148 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 37. NO. I . MARCH 1988

Zero crossing dercctor

0 (High) I (Low)

Fig. 1. The electronic bridge.

Time _.c I wulll 0 ( A . 8 . C

Time - IlllUl E ( X . 6 . C )

T i m e - Fig. 2. Signal waveforms.

degrees (frequency < 50 Hz), the leading edge of X co_mes earlier than B and flip-flop will indicate one. Therefore when X is one the signal E is connected to the up terminal and D to the down termi- nal. The various waveforms are shown in Fig. 2.

If an analog output is required, the bridge circuit without high- frequency signal C c a n be used. The output D ( A . B ) and E ( A . B ) can be filtered using a low-pass filter and the difference voltage amplified and measured.

The circuit as shown in Fig. 1 was fabricated in the laboratory. The results showed a linear relationship between frequency devia- tion and pulse count in the frequency range of 45-55 Hz, for nom- inal frequency of 50 Hz. For high-frequency clock ( C ) of 1 MHz, the relationship between the pulse count and the frequency devia- tion is given by f = 50 f C (a + PC * ) where C is the pulse count andfthe actual frequency, a = 3.9 X and = 2.38 X lo-.

Since in the power system the frequency is maintained to within k 1 percent of its nominal value this circuit is well suited for these applications.

IV. CONCLUSION A very simple frequency-deviation measuring instrument that

works on the principle of a two-arm bridge is described. The circuit was fabricated and tested in the laboratory. The results indicate good linearity between frequency deviation and voltage or pulse count over the normal range of power system frequencies.

The same instrument along with a variable frequency supply can also be used to measure a capacitance or a resistance.

REFERENCES

[ I ] 0. W. Hanson, C. J. Goodwin, and P. L. Dandeno, Influence of excitation and speed control parameters in stabilizing intersystem os- cillation, IEEE Trans. Power App. System, vol. PAS-87, pp. 1426- 1434; June 1968.

[2] R . M. Shier and A. L. Blythe, Field tests of dynamic stability using a stabilizing signal and computer program verification, IEEE Trans. Power App. Syst., vol. PAS-87, pp. 315-322; Feb. 1968.

[3] F. W. Keay and W. H. South, Design of a power system stabilizer sensing frequency deviation, IEEE Trans. Power App. Sysr., vol PAS- 90, pp.707-712, Mar./Apr. 1971.

[4] H. E. Lokay and V. Burtnyk, Applicaton of underfrequency relays for automatic load shedding, IEEE Trans. Power App. Sysr., vol. PAS-87, Mar. 1968.

[5] S. H. Honrowitz, A. Politis, and A. F. Gabrielle, Frequency actuated load shedding and restoration Part 11: Implementation, IEEE Trans. Power App. Sysr., vol. PAS-90, pp. 1460-1468, JulylAug. 1971.

[6] T. Kasparis, N. C. Voulgaris, and C. C. Halkias, A method for the precise measurement of the difference between two low frequencies, IEEE Trans. Insrrum. Mens., vol. IM-34, pp. 95-96, Mar. 1985.

Linear Voltage Controlled Oscillator

SISIR K. SAHA AND LAKHMI C. JAIN

Abstract-This paper describes a new sinusoidal oscillator whose frequency of oscillation can be controlled by a controlling voltage. The circuit gives ultra-low distortion and stable output by virtue,of an au- tomatic gain control (AGC) loop. The oscillator is useful for the VLF (3-30 kHz) and LF (30 kHz-300 kHz) ranges of operation.

I. INTRODUCTION Sinusoidal oscillators play a very important role in most of the

existing electronic systems. These oscillators are widely used in a variety of fields, i.e., in instrumentation, control systems, etc. There are many oscillator circuits reported in the literature [ 11-[5]. A simple bridge oscillator [5] uses one operational amplifier in con- junction with two capacitors, of which one is grounded. Although these networks are simple, the approach can be troublesome if a very large time period is needed.

This paper presents a novel oscillator circuit whose frequency of oscillation is scaled by resistance ratios and a controlling voltage V , such that the frequency of oscillation bears a linear relation with

Manuscript received August 13, 1986; revised September 14, 1987. S. K. Saha is with the Department of Electrical Engineering, College of

Technology, G. B. Pant University of Agriculture and Technology, Pant- nagor, U.P., 263145, India.

L. C. Jain is with the School of Electronic Engineering, South Austra- lian Institute of Technology, Adelaide, Australia.

IEEE Log Number 8718459.

0018-9456/88/0300-0148$01 .OO 0 1988 IEEE

IEEE TRANSACTIONS ON INSTRUMENTATION A N D MEASUREMENT. VOL. 37, NO. I . MARCH 1988 149

"i

.

1-1-4 Fig. 1. Basic configuration.

Rd m

Rc W V

Fig. 2. RC implementation of the basic configuration.

Vr The circuit uses all grounded capacitors. The grounded capac- itors are suitable for large scale integration.

The Intersil 8038 integrated function generator is useful for re- alizing voltage controlled oscillators with sinewave output because of its wide sweep capability; but, because of the limitations of the 8038's integrated current source, its frequency versus voltage char- acteristic is nonlinear over a considerable period of the sweep range. VCO's based on field effect transistors also suffer from harmonic distortion and nonlinearity in voltage-to-frequency conversion in- herent in field effect transistors.

The circuit presented here is a linear voltage-to-frequency con- verter with sinewave output. The circuit is realized with opera- tional amplifiers and four quadrant analog multipliers in conjunc- tion with an RC network of which all capacitors are grounded. The positive and negative feedback paths of the basic configuration are carefully balanced to attain and sustain low distortion operation. The balance is achieved by use of an automatic gain control (AGC) arrangement. Here, the mechanism is an analog multiplier (AM) which maintains desired gain to constrain the natural frequencies of the circuit on the imaginary axis of the complex frequency plane (s-plane).

The present approach is different from that reported by Saha [5] where a scaled-resistance element is used to realize a condition for the frequency of oscillation.

11. BASIC CONFIGURATION Consider the feedback configuration of Fig. 1 which yields the

following transfer function:

' ( 1 ) -- Vo(S) - kl k2 v:(s) S2TlT2 - S [ m 1 T 2 - m2T2] + k l k 2 Q

For self-oscillation, it is required that

v , = o ml = m2.

The frequency of oscillation is 7

wo = $e. ( 3 ) The basic configuration is implemented as shown in Fig. 2 . Here,

k , = OLI VT( 1 + R ; / R l ) k2 = a2 VT( 1 + R i / R 2 )

%VxRo(Rc + Rf) R C ( & + Rb)

ml =

= Rf /Rd

m2 = Rf/Rc (4 )

where a I , a2, and cq are the gain constants of A M I , AM2, and AM,, respectively. Fig. 2 involves three operational amplifiers O A l , OA2, and OA3, and three analog multipliers AMI, AM2, and AM3. Thus,

( 5 )

150

-

IEEE TRANSACTIONS ON INSTRUMENTATION A N D MEASUREMENT, VOL. 37, NO. I , MARCH 1988

k- Ai- + OA

C

u-q>?--fl- - - - 15v

Fig. 3. Oscillator with AGC loop.

TABLE I PERFORMANCE OF THE OSCILLATOR

1 V-(Volts) 0 . 5 1 . 0 2 . 0 2 .5 j I Frequency HZ 1 5 9 1 5 3 1 8 3 1 6 3 6 6 2 7957% 1

- O s 5 I Amplitude -0 .6 0.0 0.0 I Variation (dB) 111. OSCILLATOR WITH AGC LOOP

The oscillator with its AGC loop is shown in Fig. 3. As in other sinewave oscillators, the positive and negative feedback paths must be carefully balanced to attain and sustain low-distortion operation. The balancing is achieved by use of an automatic gain control; in this circuit the mechanism is an analog multiplier ( A M 3 ) .

The AGC circuit itself comprises an active loop that serves sev- eral important purposes. The integrator OA4 filters and smooths the rectified output to provide a dc control voltage VI for the input to A M 3 . Low ripple on the control voltage is necessary to prevent intermodulation distortion on the output. The high dc gain of the integrator automatically adjusts the loop to the required dc input for AM3 in spite of parameter variations. The output voltage is regulated to a value that causes the average current in R I 2 to equal that in R I 3 . Thus RI3 and - 15 V serve as reference. The AGC loop tracks this reference to maintain the output peak voltage at about 10 V, and the distortion in the output is considerably less. A pro- totype of this circuit uses 741 operational amplifiers and XR2208 analog multipliers. Vr was varied and frequency was measured at different values of VP The performance of the oscillator is shown in Table I.

IV. CONCLUSION This paper describes a sinusoidal oscillator whose frequency of

oscillation bears a linear relation with the controlling voltage VP If the circuit is fabricated in IC technology, the frequency of os-

cillation can be made stable over a wide temperature range. The automatic gain (AGC) loop is incorporated in the basic configura- tion for amplitude stabilization. The circuit is suitable where good amplitude stability is required. Its use of grounded capacitors makes it suitable for IC implementation for frequencies in the VLF and LF ranges.

ACKNOWLEDGMENT

The authors would like to thank the reviewers for their helpful comments.

REFERENCES

[ I ] W . G. Howard and D. 0. Pederson, Integrated voltage controlled oscillators, in Proc. Nut. Electron. Cant. vol. 23, pp. 279-284, 1967.

[2] Y. Sun, Generation of sinusoidal voltage (current) controlled oscil- lator for integrated circuits, IEEE Trans. Circuit Theoql, vol. CT- 19, pp. 137-141, Mar. 1972.

[3] R. S. Sidorwisz, An abundance of sinusoidal RC oscillator, in Proc. Inst. Elec. Eng., vol. 19, pp. 279-301, May 1972.

[4] S . K . Saha, Electronically tunable RC sinusoidal oscillator, IEEE Trans. Instrum. Meas., vol. IM-24, pp. 156-159, June 1975.

[5] J . D. Ryder, Electronic Fundamentals and Applications. India Pren- tice-Hall, 1976.

[6] S . K . Saha, Linear VCO with sine wave output, IEEE Trany. In- strum. Meas., vol. IM-35, no. 2, pp. 152-155. June 1986.