizer . . . . . . . . . . . . . . . . . . .
2.4
Scattered diagram of a third order integer-N frequency synthesizer . . . . . . . . . . . . . . . .
2.5
Integrated diagram of an integer-N frequency synthesizer . . . . . . . . . . . . . . . . . . . . .
2.6
Scattered diagram of a third order integer-N frequency synthesizer with an interpoled non-linearity
of VCO and with dual-modulus feedback divider . . . . . . . . . . . . . . . . . . . . . . . . . .
35
35
37
39
42
Fractional N/N+1 Frequency synthesizers
2.7
Modulated fractional frequency synthesizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
44
44
CONTENTS
2
3 Communication systems
46
PSK/QAM Transmission
3.1
Scattered diagram of base band QPSK transmission chain . . . .
3.2
Integrated diagram of base band QPSK transmission chain . . . .
3.3
Base band single user QPSK spread-spectrum transmission chain
3.4
Scattered diagram of sample-based 16-QAM chain transmission .
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46
46
49
51
53
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55
55
56
58
60
61
FSK chaotic transmission
3.10 Chaotic frequency hopping emitter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.11 Chaotic frequency hopping transmission system . . . . . . . . . . . . . . . . . . . . . . . . . .
62
62
64
4 Electrical circuits
4.1
Resitif attenuator/coupler . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
67
67
II Simulation Scilab scripts
69
1 Simulations of chaotic systems
1.1
Output probability density of autonomous second order IIR filter . . . . . . . . . . . . . . . . .
1.2
BER estimation of pair chaotic encoder/decoder with introduction of jitter in receiver clock . . .
71
71
75
2 Simulations of oscillators and Phase Locked Loops
2.1
Output spectra of Integer N frequency synthesizer . . . . . . . . . . . . . . . . . . . . . . . . .
2.2
Output jitter of integer-N frequency synthesizer . . . . . . . . . . . . . . . . . . . . . . . . . .
2.3
Gaussian modulated fractional frequency synthesizer . . . . . . . . . . . . . . . . . . . . . . .
78
78
82
85
3 Simulations of communication systems
3.1
Output spectra of Delta-Sigma modulator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
3.2
BER estimation of single user QPSK transmission . . . . . . . . . . . . . . . . . . . . . . . . .
3.3
Rayleigh noise generator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
88
88
92
96
Delta-Sigma Transmission
3.5
Scattered diagram of first order Delta-Sigma modulator . .
3.6
Scattered diagramm of second order Delta-Sigma modulator
3.7
Integrated diagram of Delta-Sigma modulator . . . . . . .
3.8
Delta-sigma modulator with two in-loop integrators . . . .
3.9
Delta-sigma modulator with three in-loop integrators . . . .
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I. SCICOS DIAGRAMS
3
Part I
Scicos Diagrams
I. SCICOS DIAGRAMS
4
I. 1. CHAOTIC DYNAMICAL SYSTEMS
5
Chapter 1
Chaotic dynamical systems
1.1 Lorentz’s system
−1
a
1/s
MScope
b
1/s
−1
1/s
−c
1.1.1 Description
The Lorentz’s system is defined by the following continuous system :
dx(t)
dt
dy(t)
dt
dz(t)
dt
= a (−x(t) + y(t))
(1.1)
= bx(t) − y(t) − x(t)y(t)
(1.2)
= −cx(t) + x(t)y(t)
(1.3)
The state variables x(t), y(t) and z(t) are temperature of the air, speed of wind and a third caracteristic which
represents the variation of temperature in accord to the altitude.
I. 1. CHAOTIC DYNAMICAL SYSTEMS
6
1.1.2 Context
Tsampl=3e-3
a=10
b=28
c=8/3
ci=[5.5;5;20]
Tfin=20
1.1.3 Scope Results
25.0
12.5
50
0.0
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45
−12.5
−25.0
40
+
10
11
12
13
14
15
16
17
18
19
20
35
25.0
30
12.5
0.0
25
−12.5
−25.0
20
+
10
11
12
13
14
15
16
17
18
19
20
50.0
15
10
37.5
5
25.0
+
0
−30
12.5
0.0
−24
−18
−12
−6
0
6
+
10
11
12
13
14
15
16
17
18
19
(a) Temporal wave forms of state variables
20
(b) Phase plan
12
18
24
30
I. 1. CHAOTIC DYNAMICAL SYSTEMS
7
1.2 Discrete Van Der Pol’s system (trapezoidal méthode)
1
u^a
−1
Trapezoidal
−1
Trapezoidal
MScope
1.2.1 Description
The Van Der Pol’s Equation is written with the equation :
x + x2 − 1 x˙ + x = 0
(1.4)
It is fully described by the following system of state equation :
x˙ = y
y˙ =
1−x
(1.5)
2
y−x
1.2.2 Context
Te=0.01
Tfin=90
ci=[-1;0]
1.2.3 Scope Results
1.2.4 Mod_num blocks
• TRAPINTEGRAL_f - Single step integrator block by trapezoidal method
1.2.5 See Also
• EULERINTEGRAL_f - Single step integrator block by Euler method (Scicos Block)
(1.6)
I. 1. CHAOTIC DYNAMICAL SYSTEMS
8
2
4.0
1
3.2
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2.4
−1
−2
1.6
+
0
0.8
9
18
27
36
45
54
63
72
81
90
0.0
5.0
−0.8
−1.6
2.5
−2.4
0.0
−3.2
−2.5
−5.0
+
−4.0
−2.5
+
0
9
18
27
36
45
54
63
72
81
−2.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
1.5
2.0
2.5
90
(a) Time domain wave forms of state variables
(b) Phase plan
1.3 Discrete forced Van Der Pol’s system (Euler method)
1
u^a
−1
Euler
−1
Euler
MScope
Trig. Function
cos
wo
A
Euler
1.3.1 Description
This system illustrates the use of a single step integrator in order to resolve continuous system. Here the system is
resolved with the backward Euler method. The forced Van Der Pol’s oscillator is described with the system of state
equation :
x˙ = y
y˙ =
z˙ =
1−x
2π
T
(1.7)
2
y − x + A cos (z)
where parameters T is the period of the driven oscillator and A it’s amplitude.
1.3.2 Context
Te=0.01
(1.8)
(1.9)
I. 1. CHAOTIC DYNAMICAL SYSTEMS
9
Tfin=90
ci=[-1;0]
A=0.5;
wo=1.1;
To=2*%pi/wo;
1.3.3 Scope Results
2.50
1.25
4.0
0.00
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3.2
−1.25
−2.50
2.4
+
0
9
18
27
36
45
54
63
72
81
90
1.6
5.0
0.8
2.5
0.0
0.0
−2.5
−5.0
−0.8
+
0
9
18
27
36
45
54
63
72
81
90
1.0
−1.6
−2.4
0.5
−3.2
0.0
+
−4.0
−2.5
−0.5
−1.0
−2.0
−1.5
−1.0
−0.5
0.0
0.5
1.0
+
0
9
18
27
36
45
54
63
72
81
90
(a) Time domain wave forms of state variables
(b) Phase plan
1.3.4 Mod_num blocks
• EULERINTEGRAL_f - Single step integrator block by Euler method
1.3.5 See Also
• EULERINTEGRAL_f - Single step integrator block by Euler method (Scicos Block)
1.5
2.0
2.5
I. 1. CHAOTIC DYNAMICAL SYSTEMS
10
1.4 Duffing-Van Der Pol’s system
To
−1
u^a
1
mu
−1
Te
u^a
1/s
MScope
1/s
v
w
1.4.1 Description
Add here a paragraph of the function description.
1.4.2 Context
Te = 5e-3
mu=0.2
v=17
w=4
To=2*%pi/w
Tfin = 40
1.4.3 Scope Results
Trig. Function
cos
I. 1. CHAOTIC DYNAMICAL SYSTEMS
11
4
2
12.0
0
9.6
−2
−4
7.2
+
0
4
8
12
16
20
24
28
32
36
40
4.8
12
2.4
6
0
0.0
−6
−12
−2.4
+
0
4
8
12
16
20
24
28
32
36
40
−4.8
1.10
−7.2
0.55
−9.6
0.00
+
−12.0
−4.0
−0.55
−1.10
−3.2
−2.4
−1.6
−0.8
0.0
0.8
1.6
2.4
3.2
4.0
+
0
4
8
12
16
20
24
28
32
36
40
Scope results
Scope results
1.5 Rössler’s system
−1
g
ScopeXYZ
1/s
MScope
1/s
a
b
1/s
1.5.1 Description
The Rössler’s system is defined with the following system of state equations :
˜ = − (Y + Z)
X
Y˜ = X + αY
Z˜ = β + Z (X − γ)
1.5.2 Context
Te=0.01
(1.10)
(1.11)
(1.12)
I. 1. CHAOTIC DYNAMICAL SYSTEMS
12
a=0.2
b=0.2
g=-5.7
ci=[-5;5;0.1]
Tfin = 150
1.5.3 Scope Results
12
6
10.0
0
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7.8
−6
−12
5.6
+
0
15
30
45
60
75
90
105
120
135
150
3.4
12
1.2
6
0
−1.0
−6
−12
−3.2
+
0
15
30
45
60
75
90
105
120
135
150
−5.4
25.0
−7.6
18.8
−9.8
12.5
+
−12.0
−10.0
6.2
0.0
−7.8
−5.6
−3.4
−1.2
1.0
3.2
+
0
15
30
45
60
75
90
105
120
135
150
(a) Time domain wave forms of state variables
(b) Phase plan
ZAXES
25.0
12.5
0.0
12
12
0
0
YAXES
−12
−12
(c) 3d phase plan
1.5.4 Mod_num blocks
• SCOPXYZ_f - 3D trajectory scope block
XAXES
5.4
7.6
9.8
12.0
I. 1. CHAOTIC DYNAMICAL SYSTEMS
13
1.6 Duffing’s oscillator
−1
Te
X1’
X1
u^a
To
1/s
X2’
X2
1/s
MScope
−a
w
X3’
X3
Trig. Function
cos
g
1/s
1.6.1 Description
The Duffing’s equation is described by this non-linear differential equation :
y (t)
dt
= x (t) − x3 (t) − ǫy (t) + γ cos (ωt)
(1.13)
where ǫ and γ are parameters and ω a pulsation.
This forced oscillator should be written as a three dimensional state equation system :
x˜1 = x2
x˜2 = x1 −
2π
x˜3 =
T
1.6.2 Context
Te=0.02
Tfin=200
g=0.3
a=0.15
w=1
To=2*%pi/w
ci1=0.1
ci2=0.1
ci3=0
1.6.3 Scope Results
(1.14)
x31
− ǫy + γ cos (x3 )
(1.15)
(1.16)
I. 1. CHAOTIC DYNAMICAL SYSTEMS
14
3.0
1.5
1.80
0.0
1.44
−1.5
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. .. . ........... . . . . . . . .. . . . . . ..... . . . .. .. .... .. . . . . . . . . .
.. ... .. . .. . .. .. .
. . . . . ...... . . . . .............. . . . . .
.. ...
1.08
+
−3.0
100
110
120
130
140
150
160
170
180
190
200
0.72
2
0.36
1
0
0.00
−1
−0.36
+
−2
100
110
120
130
140
150
160
170
180
190
200
−0.72
0.50
−1.08
0.25
−1.44
0.00
+
−1.80
−2.0
−0.25
−1.6
−1.2
−0.8
−0.4
0.0
0.4
+
−0.50
100
110
120
130
140
150
160
170
180
190
200
(a) Time domain wave forms
(b) Phase plan
1.50
1.25
. .......
......... .......................................... .....
... .... ...
...
......
................... ... ........
...... ... .
...... ... . ..................... .... ..
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1.00
0.75
0.50
0.25
0.00
−0.25
−0.50
−0.75
+
−1.00
−1.60
−1.29
−0.98
−0.67
−0.36
−0.05
0.26
0.57
0.88
1.19
1.50
(c) Poincare section
1.7 Chua’s system
−1
CHUAFONC
−1
15.6
MScope
1/s
−1
1/s
−25.58
1/s
0.8
1.2
1.6
2.0
I. 1. CHAOTIC DYNAMICAL SYSTEMS
15
1.7.1 Description
This system takes an important place in the understanding of the synchronization of chaotic systems. He is originally studed with the electronic circuit shown in the following Figure. This circuit is composed with passive
elements and with an active non-linear element.
R
C2
L
Inl
Diode
de Chua
C1
V2
V1
I1
Circuit de Chua
Figure 1.1: Chua’s circuit
This circuit is described by the following state equations:
1 1
dV1
=
(V2 − V1 ) − iN L
dt
C1 R
dV2
1
1
=
il − (V2 − V1 )
dt
C2
R
dil
1
= − V2
dt
L
(1.17)
1
[Ga − Gb ] [|V1 + E| − |V1 − E|]
(1.18)
2
Ga
Gb
C2 2
C2
R , m0 =
, m1 =
and renamming state variables, the new
,β =
By changing parameters with α =
C1
L
R
R
sate equations are:
f (V1 ) = Gb V1 +
x
˜1 = α [x2 − x1 − h (x1 )]
(1.19)
x
˜ 2 = x3 − x 2 − x1
x
˜3 = −βx2
h(x) = m1 x +
1
[m0 − m1 ] [|x + E| − |x − E|]
2
1.7.2 Context
Tsampl = 1e-2
Tfin = 60
m0=-8/7
m1=-5/7
ci=[1.6;0;-1.6]
1.7.3 Scope Results
1.7.4 Mod_num blocks
• CHUAFONC_f - Chua’s non-linear function block
(1.20)
I. 1. CHAOTIC DYNAMICAL SYSTEMS
16
4
2
4.0
.... .. ...
. . . . .. . . . . . . . . .. ... .. ...... .. .
. ... ....... .
. ..
. . .. . . .. .. .. .. ... ....... .. .. .. . ........... .
. .. . .
.......... .. . . . ..... ..
.... .... .. ....
. .. . . .. . ......
.... ... ......
. .
... .
............
.. ...... .... ..... .....
.............
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................
. .. .. ..
..
...................
.. .. ..
.......... ... .... .................................................................. .... ... .......
.... .... .... .. .. .....
...... .. .. ......... ........ ....
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..... .... ... .......... ........ ......... ..................... ........ .......... ....... ... ... ........
...... .. .. .. ...... .. . ...
......... ......... ... ... .. ... ...........
... .. .. ... ...... . .. ....
.... ..... ......... ..... ... ...... ....
.
.
.
.
..
.. .
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. .. . . .. ... . . ...
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..................
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......
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..
.....
.................
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..... ................. ...... ......................
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...
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...
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............
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... ... .. .. .. ............ ... .... .............. ... ............................................ ............................ ....................... ....................
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.. . . . .. ..... . .. ........ . . ... .. ..... ... ....... .. .. ... .... .. ......... ... .. ..
.. . . . . ...... .. .. ....... .. .. .... .. .. ................. .. .. .. .. . .. ................. ... ...
.. . . . . ..... .. .. ........... . . .. .. ... .. .. ..... .. .... . ...... ..... .......... . ... ....
.. . .. . . ....... . .. ......... . ...... .. .. .............. .. .. ... .. ............ .... ...... .. ....
... . . .. ....... .. .. ........ .. ...... ... .............. .. .. ... .. .. .. .... ... .. ...
... .. .. .. .............. ... .... ................. .................... .................... ........ ............................... ............... ... .......
...... .. ................. .... .................................................................................................................... .... ............... ...... .....
...... ... ................ .... ......................................................................... ... ............. ...... .....
....... .. .................. .... ..................................................................... ..... ............. ..... .....
.... . . .. ... ................ ..... ........................... ..... ................. ...... .....
.. . . . . . ...... ....... . ..... .
.. . . . . . .
. .. .. . . . . . . ......... .... . . . .. ..........................................................
. .. .. . . . . . . ................ .......................................... ...... ... .. ........
. ... . .. . . . . . ............... .. .. .. .. .. . ........ . .. . . . . ........
.. . . . . . . . . . . . . . . . . . . . . . . . . .....
. .. ...... . . . .. . . . . . . . . .. . . . .. .......
. .. .. .. ... .. . . . . . .. .. .. .... .
. .. .. .. .... .
0
3.2
−2
−4
2.4
+
30
33
36
39
42
45
48
51
54
57
60
1.6
1.0
0.8
0.5
0.0
0.0
−0.5
−1.0
−0.8
+
30
33
36
39
42
45
48
51
54
57
60
4
−1.6
−2.4
2
−3.2
0
+
−4.0
−1.0
−2
−4
−0.8
−0.6
−0.4
−0.2
0.0
0.2
+
30
33
36
39
42
45
48
51
54
57
60
(a) Temporal wave forms of state variables
1.7.5 See Also
• SYSTEMG_f - Chua sub-system G block (Scicos Block)
• SYSTEMH_f - Chua sub-system H block (Scicos Block)
(b) Phase plan
0.4
0.6
0.8
1.0
I. 1. CHAOTIC DYNAMICAL SYSTEMS
17
1.8 Sub-system of Chua’s circuit
Chua
sub−system H
Chua
sub−system G
Mux
MScope
Chua
sub−system G
Chua
sub−system H
Mux
1.8.1 Description
The Chua’s circuit, shown in Fig.1.2 is able to be decomposed in two sub-systems G et H.
R
C2
L
Inl
Diode
de Chua
C1
V2
V1
I1
Sous−système G
Sous−système H
Figure 1.2: Decomposition of Chua’s circuit
Making this decomposition, the Chua’s circuit should be presented by an closed loop system (see Fig.1.3).
1.8.2 Context
Tsampl = 1e-2
Tfin = 30
m0=-8/7
m1=-5/7
ci_master=[1.6;0;-1.6]
ci_slave=[0;0;0]
I. 1. CHAOTIC DYNAMICAL SYSTEMS
18
V1
Sub−system
G
Sub−system
G
^
V2
Sub−system
H
V2
Sub−system
H
Master system
Closed Loop
Slave System
Open Loop
Figure 1.3: System of Chua’s circuit
3.0
1.5
0.0
−1.5
−3.0
+
0
3
6
9
12
15
18
21
24
27
30
3
6
9
12
15
18
21
24
27
30
0.50
0.25
0.00
−0.25
−0.50
+
0
Temporal wave forms of state variables : (red line) master
system; (blue line) slave system
1.8.3 Scope Results
1.8.4 Mod_num blocks
• SYSTEMG_f - Chua sub-system G block
• SYSTEMH_f - Chua sub-system H block
1.8.5 See Also
• SYSTEMG_f - Chua sub-system G block (Scicos Block)
• SYSTEMH_f - Chua sub-system H block (Scicos Block)
^
V1
I. 1. CHAOTIC DYNAMICAL SYSTEMS
19
1.9 Master-slave synchronization of Chua’s circuit
sinusoid
generator
+
Chua
sub−system H
Chua
sub−system G
MScope
−
Mux
Chua
sub−system G
ScilabGraphic2
MScope
Chua
sub−system H
ScilabGraphic1
1.9.1 Context
Tsampl = 10e-3
Tfin = 55.5
m0=-8/7
m1=-5/7
ci_master=[1.6;0;-1.6]
ci_slave=[0;0;0]
ampl=1e-6
T=4
1.9.2 Scope Results
0.50
3.0e−06
0.25
0.00
1.5e−06
−0.25
+
−0.50
28.0
30.8
33.6
36.4
39.2
42.0
44.8
47.6
50.4
53.2
56.0
30.8
33.6
36.4
39.2
42.0
44.8
47.6
50.4
53.2
56.0
0.0e+00
0.50
0.25
−1.5e−06
0.00
−0.25
+
−3.0e−06
37.00
38.85
40.70
42.55
44.40
46.25
48.10
49.95
51.80
53.65
55.50
+
−0.50
28.0
(a) red line: master system output wave form; blue line:
slave system output wave form
(b) red line: master system input message; blue line: slave
system output message
1.9.3 Mod_num blocks
• SYSTEMG_f - Chua sub-system G block
• SYSTEMH_f - Chua sub-system H block
1.9.4 See Also
• SYSTEMG_f - Chua sub-system G block (Scicos Block)
I. 1. CHAOTIC DYNAMICAL SYSTEMS
• SYSTEMH_f - Chua sub-system H block (Scicos Block)
20
I. 1. CHAOTIC DYNAMICAL SYSTEMS
21
1.10 2D bifurcation of the logistic map
0.7
0.3/Tfin
LOGISTIC
1/z
1.10.1 Description
The logistic equation is defined by the one-dimensional discrete-time system given by :
x [k + 1] = f (x [k] , R) = 4Rx [k] (1 − x [k])
(1.21)
This application should be modelled by the following block diagram Fig.1.4, where output of the non-linear function F(t) is feed-backed to the input via a delayed block.
x [k]
F ()
Logistic
Function
x [k + 1]
Delay
T
Figure 1.4: Block diagram of logistic application
1.10.2 Context
Te = 1
ci=0.5
Tfin = 0.5e5*Te
1.10.3 Scope Results
1.10.4 Mod_num blocks
• LOGISTIQUE_f - Logistic function block
I. 1. CHAOTIC DYNAMICAL SYSTEMS
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
22
......
..................................
. .............................................................
......................................................................................
. ............................ .................... ................................ .............
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............................. ........................................... ........................................ ........ . ..................... ............. ....
........................
..................................
.............................. .................................................................................................................................................................................................................................. .......................................................................................
.............................
............................. ...... ......... ............................... . ............. ........ ........ .. ...... ................ ......... ..........
.........................
............................... ............................................ ............ ...... ...........
............... ....... .................. .. ...
.....................
.
............... .......................................... .............. .............
.
..
..................
.................................................................. ...... ............................ ...........................................................................
...............
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.. . .. .. . . ..
.
.
............................................................. .................... ........... .......
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.
.
.
................................................. ........... .............. ... .. .......... ............................... ..... ...... ..... .
...........
.................................... ....... ... .............. .......... ... ...... ....... ...................... .. .
.........
....
.. ................... ......... ......... ................... . . .... ..... . ..... . ...... .......
....
.
........................................................................ ................... .............................. ....................................................................
.
.
..................................... ......... ...... ............... ....... ..... ........ ......................
..
.........................................
.................... ................................... ....................... ........... . .......... . ............................
........................................................................
..
..................................... . .............. ...... ..................... ..... ........ .. .. ....... ........ .... .....
..
.
.... .... ....... ...... ...................... ........................ ...... . ............. ... .. .................. . ... ..
......... ..... ........... ........................ ...................................... .... . ............. ............................... ...
....
..
.............. .......... ...... ..................... ................ ............ . ..... .... ... . ............... ..... .......
........
.
............... ...................... .. ...... ... .. .. ...... ............... ............ ....... ......... ... . .
.........
............................. ............ ............................ ........... ............ ............................ ................... ............................................ .....
..........
.
.
.
...........
. . . .. .
. ..
. .. .
. . .. . . ..
.............
...................... .. . ...... ................................ ......... .................. ... ................. ............ ... ....................... .....................
..............
........ ...... ... .... ........ ........ ..... .. ............ ... .. ..... . ... ........... .............. .. . ......... ........... .. ..
................
............ .. ................................................................................... .................................................... ................................. .................... ... ...................
.................
.
..........
...................
............................... ..... ............................. ........ ................ ... . .... . .... ........................................ ........ ..............
.......
....................
............................. .............. . ................ .. ........................ ........ .. ................................... .. ...........................
..
......................
........ .... ....... . .. ... .... .... ................. ..... . .. ........... . .... ............... ....... ...... . ........... . .
........................ ....
..................... ........... ..... ....... .... . ....... . . ... ...... . ..................... ...... . .. .. .. ..
...............
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.................... ............ ............. ........ . ........................ .
............ ............ ................ .............................
...
.. ...... . .. .. . .
.. .. ... .. . ..
.
.
.
.....
......................... . ........... ..... .. .. ......... . ............. .... ... . . ... ................ ... ....... .... .............
...........
.............. .............................................................. .......................... ............... .... ...................................... .... . ...... ......................................... ....... ...................
........... ........................ ............. .... ..... .......... ............... ....... . .... ........ ....... ... .. . ....
................................ ..................... ..... .... . . . ... ................. . . .. .... ................. .. ...........
. . .. . . . .
......................... ........... . ....... .. . ...... . .. ....... . ... ...
.
............... ............................. ...... ....... ... ...................... . ........ ........................................... ...............
.................................... ............... .. .................... ...... . .... .... .......................... .. ...... ..
............................. ........... . . ............. . .... . . .... .......... ......... .... ....... ... ... .......
................................... ............. ......... ......... .. .... .... ........... .... . ......
......................... ........ . .............. ........ ... ........ ..... ............. ........ .... .
............. .............. .....................
.............. . ....................... .
......... ............. ..........
.................... ...... ... . ................... .. ..............................................
............ ............. .. ........... . .... ...... ............ ....
....................... ............... ... ...................................
................... .... ......... .. .... ......... .................. ....
...... .................... ........ .. ......... ...... .
....................... ... .... . ........... .. .... ... ..
................ ............... ... ................ .
....................................... ........... .....
.......................... .....................
...................... .... .........
............... .................
.............................
. ............
.................
.........
+
0.0
0.70
0.73
0.76
0.79
0.82
0.85
0.88
0.91
0.94
0.97
1.00
B u ca on d ag am
1.11 3D bifurcation of the logistic map
0.7
0 3/Tfin
ScopeXYZ
1/z
1 11 1 Description
Add here a paragraph of the function description
1 11 2 Context
Te = 1
ci=0.5
Tfin = 5e5*Te
I. 1. CHAOTIC DYNAMICAL SYSTEMS
23
1.11.3 Scope Results
x[k−1]
1.0
.
.
.
..
.................................
...
..
0.0
0.5
0.5
x[k]
0.0
0.70
0.85
R
1.0
1.00
Scope esu s
1 11 4 Mod_num blocks
• LOGISTIQUE_f - Logistic function block
• SCOPXYZ_f - 3D trajectory scope block
I. 1. CHAOTIC DYNAMICAL SYSTEMS
24
1.12 Henon’s system
1
1/z
u^a
−1
1.4/Tfin
b
1/z
1.12.1 Description
Henon’s map is defined with the followind discret state sytem :
xk+1 = yk + 1 − αx2k
(1.22)
yk+1 = βxk
(1.23)
1.12.2 Context
Te=1
Tfin=5e4*Te
b=0.3
1.12.3 Scope Results
2.0
1.6
1.2
0.8
0.4
0.0
−0.4
−0.8
−1.2
.........................................................................................
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...
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................
.............................................. ...............
. .. ......... .............................
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...
.... . . .... . ... ...
................................... . ........... .
..............
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............ ... ......................
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.... . . ..... . . . .
..................... ..............................
. ........ ...................... .......
. ............ ..........
.............. .........................................................................
. ....................................... ...................
..............................................
..................... . ...
.. ........
−1.6
+
−2.0
0.00
0.14
0.28
0.42
0.56
0.70
0.84
0.98
B u ca on d ag am
1.12
1.26
1.40
I. 1. CHAOTIC DYNAMICAL SYSTEMS
25
1.13 Chaotic first order Delta-Sigma modulator
0
+
−
1−bit quantizer
1/z
2/Tfin
1/z
1.13.1 Context
Te=1
Tfin=5e4*Te
1.13.2 Scope Results
1.0
0.8
0.6
0.4
0.2
0.0
−0.2
−0.4
−0.6
−0.8
−1.0
........
................................. .. ... . .... . . .. .... .. .. . . .. .. . ... .. . ... . . .. . .. .. .... . . . . .. .
........
..................................................................................................................................................................................... ....... ................................................................................... ................. .....................
........
.........
. ......................... . ................................................................................................................................ ................... ............. ......................... ................. ............ ............... ............................
..........
. ................................................................................................................................................................ ..................... ................ .................... .... .... ................................................
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................................................................ ... . ............ . . ...... .... ....... .......... ............. ........ .. ..... . .... ..................... ... .................
...........
.
............
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.
............
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.
.............
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..
..............
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..................
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....................
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............................ ..
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. .. . . . . . .... . . .
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.
. ... . .... . . .. . .. . . .. . . . . ... . . . ... . ... . .
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......... ..... ...................... .. . ...................... .............. . .................... ........ ........................ ..... ............ ...
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.
.
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..
. ... ...... ... ............................................................................................... . ............................... . .... ..... ......................
................... ................. ................................... ................................................ ............ ............................................. .
...
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.
.............................................................................................................. ..................................................................................... ......
....
... . ............ . .......... ... ...... ...... ....... .......... . .......... ................... ...... ..... ..
....
........ .. ................................. . ...................... ..................................... ....................... .......
.
...... .... ................................................ ... ... ...... .... ...... . . ............... . ..... ............... ...
. ....... .. ........................ .................... ..... ... ............................ . .................................
...............
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... .. ... . . . . . .... .... .. .... .. . .. . . . .... .. ... ... ..... .. ... .... . .
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.......... .. ... ....................................... ............... ........... .................. ................................................... ............................................
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... .......................... ........................... ............. ............... .. . ........... ... ...... ........................................ ....... ..................
..............
. ......... ....... .................. .. ............ ......... . . ...... ....... .... ... ........ ................. .. ....... ................
............
. ................ ........... ... .... ....... .......... ...... .......... . ................ . ............ ........ ........ . ....... ............
............
............... .......................................... ................ .......... .. ... . .............. .. ............. ............................ .................
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..
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.........
.................................................................................. ..... ........ ........ ....... .... .. .. . ........... .... ...... .... .... . .. ....... .... ...
.........
..................... . ........................................................... . .......... ......... . . ... .. . ......... ..... ............. .......... ........... .......... .....
.........
............ . ........................................................................................................................................................................................... .. ......................... .................................................. ....................
........
... ..... ... . . . .. . . ... .. . . .. . .. . ... .. .. .. . . . . . . .. . .
+...........
.............................................................................. .................. ........... ..... ... .... . ... ...... . .. .... ....... . . ....... ........ .. .......... . .. ... ...... ....
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
B u ca on d ag am
1 13 3 Mod_num blocks
• COMP_f - One bit Quantizer block
1.6
1.8
2.0
I. 1. CHAOTIC DYNAMICAL SYSTEMS
26
1.14 Frey’s chaotic encoder
IMODULO
1/z
MScope
1/z
LCMODULO
1.14.1 Context
Te = 1
Tfin = 4490
Nbit=16
Intmax = 2^(Nbit-1)
N = 1
ci1 = 1000
ci2 = 0
1.14.2 Scope Results
32768
32768
16384
26214
0
19661
−16384
13107
+
−32768
4400
6554
4410
4420
4430
4440
4450
4460
4470
4480
4490
4500
0
32768
.. ..
... ...
... ....
.... ...
... ...
.... .....
.... ...
... .......
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... ...
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−6554
−13107
16384
−19661
0
−26214
−16384
+
−32768
−32768
+
−32768
4400
4410
4420
4430
4440
4450
4460
4470
4480
4490
−26214
−19661
−13107
−6554
0
6554
4500
(a) time domain wave forms of state variables
1.14.3 Mod_num blocks
• IMODULO_f - Integer modulo function block
(b) phase plan
13107
19661
26214
32768
I. 1. CHAOTIC DYNAMICAL SYSTEMS
• LCMODULO_f - Left shift circulate integer modulo function block
1.14.4 See Also
• IMODULO_f - Integer modulo function block (Scicos Block)
• IMODULOB_f - Integer modulob function block (Scicos Block)
• FMODULOB_f - Float modulob function block (Scicos Block)
• FMODULOC_f - Float moduloc function block (Scicos Block)
• LCMODULO_f - Left shift circulate integer modulo function block (Scicos Block)
27
I. 1. CHAOTIC DYNAMICAL SYSTEMS
28
1.15 Second order Infinite Impulse Response filter
IMODULO
y[k−1]
a
1/z
IMODULO
y[k−2]
b
1/z
MScope
IMODULO
1.15.1 Description
The Fig. 1.5 presents the block diagram of an ideal second order digital filter.
y [k]
x [k]
Z −1
a
y [k − 1]
Z −1
b
y [k − 2]
Figure 1.5: Block diagram of a linear second order digital recursive filter
The differential discret equation that described the system is given by:
y (z) = y (z) az −1 + bz −2 + x (z)
(1.24)
This linear system is traditionaly studed by the Z function transfert :
H (z) =
y (z)
1
=
x (z)
1 + az −1 + bz −2
(1.25)
With H (Z), we determinate the stability domain of the filter in accord to the two gain paramter a et b. The Fig.1.6
represents the stability domain of the second order recursive filter.
I. 1. CHAOTIC DYNAMICAL SYSTEMS
29
b
b=
a2
4
+1
Pôles complexes
-2
+2
a
Pôles réels
+1
b=a-1
b=-a-1
Figure 1.6: Stability domain of the second order recursive filter
Now, we replace the ideal operators (adder and multiplactor) by real operaters that are presents in Digital Signal
Processors (DSP) when realising recursive filters. The associated non-linear function is the modulo function, wich
represents the effect of the overflow that occurs in digital implementation. The non-linear system is then described
by a non-linear discret state equations system :
1.15.2 Context
Te = 1
Tfin = 1e4*Te
Nbit = 31
a=0.5
b=-1
ci=0.675
Intmax = 2^(Nbit-1);
ci1=-int(ci*Intmax)
ci2=int(ci*Intmax)
1.15.3 Scope Results
1.1e+09
1.07e+09
5.4e+08
8.59e+08
0.0e+00
6.44e+08
−5.4e+08
4.29e+08
+
−1.1e+09
9900
2.15e+08
9910
9920
9930
9940
9950
9960
9970
9980
9990
10000
0.00e+00
1.1e+09
−2.15e+08
−4.29e+08
5.4e+08
−6.44e+08
0.0e+00
−8.59e+08
−5.4e+08
.
.
..
....
....
.........
.
.............
.
......... .............
. ..
..
. .. . .....................
. . .... .. .
.................... . ......... .......
........... . .. . . .....
. .. .
......
.. ..
...... .
.
.... .. ........ ..... ..
. ... ..... .
. . ............... .. ... .............
. . .. ... ...
. . ..... . . ........ .
+. ..
... ... ..................... .. .. .... ... ......... . ....... . .. ....... .....
..
... . ............ ... .... ...... ... ............... ..... .... ...... ... . . . . ....... ..
.
.. ... .... .......
...
.. ...... .. ............. .. ...... ...........
........ ... ..... . ........
..... ... ....
...
. ............
............
.......
...... . .............. .......... ...
......... .. ...........
..... ......... . .. . .......
........ .......... ..........
.........
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........... .
......
. ....
........
.....
....
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.
..
.
....
.....
.
.. ..
......
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................
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...
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.
.
.
.. .
..
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. ............ . . ... ..........
.
.......
.
.
.
.....
..
. ........
......
... .......
.. .........
.... . . ........
.. .......... .............. . . ............... .
..................... .. . .......... .. ..................................... ............ . ..
.
.
. ...........
.. .
. ...... .....
........
. ....
.. .....
....
................ .. .......
. ... . ................... ....
...... ......... . ..... . .....
.. ... .. . . . .. . ............
.
........
. .........
...
.. .......
.......
.
.
...........
.
.
.
.
.
.
.. .. ....... .
...... .....
. ............
.
....................... ...... .... . ..
.
.
.
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..
.......... . . . ..... . . .
. . . . ....
... ................
....... . . .
.
. . ..... . ......... ...................... ...
... ...... ..... . ....... ......... ......... ... ........... .... ...... .. ....
. ................................ . .....
.
.
−1.07e+09
−1.07e+09 −8.59e+08 −6.44e+08 −4.29e+08 −2.15e+08 0.00e+00 2.15e+08 4.29e+08 6.44e+08 8.59e+08 1.07e+09
+
−1.1e+09
9900
. ................. . .. . . ........... . . . ......... ......................... ......... ..... .. .. .. ...........
....... .. .....
. ... . ..... ......
...... .. . .... . ....
. ....... . .......
........ .. . ........... ... . ............. ..
..... ..........
...... . ......... ...... ...
. .. .
.................
...........
........
..............
......... . ....... ..................... .........
..
. ... .. . . .... . ....
..
......... ... .. ......... .
....... ... ............... ....
.........
.
. .....
............................. .. . ....... .. .......................... .. ... .. .
........ . ..... ... ............ . ...... . .......................
. .
. . .. . .. .. .....
... . . . .
.
.
.
.
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.
.
.
.
.
. . ...
.
.. .
..
....
....
.
.
.
.. .
....
.. . . . . ...
.. ........ . . .................
... ....... . . ..
...........................................
...
.
.
.
... .. .. ... .
...... ...........
................
.........
.
......
.
..
.. . . . . ...... ...... ....
. ............ ..........
.................. .........
..........
.......
..
9910
9920
9930
9940
9950
9960
9970
9980
9990
10000
(a) Temporal wave forms of discrete state variables
1.15.4 Mod_num blocks
• IMODULO_f - Integer modulo function block
(b) Phase plan
I. 1. CHAOTIC DYNAMICAL SYSTEMS
30
1.16 Master-slave synchronization of second order IIR filter
sinusoid
generator
MScope
+
1/z
sinusoid
generator
1/z
MScope
−
a
IMODULO
IMODULO
IMODULO
y[k−1]
1/z
a
1/z
b
IMODULO
IMODULO
y[k−2]
1/z
b
IMODULO
1.16.1 Context
Te = 1
Te_rec = 1
Tfin = 100
Nbit = 16
a=0.5
b=-1
ci=0.675
Intmax = 2^(Nbit-1);
ci1=-int(ci*Intmax)
ci2=int(ci*Intmax)
p_source=2*%pi*0.01
a_source=2^(Nbit-1)-1
1.16.2 Scope Results
32768
32768
16384
0
16384
−16384
−32768
+
0
10
20
30
40
50
60
70
80
90
100
0
32768
16384
−16384
0
−16384
−32768
−32768
0
+
0
+
10
20
30
40
50
60
70
80
90
10
20
30
40
50
60
70
80
100
(a) input message of emitter; output message of emitter
1.16.3 Mod_num blocks
• IMODULO_f - Integer modulo function block
1.16.4 See Also
• IMODULO_f - Integer modulo function block (Scicos Block)
• IMODULOB_f - Integer modulob function block (Scicos Block)
• FMODULO_f - Float modulo function block (Scicos Block)
(b) output message of receiver
90
100
I. 1. CHAOTIC DYNAMICAL SYSTEMS
• FMODULOB_f - Float modulob function block (Scicos Block)
• FMODULOC_f - Float moduloc function block (Scicos Block)
31
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
32
Chapter 2
Oscillators and Phase Locked Loop systems
2.1 Continous Voltage Controled Oscillator
Tsampl
MScope
sinusoid
generator
AC(t)
SCOPE
Theta(t)
u3(t)
Trig. Function
cos
kv
Ys(t)
− to +
Phi(t)
1/s
1
DC
wo
freq_div
wo t
EVENT SCOPE 1
EVENT SCOPE 2
2.1.1 Description
This diagram realizes an open loop model of a continous Voltage Controled Oscillator.
Regular output of the VCO is described with the following formula :
Z t
kv u3 (τ ) dτ
ys (t) = cos (ω0 t) +
(2.1)
0
Integration of input voltage and detection of crossing are made with the integral block and zeros crossing block
of scicos which use the integrated lsoda solver.
2.1.2 Context
Fo = 10e6;
To = 1 / Fo;
wo=2*%pi * Fo;
alpha=60e6;
kv=60e6
j_vco=100e6;
N=3;
Nsampl = 80;
Tsampl = To/(Nsampl);
Fsampl = 1 / Tsampl;
Tfin=15*To
2.1.3 Scope Results
2.1.4 See Also
• discr_vco - Discrete Voltage Controled Oscillator (Scicos Diagram)
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
33
2.0
1.0
1.5
0.9
1.0
0.8
0.5
0.7
+
0.0
0.00e+00 1.50e−07 3.00e−07 4.50e−07 6.00e−07 7.50e−07 9.00e−07 1.05e−06 1.20e−06 1.35e−06 1.50e−06
0.6
0.5
1.0
0.4
0.3
0.5
0.2
0.0
0.1
−0.5
+
0.0
0.00e+00 1.50e−07 3.00e−07 4.50e−07 6.00e−07 7.50e−07 9.00e−07 1.05e−06 1.20e−06 1.35e−06 1.50e−06
+
−1.0
0.00e+00 1.50e−07 3.00e−07 4.50e−07 6.00e−07 7.50e−07 9.00e−07 1.05e−06 1.20e−06 1.35e−06 1.50e−06
Input and output voltage of VCO
Events generated by the - to + block
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
+
0.0
0.00e+00 1.50e−07 3.00e−07 4.50e−07 6.00e−07 7.50e−07 9.00e−07 1.05e−06 1.20e−06 1.35e−06 1.50e−06
Events generated by the frequency divider block
• VCO_f - Discrete Voltage Controlled Oscillator block (Scicos Block)
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
34
2.2 Discrete Voltage Controled Oscillator
Tsampl
Random
Generator
n(t)
MScope
Trig. Function
cos
Ys(t)
Muller Law
sinusoid
generator
AC(t)
kv
Phi(t)
Euler
1
SCOPE
Theta(t)
u3(t)
DC
Time signal
wo
VCOEVT
wo t
freq_div
EVENT SCOPE 1
EVENT SCOPE 2
2.2.1 Description
This diagram is an open loop model of a discrete Voltage Controled Oscillator.
Regular output voltage can be described with this continous equation :
Z t
kv u3 (τ ) + n(τ )dτ
ys (t) = cos (ω0 t) +
(2.2)
0
The noise introduces in the the tunning voltage ist a White Gaussian Noise.
The integral of the input voltage is realized with the EULERINTEGRAL block which use the discrete backwardEuler formula and the VCOEVT block produces the event corresponding to a zero crossing with a discrete method
of detection.
2.2.2 Context
Fo = 10e6;
To = 1 / Fo;
wo=2*%pi * Fo;
alpha=60e6;
kv=60e6
j_vco=100e6;
N=3;
Nsampl = 80;
Tsampl = To/(Nsampl);
Fsampl = 1 / Tsampl;
Tfin=15*To
2.2.3 Scope Results
2.2.4 Mod_num blocks
• NOISEBLK_f - Gaussian White Noise Generator block
• Time_f - Discrete time estimator bloc
• VCOEVT_f - Discrete zero crossing block
• EULERINTEGRAL_f - Single step integrator block by Euler method
2.2.5 See Also
• scicos_vco - Continous Voltage Controled Oscillator (Scicos Diagram)
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
35
2.0
1.0
1.5
0.9
1.0
0.8
0.5
0.7
+
0.6
0.0
0.00e+00 1.50e−07 3.00e−07 4.50e−07 6.00e−07 7.50e−07 9.00e−07 1.05e−06 1.20e−06 1.35e−06 1.50e−06
0.5
1.0
0.4
0.3
0.5
0.2
0.0
0.1
−0.5
+
0.0
0.00e+00 1.50e−07 3.00e−07 4.50e−07 6.00e−07 7.50e−07 9.00e−07 1.05e−06 1.20e−06 1.35e−06 1.50e−06
+
−1.0
0.00e+00 1.50e−07 3.00e−07 4.50e−07 6.00e−07 7.50e−07 9.00e−07 1.05e−06 1.20e−06 1.35e−06 1.50e−06
Input and output voltage of VCO
Events generated by the VCOEVT block
1.0
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
+
0.0
0.00e+00 1.50e−07 3.00e−07 4.50e−07 6.00e−07 7.50e−07 9.00e−07 1.05e−06 1.20e−06 1.35e−06 1.50e−06
Events generated by the frequency divider block
2.3 Simple scicos diagram of an integer-N frequency synthesizer
random
generator
Event
Delay
CPF
+
−
num(s)
den(s)
Icp
Ileak
MScope
SCOPE
− to +
Trig. Function
cos
alpha
1/s
freq_div
wo
Trig. Function
tanh
beta2
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
36
2.3.1 Context
F_cpf = 50e6;
T_cpf = 1/F_cpf;
sig_ref=T_cpf*0.1/100
Fo = 2.045e9;
To = 1 / Fo;
wo=2*%pi * Fo;
kv = 100.5e6;
alpha=6.91e9;
beta2=0.15;
j_vco=1e6;
N=52;
Fd=N*F_cpf;
Nsampl = 4;
Tsampl = 1/(Fd*Nsampl);
Fsampl = 1 / Tsampl;
Icp = 5e-3;
Ileak=10e-6;
fn=F_cpf/180;
phi=%pi/4;
kv=kv*2*%pi
[tau1,tau,tau2]=calcul_3eme_ordre(fn,phi,kv,Icp,N);
s=poly(0,’s’);
num=1+tau1*s;
den=tau*s*(1+tau2*s);
kv=kv/(2*%pi)
Tfin=1000*T_cpf
2.3.2 Scope Results
0.0050
0.0025
0.0000
−0.0025
+
−0.0050
0.0e+00
2.0e−06
4.0e−06
6.0e−06
8.0e−06
1.0e−05
1.2e−05
1.4e−05
1.6e−05
1.8e−05
2.0e−05
2.0e−06
4.0e−06
6.0e−06
8.0e−06
1.0e−05
1.2e−05
1.4e−05
1.6e−05
1.8e−05
2.0e−05
4
3
2
1
+
0
0.0e+00
Scope results
2.3.3 Mod_num blocks
• CPF_f - Tri-state Phase/Frequency Comparator block
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
37
2.4 Scattered diagram of a third order integer-N frequency synthesizer
Random
Generator
Phase
Modulator
Muller Law
T_cpf
CPF
+
−
num(s)
den(s)
Icp
Ileak
MScope
SCOPE
Tsampl
Trig. Function
tanh
alpha
VCOEVT
Trapezoidal
400*T_cpf
Counter
Modulo 3
Random
Generator
Muller Law
wo
Time signal
N
2.4.1 Context
lines(-1);
F_cpf = 50e6;
T_cpf = 1/F_cpf;
sig_ref=T_cpf*0.2/100
Fo = 2.045e9;
To = 1 / Fo;
wo=2*%pi * Fo;
kv = 100.5e6;
alpha=6.91e9;
beta2=0.15;
j_vco=1e6;
N=52;
Fd=N*F_cpf;
Nsampl = 2;
Tsampl = 1/(Fd*Nsampl);
Fsampl = 1 / Tsampl;
Icp = 5e-3;
Ileak=1e-6;
fn=F_cpf/180;
phi=%pi/4;
kv=kv*2*%pi
[tau1,tau,tau2]=calcul_3eme_ordre(fn,phi,kv,Icp,N);
s=poly(0,’s’);
num=1+tau1*s;
den=tau*s*(1+tau2*s);
kv=kv/(2*%pi)
Tfin=2e3*T_cpf
2.4.2 Scope Results
2.4.3 Mod_num blocks
• TRAPINTEGRAL_f - Single step integrator block by trapezoidal method
• VCOEVT_f - Discrete zero crossing block
• CPF_f - Tri-state Phase/Frequency Comparator block
• Time_f - Discrete time estimator bloc
beta2
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
38
0.0050
0.0025
0.0000
−0.0025
+
−0.0050
0.0e+00
4.0e−06
8.0e−06
1.2e−05
1.6e−05
2.0e−05
2.4e−05
2.8e−05
3.2e−05
3.6e−05
4.0e−05
4.0e−06
8.0e−06
1.2e−05
1.6e−05
2.0e−05
2.4e−05
2.8e−05
3.2e−05
3.6e−05
4.0e−05
5.0
4.5
4.0
3.5
+
3.0
0.0e+00
Scope results
• NOISEBLK_f - Gaussian White Noise Generator block
• PEVTDLY_f - Phase modulator event generator block
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
39
2.5 Integrated diagram of an integer-N frequency synthesizer
Random
Generator
Muller Law
PFD
Sec Order
Loop
Filter
MScope
SCOPE
VCO
%N
N
2.5.1 Context
F_cpf = 20e6;
T_cpf = 1/F_cpf;
sig_ref=(2*%pi*0.2/100)
Fo = 2.045e9;
To = 1 / Fo;
wo=2*%pi * Fo;
kv = 100.5e6;
alpha=6.91e9;
beta2=0.15;
j_vco=1e6;
Fd=2.5e9;
N=int(Fd/F_cpf)
Nsampl = 2;
Tsampl = T_cpf/(Nsampl);
Fsampl = 1 / Tsampl;
Icp = 5e-3;
Ileak=1e-6;
Ileak_sig=1e-12;
fn=F_cpf/180;
phi=%pi/4;
Tfin=0.8e3*T_cpf
2.5.2 Scope Results
2.5.3 Mod_num blocks
• PFD_f - Phase/Frequency tristate Detector block
• VCO_f - Discrete Voltage Controlled Oscillator block
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
40
0.0050
3.1e+09
0.0025
3.0e+09
0.0000
2.9e+09
−0.0025
2.8e+09
+
−0.0050
0.0e+00
4.0e−06
8.0e−06
1.2e−05
1.6e−05
2.0e−05
2.4e−05
2.8e−05
3.2e−05
3.6e−05
4.0e−05
2.7e+09
2.6e+09
3.50
2.5e+09
2.62
2.4e+09
1.75
2.3e+09
0.88
2.2e+09
0
+
0.00
0.0e+00
4.0e−06
8.0e−06
1.2e−05
1.6e−05
2.0e−05
2.4e−05
2.8e−05
3.2e−05
3.6e−05
2
4
Time domain wave forms (a)Charge pump output current;
(b)VCO input voltage
Magnitude
40
0
0
db
db
12
20
−20
−40
−20
−60
−40
−80
−60
−100
4
10
5
10
6
7
10
Hz
−80
8
10
10
4
5
10
6
10
10
Hz
Phase
7
10
8
10
Phase
−135
−0
−140
−20
−145
−40
−150
−60
degrees
degrees
10
Magnitude
60
20
−155
−160
−165
−80
−100
−120
−170
−140
−175
−180
8
Non linear voltage/frequency caracteristic of VCO
40
−120
6
4.0e−05
−160
4
10
5
10
6
7
10
Hz
−180
8
10
10
4
5
10
6
10
Open-loop transfert function
10
Hz
Closed-loop transfert function
Magnitude
5
0
−5
db
−10
−15
−20
−25
−30
−35
4
10
5
10
6
10
Hz
7
10
8
10
Phase
180
160
degrees
140
120
100
80
60
40
20
0
4
10
7
10
5
10
6
10
Hz
7
10
FM-response transfert function
• PCLOCK_f - Integrated phase modulator event generator block
• NOISEBLK_f - Gaussian White Noise Generator block
8
10
8
10
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
• SOLOOPFILTER_f - Second order Loop Filter for PLL type 2 block
41
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
42
2.6 Scattered diagram of a third order integer-N frequency synthesizer with an
interpoled non-linearity of VCO and with dual-modulus feedback divider
Random
Generator
Phase
Modulator
Muller Law
freq_div
CPF
+
−
Sec Order
Loop
Filter
Io
Ileak
MScope
Random
Generator
VCOEVT
Muller Law
Trig. Function
sin
Prescaler
P/P+1
1/s
wo
counter
A
B COUNTER
2.6.1 Context
F_ref=250e6
T_ref=1/F_ref
sig_ref=0.2*T_ref
R=5
F_cpf = F_ref/R;
T_cpf = 1/F_cpf;
Io=5e-3
Ileak=1e-8
Fo = 2.045e9;
To = 1 / Fo;
wo=2*%pi * Fo;
j_vco=2e6;
y_tab=read(MODNUM+’/scs_diagr/pll/synthe/vcotab’,12,9);
d_tab=splin(y_tab(:,1),((y_tab(:,2)*1e6)-Fo)*2*%pi)
i_tab=1:0.1:12;
f_tab=interp(i_tab,y_tab(:,1),((y_tab(:,2)*1e6)-Fo)*2*%pi,d_tab);
A=4;
B=6;
P=8;
N=B*P+A;
Fd=N*F_cpf;;
fn=F_cpf/180
mphi=%pi/4
kv=80e6
Nsampl = 2;
Tsampl = 1/(Nsampl*Fd);
Fsampl = 1 / Tsampl;
Tfin=0.9e3*T_cpf
2.6.2 Scope Results
2.6.3 Mod_num blocks
• NOISEBLK_f - Gaussian White Noise Generator block
interp
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
0.0050
0.0025
0.0000
−0.0025
+
−0.0050
0.00e+00 1.80e−06 3.60e−06 5.40e−06 7.20e−06 9.00e−06 1.08e−05 1.26e−05 1.44e−05 1.62e−05 1.80e−05
5.00
3.75
2.50
1.25
+
0.00
0.00e+00 1.80e−06 3.60e−06 5.40e−06 7.20e−06 9.00e−06 1.08e−05 1.26e−05 1.44e−05 1.62e−05 1.80e−05
Scope results
• PEVTDLY_f - Phase modulator event generator block
• SOLOOPFILTER_f - Second order Loop Filter for PLL type 2 block
• VCOEVT_f - Discrete zero crossing block
• CPF_f - Tri-state Phase/Frequency Comparator block
43
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
44
2.7 Modulated fractional frequency synthesizer
0
PFD
num(s)
den(s)
MScope
Icp/Vtune
VCO
%N
N
MASH
Sigma/Delta
2freq clock
f/n f
FIR
Random
Integer
Generator
Gauss
MScope
Symbole émis
2.7.1 Context
lines(-1);
F_cpf = 20e6;
T_cpf = 1/F_cpf;
sig_ref=T_cpf*0.02/100
Fo = 2.045e9;
To = 1 / Fo;
wo=2*%pi * Fo;
kv = 100.5e6;
alpha=6.91e9;
beta2=0.15;
j_vco=0.2e6;
Fd=2.5e9;
N=int(Fd/F_cpf)
Nsampl = 2;
Tsampl = 1/(F_cpf*Nsampl);
Fsampl = 1 / Tsampl;
Icp = 5e-3;
Ileak=0.1e-6;
fn=F_cpf/180;
phi=%pi/4;
Ts=3/fn
Nech=12
Te=Ts/Nech
Nbit=3
M=32
[tau1,tau,tau2]=calcul_3eme_ordre(fn,phi,kv*2*%pi,Icp,N);
s=poly(0,’s’);
num=1+tau1*s;
den=tau*s*(1+tau2*s);
Tfin=10e3*T_cpf
2.7.2 Scope Results
2.7.3 Mod_num blocks
• PFD_f - Phase/Frequency tristate Detector block
I. 2. OSCILLATORS AND PHASE LOCKED LOOP SYSTEMS
1.10
45
0.0050
0.55
0.0025
0.00
−0.55
0.0000
+
−1.10
2.50e−04 2.75e−04 3.00e−04 3.25e−04 3.50e−04 3.75e−04 4.00e−04 4.25e−04 4.50e−04 4.75e−04 5.00e−04
−0.0025
36
+
18
−0.0050
2.50e−04 2.75e−04 3.00e−04 3.25e−04 3.50e−04 3.75e−04 4.00e−04 4.25e−04 4.50e−04 4.75e−04 5.00e−04
0
−18
3.100
+
−36
2.50e−04 2.75e−04 3.00e−04 3.25e−04 3.50e−04 3.75e−04 4.00e−04 4.25e−04 4.50e−04 4.75e−04 5.00e−04
2.975
3.5
2.850
1.5
−0.5
2.725
−2.5
+
+
−4.5
2.50e−04 2.75e−04 3.00e−04 3.25e−04 3.50e−04 3.75e−04 4.00e−04 4.25e−04 4.50e−04 4.75e−04 5.00e−04
2.600
2.50e−04 2.75e−04 3.00e−04 3.25e−04 3.50e−04 3.75e−04 4.00e−04 4.25e−04 4.50e−04 4.75e−04 5.00e−04
Scope results
• VCO_f - Discrete Voltage Controlled Oscillator block
• PCLOCK_f - Integrated phase modulator event generator block
• MASHBLK_f - Delta-Sigma modulator block
• RIFGEN_f - Generic Finite Impulse Response filter block
• GENINT_f - Random Integer Generator block
Scope results
I. 3. COMMUNICATION SYSTEMS
46
Chapter 3
Communication systems
3.1 Scattered diagram of base band QPSK transmission chain
Random
Integer
Generator
N15
Convol
N15
Convol
I/Q
Mod
PSK
M − PSK
Modulator
Mux
Right Shift
Register
VectoMemo
Scope
0000000.
Bit Error
Counter
VectoMemo
Scope
Random
Generator
Ts
M
15
1−bit quantizer
I/Q
Demod
PSK
M − PSK
Demodulator
Mux
Convol
0
Demux
Ts
M
15
0
Convol
1−bit quantizer
M
15
Mux
Vector
ScopeXY
3.1.1 Description
Long description
3.1.2 Context
Te=0.1;
Nu=350;
Nech=15;
N=Nu*Nech;
Nbit=2;
nb_coef=127;
r=0.35;
Vector
ScopeXY
Demux
Muller Law
I. 3. COMMUNICATION SYSTEMS
47
fe=Nech;
gain_em=1;
gain_rec=1/Nech;
pulse=zeros(1,1);
t_Ts=1/fe*(-nb_coef/2:nb_coef/2-1);
pulse = 4*r/%pi*(cos((1+r)*%pi*t_Ts) + (sin((1-r)*%pi*t_Ts)./(4*r*t_Ts)))./(1-(4*r*t_Ts).^2);
Nb_vec=3;
nb_event=3;
Tfin=Te*Nb_vec
sigma=0.2;
3.1.3 Scope Results
1.5
1.5
1.2
1.2
.
. . .. . .. .
.
. .. .
. . . . .... ........ . . . . ...
.
. ...... .. .. .
. . ... . ......... .......... . ..
..
..
..
.
.... . ... ...... . .... .
.
.
.
.. .... . . ..... . . . .
.. .... ... .. .. . .. .
.
. . . . . ..
0.9
0.6
0.9
0.6
0.3
0.3
0.0
0.0
−0.3
−0.3
. ... . .
.
. . ... .. .. . .
.. ........ ............. .... ...
.. .
. .. . .......... .. ... .
. ..
.
−0.6
−0.9
.
. .. . . . .
.
. . .. ... .
. ... ... .... ... .. ...... . ..
.. . . .
.
. ... ..... .... .. ... . .. .
. .. .. . ..
.
−0.6
−0.9
−1.2
−1.2
−1.5
−1.5
−1.5
−1.2
−0.9
−0.6
−0.3
0.0
0.3
0.6
0.9
1.2
1.5
1.0
3.9
6.8
9.7
12.6
(a)
1.5
1.2
1.2
0.9
0.9
0.6
0.6
0.3
0.3
0.0
0.0
−0.3
−0.3
−0.6
−0.6
−0.9
−0.9
−1.2
−1.2
−1.5
3.9
6.8
9.7
12.6
15.5
18.4
21.3
24.2
27.1
30.0
0.3
0.6
0.9
1.2
1.5
(b)
1.5
1.0
15.5
18.4
21.3
24.2
27.1
30.0
−1.5
−1.5
−1.2
(c)
3.1.4 Mod_num blocks
• VECTOMEMOSCOPE_f - Vectorial scope with memory block
• SCOXYVEC_f - Scicos Vector Scope visualization block
• CONVOLGEN_f - Convolution block
• INTSYMB_f - Discrete Symbol Integrator block
−0.9
−0.6
−0.3
0.0
(d)
I. 3. COMMUNICATION SYSTEMS
• MODPSK_f - M-ary Phase Shift Keying Modulator Block
• DEMODPSK_f - M-ary Phase Shift Keying demodulator Block
• OVERLAPRSR_f - Memory discrete shift register for multiplexed signal block
• NOISEBLK_f - Gaussian White Noise Generator block
• GENINT_f - Random Integer Generator block
• BITERROR_f - Binary error estimation block
• COMP_f - One bit Quantizer block
• UPSMPL_f - Up-sample block
• DOWNSMPL_f - Down-sample block
48
I. 3. COMMUNICATION SYSTEMS
49
3.2 Integrated diagram of base band QPSK transmission chain
VectoMemo
Scope
Random
Integer
Generator
A.W.G.N
GENERIC
Bit Error
Counter
0000000.
Symbol
Generator
VectoMemo
Scope
QPSK
Receiver
3.2.1 Context
Te=0.1;
Nu=128;
Nech=15;
N=Nu*Nech;
Nbit=2;
nb_coef=127;
r=0.35;
fe=Nech;
gain_em=1;
gain_rec=1/Nech;
p=filter_tap(1,nb_coef,Nech,r,1);
m1=2^(int(log(N+nb_coef-1)/log(2))+1);
Nb_vec=3;
nb_event=3
Tfin=Te*Nb_vec;
sigma=0.2;
3.2.2 Scope Results
1.5
1.5
1.2
1.2
0.9
0.9
0.6
0.6
0.3
0.3
0.0
0.0
−0.3
−0.3
−0.6
−0.6
−0.9
−0.9
−1.2
−1.2
−1.5
−1.5
1.0
3.9
6.8
9.7
12.6
15.5
18.4
21.3
24.2
27.1
30.0
1.0
3.9
Scope results
3.2.3 Mod_num blocks
• AWGN_f - Additive White Gaussian Noise Channel block
• GENINT_f - Random Integer Generator block
• GENSYMB_f - Symbol generator block
• QPSKREC_f - Quaternary Phase Shift Keying receiver block
6.8
9.7
12.6
15.5
18.4
Scope results
21.3
24.2
27.1
30.0
I. 3. COMMUNICATION SYSTEMS
• BITERROR_f - Binary error estimation block
• VECTOMEMOSCOPE_f - Vectorial scope with memory block
50
I. 3. COMMUNICATION SYSTEMS
51
3.3 Base band single user QPSK spread-spectrum transmission chain
N
Codinservec
Random
Integer
Generator
I/Q
Mod
PSK
Convol
Gold
Generator
Demux
0000000.
Right Shift
Register
Bit Error
Counter
Mux
N
Codinservec
Convol
Random
Generator
VectoMemo
Scope
Mux
Ts
Ts
M
M
Convol
0
Decodvec
0
1−bit quantizer
1−bit quantizer
I/Q
Demod
PSK
Gold
Generator
Ts
M
Ts
Demux
Decodvec
0
M
0
1−bit quantizer
Demux
Convol
1−bit quantizer
3.3.1 Context
Te=0.1;
Nu=4;
Nbit=2;
l_g=5;
Nc=(2^l_g)-1;
ci_g1=[21;21];ci_g2=[13;10]
coef_g1=[9;9];coef_g2=[15;15]
nb_coef=127;
Nech=15;
N=Nu*Nc;
N1=N*Nech
r=0.35;
fe=Nech;
gain_em=1;
gain_rec=1/Nech;
pulse=zeros(1,1);
t_Ts=1/fe*(-nb_coef/2:nb_coef/2-1);
pulse = 4*r/%pi*(cos((1+r)*%pi*t_Ts) + (sin((1-r)*%pi*t_Ts)./(4*r*t_Ts)))./(1-(4*r*t_Ts).^2);
Nb_vec=3;
nb_event=4;
Tfin=Te*Nb_vec;
sigma=0.4;
3.3.2 Scope Results
1.5
1.2
0.9
0.6
0.3
0.0
−0.3
−0.6
−0.9
−1.2
−1.5
1.0
3.9
6.8
9.7
12.6
15.5
18.4
Scope results
3.3.3 Mod_num blocks
• CODINSERVEC_f - Sequence/symbol modulation block
21.3
24.2
27.1
30.0
Muller Law
I. 3. COMMUNICATION SYSTEMS
• DECODVEC_f - Sequence/symbol demodulation block
• GENGOLD_f - Gold sequence generator block
• CONVOLGEN_f - Convolution block
• DEMODPSK_f - M-ary Phase Shift Keying demodulator Block
• OVERLAPRSR_f - Memory discrete shift register for multiplexed signal block
• MODPSK_f - M-ary Phase Shift Keying Modulator Block
• INTSYMB_f - Discrete Symbol Integrator block
• GENINT_f - Random Integer Generator block
• NOISEBLK_f - Gaussian White Noise Generator block
• VECTOMEMOSCOPE_f - Vectorial scope with memory block
• BITERROR_f - Binary error estimation block
• COMP_f - One bit Quantizer block
• UPSMPL_f - Up-sample block
• DOWNSMPL_f - Down-sample block
52
I. 3. COMMUNICATION SYSTEMS
53
3.4 Scattered diagram of sample-based 16-QAM chain transmission
MScope
N
Random
Integer
Generator
I/Q
MQAM
FIR
I
RRCF
Q
Re
Mod I/Q
Img
MScope
N
FIR
RRCF
MScope
Memo Scope
FIR
Re
I
Demod I/Q
Img
Q
RRCF
FIR
RRCF
3.4.1 Context
Tsymbole = 0.1
Nech = 12
Tech = Tsymbole /Nech
Nsampl = 20
Tsampl = Tech/Nsampl
nb_coef=127
r=0.35
wo=2*%pi/(Tsymbole/20)
Tfin=300*Tsymbole
3.4.2 Scope Results
1.50
0.08
0.75
0.06
0.04
0.00
0.02
−0.75
0.00
+
−1.50
29.50
29.55
29.60
29.65
29.70
29.75
29.80
29.85
29.90
29.95
30.00
0
20
40
60
80
X
Scope results
Scope results
100
120
I. 3. COMMUNICATION SYSTEMS
54
16
1.50
12
8
0.75
4
+
0
25.0
25.5
26.0
26.5
27.0
27.5
28.0
28.5
29.0
29.5
30.0
0.00
4
2
−0.75
0
+
−2
−1.50
25.0
+
−4
25.0
25.5
26.0
26.5
27.0
27.5
28.0
28.5
29.0
29.5
25.5
26.0
26.5
27.0
27.5
28.0
28.5
29.0
29.5
30.0
25.5
26.0
26.5
27.0
27.5
28.0
28.5
29.0
29.5
30.0
30.0
4
1.50
2
0
0.75
−2
+
−4
25.0
25.5
26.0
26.5
27.0
27.5
28.0
28.5
29.0
29.5
30.0
0.00
1.50
0.75
−0.75
0.00
+
−0.75
−1.50
25.0
+
−1.50
25.0
25.5
26.0
26.5
27.0
27.5
28.0
28.5
29.0
29.5
30.0
Scope results
Scope results
1.5
1.2
0.9
0.6
0.3
0.0
−0.3
−0.6
−0.9
−1.2
−1.5
1.0
3.3
5.6
7.9
10.2
12.5
14.8
17.1
19.4
21.7
Scope results
3.4.3 Mod_num blocks
• GENINT_f - Random Integer Generator block
• RIFGEN_f - Generic Finite Impulse Response filter block
• MODQAM_f - Quadrature Amplitude Modulation modulator Block
• MODIQ_f - I/Q modulator Block
• DEMODIQ_f - I/Q demodulator Block
• MEMOSCOPE_f - Memory sequential scope block
• UPSMPL_f - Up-sample block
24.0
I. 3. COMMUNICATION SYSTEMS
55
3.5 Scattered diagram of first order Delta-Sigma modulator
sinusoid
generator
num(s)
den(s)
+
−
MScope
1−bit quantizer
1/z
1
3.5.1 Context
M=1
Te=0.1
Ne=500
To=Te*Ne
w=2*%pi/To
Tfin=2*To
3.5.2 Scope Results
1.0
0.5
0.0
−0.5
−1.0
×××××××××××××××××××××××
××××××××××××××××××××××××××××××
×××××
×××××××
××××××
××××
××××
×××××
××××
××××
××××
××××
××××
××××
××××
×××
×××
×××
×××
×××
×××
××××
×××
×××
×××
×××
×××
×××
×
×××
×
×
×××
×
×××
×
×××
×××
×××
×
×××
×
×
×
×
×××
×
×××
××
××
×××
×××
×××
×××
×××
×
×××
×
×
×××
×××
×××
×××
×××
×××
×××
×
×
×××
××
×××
×××
××××
×××
××××
×
××××
×
×
××××
××××
××××
××
×××××
×××××
××××
××××
×
×
×
×
×
×
×
×
××××××
×××××××
××××××××××××××××××××××××××
×××××××××××××××××××××××××
+
0
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
1.10
0.55
0.00
−0.55
−1.10
+
0
1.0
0.5
0.0
−0.5
−1.0
+
0
Scope results
3.5.3 Mod_num blocks
• COMP_f - One bit Quantizer block
3.5.4 See Also
• mash_2eme_ordre - Scattered diagramm of second order Delta-Sigma modulator (Scicos Diagram)
• mash_gauss - Integrated diagram of Delta-Sigma modulator (Scicos Diagram)
• MASHBLK_f - Delta-Sigma modulator block (Scicos Block)
• mash_gauss_sim - Output spectra of Delta-Sigma modulator (Scilab simulation Script)
I. 3. COMMUNICATION SYSTEMS
56
3.6 Scattered diagramm of second order Delta-Sigma modulator
sinusoid
generator
+
−
1−bit quantizer
1/z
1
+
Q(z)
−
+
−
1/z
−
+
1−bit quantizer
1/z
MScope
num(s)
den(s)
1
3.6.1 Context
M=1
Te=0.1
Ne=500
To=Te*Ne
w=2*%pi/To
Tfin=2*To
3.6.2 Scope Results
2.10
1.05
0.00
−1.05
−2.10
+
0
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
1.0
0.5
0.0
−0.5
−1.0
+
0
Scope results
3.6.3 Mod_num blocks
• COMP_f - One bit Quantizer block
3.6.4 See Also
• mash_1er_ordre - Scattered diagram of first order Delta-Sigma modulator (Scicos Diagram)
• mash_gauss - Integrated diagram of Delta-Sigma modulator (Scicos Diagram)
• MASHBLK_f - Delta-Sigma modulator block (Scicos Block)
I. 3. COMMUNICATION SYSTEMS
• mash_gauss_sim - Output spectra of Delta-Sigma modulator (Scilab simulation Script)
57
I. 3. COMMUNICATION SYSTEMS
58
3.7 Integrated diagram of Delta-Sigma modulator
2freq clock
f/n f
Random
Integer
Generator
FIR
num(s)
den(s)
MASH
Sigma/Delta
MScope
Gauss
MScope
3.7.1 Context
M=1
Te=1
Nech=12
order=3
Tsym=Te*Nech
Nsampl=500
Tsampl=Tsym/Nsampl
fc=0.03*(1/Tsampl)
eps=0.7
tau=1/(2*%pi*fc)
Tfin=8*Tsym
3.7.2 Scope Results
8
1.10
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⊕
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4
0
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0.55
0.00
⊕
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−4
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⊕
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⊕
⊕
⊕⊕⊕
−8
⊕ ⊕ ⊕⊕ ⊕⊕ ⊕ ⊕
⊕
⊕ ⊕⊕⊕⊕
⊕⊕⊕ ⊕
0.0
9.6
19.2
28.8
38.4
48.0
57.6
67.2
76.8
86.4
−0.55
⊕⊕
+
96.0
−1.10
1.0
1.10
0.5
0.55
0.0
0.00
9.6
19.2
28.8
38.4
48.0
57.6
67.2
76.8
86.4
96.0
9.6
19.2
28.8
38.4
48.0
57.6
67.2
76.8
86.4
96.0
−0.55
−0.5
−1.0
+
0.0
+
0.0
9.6
19.2
28.8
38.4
48.0
57.6
67.2
76.8
86.4
96.0
−1.10
+
0.0
Scope results
3.7.3 Mod_num blocks
• RIFGEN_f - Generic Finite Impulse Response filter block
• GENINT_f - Random Integer Generator block
• MASHBLK_f - Delta-Sigma modulator block
Scope results
I. 3. COMMUNICATION SYSTEMS
3.7.4 See Also
• mash_1er_ordre - Scattered diagram of first order Delta-Sigma modulator (Scicos Diagram)
• mash_2eme_ordre - Scattered diagramm of second order Delta-Sigma modulator (Scicos Diagram)
• mash_gauss_sim - Output spectra of Delta-Sigma modulator (Scilab simulation Script)
59
I. 3. COMMUNICATION SYSTEMS
60
3.8 Delta-sigma modulator with two in-loop integrators
sinusoid
generator
+
−
1/z
1−bit quantizer
1/z
M
num(s)
den(s)
3.8.1 Context
M=1
Te=0.1
Ne=500
To=Te*Ne
w=2*%pi/To
Tfin=2*To
3.8.2 Scope Results
1.10
0.55
0.00
−0.55
−1.10
+
0
10
20
30
40
50
60
70
80
90
100
10
20
30
40
50
60
70
80
90
100
1.0
0.5
0.0
−0.5
−1.0
+
0
Scope results
3.8.3 Mod_num blocks
• COMP_f - One bit Quantizer block
MScope
I. 3. COMMUNICATION SYSTEMS
61
3.9 Delta-sigma modulator with three in-loop integrators
2
1
sinusoid
generator
+
0.25
−
1−bit quantizer
sinusoid
generator
1/z
1/z
1/z
M
num(s)
den(s)
MScope
3.9.1 Context
M=1
Te=1
Ne=100
To=Te*Ne
w=2*%pi/To
Tsampl=Te/Ne
Nsampl=2^14
Tfin=Nsampl*Tsampl
3.9.2 Scope Results
1.10
0.55
0.00
−0.55
+
−1.10
100
110
120
130
140
150
160
170
180
190
200
110
120
130
140
150
160
170
180
190
200
1.0
0.5
0.0
−0.5
+
−1.0
100
Scope results
3.9.3 Mod_num blocks
• COMP_f - One bit Quantizer block
I. 3. COMMUNICATION SYSTEMS
62
3.10 Chaotic frequency hopping emitter
0
PFD
num(s)
den(s)
CAN
GENERIC
Destockbit
0
MScope
Icp/Vtune
VCO
%N
Memo Scope
N
MASH
Sigma/Delta
FIR
Gauss
MScope
Symbole émis
3.10.1 Description
Add here a paragraph of the function description.
3.10.2 Context
nb_coef=85
lines(-1);
F_cpf = 20e6;
T_cpf = 1/F_cpf;
sig_ref=T_cpf*0.02/100
Fo = 2.045e9;
To = 1 / Fo;
wo=2*%pi * Fo;
kv = 100.5e6;
alpha=6.91e9;
beta2=0.15;
j_vco=0.2e6;
Fd=2.5e9;
N=int(Fd/F_cpf)
Nsampl = 2;
Tsampl = 1/(F_cpf*Nsampl);
Fsampl = 1 / Tsampl;
Icp = 5e-3;
Ileak=0.1e-6;
fn=F_cpf/180;
phi=%pi/4;
Ts=3/fn
Nech=12
Te=Ts/Nech
M=32
Nbit=3
a=0.5
b=-1
[tau1,tau,tau2]=calcul_3eme_ordre(fn,phi,kv*2*%pi,Icp,N);
s=poly(0,’s’);
num=1+tau1*s;
den=tau*s*(1+tau2*s);
Tfin=170e3*T_cpf
3.10.3 Scope Results
3.10.4 Mod_num blocks
• PFD_f - Phase/Frequency tristate Detector block
• VCO_f - Discrete Voltage Controlled Oscillator block
• PCLOCK_f - Integrated phase modulator event generator block
MScope
I. 3. COMMUNICATION SYSTEMS
63
8
0.0050
4
0.0025
0
0.0000
−4
−0.0025
+
−8
8.00e−03 8.05e−03 8.10e−03 8.15e−03 8.20e−03 8.25e−03 8.30e−03 8.35e−03 8.40e−03 8.45e−03 8.50e−03
+
−0.0050
8.00e−03 8.05e−03 8.10e−03 8.15e−03 8.20e−03 8.25e−03 8.30e−03 8.35e−03 8.40e−03 8.45e−03 8.50e−03
32
2.900
16
2.875
0
2.850
−16
2.825
+
−32
8.00e−03 8.05e−03 8.10e−03 8.15e−03 8.20e−03 8.25e−03 8.30e−03 8.35e−03 8.40e−03 8.45e−03 8.50e−03
+
2.800
8.00e−03 8.05e−03 8.10e−03 8.15e−03 8.20e−03 8.25e−03 8.30e−03 8.35e−03 8.40e−03 8.45e−03 8.50e−03
Scope results
Scope results
2048
2.890
1024
2.883
−0
2.876
−1025
2.869
+
2.862
−2049
8.00e−03 8.05e−03 8.10e−03 8.15e−03 8.20e−03 8.25e−03 8.30e−03 8.35e−03 8.40e−03 8.45e−03 8.50e−03
2.855
2048
2.848
2.841
1024
2.834
−0
2.827
−1025
2.820
1.0
24.9
48.8
72.7
96.6
120.5
144.4
168.3
192.2
216.1
240.0
+
−2049
8.00e−03 8.05e−03 8.10e−03 8.15e−03 8.20e−03 8.25e−03 8.30e−03 8.35e−03 8.40e−03 8.45e−03 8.50e−03
Scope results
• MASHBLK_f - Delta-Sigma modulator block
• RIFGEN_f - Generic Finite Impulse Response filter block
• CAN_f - Analog to Digital Converter block
• MEMOSCOPE_f - Memory sequential scope block
• DESTOCKBIT_f - Binary shift register block
Scope results
I. 3. COMMUNICATION SYSTEMS
64
3.11 Chaotic frequency hopping transmission system
MScope
0
PFD
num(s)
den(s)
CAN
GENERIC
sinusoid
generator
MScope
Destockbit
S/H
Icp/Vtune
MScope
VCO
%N %M
N
MASH
Sigma/Delta
Message
FIR
Gauss
MScope
PFD
num(s)
den(s)
MScope
MScope
CAN
sig
GENERIC
Icp/Vtune
VCO
%N
N
Memo Scope
3.11.1 Description
Add here a paragraph of the function description.
3.11.2 Context
nb_coef=85
lines(-1);
F_cpf = 20e6;
T_cpf = 1/F_cpf;
sig_ref=T_cpf*0.02/100
Fo = 2.045e9;
To = 1 / Fo;
wo=2*%pi * Fo;
kv = 100.5e6;
alpha=6.91e9;
beta2=0.15;
j_vco=0.2e6;
Fd=2.5e9;
N=int(Fd/F_cpf)
Nsampl = 2;
Tsampl = 1/(F_cpf*Nsampl);
Fsampl = 1 / Tsampl;
Icp = 5e-3;
Ileak=0.1e-6;
fn=F_cpf/280;
phi=%pi/4;
Ts=3/fn
Nech=12
Te=Ts/Nech
M=32
Nbit=3
a=0.5
b=-1
[tau1,tau,tau2]=calcul_3eme_ordre(fn,phi,kv*2*%pi,Icp,N);
s=poly(0,’s’);
num=1+tau1*s;
den=tau*s*(1+tau2*s);
fn2=F_cpf/100;
[tau1,tau,tau2]=calcul_3eme_ordre(fn2,phi,kv*2*%pi,Icp,N);
MScope
MScope
sig
Message
I. 3. COMMUNICATION SYSTEMS
65
num2=1+tau1*s;
den2=tau*s*(1+tau2*s);
Tfin=0.00504
3.11.3 Scope Results
2048
2048
1024
1024
−0
−0
−1025
−1025
+
−2049
0.00000
+
0.00050
0.00101
0.00151
0.00202
0.00252
0.00302
0.00353
0.00403
0.00454
0.00504
−2049
0.00000
0.00050
0.00101
0.00151
Scope results
0.00252
0.00302
0.00353
0.00403
0.00454
0.00504
0.00353
0.00403
0.00454
0.00504
Scope results
32
3.10
16
3.05
0
3.00
−16
2.95
+
−32
0.00000
0.00202
+
0.00050
0.00101
0.00151
0.00202
0.00252
0.00302
0.00353
0.00403
0.00454
0.00504
2.90
0.00000
0.00050
Scope results
3.11.4 Mod_num blocks
• PFD_f - Phase/Frequency tristate Detector block
• VCO_f - Discrete Voltage Controlled Oscillator block
• PCLOCK_f - Integrated phase modulator event generator block
• MASHBLK_f - Delta-Sigma modulator block
• RIFGEN_f - Generic Finite Impulse Response filter block
• CAN_f - Analog to Digital Converter block
• DESTOCKBIT_f - Binary shift register block
0.00101
0.00151
0.00202
0.00252
0.00302
Scope results
I. 3. COMMUNICATION SYSTEMS
66
2048
3.10
1024
3.05
−0
3.00
−1025
2.95
+
−2049
0.00000
+
0.00050
0.00101
0.00151
0.00202
0.00252
0.00302
0.00353
0.00403
0.00454
0.00504
2.90
0.00000
0.00050
0.00101
0.00151
Scope results
0.00252
0.00302
0.00353
0.00403
0.00454
0.00504
0.00353
0.00403
0.00454
0.00504
Scope results
2048
4.00
1024
1.75
−0
−0.50
−1025
−2.75
+
−2049
0.00000
0.00202
+
0.00050
0.00101
0.00151
0.00202
0.00252
0.00302
0.00353
0.00403
0.00454
0.00504
Scope results
• MEMOSCOPE_f - Memory sequential scope block
−5.00
0.00000
0.00050
0.00101
0.00151
0.00202
0.00252
0.00302
Scope results
I. 4. ELECTRICAL CIRCUITS
67
Chapter 4
Electrical circuits
4.1 Resitif attenuator/coupler
V
−
+
V
R=18
C= 100e−12
R=50
1
~
+
MScope
−
R=18
C= 100e−12
R=18
+
R=26
−
V
R=26
C= 100e−12
R=35
R=50
4.1.1 Description
This diagram is a power attenuator realised with resistors.
This stage is often find in microwave synthesizer at the power output of the VCO.
4.1.2 Context
do_tild=mdo_tild
%scicos_solver=100
f_sin=2.4e9;
T_sin=1/f_sin;
Nsampl=50;
Tsampl=T_sin/Nsampl; f_sin=2.4e9;
Tfin=10*T_sin
4.1.3 Scope Results
4.1.4 Mod_num blocks
• mResistor - Modified Resistor block
I. 4. ELECTRICAL CIRCUITS
68
1.0
0.5
0.0
−0.5
+
−1.0
0.00e+00 4.17e−10 8.33e−10 1.25e−09 1.67e−09 2.08e−09 2.50e−09 2.92e−09 3.33e−09 3.75e−09 4.17e−09
0.50
0.25
0.00
−0.25
+
−0.50
0.00e+00 4.17e−10 8.33e−10 1.25e−09 1.67e−09 2.08e−09 2.50e−09 2.92e−09 3.33e−09 3.75e−09 4.17e−09
0.2
0.1
0.0
−0.1
+
−0.2
0.00e+00 4.17e−10 8.33e−10 1.25e−09 1.67e−09 2.08e−09 2.50e−09 2.92e−09 3.33e−09 3.75e−09 4.17e−09
Scope results
II. SIMULATION SCILAB SCRIPTS
69
Part II
Simulation Scilab scripts
II. SIMULATION SCILAB SCRIPTS
70
II. 1. SIMULATIONS OF CHAOTIC SYSTEMS
Chapter 1
Simulations of chaotic systems
1.1 Output probability density of autonomous second order IIR filter
1.1.1 Simulation script(s)
function [x,y]=mhistplot(n,data)
p=size(data,’*’)
data=data(:)
if size(n,’*’)==1 then
x = linspace(min(data), max(data), n+1)’;
else
x=n(:)
end,
n=prod(size(x));
[ind , y] = dsearch(data, x);
y=[y;y(n-1)];
nx=maxi(min(15,prod(size(x))-1),1);
endfunction
set("figure_style","old")
load SCI/macros/scicos/lib
exec(loadpallibs,-1)
%tcur=0;%cpr=list();alreadyran=%f;needstart=%t;needcompile=4;%state0=list();
prot=funcprot();funcprot(0);
deff(’disablemenus()’,’ ’)
deff(’enablemenus()’,’ ’)
funcprot(prot)
load(MODNUM+’/simu/lin_chua_sim/lin_chua_sim.cos’)
context=scs_m.props("context");
execstr(context);
tolerances=scs_m.props.tol;
solver=tolerances(6);
scs_m.props.context(3)=’Nbit=16’;
ci=0.66:2e-3:0.68;
Nbsampl=1e4;
Nbsampl=5e3;
z=zeros(size(ci,2),Nbsampl);
for j=1:size(ci,2)
scs_m.props.context(6)=’ci=’+string(ci(j));
71
II. 1. SIMULATIONS OF CHAOTIC SYSTEMS
%scicos_context=struct();
[%scicos_context,ierr]=script2var(scs_m.props.context,%scicos_context);
[scs_m,%cpr,needcompile,ok]=do_eval(scs_m,%cpr);
[%cpr,%state0_n,needcompile,alreadyran,ok]=do_update(%cpr,%state0,needcompile);
%state0=%state0_n;
%tcur=0;
%cpr.state=%state0;
tf=scs_m.props.tf;
[state,t]=scicosim(%cpr.state,%tcur,tf,%cpr.sim,’start’,tolerances);
timer();
y=[];
%tcur=0;
for i=1:Nbsampl
tf=i*Te;
[state,t]=scicosim(%cpr.state,%tcur,tf,%cpr.sim,’run’,tolerances);
%cpr.state=state;
%tcur=tf;
Nblock=3;
y(1,i)=state("z")(%cpr.sim("zptr")(Nblock):%cpr.sim("zptr")(Nblock+1)-1);
Nblock=6;
y(2,i)=state("z")(%cpr.sim("zptr")(Nblock):%cpr.sim("zptr")(Nblock+1)-1);
end
z(j,:)=y(1,:);
Tsim=timer();disp(’Tsim:’+string(Tsim));
end
clear y;
k=200;
c=zeros(size(ci,2),k+1);
for j=1:size(ci,2)
[a,b]=mhistplot(k,z(j,:));
c(j,:)=matrix(b,1,k+1);
end
x=(1:size(ci,2))/size(ci,2);
y=(1:k+1)/k;
z=c/max(c);
set("figure_style","new");
scf(100);
plot3d(x,y,z,11,45,’X@Y@Z’,[2,2,4])
lin_chua_sim.sce
72
II. 1. SIMULATIONS OF CHAOTIC SYSTEMS
73
1.0
0.8
0.0
0.6
Z
0.2
0.4
0.4
0.2
0.6
0.0
0.8
0.0
0.1
0.2
0.3
0.4
0.5
Y
0.6
0.7
0.8
X
1.0
0.9
1.0
1.1
Scope results
1.1.2 Scope Results
1.1.3 Scicos diagram(s)
IMODULO
y[k−1]
a
1/z
IMODULO
y[k−2]
b
IMODULO
lin_chua_sim.cos
1.1.4 Mod_num blocks
• IMODULO_f - Integer modulo function block
1/z
II. 1. SIMULATIONS OF CHAOTIC SYSTEMS
1.1.5 See Also
• lin_chua - Second order Infinite Impulse Response filter (Scicos Diagram)
74
II. 1. SIMULATIONS OF CHAOTIC SYSTEMS
75
1.2 BER estimation of pair chaotic encoder/decoder with introduction of jitter in
receiver clock
1.2.1 Simulation script(s)
//Define simulation name
sim_name=’lin_chua_teb_sim’;
//Load scicos diagram
load(MODNUM+’/simu/’+sim_name+’/’+sim_name+’.cos’)
//Define context
exec(MODNUM+’/simu/’+sim_name+’/’+sim_name+’_ctxt.sce’);
context=scs_m.props("context");execstr(context);
//Define Simulation end time
scs_m.props.tf=Tfin;
//Define other variable
//sig_log=10:2.5:32.5;
sig_log=8:2:24;
sig=[];
for k=1:size(sig_log,2)
sig(k)=1/(10^(sig_log(k)/10));
end
nb_r=size(sig,1);
teb=[];nb_error=[];
l=0
while l<2
for j=1:nb_r
//define context variable to be sweep
scs_m.props.context(13)=’sigma=’+string(sig(j))+’*Te’;
//Initialise Info and %scicos_context variable
Info=list();
if ~exists(’%scicos_context’) then %scicos_context=struct(); end
//Disp Begin simulation date
printf("Begin simulation %d, \t %s\n",j,return_date());
//Do simulation with scicos_simulate
Info=scicos_simulate(scs_m,Info,%scicos_context,"nw");
//Save result
myvar=return_state_block(Info,"toto");
nb_error(j)=myvar(1)(1);
//Processed result
teb(j)=nb_error(j)/(Nbsampl*Nbit);
//Disp processed result and end simulation time
printf("Processed Teb(%d) = %f\n",j,teb(j));
printf("End simulation %d, \t %s\n\n",j,return_date());
end
l=l+1
end
//Plot result
plot_teb(49,sig_log,teb,"1");
II. 1. SIMULATIONS OF CHAOTIC SYSTEMS
76
lin_chua_teb_sim.sce
1.2.2 Scope Results
−1
10
−2
10
−3
10
−4
10
8
10
12
14
16
18
20
22
24
Scope results
1.2.3 Scicos diagram(s)
Receiver clock
Emitter clock
Random
Generator
Event
Delay
Muller Law
Ideal channel
Random
Integer
Generator
Binary source
Recovered message
C block2
Emitter
Receiver
BER estimation
1/z
Transmission delay
lin_chua_teb_sim.cos
1.2.4 Context file(s)
scs_m.props.context=[
’Te=1;’
’Nbsampl=2^16;’
’Tfin=Nbsampl*Te;’
’Nbit=16;’
’a=0.5;’
’b=-2.5;’
’ci=0.675;’
’Intmax = 2^(Nbit-1);’
’ci1=-int(ci*Intmax);’
’ci2=int(ci*Intmax);’
’p_source=2*%pi/(4*Te);’
II. 1. SIMULATIONS OF CHAOTIC SYSTEMS
’a_source=2^(Nbit-2);’
’sigma=0’];
lin_chua_teb_sim_ctxt.sce
1.2.5 Mod_num blocks
• GENINT_f - Random Integer Generator block
• NOISEBLK_f - Gaussian White Noise Generator block
77
II. 2. SIMULATIONS OF OSCILLATORS AND PHASE LOCKED LOOPS
Chapter 2
Simulations of oscillators and Phase Locked
Loops
2.1 Output spectra of Integer N frequency synthesizer
2.1.1 Simulation script(s)
//Define simulation name
sim_name=’synthe_int_sim’;
//Define simulation path
sim_path=’synthe_int_sim’;
//Load scicos diagram
load(MODNUM+’/simu/’+sim_path+’/’+sim_name+’.cos’);
//Define context
exec(MODNUM+’/simu/’+sim_path+’/’+sim_name+’_ctxt.sce’);
context=scs_m.props("context");execstr(context);
//Define Simulation end time
scs_m.props.tf=Tfin;
//Define other variables
//Open Log file
u_log=mopen(MODNUM+’/simu/’+sim_path+’/’+sim_name+’.log’,’a’);
//Set flag (for display saved information in scilab window)
flag=1;
//Save inital state of simulation in Log file
wlog_init(u_log,flag);
//Save context in log file
wlog_ctxt(u_log,flag);
//Loop for iterative simulation
j=1;
//Save and display begin simulation date j
wlog_bst(u_log,j,flag);
//substitue context variable to be sweep
//scs_m.props.context=subst_ctxt(’varname’,’varname=’);
//Initialise Info and %scicos_context variable
//if exists(’Info’)==0 then
clear Info;
Info=list();
//end
//if exists(’%scicos_context’)==0 then %scicos_context=struct(); end
clear %scicos_context;
%scicos_context=struct();
//Do simulation with scicos_simulate
Info=scicos_simulate(scs_m,Info,%scicos_context);
78
II. 2. SIMULATIONS OF OSCILLATORS AND PHASE LOCKED LOOPS
79
//Load result
myvar=return_state_block(Info,"z_buf");
//Save and display util variable
//wlog_sv(u_log,tlist([’varname’],varvalue),flag);
//Save and Disp final simulation date j
wlog_fst(u_log,j,flag);
//post-processed result
//Save and display post-processed vector(matrix)
//wlog_psv(u_log,tlist([’varname’],varvalue,flag);
//Close final state of simulation in Log file
wlog_final(u_log,flag);
//close log file
mclose(u_log);
plot_spectre2(myvar(1)(1:Nsav),Tsampl,Tacqui,N*F_cpf,0.9e6,10,0);
plot_spectre2(myvar(1)(1:Nsav),Tsampl,Tacqui,N*F_cpf,0.5e6,11,1);
synthe_int_sim.sce
2.1.2 Scope Results
−100
−50
−100
−150
−150
−200
−200
2.40e+09 2.41e+09 2.42e+09 2.43e+09 2.44e+09 2.45e+09 2.46e+09 2.47e+09 2.48e+09
(a) Output spectrum of synthesizer
2
10
3
10
4
10
5
10
6
10
7
10
(b) Output noise spectrum of synthesizer
8
10
II. 2. SIMULATIONS OF OSCILLATORS AND PHASE LOCKED LOOPS
2.1.3 Scicos diagram(s)
Random
Generator
PFD
Z_buf
num(s)
den(s)
VCO
%N
N
synthe_int_sim.cos
2.1.4 Context file(s)
scs_m.props.context=[
’F_cpf = 20e6;’
’T_cpf = 1/F_cpf;’
’sig_ref=(2*%pi*0.01/100)’
’Fo = 2.045e9;’
’To = 1 / Fo;’
’wo=2*%pi * Fo;’
’kv = 100.5e6;’
’alpha=6.91e9;’
’beta2=0.15;’
’Fd=2.45e9;’
’N=int(Fd/F_cpf)’
’j_vco=2e6/N;’
’Nsampl = 16;’
’Tsampl = T_cpf/Nsampl;’
’Fsampl = 1 / Tsampl;’
’Icp = 5e-3;’
’Ileak=10e-6;’
’Ileak_sig=1e-12;’
’fn=F_cpf/180;’
’phi=%pi/4;’
’[tau1,tau,tau2]=calcul_3eme_ordre(fn,phi,kv*2*%pi,Icp,N);’
’s=poly(0,’’s’’);’
’num=1+tau1*s;’
80
II. 2. SIMULATIONS OF OSCILLATORS AND PHASE LOCKED LOOPS
’den=tau*s*(1+tau2*s);’
’Nsav=2^21+2^20’
’Tse=Tsampl’
’Tacqui=1e-4’
’Tfin=Tacqui+Nsav*Tse’
];
synthe_int_sim_ctxt.sce
2.1.5 Mod_num blocks
• PFD_f - Phase/Frequency tristate Detector block
• VCO_f - Discrete Voltage Controlled Oscillator block
• PCLOCK_f - Integrated phase modulator event generator block
• NOISEBLK_f - Gaussian White Noise Generator block
• ZBUF_f - Discrete buffer block
81
II. 2. SIMULATIONS OF OSCILLATORS AND PHASE LOCKED LOOPS
82
2.2 Output jitter of integer-N frequency synthesizer
2.2.1 Simulation script(s)
//Define simulation name
sim_name=’synthe_int_jit_sim’;
//Define simulation path
sim_path=’synthe_int_jit_sim’;
//Load scicos diagram
load(MODNUM+’/simu/’+sim_path+’/’+sim_name+’.cos’);
//Define context
exec(MODNUM+’/simu/’+sim_path+’/’+sim_name+’_ctxt.sce’);
context=scs_m.props("context");execstr(context);
//Define Simulation end time
scs_m.props.tf=Tfin;
//Define other variables
j=1;
//substitue context variable to be sweep
//scs_m.props.context=subst_ctxt(’varname’,’varname=’);
//Initialise Info and %scicos_context variable
clear Info;Info=list();
clear %scicos_context;
%scicos_context=struct();
//Do simulation with scicos_simulate
Info=scicos_simulate(scs_m,Info,%scicos_context);
//Load result
myvar=return_state_block(Info,"z_buft");
f=scf(10);
plot2d(1:Nsav,myvar(1)(1:Nsav)-1/Fd,rect=[0 min(myvar(1)(1:Nsav)-1/Fd) Nsav max(myvar(1)(1:N
xtitle(’Period jitter for ’+scs_m.props.context(3)+’;’+scs_m.props.context(12));
g=scf(20);
histplot(100,myvar(1)(1:Nsav)-1/Fd);
xtitle(’Probility density of period jitter for ’+scs_m.props.context(3)+’;’+scs_m.props.cont
synthe_int_jit_sim.sce
2.2.2 Scope Results
Period jitter for sig_ref=T_cpf*0.1/100;j_vco=10e6;
0.0050
0.0025
4e−13
0.0000
3e−13
−0.0025
2e−13
+
−0.0050
4.0e−05
1e−13
4.4e−05
4.8e−05
5.2e−05
5.6e−05
6.0e−05
6.4e−05
6.8e−05
7.2e−05
7.6e−05
8.0e−05
0e+00
3.50
−1e−13
2.62
−2e−13
1.75
−3e−13
0.88
−4e−13
0
+
0.00
4.0e−05
4.4e−05
4.8e−05
5.2e−05
5.6e−05
6.0e−05
6.4e−05
6.8e−05
7.2e−05
7.6e−05
1000
2000
3000
4000
5000
6000
7000
8000
8.0e−05
(a) Charge pump output current; input voltage of VCO
(b) Evolution of period jitter
9000
10000
II. 2. SIMULATIONS OF OSCILLATORS AND PHASE LOCKED LOOPS
Probility density of period jitter for sig_ref=T_cpf*0.1/100;j_vco=10e6;
4.5e+12
4.0e+12
3.5e+12
3.0e+12
2.5e+12
2.0e+12
1.5e+12
1.0e+12
5.0e+11
0.0e+00
−5e−13
−4e−13
−3e−13
−2e−13
−1e−13
0e+00
1e−13
2e−13
3e−13
4e−13
5e−13
(c) Probability density of period jitter
2.2.3 Scicos diagram(s)
Random
Generator
Tcpf
num(s)
den(s)
PFD
Tsampl
MScope
SCOPE
VCO
freq_div
Z_buft
83
II. 2. SIMULATIONS OF OSCILLATORS AND PHASE LOCKED LOOPS
synthe_int_jit_sim.cos
2.2.4 Context file(s)
scs_m.props.context=[
’F_cpf = 20e6;’
’T_cpf = 1/F_cpf;’
’sig_ref=T_cpf*0.1/100’
’Fo = 2.045e9;’
’To = 1 / Fo;’
’wo=2*%pi * Fo;’
’kv = 100.5e6;’
’alpha=6.91e9;’
’beta2=0.15;’
’Fd=2.44e9;’
’N=int(Fd/F_cpf)’
’j_vco=10e6;’
’Nsampl = 2;’
’Tsampl = To/Nsampl;’
’Fsampl = 1 / Tsampl;’
’Icp = 5e-3;’
’Ileak=0;’
’Ileak_sig=1e-6;’
’fn=F_cpf/180;’
’phi=%pi/4;’
’[tau1,tau,tau2]=calcul_3eme_ordre(fn,phi,kv*2*%pi,Icp,N);’
’s=poly(0,’’s’’);’
’num=1+tau1*s;’
’den=tau*s*(1+tau2*s);’
’Nsav=10000’
’Tfin=Nsav*Tsampl*30’
];
synthe_int_jit_sim_ctxt.sce
2.2.5 Mod_num blocks
• PFD_f - Phase/Frequency tristate Detector block
• VCO_f - Discrete Voltage Controlled Oscillator block
• PCLOCK_f - Integrated phase modulator event generator block
• NOISEBLK_f - Gaussian White Noise Generator block
• ZBUFT_f - Event discrete buffer block
84
II. 2. SIMULATIONS OF OSCILLATORS AND PHASE LOCKED LOOPS
85
2.3 Gaussian modulated fractional frequency synthesizer
2.3.1 Description
Add here a paragraph of the function description.
2.3.2 Simulation script(s)
//stacksize(1.8e8);
sim_name=’synthe_sd_quick’;
sim_path=’synthe_sd_quick_sim’;
load(MODNUM+’/simu/’+sim_path+’/’+sim_name+’_sim.cos’);
exec(MODNUM+’/simu/’+sim_path+’/’+sim_name+’_ctxt.sce’);
context=scs_m.props("context");execstr(context);
scs_m.props.tf=Tfin;
if exists(’Info’)==0 then Info=list(); end
if exists(’%scicos_context’)==0 then %scicos_context=struct(); end
Info=scicos_simulate(scs_m,Info,%scicos_context,"nw");
myvar=return_state_block(Info,"z_buf");
clear Info;
timer();
fc=2.49e9-2.5e6/2;
//step=plot_spectre2(myvar(1),Tsampl,Tacqui,fc,0.015e6,10,0);
step=1/(Nsav*Tsampl);
DSP=10*log10((1/(Nsav)*abs(fftshift(fft(myvar(1)(1:Nsav),-1))))^2);
lwin=0.45e6;
clf(10);
scf(10);
//plot2d((((Fd/step)-lwin):((Fd/step)+lwin))*step,DSP(Nsav/2+((Fd/step)-lwin:((Fd/step)+lwin
nNsav=2^17;
sm=pspect(nNsav/16,nNsav,’re’,myvar(1)(1:Nsav)’);
smsize=maxi(size(sm))/2;fr=(1:smsize)/(2*smsize);
nstep=1/(2*Tsampl*smsize);
Fc=Fd+F_cpf/2; Fdecal=50e6; Fmin=Fd-Fdecal; Fmax=Fd+F_cpf+Fdecal;
vec=int(Fmin/nstep:Fmax/nstep);
plot2d(vec*nstep,10*log10(1/(Nsav)*sm(vec))); xgrid();
t_cpu=timer();
Nbsym=int(Tfin/Ts);
var_tt="Center Freq.=%e, Sampling Freq.=%e\nNumb. of Sample=%d, Freq. step=%e\n";
printf(var_tt,fc,Fsampl,Nsav,step);
printf("t_cpu=%f, Numb. of simulated symbol=%d, symb/s=%f\n",t_cpu,Nbsym,Nbsym/t_cpu);
//plot_spectre2(myvar,Tsampl,Tacqui,N*F_cpf,0.5e6,11,1);
synthe_sd_quick.sce
II. 2. SIMULATIONS OF OSCILLATORS AND PHASE LOCKED LOOPS
86
2.3.3 Scicos diagram(s)
0
PFD
num(s)
den(s)
MScope
Icp/Vtune
Z_buf
VCO
%N
N
MASH
Sigma/Delta
2freq clock
f/n f
square wave
generator
FIR
Gauss
MScope
Symbole émis
synthe_sd_quick_sim.cos
2.3.4 Context file(s)
scs_m.props.context=[
’lines(-1);’
’F_cpf = 20e6;’
’T_cpf = 1/F_cpf;’
’sig_ref=T_cpf*0.02/100’
’Fo = 2.045e9;’
’To = 1 / Fo;’
’wo=2*%pi * Fo;’
’kv = 100.5e6;’
’alpha=6.91e9;’
’beta2=0.15;’
’j_vco=0.0e6;’
’Fd=2.5e9;’
’N=int(Fd/F_cpf)’
’Nsampl = 4;’
’Tsampl = 1/(Fd*Nsampl);’
’Fsampl = 1 / Tsampl;’
’Icp = 5e-3;’
’Ileak=0.05e-6;’
’fn=F_cpf/280;’
’phi=%pi/4;’
’Ts=3/fn’
’Nech=12’
’BT=0.7’
’nb_coef=85’
’Te=Ts/Nech’
’Nbit=3’
’M=32’
’order_sd=3’
’[tau1,tau,tau2]=calcul_3eme_ordre(fn,phi,kv*2*%pi,Icp,N);’
II. 2. SIMULATIONS OF OSCILLATORS AND PHASE LOCKED LOOPS
’s=poly(0,’’s’’);’
’num=1+tau1*s;’
’den=tau*s*(1+tau2*s);’
’Tacqui=20e-5’
’Nsav=2^21’
’Tfin=Tacqui+Nsav*Tsampl’
];
synthe_sd_quick_ctxt.sce
2.3.5 Mod_num blocks
• PFD_f - Phase/Frequency tristate Detector block
• VCO_f - Discrete Voltage Controlled Oscillator block
• PCLOCK_f - Integrated phase modulator event generator block
• MASHBLK_f - Delta-Sigma modulator block
• RIFGEN_f - Generic Finite Impulse Response filter block
• ZBUF_f - Discrete buffer block
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II. 3. SIMULATIONS OF COMMUNICATION SYSTEMS
88
Chapter 3
Simulations of communication systems
3.1 Output spectra of Delta-Sigma modulator
3.1.1 Description
This simulation script enables the analysis of spectrum of a MASH ∆ − Σ modulator when the modulator works
with a gaussian filtered input symbol.
3.1.2 Simulation script(s)
//Define simulation name
sim_name=’mash_gauss_sim’;
sim_path=’mash_gauss_sim’;
//Load scicos diagram
load(MODNUM+’/simu/’+sim_path+’/’+sim_name+’.cos’);
//Define context
exec(MODNUM+’/simu/’+sim_path+’/’+sim_name+’_ctxt.sce’);
context=scs_m.props("context");execstr(context);
//Define Simulation end time
scs_m.props.tf=Tfin;
//Define other variables
for nb_r=1:3
//substitue context variable to be sweep
scs_m.props.context=subst_ctxt(scs_m,’order=’,’order=’+string(nb_r));
//Initialise Info and %scicos_context variable
Info=list();
if exists(’%scicos_context’)==0 then %scicos_context=struct(); end
//Do simulation with scicos_simulate
Info=scicos_simulate(scs_m,Info,%scicos_context,"nw");
//Load result
myvar=return_state_block(Info,"z_buf");
if nb_r==1 then
//draw time domain wave form of gaussian filtered input signal
scf(10);
myvart=myvar(1)(1:Nsav);
plot2d(0:Nsav-1,myvart,rect=[0 -1 Nsav-1 1]);
//compute fft of gaussian input signal
DSP1=1/Nsav*abs(fftshift(fft(myvart,-1))^2);
DSP1_log=10*log10(DSP1(Nsav/2:Nsav));
//draw output sprectrum of gaussian filtered input signal
scf(20);
plot2d(0:Nsav/2,DSP1_log,rect=[0 min(DSP1_log) Nsav/2 max(DSP1_log)]);xgrid();
end
//draw time domain wave form of sigma-delta modulator output
II. 3. SIMULATIONS OF COMMUNICATION SYSTEMS
89
scf(10+nb_r);
plot2d(Nsav/4:Nsav/4+600,myvar(2)(Nsav/4:Nsav/4+600),rect=[Nsav/4 -2^nb_r Nsav/4+600 2^nb_
//compute fft of sigma-delta modulator output
myvart=myvar(2)(1:Nsav);
DSP2=1/Nsav*abs(fftshift(fft(myvart,-1))^2);
DSP2_log=10*log10(DSP2(Nsav/2:Nsav));
//draw output sprectrum of sigma-delta modulator
scf(20+nb_r);
plot2d(0:Nsav/2,DSP2_log,rect=[0 min(DSP2_log) Nsav/2 max(DSP2_log)]);xgrid();
end
mash_gauss_sim.sce
3.1.3 Scope Results
1.0
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−10
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(a) Time domain wave form of gaussian filtered input signal
5000
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(b) Spectrum of gaussian filtered input signal
2.0
20
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0
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−1.0
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−1.5
−60
−2.0
16400
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16900
(c) Time domain output wave form of first order Σ-∆ modulator
0
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(d) Spectrum of output wave form of first order Σ-∆ modulator
II. 3. SIMULATIONS OF COMMUNICATION SYSTEMS
90
4
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2
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1
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−1
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16400
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0
(e) Time domain output wave form of second order Σ-∆
modulator
5000
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(f) Spectrum of output wave form of second order Σ-∆
modulator
8
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16400
16500
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16900
0
(g) Time domain output wave form of third order Σ-∆
modulator
5000
10000
15000
20000
2freq clock
f/n f
Z_buf
FIR
30000
(h) Spectrum of output wave form of third order Σ-∆ modulator
3.1.4 Scicos diagram(s)
Random
Integer
Generator
25000
Z_buf
MASH
Sigma/Delta
Gauss
mash_gauss_sim.cos
num(s)
den(s)
II. 3. SIMULATIONS OF COMMUNICATION SYSTEMS
3.1.5 Context file(s)
scs_m.props.context=[
’M=1 ’
’Te=1’
’Nech=12’
’order=3’
’Tsym=Te*Nech’
’Nsampl=500’
’Tsampl=Tsym/Nsampl’
’fc=0.03*(1/Tsampl)’
’eps=0.7’
’tau=1/(2*%pi*fc)’
’Nsav=2^16’
’Tfin=Nsav*Tsampl’
];
mash_gauss_sim_ctxt.sce
3.1.6 Mod_num blocks
• RIFGEN_f - Generic Finite Impulse Response filter block
• GENINT_f - Random Integer Generator block
• MASHBLK_f - Delta-Sigma modulator block
• ZBUF_f - Discrete buffer block
3.1.7 See Also
• mash_1er_ordre - Scattered diagram of first order Delta-Sigma modulator (Scicos Diagram)
• mash_2eme_ordre - Scattered diagramm of second order Delta-Sigma modulator (Scicos Diagram)
• mash_gauss - Integrated diagram of Delta-Sigma modulator (Scicos Diagram)
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II. 3. SIMULATIONS OF COMMUNICATION SYSTEMS
3.2 BER estimation of single user QPSK transmission
3.2.1 Simulation script(s)
//Define simulation name
sim_name=’qpsk_teb_sim’;
//Define simulation path
sim_path=’qpsk_teb_sim’;
//Load scicos diagram
load(MODNUM+’/simu/’+sim_path+’/’+sim_name+’.cos’);
//Define context
exec(MODNUM+’/simu/’+sim_path+’/’+sim_name+’_ctxt.sce’);
context=scs_m.props("context");execstr(context);
//Define Simulation end time
scs_m.props.tf=Tfin;
//Define other variables
//sig_log=-13:1:0;
sig_log=-13:1:-2;
Eb=cos(%pi*(1/(2^Nbit)));
sig=[];
for i=1:size(sig_log,2)
sig(i)=Eb/10^(sig_log(i)/10);
end
nb_r=size(sig,1);
nb_error_sav=zeros(nb_r,1);
//Open Log file
u_log=mopen(MODNUM+’/simu/’+sim_path+’/’+sim_name+’.log’,’a’);
//Set flag (for display saved information in scilab window)
flag=0;
//Save inital state of simulation in Log file
wlog_init(u_log,flag);
//Save context in log file
wlog_ctxt(u_log,flag);
//Save and display util variable
wlog_sv(u_log,tlist([’sig_log’],sig_log),flag);
l=1;
nbit_tot=0;
cpu_tot=0;
//while %t
while l<3
nb_error=zeros(nb_r,1);
//Loop for iterative simulation
for j=1:nb_r
//Save and display begin simulation date j
wlog_bst(u_log,j,flag);
//substitue context variable to be sweep
scs_m.props.context=subst_ctxt(scs_m,’sigma’,’sigma=’+string(sig(j)));
//Initialise Info and %scicos_context variable
//if exists(’Info’)==0 then Info=list(); end
Info=list();
if exists(’%scicos_context’)==0 then %scicos_context=struct(); end
//Do simulation with scicos_simulate
timer();
Info=scicos_simulate(scs_m,Info,%scicos_context,"nw");
cpu_time=timer();
nb_bit=Nu*Nbit*(Nb_vec-nb_event);
//Load result
myvar=return_state_block(Info,"teb2");
nb_error(j)=myvar(1)(1);
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II. 3. SIMULATIONS OF COMMUNICATION SYSTEMS
93
cpu_tot=cpu_tot+cpu_time;
nbit_tot=nbit_tot+nb_bit;
bit_s=nbit_tot/cpu_tot;
printf("cpu_tot=%f,\t nbit_tot=%d,\t bit/s=%f\n",cpu_tot,nbit_tot,bit_s);
//Save and display util variable
wlog_sv(u_log,tlist([’nb_error’],nb_error(j)),flag);
//Save and Disp final simulation date j
wlog_fst(u_log,j,flag);
end
//post-processed result
//nb_bit=Nu*Nbit*(Nb_vec-nb_event);
nb_error_sav=nb_error_sav+nb_error;
teb=nb_error_sav/(l*nb_bit);
plot_teb(49,sig_log,teb,"1");
//Save and display post-processed vector(matrix)
wlog_psv(u_log,tlist([’nb_bit’;’nb_error_sav’;’teb’;’l’],nb_bit,nb_error_sav,teb,l,1));
//
l=l+1;
end
//Close final state of simulation in Log file
wlog_final(u_log,flag);
//close log file
mclose(u_log);
qpsk_teb_sim.sce
3.2.2 Scope Results
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Scope results
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II. 3. SIMULATIONS OF COMMUNICATION SYSTEMS
94
3.2.3 Scicos diagram(s)
Random
Integer
Generator
N
Convol
N
Convol
I/Q
Mod
PSK
Mux
Right Shift
Register
Random
Generator
Bit Error
Counter
Ts
M
Mux
Muller Law
Convol
0
1−bit quantizer
I/Q
Demod
PSK
Demux
Ts
M
0
Convol
1−bit quantizer
qpsk_teb_sim.cos
3.2.4 Context file(s)
scs_m.props.context=[
’Te=0.1;’
’Nu=16;’
’Nech=15;’
’N=Nu*Nech;’
’Nbit=2;’
’nb_coef=127; ’
’r=0.35; ’
’fe=Nech; ’
’gain_em=1; ’
’gain_rec=1/Nech; ’
’pulse=zeros(1,1); ’
’t_Ts=1/fe*(-nb_coef/2:nb_coef/2-1); ’
’pulse = 4*r/%pi*(cos((1+r)*%pi*t_Ts) + (sin((1-r)*%pi*t_Ts)./(4*r*t_Ts)))./(1-(4*r*t_Ts).^2
’Nb_vec=2^11; ’
’nb_event=3;’
’Tfin=Te*Nb_vec’
’sigma=0.6;’
];
qpsk_teb_sim_ctxt.sce
3.2.5 Mod_num blocks
• CONVOLGEN_f - Convolution block
• INTSYMB_f - Discrete Symbol Integrator block
• MODPSK_f - M-ary Phase Shift Keying Modulator Block
• DEMODPSK_f - M-ary Phase Shift Keying demodulator Block
• OVERLAPRSR_f - Memory discrete shift register for multiplexed signal block
• NOISEBLK_f - Gaussian White Noise Generator block
• GENINT_f - Random Integer Generator block
II. 3. SIMULATIONS OF COMMUNICATION SYSTEMS
• BITERROR_f - Binary error estimation block
• COMP_f - One bit Quantizer block
• UPSMPL_f - Up-sample block
• DOWNSMPL_f - Down-sample block
95
II. 3. SIMULATIONS OF COMMUNICATION SYSTEMS
3.3 Rayleigh noise generator
3.3.1 Simulation script(s)
//Simulateur de processus de Rayleigh
//Le code original est un code Matlab qui a été fourni
//par J.P Cances (ENSIL) dans le cours de DEA en Traitement du
//signal numérique.
//Le code délivre un processus aléatoire de Rayleigh dont la Densité
//Spectrale de Puissance est déterminée par la vitesse d’un véhicule
//en mouvement (spectre de Jakos)
//RAZ des variables
//clear;
//polyfit est une fonction qui permet de déterminer les coefficients
//d’un pôlynôme donnée par un vecteur P(X). A l’origine c’est une fonction
//matlab qui a été traduite en scilab (trouvé sur le site des
//Newsgroup de scilab).
//getf(’./polyfit.sci’);
///////////////////////////////////
//Paramètres d’entrée de la simulation
////////////////////////////////////
fd = 0.02; //définition de la fréquence Doppler normalisée
fs = 1;
//definition de la fréquence d’échantillonnage
Ns=1024;
//définition du nombre d’échantillon de Rayleigh à produire
//Calcul du nombre d’échantillons aléaotoires en entrée
N = 8;
while (N)
if (N<2*fd*Ns/fs)
N = 2*N;
else
break;
end
end
//Nombre de points de la fft inverse (pour lissage)
N_inv = ceil(N*fs/(2*fd));
//calcul de l’intervalle fréquentiel après la fft
delta_f = 2*fd/N;
//calcul de l’intervalle temporel des échantillons de sorties
delta_T_inv = 1/fs;
//Calcul de deux processus aléatoire gaussien (WGN)
I_input_time = rand(1,N,’normal’);
Q_input_time = rand(1,N,’normal’);
//Calcul des fft des deux processus
I_input_freq = fft(I_input_time,1);
Q_input_freq = fft(Q_input_time,1);
96
II. 3. SIMULATIONS OF COMMUNICATION SYSTEMS
/////////////////////////////////////////////////////
//Calcul de la fonction de transfert du filtre Doppler
/////////////////////////////////////////////////////
//Composante continue
SEZ(1) = 1.5/(%pi*fd);
// 0 < f < fd
for j=2:N/2
f(j) = (j-1)*delta_f;
SEZ(j) = 1.5/(%pi*fd*sqrt(1-(f(j)/fd)^2));
SEZ(N-j+2) = SEZ(j);
end
//utilisation de polyfit pour le calcul de la composante à f = fd
k=3;
p=polyfit( f(N/2-k:N/2), SEZ(N/2-k:N/2), k);
//approximation de la composante à partir des coef donné par polyfit
l=size(p,’c’);
polyn=0;
x=poly(0,"x");
for i=1:l
polyn=polyn+p(i)*x^(i-1);
end
SEZ(N/2+1)=horner(polyn,f(N/2)+delta_f);
//mise en forme et affichage de la fonction de transfert
SEZ=matrix(SEZ,1,N);
xset("window",1);xset("wdim",300,200);xbasc(1);plot2d(SEZ);
//Réalisation du filtrage
I_output_freq = I_input_freq .* sqrt(SEZ);
Q_output_freq = Q_input_freq .* sqrt(SEZ);
//insertion de zéros pour le lissage
I_temp = [I_output_freq(1:N/2) zeros(1,N_inv-N) I_output_freq(N/2+1:N)];
Q_temp = [Q_output_freq(1:N/2) zeros(1,N_inv-N) Q_output_freq(N/2+1:N)];
//calcul des fft inverses des processus filtrés
I_output_time = fft(I_temp,-1);
Q_output_time = fft(Q_temp,-1);
//calcul du module de l’amplitude au carrée de la réponse temporelle
for j=1:N_inv
r(j) = sqrt( (abs(I_output_time(j)))^2 + (abs(Q_output_time(j)))^2);
end
//normalisation de la réponse temporelle
rms = sqrt( mean (r.*r) );
r = r(1:Ns)/rms;
//affichage du processus de Rayleigh
xset("window",2);xset("wdim",300,200);xbasc(2);plot2d(r);
rayleigh_sim.sce
97
II. 3. SIMULATIONS OF COMMUNICATION SYSTEMS
2.5
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(a) Rayleigh noisy sample
3.3.2 Scope Results
3.3.3 See Also
• polyfit - polyfit mtlb equivalent function (Scilab Function)
10
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(b) Impulse response of Doppler filter
70