Academic Open Internet Journal

ISSN 1311-4360

www.acadjournal.com

Volume 21, 2007

 

 

A Single Resistance Controlled Eight Possible Oscillator circuits for Analog Signal Processing Applications

 

A. Kumar* and A. L. Vyas

anuj_chauhan97@yahoo.co.in

Advanced Instrumentation Lab

Instrument Design and Development Centre

Indian Institute of Technology Delhi, New Delhi-110016, India

 

 

 

Abstract

 A single resistance controlled oscillator using two current conveyors, two (or three) grounded capacitors and three (or two) grounded resisters are presented. This paper presents the condition of oscillation and the frequency of oscillation for eight oscillator possible circuits. The proposed circuits enjoy oscillation control through a single grounded passive element. The group of passive component oscillator provides the following advantages e.g. the oscillation frequency can be independently controlled by grounded resistors and all the passive components which are suitable for IC implementation are grounded. The proposed circuit has very good frequency stability. Experimental results are found to be in conformity with the theoretical analysis.

Keywords Current Conveyor, Multisim, Passive Components

 

*Corresponding Authors  Advanced Instrumentation Lab, Instrument Design and Development Centre, Indian Institute of Technology Delhi, New Delhi – 110016, India.

Phone no. +919312232268

E- mail anujchauhan97@gmail.com

 

Introduction

 The application and advantages in the realization of RC sinusoidal oscillators using current conveyors have received considerable attention [1]. In 1992, Abuelma’ atti etal. proposed a single resistance controlled sinusoidal oscillator [2] using a plus type second generation current conveyor (CCII +), two capacitors (one of which is grounded and the other of which is floating), and three resistors (two of which are grounded and one of which is floating). That proposed configuration provides the interesting property of independent control to maintain sustained oscillations and to adjust oscillation frequency. Both controls are achieved using two single resistors (one of which is grounded and the other of which is floating). In 1993, Bhaskar and Senani proposed a good minimum component CC based single resistance controlled oscillator (SRCC) configuration [3] using a minus type second generation current conveyor (CCII-), two grounded capacitors, three resistors (one of which is grounded and two of which are floating) and a voltage buffer. This proposed configuration has the following advantageous features: independent frequency control, through a single grounded resistors, ease of convertibility into a voltage controlled oscillator, use of two grounded capacitors, a buffered output and very good frequency stability.

In 1994, C.M. Chang proposed novel current conveyors based single resistance controlled oscillator configuration [4] using a three current conveyor, three grounded resistors and two grounded capacitors and enjoys independent oscillation and frequency control. However, the major disadvantage of the circuit is use of three current conveyors, two of them are positive second generation current conveyors (CCII+) and third is negative first generation current conveyor (CCI-).

The purpose of this paper is to propose eight single resistance controlled oscillator circuit using one negative second generation current conveyor (CCII-) and one positive first generation current conveyor (CCI+), three (or two) grounded resistors and two (or three) grounded capacitors. The circuit enjoys independent control of oscillation and frequency and some of them can be easily converted to voltage controlled oscillators. The proposed circuits finally designed based on current conveyor CMOS realizations.

Proposed description

The current conveyors are three port networks with terminals X, Y and Z. The first generation current conveyor CCI forces both the current and voltages in ports X and Y to be equal and a replica of the current is mirrored to the output port Z. Only one of the virtual grounds in terminal X and Y of the first generation current-conveyor is used and the unused terminal must be grounded or otherwise connected to a suitable potential. This grounding must be done carefully since a poorly grounded input terminal may cause unwanted negative impedance at the other input terminal. More ever, for many applications a high impedance input terminal is preferable. For these reasons, the second generation current conveyor was developed. It has one high and one low impedance input rather than the two low input impedance of the CCI [6].

Second generation current-conveyor differs from the first generation conveyor, in which terminal Y is a high impedance port, i.e. there is no current flowing into Y instead Y terminal is a voltage input and the Z terminal is a current output. The X terminal can be used both as a voltage output and as a current input. Therefore, this conveyor can easily be used to process both current and voltage signals unlike the operational amplifiers first generation current conveyor. The second generation negative current conveyor (CCII-), the currents IX and IZ have opposite direction as in a current buffer.         

The proposed oscillator using the plus/minus type second -/first- generation current conveyor [5, 6] (CCII/CCI) is shown in fig. 1. Using standard notation, the port relations [5, 6] of a CCI and a CCII can be characterized by VX=VY, IZ=IX and IY=IX for CCI and IY=0 for CCII respectively. The characteristic equation for the proposed oscillator in fig. 1 can be given as

 

Y1Y2 + Y3Y4 –Y2Y4 = 0                                   (1)

 

Using equation 1, eight oscillator circuits can be derived and summarized for the condition of oscillation and frequency of oscillation. These circuits were derived from fig. 1. On the assumption that only five passive elements are used, obviously, by increasing the number of usable passive elements, a larger number of oscillator circuits can be derived from figure 1. The frequency of oscillation of circuits 1 to 4 can be adjusted by tuning a single element (capacitor or resistor) without disturbing the condition of oscillation while the condition of oscillation can be adjusted by tuning other elements (resistor or capacitor) without disturbing the frequency of oscillation. Thus the circuits enjoy independent oscillation and frequency control. But the frequency of oscillation of the circuits 5 to 8 can be adjusted without disturbing the condition of oscillation while the condition of oscillation can not be adjust without disturbing the frequency of oscillation.

 

 

 

 Circuit 1:

 

 The passive element of circuit 1

                        Y1= SC1    Y2 = SC2+G2   Y3 = SC3   Y4 = G4

Characteristic equation –

            -S 2 C1C3 R2 R4 + 1 + S C2 R2 – S C3 R2 = 0

Frequency of oscillation –

            W0 2 =              

Condition of oscillation – C2  = C3

The frequency of oscillation can be adjusted by tuning C1 or G2 or G4 without disturbing the condition of oscillation while the condition of oscillation can be adjusted by tuning C2 without disturbing the frequency of oscillation.

Circuit 2

 The passive element of circuit 2

            Y1 = G1+SC1  Y2 = G2  Y3 = SC3  Y4 = G4

Characteristic equation –

            SC3R2R4  + S2C1R1C3R2R4 + R1 – SC3R1R2 = 0

Frequency of oscillation –

            W0 2 =   

Condition of oscillation – G4 = G1

The frequency of oscillation can be adjusted by tuning C1 or C3 or G2 without disturbing the condition of oscillation while the condition of oscillation can be adjusted by tuning G1 without disturbing the frequency of oscillation.

Circuit 3

The passive element of circuit 3

            Y1 = G1   Y2 = G2 +SC2  Y3 = G3  Y4 = SC4

Characteristic equation –

            R2  + SC4 R1 R3 + S2C2R2C4R1R3 – SC4R1R2 = 0

Frequency of oscillation –

            W0 2 =   

Condition of oscillation – G2 = G3

The frequency of oscillation can be adjusted by tuning C2 or C4 or G1 without disturbing the condition of oscillation while the condition of oscillation can be adjusted by tuning G2 without disturbing the frequency of oscillation.

 

Circuit 4

 The passive element of circuit 4

            Y1 = G1 + SC1   Y2 = C2  Y3 = G3   Y4 = SC4

Characteristic equation –

            1 + SC1R1 + S2C2C4R1R3 – SC4R1=0

Frequency of oscillation –

            W0 2 =   

Condition of oscillation – C1 = C4

The frequency of oscillation can be adjusted by tuning C2 or G1 or G3 without disturbing the condition of oscillation while the condition of oscillation can be adjusted by tuning C1 without disturbing the frequency of oscillation.

Circuit 5

The passive element of circuit 5

            Y1 = SC1   Y2 = G2   Y3 = SC3  Y4 = G4+SC4

Characteristic equation –

            S2C1C3R2R4 + 1 + SC4R4 – SC3R2 – S2C4C3R4R2 = 0

Frequency of oscillation –

            W0 2 =   

Condition of oscillation – C4G2 = C3G4The frequency of oscillation can be adjusted by tuning C1 without disturbing the condition of oscillation while the condition of oscillation can not be adjusted without disturbing the frequency of oscillation.

Circuit 6

The passive element of circuit 6

            Y1 = G1   Y2 = SC2   Y3 = G3+SC3   Y4 = SC4

Characteristic equation –

            1 + SC3R3 + S2C2C4R1R3 – SC4R1 – S2C3C4R1R3 = 0

Frequency of oscillation –

 W0 2 =   

Condition of oscillation – C3 G1 = C4G3

The frequency of oscillation can be adjusted by tuning C2 without disturbing the condition of oscillation while the condition of oscillation can not be adjusted without disturbing the frequency of oscillation.

Circuit 7

The passive element of circuit 7

            Y1 = SC1   Y2 = G2     Y3 = G3 + SC3   Y4 = G4

Characteristic equation –

            R2R4SC1 + S2C3R3C1R2R4 + R3 – R2 – SC3R3R2 = 0

 

 

Frequency of oscillation –

             W0 2 =   

Condition of oscillation – C1G3 = C3G4

The frequency of oscillation can be adjusted by tuning G2 without disturbing the condition of oscillation while the condition of oscillation can not be adjusted without disturbing the frequency of oscillation.

Circuit 8

 

The passive element of circuit 8

            Y1 = G1   Y2 = SC2    Y3 = G3    Y4 = G4+ SC4

Characteristic equation -  

            R4 + SC2R1R3 + S2C2C4R4R1R3 – R1 – SC4R4R1 = 0

Frequency of oscillation-

           

            W0 2 =   

Condition of oscillation – G4C2 = G3C4

The frequency of oscillation can be adjusted by tuning G1 without disturbing the condition of oscillation while the condition of oscillation can not be adjusted without disturbing the frequency of oscillation.

Frequency stability

            The passive sensitivities of circuit 1 to 4 sinusoidal oscillator are  0.5. Thus these four circuits 5 to 8 enjoy low sensitivity characteristics. The classical frequency stability factor Sf is defined as [4]. Sf =   Where  and  represents the phase function of the open loop transfer function of fig. 1 Sf  can be found to be

SF =  =2 if N >>1.

 

Experimental Results

 

The proposed circuits 1 to 8 were simulated using Multisim. To verify the theoretical analysis, we implemented the proposed oscillator circuit 3. The CCII- and CCI+ were realized by a commercial operational amplifier (LF 356) and bipolar transistor array (CA 3096) [11, 12]. Fig. 3 shows the experimental results of the oscillator frequency of circuit 3 by varying the value of the resistor R2 with C2 = C4 = 1.2 nf and R1 = R3 = 10K, experimental results, which confirm the theoretical analysis are obtained.

 

 

Figure 2. Experimental results of oscillation frequency of circuit 3 by changing value of register R2 (if C2=C4=1.2nF and R1=R3=10KΩ)

 

Conclusion

 

A single resistance controlled eight sinusoidal oscillator circuits using a CCI+ and CCII- is presented. The proposed circuits requires only five grounded passive elements; namely two (or three) grounded capacitor and three or (two) grounded resistors. Some of the proposed circuits enjoy independent control of the frequency and the condition of oscillation. The use of grounded capacitors makes the circuits attractive for integration and the use of grounded resistors for independent control of the frequency of oscillation, makes some of the circuits attractive for realization of voltage controlled oscillators.

References

 

[1]  B. Wilson, “Recent developments in current conveyors and current mode circuits”, IEE Proc. G, 137, (2), pp. 63 – 77,1990.

[2]  M. T. Abuelma’ Atti, S. Celma, P.A. Martinez, and A. Carlosena, “Minimal realization for single resistor controlled sinusoidal oscillator using single CCII (comment)”, Electron. Lett., 28, (13), pp. 1264 – 1265, 1992.

[3]  D. R. Bhaskar, R. Senani, “New current conveyor based single resistance controlled / voltage controlled oscillator employing grounded capacitors”, Electron. Lett.,  29, (7), pp. 612 – 614, 1993.

[4]  C. M Chang, “Novel current conveyor based single resistance – controlled /voltage – controlled oscillator employing grounded resistors and capacitors”, Electron. Lett., 30, (3), pp. 181 – 182, 1994.

[5]  A. S. Sedra and K. C. Smith, “A second generation current conveyor and its application”, IEEE Trans., CT – 17, pp. 132 – 133, 1970.

[6] M. Bhusan, and R. W. Newcomb, “Grounding of capacitors integrated circuits”, Electron. Lett., (3), pp. 148 – 149, 1967.

[7]  M. Hribsek, and R. W. Newcomb, “VCO – controlled by one variable resistor”, IEEE Trans., CAS – 23, pp. 166 – 169, 1976.

[8]  K. C. Smith, and A. S. Sedra, “The current conveyor: A new circuit building block”, IEEE Trans., CT-56, pp. 1368 – 1369, 1968.

[9]  R. Senani, “On the transformation of RC active oscillators”, IEEE Trans., CAS – 24, pp. 1091 – 1093, 1987.

[10]  K. Chan, R. Duncan, A. Sedra, “High performance current amplifier and current     conveyor”, in proc. IEEE Int. Symposium on circuit and system (ISCAS - 92), San Diego, pp. 2344-2347, 1992.

[11] B. Wilson, “High performance current conveyor implementation”, Electron. Lett.,  20, pp. 990-991, 1984.

[12] A. Fabre, “Wideband translinear current conveyor”, Electron. Lett., 20, pp. 241-242, 1984.

 

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