Hardware Reference
In-Depth Information
s
ʲ
1
ʱ
1
ʲ
2
C
0
1
C
0
2
R
0
1
R
0
2
and
ω
0
¼
for the Fig
:
7
:
7b
ð
7
:
20
Þ
Where
C
1
¼
C
z
2
,
C
2
¼
C
z
2
,
R
1
C
1
þ
C
y
1
þ
C
y
2
þ
C
2
þ
C
y
2
þ
C
z
1
þ
R
x
1
and
R
2
¼
¼
R
1
þ
R
2
þ
R
x
2
for the Fig7
:
7a
ð
7
:
21
Þ
C
1
¼
C
z
2
,
C
2
¼
C
z
1
,
R
1
¼
R
x
1
and
R
2
C
1
þ
C
y
1
þ
C
y
2
þ
C
2
þ
R
1
þ
¼
R
2
þ
R
x
2
for the Fig
:
7
:
7b
ð
7
:
22
Þ
Fongsamut et al. have demonstrated [
47
] that since the value of voltage gain
ʲ
is
much closer to unity than the current gain
, therefore by comparing the above
equations, it is obvious that the FO of the circuit of Fig.
7.7b
would be in a closer
agreement of the theoretical value than that of the circuit of Fig.
7.7a
. Using the
translinear current conveyor as well as using CCII+ from AD844 and CCII
α
implemented from two AD844s, the validity of this assertion has been confirmed
in [
47
].
The difficulty of adjusting the CO through a variable capacitance is eliminated if
an SRCO could be synthesized with at least three resistors such that one of the two
resistors can control the CO and the remaining third resistor controls the FO. Such a
circuit using a CCII
and a voltage follower was first proposed by Bhaskar and
Senani [
18
] and is shown in Fig.
7.8
.
The CO and FO for this circuit are given by
R
1
R
2
¼
C
2
C
1
CO
ð
7
:
23
Þ
:
r
1
R
3
R
2
C
1
C
2
1
2
ˀ
f
o
¼
ð
:
Þ
andFO
:
7
24
Slightly different version of this circuit is also possible with the same functionalities
but slightly altered expression for CO when the resistor R
2
, instead of being
connected to V
o
, is returned to the Z- terminal of the CCII
. The resulting CO is
then given by
C
1
þ
1
R
1
R
2
¼
C
2
CO
:
ð
7
:
25
Þ
whereas the expression for the FO remains the same as earlier.
A remarkable property of this circuit is that with R
1
¼
R
2
¼
R; C
1
¼
C
2
¼
C and
R/n, the frequency stability factor
S
F
, for the resistor ratio n much larger than
R
3
¼
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