Realization of Sinusoidal Oscillators Using CCs - Current Conveyors: Variants, Applications and Hardware Implementations - page 189

Fig. 7.1 Soliman ' s single-
capacitor-controlled
oscillator [ 3 ]

C 2

R 1

x

CCII+

z V 0

C 1

R 2

y

R 0

R 0

1
R 2 ¼

1
R 0 þ

2
R 1

CO : ð 7 : 1 Þ

and the frequency of oscillation (FO) as

r

2
C 1 C 2

1
R 1

FO

: ω 0 ¼

ð 7 : 2 Þ

From the above equations, it is seen that the condition of oscillation can be con-
trolled by the grounded resistor R 2 whereas the frequency of oscillation is adjustable
through a single variable capacitor C 2 or C 1 . It is worth pointing out that because
none of the two capacitors appears in the CO, with one of the external capacitor
namely C 1 taken out, the remaining circuit must be a lossless grounded inductor
subject to the fulfillment of the same condition as given in Eq. ( 7.1 ). It is, indeed, true
as was subsequently shown by Soliman himself (in [9] of Chap. 5 , see Fig. 5.20 of
Sect. 5.3.2) that with C 1 omitted, the remaining circuit is, indeed, an active gyrator.
In the same year, Soliman came up with another single CCII+ based circuit
which could realize an ideal FDNR, a lossy FDNR, a parallel tuned circuit or an
oscillator from the same structure subject to the fulfillment of appropriate condition
in terms of RC elements used in the circuit. This circuit is shown in Fig. 7.2
The CO and FO for this circuit in oscillator mode are given by:

R 1
R 4

2 R 3
R 1 þ

R 2 þ R 3

CO : C 2 R 2 1 þ C 1 R 1 1 þ ¼ 0 ð 7 : 3 Þ

R 4

t

1

8
<

9
=

1
R 3 R 4

1

f 0 ¼ ð : Þ

FO : 7 4

2 ˀ C 1 : ;

R 1
R 3

R 1 2 þ

provided that the following conditions should be satisfied:

, R 2 ¼

R 3
R 2

C 2 ¼ C 1 1 þ ð R 1 þ R 3 Þ and R 3 > R 4 ð 7 : 5 Þ