Hardware Reference
In-Depth Information
The phase between the two generated signals V
2
and V
1
is given by:
tan
1
tan
1
ˆ ¼
ω
C
1
R
1
ω
C
2
R
2
ð
7
:
33
Þ
C
3
R
3
R
2
Using the value of C
1
from Eq. (
7.32
) i.e.
C
1
¼
, the phase different
˕
can be
then represented as:
r
C
3
R
1
R
3
C
2
R
2
r
C
2
R
2
C
3
R
1
R
3
¼
2
tan
1
tan
1
ˆ ¼
ð
7
:
34
Þ
which shows that V
2
and V
1
are, indeed, in quadrature.
The experimental results of this circuit were taken with CCII+ realized by
AD844 IC biased with power supply
12 V and component values taken as
C
1
¼
. A typical wave-
form obtained from this circuit is shown in Fig.
7.13
b while the variation of the
oscillation frequency with the resistance R
1
is shown in Fig.
7.13c
.
A voltage-mode (VM) two-phase quadrature oscillator using only CCII+ s
proposed by Minhaj [
49
] is shown in Fig.
7.14
.
The CO and FO for this circuit are given by:
C
2
¼
C
3
¼
10 nF, R
¼
9.9 K
ʩ
,R
2
¼
9.88 K
ʩ
,R
3
¼
9.78 K
ʩ
r
1
C
1
C
2
R
2
R
3
CO
R
1
R
4
and FO
:
ω
o
¼
ð
7
:
35
Þ
:
It is easy to see that because of the second CCII+ configured as a non-inverting
integrator, its input and output i.e. the two outputs V
2
and V
4
of the circuit will be in
quadrature.
A generalized circuit for realizing a multiphase oscillator which consists of
n
'
numbers of identical CCII-RC sections was presented by Wu et al. [
27
] and is
shown in Fig.
7.15
. The condition for which the proposed circuit will provide the
sustained oscillations of frequency (
'
ˉ
0
) is given by:
n
n
ð
j
ω
0
þ ω
2
Þ
ω
1
ð
Þ
¼
0
ð
7
:
36
Þ
The Eq. (
7.36
) would have a solution only if the value of n is odd (
n
3). By
equating the real and imaginary parts of Eq. (
7.36
) to zero, the CO and FO can be
then expressed as:
R
1
sec
n
andFO
:
ω
0
¼ ω
1
sin
n
CO
R
2
ð
7
:
37
Þ
:
The circuit was experimentally tested using AD844AN CFOAs for a three phase
oscillator. Since FO of each phase is independently controllable by a grounded
resistor, this makes it possible for the circuit to be converted into a voltage
controlled multiphase oscillator. Another notable feature of the circuit is its suit-
ability for IC fabrication because of the use of AGPEs.
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