Hardware Reference
In-Depth Information
R
4
X
CCII
Z
Y
I
R
3
+
+
C
1
C
3
V
C
1
V
C
3
+
−
−
R
2
C
2
V
C
2
−
Fig. 8.29 A classical Wien Bridge oscillator converted into a chaotic oscillator as proposed by
Elwakil and Soliman [
13
]
where the no-dimensional variables and other assumed relations are: X
¼
V
C1
/V
T
,
¼
¼
ʱ
¼
R
2
/R
J
,t
n
¼
t/R
2
C
2
and C
1
¼
C
3
¼
2C, C
2
¼
Y
V
C2
/V
T
and Z
V
C3
/V
T
,
C
and the JFET is characterized by the following v-i relation:
1
R
J
V
GD
V
GD
V
T
I
¼
ð
8
:
44
Þ
V
T
V
GD
<
V
T
where R
J
is the JFET small signal resistance at the operating point, V
GD
is the JFET
gate to drain voltage, V
T
is the threshold voltage approximately equal to minus
0.66 V for the JFET J2N4338. The various coefficients appearing in the dimen-
sionless state space equations are given by:
,
b
R
4
R
4
þ
R
2
R
X
R
2
þ
R
3
R
4
R
4
R
4
þ
R
2
R
X
R
2
R
4
a
¼
1
¼
;
ð
8
:
45
Þ
R
3
R
3
and
e
R
3
2
R
4
,
d
R
2
2
R
4
R
4
R
X
þ
R
3
R
2
þ
1
2
R
2
R
4
þ
R
2
R
X
c
¼
¼
1
¼
ð
8
:
46
Þ
The experimental tests of this circuit using AD844 CCII+ biased with
9 V supply
with C
1
¼
C
3
¼
2 nF, C
2
¼
1nF,R
2
¼
5K
ʩ
potentiometer, R
3
¼
500
ʩ
and R
4
as a
2K
potentiometer demonstrated chaotic behavior.
Chua
ʩ
s circuit is one of the most investigated chaotic oscillator which consists of
a third order linear part composed of two grounded capacitors, a grounded inductor
and a resistor along with a nonlinear negative resistor popularly known as Chua
'
s
diode characterized by a three segment piecewise linear v-i characteristic having
specified slopes of the three segments. A CCII+ based Chua
'
s oscillator was
presented by Sanchez-Lopez et al. in [
20
], which is shown here in Fig.
8.30
.
'
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