 Open Access
 Total Downloads : 185
 Authors : Ashwani Kumar Gaur, Anuj Singal, Dr. Pardeepkumar
 Paper ID : IJERTV3IS11174
 Volume & Issue : Volume 03, Issue 01 (January 2014)
 Published (First Online): 30012014
 ISSN (Online) : 22780181
 Publisher Name : IJERT
 License: This work is licensed under a Creative Commons Attribution 4.0 International License
Performance Analysis of Tunable Frequency Sinusoidal Oscillator Employing CCII+ Based AD844
Ashwani Kumar Gaur 
Anuj Singal 
Dr. Pardeepkumar 
GJUST, Hisar 
GJUST, Hisar 
YMCA UST Faridabad 
Abstract
This paper presents realization of canonic tunable fre
0 1 0
quency sinusoidal oscillator and its physical implemen
= 1 0 0
tation using commercially available IC AD844. These oscillators employ second generation current conveyor as there functional block. State variable equation matrix are used to determine values of passive elements and
0 Â±1 0
give tuning law for oscillation. THD and DC component of generated waveform are used to determine the quality of sinusoidal wave.

Introduction
Single element controlled, specifically a resistor or in some cases a grounded capacitor, oscillator finds appli cation in numerous of measurement and instrumenta tion. Such oscillators are also used to generate low fre quency sinusoidal signal.
Current feedback operational Amplifiers (CFOAs) such as AD844 having four terminals, particularly the com pensation terminal, have become more popular than traditional voltage mode opamps (VOA). Advantages provided are such as nearly constant bandwidth inde pendent of gain, higher slew rate, ease of designing cir cuits with generalized second order deferential equation for oscillators, low distortion level and least no. of ex ternal elements is attracting prominent circuit designers. The CFOAs used has a terminal characteristics that of second generation current conveyor CCII+ [16] charac terized by hybrid matrix
Where x, y are input terminal and z is output terminal.
CCII+
Z
Y+
X
Fig.1. Second Generation Current Conveyor.
Although a no. of CFOAs based sinusoidal oscillators have been evolved[811,1318] none of them employ both grounded resistors as well as capacitor. Here pro vided two CFOAs, condition for sinusoidal oscillators are characterized using state variable equation [11], in such a way that there is noninteracting control between condition of oscillation (CO) and frequency of oscilla tion(FO). The second order generalized state variable equation can be stated using eq. (1). Characteristics equ ation (CE) for oscillators is equal to zero so from (1) and (2) [i.e. for loop gain L(s)] we have eqn. (3).
1 = 11 12 1 (1)
2
21 22 2
1L(s) = 0 (2)
2 11 + 22 + 11221221 = 0
(3)
From (3) condition of oscillation and frequency of oscilla tion can be given by (4) and (5)
(11 + 22) = 0 (4)
Circuit 1:
Assuming the matrix [A] as
1
1
[A1] = 1.3
2.1
1
1.3
1
2.2
Or 11 = 22
= 1122 1221 (5)
Now from eqn. (4) and eqn. (5) we have condition of os cillation (CO) and FO are given by
The proposed methodology involved selecting the pa
1
1.3
1
2.2
= 0 (7)
rameter where i = 1, 2 and j = 1, 2, inaccordance with the required features, converting [A] matrices into node equations, and, finally, synthesizing the resulting node equations by physical circuits using CFOA and RC ele ment.

Configuration of Oscillators
Most of the SRCOs are based on the tuning law giv
1 = 1
1.3 2.2
3 = 2
2 1
Frequency is given by
0
= 1
13
. 1
22
+ 1
13
. 1
21
(8)
(9)
en by eq. (67)
CO: R1= R3 (6)
1
1
= 2
1213
(10)
FO: 0
= 1
1.2.2.3
(7)
1 < 1 (From sensitivity calculation)
2
Characteristic eqn. for the above state variable equation
From equation (6), (7) condition of oscillation is controlled by R1 and that of frequency of oscillation
can be stated as
S2 S 1 1 + 1 . 1 1 . 1 = 0
by R3 respectively. However oscillators presented in this paper have been configured with a novel ap proach as of given by (6)& (7). This approach re
13
22
13
22
13
21
(11)
quires following steps
Nodal eqn. for the state variable equation can be stated as

Determining the elements of [A] matrices.
1 1 = 12 = 1 2
(12)

Converting [A] matrices in node equation.
3
3
3

Synthesizing the node equation into physical
2 2 = 1 2 (13)
circuits using corresponding elements and
1
2
CFOAs
Here we have discussed two circuits with different arrangement of elements of matrix [A], hence giving out different circuit configuration.
Here, X1 and X2 are the voltages across C1 and C2
1 , 2 , 1 , 2 are the branch currents. Realizing the corre
3 3 1 2
sponding circuit using CCII+ port characteristic Fig 2 gives the equivalent circuit diagram.
Passive Sensitivity:Frequency sensitivity of the oscil lator is defined as deflection produced in the operating frequency due to change in any of the passive components and is given as:
Circuit 2:
In this circuit 5 passive elements are used. The state vari able matrix is given as
=
(14)
1 ( 1 1 ) 1
[A2] = 12
3
13 (19)
1 ( 1 1 ) 1
2 3 1 23
CE can be stated as
S2 1 1 1 1
+ 1 1 1 . 1 +
1
2
3
23
1
2
3
23
1 . 1 1 1 = 0 (20)
13 2 3 1
2 1 1 1 1
+ 1
1 + 1 1
1
2
3
23
123
2
3
3
1 = 0 (21)
1
From above eqn. (21) FO and CO can be stated as
CO: 1 1 1 1
= 0 (22)
1
2
3
2.3
1 1 1 = 1
(23)
1
2
3
23
Fig 2: Circuit1corresponding to eq. (12) and (13).
3 1 1 = 1
(24)
where, Rx is any passive component on which frequency
2
3
2
depends.Frequency sensitivity of different component is
3 = 1 + 1
(25)
0 =
found to be as follows
2
2
1 = 2 = 3 = 1
(15)
FO: 1
1 + 1 (26)
2
1.2.3
2
1
For R1, R2 sensitivity is found to be
1 = 1 1
(16)
0 2
1 1
=
1.2.3.1
(27)
1
2 1
2
Passive sensitivity:
Hence for system to be stable 1 < < 1 , therefor1 <
1
2
3 1
for1 < 1
2
Similarly for 2 = 1 . 1
(17)
2
0 = 0 = 0 = 2 (28)
As frequency of oscillation is given by same expression so sensitivity of different passive elements is same as that
1
2 2
1
of found in circuit 1
If R1 and R2 are taken in such a way that 2 = then
2 = . 1
frequency stability factor is stated as:
1
1
0 2
1 = 1
2
1
1
(29)
(30)
SF =2 1 ( 1) (18)
0
1
2 1
2
= 2 ; for n >> 1
Hence for system to be stable 1 < < 1 , therefor1 <
ble 1. The values are selected in accordance to eq. (9),
0
1
2
(10) for circuit 1and eq. (25), (27) for circuit 2. The slight variation is for initialization of oscillation. Fig.4 gives the
Now taking 3 = 2 the stability of the circuit can be stated
2
as
schematic generated in SPICE for circuit 1 for which gen erated sinusoidal output waveform is given by in Fig 5. To detect the harmonics generated Fourier transform for
the generated signal is taken which indicates a very nar
SF = 8 1
2 1
= 2 ; 1
(31)
row spectrum given by Fig 6. Table 2 and 3 shows the normalized component, Fourier component and normal ized phase component for circuit 1 and circuit2 respec tively. Overall deviation from the main frequency compo
The node equation corresponding to state variable matrix can be stated as
C1 1 = 1 1+2 (32)
nent is given by THD and the DC component which are quit low as compared to conventional oscillators.
Table 1 : Values of elements used in
2
3
simulation
PARAMETERS
Values
Circuit 1
Circuit 2
VDD
5V
5V
VSS
5V
5V
R1
3.2K
4K
R2
11.6K
4.9K
R3
10K
10K
RL
100k
100K
C1
1E9 F
1nF
C2
1E9 F
1Nf
C2 2 = 1 + 12 (33)
1
3
Realizing the circuit corresponding node equations with x1 and x2 as node voltage across capacitor C1 and C2, is shown in fig 3
Fig 3: Circuit2 corresponding to eq. (32) and (33).
3 Performance Analysis and Experimental Re sults
The above synthesized circuit have been realized using AD844 ICs model files in SPICE. The value of circuit elements used for each of the two circuits is listed in Ta
Fig 4: Sinusoidal waveform generated for circuit 1
Fig : 5 FFT for Circuit1
Fig :6 Variation of frequency f0 with R1
Table 2: Fourier component for the transient response of circuit1
HAR MONICNO
FRE QUENCY(HZ)
FOURIERCOM PONENT
NORMALIZED COMPONENT
PHASE(D EG)
NORMALIZED PHASE (DEG)
1.
2.200E+04
7.969E01
1.000E+00
4.743E+01
0.000E+00
2.
4.400E+04
1.876E02
2.354E02
1.541E+02
2.490E+02
3.
6.680E+04
2.926E03
3.671E03
6.298E+01
2.053E+02
4.
8.800E+04
8.019E03
1.006E02
6.298E+01
3.546E+02
Table 3: Fourier component for the transient response of circuit2
HARMONICNO
FREQUENCY(HZ)
FOURIER COMPONENT
NORMALIZED COMPONENT
PHASE (DEG)
NORMALIZEDPHASE (DEG)
1.
1.033E+04
1.359E03
1.000E+00
8.792E+01
0.000E+00
2.
2.066E+04
1.355E03
9.964E01
8.584E+01
9.000E+01
3.
3.099E+04
1.346E03
9.904E01
8.377E+01
1.800E+02
4.
4.132E+04
1.335E03
9.820E01
8.171E+01
2.700E+02

Practical feasibility and significance

Both of the discussed oscillators contain a difference term in the expression for their FO which could be generalized to give eq. (34)
0
= 1
(34)
Where is the ratio of frequency controlling resistor and thus qualify to be used for generating very low frequency oscillations. These oscillators could be practically imple mented using commercially available AD844 ICs which nearly accurate and stable frequency output as shown in fig 6 for circuit 1 the output of sinusoidal waveform from a Digital oscilloscope.
Table 4: Output parameters for circuit 1 and 2.
Output Parameters 
Circuit 1 
Circuit 2 
Total Harmonic Dis tortion (THD) 
2.59E02 
1.71E+0 0 
DC component 
1.59E02 
6.81E04 
5.Conclusion
Two new sinusoidal circuits employing CFOAs have been analysed each having grounded capacitor. The circuits have been derived by employing new tuning laws. Several others laws may be undertaken to real ize sinusoidal oscillators. More over these circuits
Fig 7: Sinusoidal Waveform from DSO for circuit1
can be physically realized with bare minimum four passive elements and are suitable for is generation of VLF oscillation. Output waveform for such a circuit is shown in fig 7. It believed that aforementioned oscillators would found several applications in fur ther to those discussed here.
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