NEW QUARTZ CRYSTALOSCILLATORS USING THE CURRENT …

Active and Passive Elec. Comp., 2000, Vol. 23, pp. 131 -136 (C) 2000 OPA (Overseas Publishers Association) N.V.Reprints available directly from the publisher Published by license underPhotocopying permitted by license only the Gordon and Breach Science

Publishers imprint.Printed in Singapore.

NEW QUARTZ CRYSTAL OSCILLATORSUSING THE CURRENT-FEEDBACK

OPERATIONAL AMPLIFIER

MUHAMMAD TAHER ABUELMA’ATTI*and AHMAD AL-GHAZWANI

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

(Received 7 February 2000; In finalform 25 April 2000)

New crystal oscillators using the current-feedback operational-amplifier (CFOA) arepresented. Each circuit uses one CFOA, a crystal and, at most, five externally connectedpassive elements. Experimental results are included.

Keywords: Oscillators; Current-feedback operational amplifier

INTRODUCTION

Quartz crystal oscillators built around various discrete and integrated-circuit active elements are available in the literature [1,2]. Of particularinterest here are crystal oscillators built around the second-generationcurrent-conveyor (CCII) [3-5]. Because the CCII minimally degradesthe quartz crystal performance, CCII-based crystal oscillators enjoygood frequency stability and are, therefore, very attractive [3].On the other hand, the current-feedback operational-amplifier

(CFOA) is a four-terminal device which is equivalent to a CCII plusan output voltage buffer and, thus, it can easily drive external loads.Moreover, the CFOA enjoys wide bandwidth which is relatively

*Corresponding author.

131

132 M.T. ABUELMA’ATTI AND A. AL-GHAZWANI

independent of the closed-loop gain and very high slew rate. Thus, theuse of CFOA in realizing crystal oscillators will be attractive.To the authors knowledge, the use of CFOA is designing crystal

oscillators has not yet been reported in the literature. It is, therefore,the purpose of this letter to present a number of CFOA-based crystaloscillators.

PROPOSED CIRCUITS

Consider the oscillator structures shown in Figure 1. Assuming idealCFOA with iz-- i, iy=O, vx= Vy, Vo= Vz routine analysis yields thecharacteristic equation given by

(Y + Y)V + ],’Y o (la)

for the oscillator structure of Figure l(a), and

(Y] + Y2)Y4- Y2Y3 0 (lb)

for the oscillator structure of Figure l(b).Using the crystal equivalent circuit shown in Figure 2, the ad-

mittance Y3 can be expressed as

r + sL1 + 1/sC + 1/sCoY3 r/sCo + Zl/Co + 1/s2C1Co (2)

Y2

(a) (b)

FIGURE Proposed crystal oscillator structures.

QUARTZ CRYSTAL OSCILLATOR 133

L1

C1

FIGURE 2 Electrical equivalent circuit of quartz crystal.

where r is the crystal internal resistance, L1 is the crystal internalinductance, C1 is the crystal internal capacitance, and Co is the elec-trostatic capacitance between the two parallel plates of the crystal.Combining Eqs. (1) and (2), new CFOA-based crystal oscillators

can be obtained, from the oscillator structures of Figure 1, using vari-ous combinations of the admittances Y1, Y2 and Y4. Following aretwo examples:

Example 1 In Figure l(a), if Y1 1/R, Y2 1/R + sC2 and Y41/R + sC4, then Eq. (l a) reduces to

(3)

Equation (3) is a fourth-order polynomial in s. Following a proceduresimilar to that described in [6], by disregarding the s4 term and sub-stituting for s3 the term

s -sw (4)

Equation (3) reduces to a second-order polynomial in s. Equating thereal and imaginary parts, of this second-order polynomial to zero,


yields

(1/CoR)((C2/C1) + 2(C4/C1)+ 2(r/R) + 1)+ (1/RC1) (5)(L1/R)((C2/Co) + 2(C4/C0) + 1) + C2r((C4/Co) + 1)

and

2/(R2CICo)(C2/Co)((C4/C1) + (r/R) + 1) +2(C4/Co)(r/R) + 2(LI /RZCo) + (C2/C

(6)

With C1 << Co, r << R, Eqs. (5) and (6) can be approximated by

L1C1(7)

and

2,.,.,3n L1C1

(8)

From (7) and (8) it obvious than wp and wn are approximately equaland thus, the circuit can oscillate at a frequency approximately givenby the series-resonance frequency of the crystal.

Example 2 In Figure l(b), if Y1 l/R, Y2= 1/R + sC2 and Y41/R + sC4, then Eq. (1b) reduces to

C4 s3 L C2 2C4_

(C:z(C4r ) 2C4r L1 r C2)RgCo R C

(1 (C2 2C4 r )+s 1+-]-+2-1 -C-- +2R2C1Co =0 (9)

Equation (9) is a fourth-order polynomial in s. Following similarprocedure as in the previous example, it is easy to, show that

w2p(1/CoR)((C2/C) + 2(C4/C) + 2(r/R) 1) (1/RC1) (10)(L1/R)((C:/Co) + 2(C4/C0) 1) + C2r((C4/Co) 1)

QUARTZ CRYSTAL OSCILLATOR 135

and

2 2/(RCCo)(C/Co)((C4/C + (r/R) 1) + 2(C4/Co)(r/R) +2(L/RCo) (C/C

(11)

With C (( C0,/" ((R, Eqs. (10) and (11) can be approximated byEqs. (7) and (8) respectively. Thus, the circuit can oscillate at a fre-quency approximately equal to the series-resonance frequency ofthe crystal.

EXPERIMENTAL RESULTS

The proposed circuits of Figure were tested using the AD844 CFOAand different crystals. A typical output waveform obtained from thecircuit of Figure l(a) with R 10kf and 20 MHz crystal is shownin Figure 3. Only three externally connected equal resistances wereused. No external capacitances were connected. In fact the parasitic

FIGURE 3 Typical output waveform obtained from the osciallator structure ofFigure l(a)with: YI=I/R, Y2=I/R+s C,. Y4=I/R/s C:. R=IOKf, Cy3pF,Cz 4.5 pFf= 20 MHz.


capacitances Cy - 3 pF and Cz 4.5 pF at terminals y and z of theCFOA were exploited to advantage. It appears that the experimentalresults are in excellent agreement with the theory presented.

CONCLUSION

New CFOA-based crystal oscillators have been presented. Each circuituses one CFOA, a crystal and, at most, five externally connectedpassive elements. In both circuits the output can be taken from alow impedance outlet, thus avoiding the degradation in the crystalperformance resulting from external loading effects. The circuit ofFigure l(b) is a "single-pin" oscillator and, therefore, may be moreattractive than that of Figure l(a).

References

[1] Matthys, R. J., Crystal Oscillator Circuits, New York: Wiley, 1983.[2] Nordholt, E. H. and Boon, C. A. M. (1990). "Single-Pin" integrated crystal

oscillators, IEEE Transactions on Circuits and Systems, 37, 175-182.[3] Ivanisevic, I. I. and Vasiljevic, D. M. (1993). The quartz crystal oscillator realization

using current conveyors, IEEE Transactions on Circuits and Systems-l: FundamentalTheory and Applications, 40, 530-533.

[4] Stiurca, D. (1996). Crystal oscillator using a current-conveyor, Electronics World,102, 324.

[5] Popovic, J., Pavasovic, A., Zivkovic-DZunja, Z. and Vasiljevic, D. (1996). CMOSRLC and crystal oscillators based on current conveyors, IEEE Transactions onUltrasonic, Ferroelectrics, and Frequency Control, 43, 410-416.

[6] Akeberg, D. and Mossberg, K. (1974). A versatile active RC building block withinherent compensation for the finite bandwidth of the amplifier, IEEE Transactionson Circuits and Systems, CAS-21, 75-78.

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttp://www.hindawi.com Volume 2010

RoboticsJournal of

Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014


Active and Passive Electronic Components

Control Scienceand Engineering

Journal of



RotatingMachinery


Hindawi Publishing Corporation http://www.hindawi.com

Journal ofEngineeringVolume 2014

Submit your manuscripts athttp://www.hindawi.com

VLSI Design



Shock and Vibration


Civil EngineeringAdvances in

Acoustics and VibrationAdvances in



Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation http://www.hindawi.com

Volume 2014

The Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014

SensorsJournal of


Modelling & Simulation in EngineeringHindawi Publishing Corporation http://www.hindawi.com Volume 2014


Chemical EngineeringInternational Journal of Antennas and

Propagation




Navigation and Observation



DistributedSensor Networks


NEW QUARTZ CRYSTALOSCILLATORS USING THE CURRENT …

Documents

Transcript of NEW QUARTZ CRYSTALOSCILLATORS USING THE CURRENT …