new sinusoidal oscillatorsusing the current...

Active and Passive Elec. Comp., 1998, Vol. 21, pp. 23-32Reprints available directly from the publisherPhotocopying permitted by license only

(C) 1998 OPA (Overseas Publishers Association) N. V.Published by license under

the Gordon and Breach SciencePublishers imprint.

Printed in India.

NEW GROUNDED-CAPACITORSINUSOIDAL OSCILLATORS USING THECURRENT-FEEDBACK-AMPLIFIER POLE

MUHAMMAD TAHER ABUELMA’ATTI*and HUSAIN ABDULLAH AL-ZAHER

King Fahd University of Petroleum and Minerals, Box 203,Dhahran 31261, Saudi Arabia

(Received 2 November 1997," ln finalform 23 January 1998)

New current-feedback-operational amplifier (CFOA)-pole-based sinusoidal oscillatorcircuits are presented. Each circuit uses two CFOAs, two (or three) grounded capacitorsand/or resistors. Experimental results are included.

Keywords." Oscillators; current-feedback amplifier

INTRODUCTION

It is well known that oscillator circuit realization using the internalpole of the voltage feedback operational amplifier (VFOA) results inreliable high frequency performance and low component count [1- 3].The current feedback operational amplifier (CFOA) has a largerbandwidth and higher slew rate compared to the conventional VFOA.Thus the realization of oscillator circuits using the internal pole of theCFOA would result in higher frequencies of operation than theirVFOA counterpart. This conjecture was examined and recently anumber of oscillator circuits, exploiting to advantage the internal poleof the CFOA, have been presented [4-12]. In [4] three sinusoidaloscillator circuits using the CFOA pole are presented. While the firstoscillator circuit uses two CFOAs and six resistors, the second

*Corresponding author.

23

24 M.T. ABUELMA’ATTI AND H. A. AL-ZAHER

oscillator circuit uses two CFOAs and eight resistors. While both circuitsuse no external capacitors, they do not enjoy the attractive feature ofindependent control of the frequency and the condition of oscillation.Thus, while the frequency of oscillation can be controlled withoutdisturbing the condition of oscillation, the condition of oscillation cannot be controlled without disturbing the frequency of oscillation. Thethird oscillator circuit uses one CFOA, three resistors and one floatingcapacitor. In this oscillator circuit, using only four passive elements, thefrequency of oscillation can not be controlled without disturbing thecondition of oscillation. In [5] a multiphase active-R sinusoidaloscillator circuit using the CFOA-pole is presented. Each phase requiresone CFOA and two resistors; one of them is floating. Moreover, thefrequency of oscillation can not be controlled without disturbing thecondition of oscillation. In [6] three single-CFOA-pole-based oscillatorcircuits are presented. For these oscillators, the frequency of oscillationand the condition of oscillation can be independently controlled.However, each circuit requires three resistors; one ofthem floating, andone floating capacitor. Moreover, the control of the frequency ofoscillation is achieved by using the floating resistor. The active-Roscillator circuits proposed in [7, 8] use two CFOAs and five resistors;three of them are floating. For these oscillators the frequency ofoscillation can not be controlled without disturbing the condition ofoscillation. The single CFOA-pole-based oscillator circuit proposed in[9] enjoys the independent control ofthe frequency ofoscillation and thecondition of oscillation. However, it requires two grounded resistors,one floating resistor and one floating capacitor. The CFOA-pole basedoscillator circuit proposed in [10] enjoys the independent control of thefrequency of oscillation and the condition of oscillation. However, ituses a floating capacitor and three resistors; one ofthem is floating. Thethree sinusoidal oscillator circuits proposed in [11] exploit to advantagethe internal pole of a single CFOA. Each circuit uses five externallyconnected passive elements; two (or three) resistors and three (or two)capacitors. In one of the circuits, all the capacitors are grounded.However, the circuit has the disadvantage of interdependent control ofthe frequency and the condition of oscillation. In two of the circuits,independent control of the frequency and the condition of oscillationcan be achieved. However, the implementation of these two circuitsrequires floating capacitors and floating resistors. The fourth circuit

SINUSOIDAL OSCILLATOR 25

requires floating capacitors and floating resistors and does not enjoy theindependent control of the frequency and the condition of oscillation.Finally, in [12] a single-resistance-controlled sinusoidal oscillator ispresented. The circuit exploits to advantage the internal poles of twoCFOAs and uses three externally connected resistors; two of them arefloating. While the frequency of oscillation can be controlled byadjusting a floating resistor without disturbing the condition ofoscillation, the condition of oscillation can not be controlled withoutdisturbing the frequency of oscillation.

It appears, therefore, that a sinusoidal oscillator circuit using theCFOA-pole and enjoying the attractive features of (i) independentcontrol of the frequency of oscillation and the condition of oscillationby using grounded elements, (ii) use of externally connected groundedcapacitors and resistors and (iii) low output impedance, is notavailable yet in the literature. It is the major intention of this paperis to present such an oscillator structure. The proposed structureexploits to advantage the internal poles of two CFOAs and usesgrounded capacitors and resistors only.

PROPOSED CIRCUIT

The proposed oscillator circuit is shown in Figure 1. Figure 2 shows asimplified equivalent circuit for the CFOA. In this equivalent circuitthe parallel combination of Cz and Rz represents the parasiticimpedance at node z of the CFOA, the parallel combination of Cyand Ry represents the parasitic impedance at node y of the CFOAa 1--el, lell << represents the current-tracking error of the CFOA,3 1- 2, 1 21 1 represents the input voltage-tracking error, and

1-3, 131 represents the output voltage-tracking error of theCFOA. Using the CFOA equivalent circuit of Figure 2, the equivalentcircuit of the proposed oscillator structure of Figure 1, is shown inFigure 3. Routine analysis yields the characteristic equation of thecircuit of Figure 1 which can be expressed as

(Gr + sCr) (GT + sCr) 0102/1fl2")’12 Y1 Y2 (1)

where Gr Gz, -i-Ga-bGy2, GT2 Gz: -t"Gb-l-Gy, Ga-- (1/Ra), Gb--(1/Rb), Gz, (1/Rz,), Gyi (1/Ry,) are the internal conductances at

-Y-II Output2

x CFA>’;-’

YI Ra XIFIGURE Proposed oscillator structure.

R

FIGURE 2 Equivalent circuit of the CFOA.

utlRARy Cy2 Rb ii2!’ i Cz2

put2

Xl

FIGURE 3 Equivalent circuit of the proposed oscillator structure.


nodes z and y of the ith CFOA, and ai, fli and 7 are the currenttracking-error, the input voltage tracking-error and the output voltagetracking-error of the ith CFOA. Using (1) several oscillator circuitscan be derived from Figure 1. Table I summarizes the admittances, thefrequency and the condition of oscillation of the resulting oscillatorcircuits using four or five passive elements only. However, for circuits1-4, the resistors Ra and Rb can be removed and the design canaccount on the internal conductances of the CFOAs. Thus, circuits 1-4 can be realised using three externally connected passive elementsonly.From the Table it can be seen that for the circuits 1-4 the frequency

of oscillation can be adjusted by tuning a single element (capacitor or

resistor) without disturbing the condition of oscillation, while thecondition of oscillation can be adjusted by tuning another element(resistor or capacitor) without disturbing the frequency of oscillation.Thus the circuits 1-4 enjoy independent oscillation and frequencycontrol. For example, for circuit 4, the frequency of oscillation can beadjusted by tuning G1 without disturbing the condition of oscillation,while the condition of oscillation can be adjusted by tuning C1 withoutdisturbing the frequency of oscillation. However, because of thedifference terms in the numerator (or denominator) of the oscillationfrequency of the circuits 1-4, it is essential to select components tosatisfy the condition CT1CT2 > C1 C2 (or GT1GT2 > G1G2).

Circuit

TABLE Frequency and Condition of Oscillation of the 6 Oscillators

Admittances Frequency of Condition ofY1 Y2 Oscillation Wo Oscillation

6 ala2fl132")’1")’2.


From the Table it can also be seen that circuits 5-6, although usingfewer components, their frequency and condition of oscillation areinterdependent. These circuits may be useful in applications wheresingle-frequency oscillators are required. The frequency ofoscillation ofthe circuits 5-6 can be adjusted by tuning the resistors R and/or Rb.

SENSETIVITY ANALYSIS

By relating a sensetivity parameter F to the element of variation xi by

sF Xi_ dFx, F dxi

it is easy to show that the Wo-sensetivities of the circuits 5 and 6 can beexpressed as

So o __So __SoGr S GT CT Cr

so so s; s; s; s4 o

Thus, the circuits 5 and 6 enjoy low active and passive Wo-sensetivities.In the case of circuits 1-4, the passive Wo-sensetivities may be

appreciably higher due to the presence of the difference terms in thedenominators. For example, for the circuits and 2, the Wo-sense-tivities can be expressed as

so =so 2-1So Soor, CT (C1 C2/CT, CT2)-1So Soc c (CC2/Cr CT)

and

so =so =s; =s so=so

Thus, while the active Wo-sensetivities of the circuits and 2 are zeros,the passive sensitivities may be appreciably high. However, careful


selection of the passive components can yield passive a;o-sensetivitiesof the same order as those of circuits 5 and 6.

Finally, the tVo-sensetivities of the circuits 3-4 can be expressed as

Thus, circuits 3 and 4 has non-zero active o-sensetivities and itspassive Wo-sensetivities may be appreciably high. However, carefuldesign may result in active and passive Wo-sensetivities of the sameorder as those of circuits 5 and 6.

EXPERIMENTAL RESULTS

The proposed sinusoidal oscillator circuits were experimentally testedusing the AD844 CFOA. The results obtained from circuits 3-6 areshown in Figure 4. Because of the large values of stray capacitancesencountered in a breadboard implementation, it is difficult tosuccessfully obtain oscillations from circuits and 2. Extra care mustbe taken to minimize the effect of the stray capacitances. Thus, circuitsand 2 are more suitable for integrated circuit implementation.For the AD844 the capacitances Cz - 5 pF, Cy--- 3 pF and the

resistances Rz 3 Mf, Ry 10Mf. However, the total parasiticcapacitance between terminals Z of the AD844 and the breadboardwas measured to be about 25 pF. Thus Crl Cr was taken as 33 pF.The experimental results confirm the validity of the proposedoscillator structure for generating high frequencies.

It is worth mentioning, however, that the experimental resultsobtained from circuits 5 and 6 are different even for same values ofexternally connected resistances. This is attributed to the influence ofthe resistance Rx at terminal X of the AD844. This resistance is about50 f and when a capacitance is connected to terminal X this resistance


6

Frequency

MHz5

a

0.1k Ik

calculated

1Ok

Resistance, Ohm

measured

FIGURE 4 Measured and calculated results obtained from. (a) Circuits 3, 4 with:Ra-’Rb- 1Kf, R2 10Kf, C1 =C2 100pF, R1 =200f- 10Kf; (b) Circuit 5 with:R2 10Kf. R,= 1Kf, C1 =470pF, Ra=200f-800f; (c) Circuit b with: Rb 1Kf,R1 10Kf, C2=300pF, Ra=200f-2Kf.

will affect the transfer function especially at high frequencies [13].Thus, with C1 470 pF for circuit 5 and C2 300 pF for circuit 6, theexperimental results are different at high frequencies. As the frequencydecreases the results obtained from the two circuits becomes closer toeach other. This effect is not observed in circuits 3 and 4. This isattributed to the symmetry between the two circuits regarding theexternally connected elements to terminals X. Moreover, circuits 3 and4 use relatively lower value for capacitances, C1 C2 100 pF. Thus,the effect of Rx would manifest itself at relatively higher frequencies.

In order to minimize the effect of the parasitic resistance Rx on thecircuit performance, it is recommended here to use CFOAs designedusing the power-supply current-sensing technique, rather than theAD844 which is built around the translinear principle [13] and suffersfrom relatively large value of the parasitic resistance R.


CONCLUSION

New grounded-capacitor grounded-resistor CFOA-pole-based sinu-soidal oscillator circuits have been presented. Each circuit uses twoCFOAs, at most five passive elements and exploits, to advantage, theinternal poles of the CFOAs. Some of the circuits enjoy independentcontrol of the frequency and the condition of oscillation. The use ofgrounded capacitors and resistors is an attractive feature forintegration. Moreover, each circuit has two low impedance outputs.Thus, in comparison to similar ideal current-conveyor-based topolo-gies [14], the proposed circuits enjoy the attractive features of usingless number of passive components while providing two low-impedance outputs and exploiting, to advantage, the nonidealities ofthe active devices.

References

[1] Abuelma’atti, M. T. and Almansoury, W. A., Identification of two-amplifier active-R sinusoidal oscillators, IEEE Proceedings, 134, Part G, 137-140.

[2] Battacharyya, B. B. and Natarajan, S. (1977). A new continuously tuneablesinusoidal oscillator without external capacitors, 1EEE Proceedings, 65, 1726-1727.

[3] Stiurca, D. (1994). On the multiphase symmetrical active-R oscillators, IEEETransactions on Circuits and Systems-lI." Analog and Digital Signal Processing, 41,156-158.

[4] Liu, S.-I., Chang, C.-C. and Wu, D.-S. (1994). Active-R sinusoidal oscillators usingthe CFA pole, International Journal of Electronics, 77, 1035-1042.

[5] Wu, D.-S., Liu, S.-I., Hwang, Y.-S. and Wu, Y.-P. (1995). Multiphase sinusoidaloscillator using the CFOA pole, IEEEproceedings-Circuits Devices Systems, 142,37-40.

[6] Senani, R. and Singh, V. K. (1996). Synthesis of canonic single-resistance-controlled-oscillators using a single current-feedback-amplifier, IEEE Proceed-ings-Circuits, Devices and Systems, 143, 71-72.

[7] Toumazou, C., Payne, A. and Pookaiyaudom, S. (1995). The active-R filtertechnique applied to current-feedback op-Amps, Proceedings of the InternationalSymposium on Circuits and Systems, pp. 1203-1206.

[8] Payne, A. and Toumazou, C. (1995). Analogue circuit design using current-feedback active-R op-amps, Electronic Engineering, 67, 77-78, 80.

[9] Abuelma’atti, M. T. and A1-Shahrani, S. M. (1996). A novel low-component-countsingle-element-controlled sinusoidal oscillator using the CFOA pole, InternationalJournal of Electronics, $0, 747-752.

[10] Martinez, P. A., Celma, S. and Sabadell, J. (1996). Designing sinusoidal oscillatorswith current-feedback amplifiers, International Journal ofElectronics, 80, 637-646.

[11] Abuelma’atti, M. T., Farooqi, A. A. and A1-Shahrani, S. M. (1996). Novel RCoscillators using the current-feedback operational amplifier, IEEE Transactions onCircuits and Systems-l: Fundamental Theory and Applications, 43, 155-157.


[12] Senani, R. and Singh, V. K. (1996). Single-resistance-controlled-oscillatorconfiguration using current feedbak amplifiers, IEEE Transactions on Circuitsand Systems-l: Fundamental Theory and Applications, 43, 698-700.

[13] Fabre, A., Saaid, O., Wiest, F. and Boueheron, C. (1996). High frequencyapplications based on a new current controlled conveyor, IEEE Transactions onCircuits and Systems-l: Fundamental Theory and Applications, 43, 82-91.

[14] Abuelma’atti, M. T., A1-Ghumaiz, A. A. and Khan, M. H. (1995). Novel CCII-based single-element controlled oscillators employing grounded resistors andapaitors, International Journal of Electronics, 75, 1107-1112.

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