120 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT; VOL. IM-36, NO.1, MARCH 1987

Inexpensive Sawtooth Wave; Adjustable andFrequency-Independent Duty-Cycle

Square-Wave OscillatorASHWANI KARNAL, KRISHNA CHANDRA TRIPATHI, AND VED PRAKASH

39011

Abstract-An inexpensive oscillator which acts as a sawtooth waveas well as an adjustable and frequency-independent duty-cycle square­wave oscillator is developed. It involves a single operational amplifieras the main component and works by using a single positive powersupply. Slight changes in the duty cycle of the oscillations at higherfrequencies have been overcome in the modified circuit by bypassingthe collector resistance of the transistor.

I. INTRODUCTION

ACIRCUIT is designed which can be classified as anonharmonic or a relaxation oscillator with the ad­

ditional facilities of adjusting the duty cycle and of chang­ing the frequency without affecting the duty cycle. Thesame circuit can be operated for sawtooth wave genera­tion as well. In most of the existing square-wave oscilla--tors, it is very difficult to change the frequency withouthaving any effect on the duty cycle. But in this circuit(Fig. 1), we can change the frequency of the oscillationswithout any effective change on the duty cycle of the os­cillations. The main feature of this circuit is that it in­volves a single operational amplifier (op amp) as the maincomponent and yet it operates as a multipurpose circuit.The duty cycle of the oscillations can be varied with thehelp of variable resistances R2 and R3• For a particularduty cycle, the frequency can still be changed with thehelp of variable resistance R1 without having any effecton the duty cycle of the oscillations. As a particular case,by putting R1 ~ 0, sawtooth wave oscillations are gen­erated. It operates using only a single positive power sup­ply, thus avoiding the need for both positive as well asnegative power supplies.

A modified circuit (Fig. 2) is also briefly discussed toaccount for certain limitations in the described circuitwhen used as a square-wave oscillator.

Manuscript received April 3, 1986; revised July 28, 1986.A. Kamal and K. C. Tripathi are with Nuclear Research Laboratory,

Bhabha Atomic Research Centre, Srinagar-190006, Kashmir, India.V. Prakash was with Nuclear Research Laboratory, Bhabha Atomic Re­

search Centre, Srinagar-190006, Kashmir, India. He is now with the AtomicMinerals Division, Department of Atomic Energy, Hyderabad, India.

IEEE Log Number 8612138.

Vee+--1~------"'-----------"

")f-.--~rv---------""""'OUT'

Fig. 1. Circuit diagram of sawtooth wave, square-wave generator.

Vee

Fig. 2. Modified circuit diagram of square wave generator.

II. WORKING OF THE CIRCUIT AND THEORETICALCONSIDERATIONS

The capacitor Cat noninverting input is chargedthroughcollector resistance R; and R1, respectively (Fig. 1). Whenvoltage at the noninverting input goes just higher than thevoltage at the inverting input, the output of the op ampchanges the state from low to high and sets the transistorQl into saturation. As soon as the transistor Ql goes intoconduction, the following two processes start:

1) the point OUT is grounded (assuming no drop acrossthe collector to the emitter when the transistor is in

0018-9456/87/0300-0120$01.00 © 1987 IEEE

KARNAL et al.: SAWTOOTH WAVE; SQUARE-WAVE OSCILLATOR 121

saturation) and the voltage at the inverting input ofthe op amp is lowered; and

2) the capacitor C begins to discharge through R I to thesaid lowered voltage which is at the inverting input.

As soon as the voltage at the noninverting input reducesto a value below the voltage at the inverting input, theoutput state of the op amp changes from high to low. Thetransistor stops conduction and goes into OFF state andthus one cycle is complete. Repetition of the cycle pro­duces the oscillatory output.

Let VI and V2 be the voltages at point A of the op ampwhen the transistor QI is OFF and in "saturation," re­spectively. Then

322816'2

uQJ

(J) 16E

20 24

R, IN K11?S

Fig. 3. Plots for finding value of K1 using Fig. 1 (circuit) for square wave.(a) 1 /-tf. (b) 0.47 uf, (c) 22 kpf.

(2)

(1)

(input impedence of op amp being very high) and

V2

::::: R2R3 V(R 2 + R4)(R3 + Rs) ee·

The discharging time td of the capacitor from VI to V2 isgiven by

(The value of R2 and R4 should be very low as comparedto R3 and Rs so that change in voltage at point B is verysmall and can be neglected.) The charging time t, of thecapacitor from V2 to VI (V2 < VI) is given by

(9)

(10)

by

A. Same Circuit as Sawtooth Wave Oscillator

If we put RI = 0 in (3) and (5), we get

(Vee - V2 )

~ ~ ReCln V - Vee I

tc(OFFtime)::::: RICIn [1 + R4(~2;'R5)] (7)

td(oNtime)::::: R1CIn[R3~R5l (8)

We see from (7) and (8) that in addition to RI and C theOFF time depends upon R2-Rs while the ON time dependsonly on R3 and Rs. Since the ON time is independent of R2

and R4 , the OFF time can be adjusted without having anyeffective change on the ON time with variable resistanceR2 • However, the ON time cannot be adjusted without anyeffect on OFF time because both R3 and Rs appear in (7).Thus it is suggested that for fixing a particular duty cycle,ON time should be adjusted first using R3 and then OFF

time, using R2 •(5)

(4)

(3)(Vee - V2 )

te~(RI+Re)Cln V -V'ee I

td ::::: RICIn (~:).

It is seen from (4) and (5) that te / td is independent ofR I and C. Therefore the frequency of the oscillations canbe varied without any effective change on the duty cycleof the oscillations.

The total time period T I = t, + td, which in terms ofresistance is given by

If Re « RJ, s, can be neglected

or

where K I is a constant determined by resistances R2-Rs(see also plot in Fig. 3).

The charging time t, (OFF time) and discharging time td

(ON time) from (4) and (5) in terms of resistances are given

From the above expressions, it is clear that the discharg­ing time of the capacitor is zero under ideal conditionswhereas the charging time of the capacitor depends uponR; and C. Thus R; and C decide the frequency of the saw­tooth waves. The wave shaping, i.e., the linearity of'theslope of sawtooth waves, can be done with the help ofresistors R2 and R3 • The total time period in terms of re­sistances in the case of sawtooth waves is

(6)

122 IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. IM-36, NO.1, MARCH 1987

or

68

4800

66

4000

64

Value of K, calculated by sub­stituting Rs-R; in (6), is

60 62

R,'N KItS

2400 3200

~ f IN HZ

58

1600

56

32

TABLE IVALUES OF K, OBTAINED FROM SLOPE OF FIG. 3 AND FROM CALCULATIONS

Fig. 4. Plots for finding value of K 2 using Fig. 1 for sawtooth waves. (a)2.2 kpf. (b) 0.22 p,f.

Fig. 5. Frequency-independent duty-cycle plot using Fig. 1 (circuit).

TABLE IIV ALUES OF K2 OBTAINED FROM SLOPES OF FIG. 4 AND FROM CALCULATIONS

z

}-Ol 34

t 2000

u~ 1800=l..

3

Values of K 1 obtained from slopes ofFig. 3(a)-(c) are

(a) K1 ::= 1.80 when C = 1 p,f(b) K} ::= 1.75 when C = 0.47 p,f(c) K} ::= 2.25 when C = 22 kpf

2200

(11)

III. EXPERIMENTAL OBSERVATIONS

A. Square-Wave Oscillator

Experimentally we have been able to obtain frequenciesof the order of -- 5 MHz using single op amp 308 thoughthe amplitude of oscillation is very small. Time period ofthe order of 0.6 h -has also been seen using the same opamp 308. We expect that frequency range can still be wid­ened by using FET input op amps.

Equation (6) has been plotted in Fig. 3. The slope ofthe curve divided by the capacitor value gives us the valueof K I • Hence after knowing the value of K I for the desiredduty cycle, the time period of the oscillations can be cal­culated from the same equation. The values of K I havebeen tabulated in Table I. From Table lone observes thatthe experimental value of K I deviates a bit from calcu­lated value. This may be due to the tolerance of the resis­tances and capacitor used.

The extent of frequency independence can be visualized_from t, / td versus frequency curve in Fig. 5. We see thati, / td is almost constant for lower frequencies but as thefrequency is increased tc / td increases because conditionRI » R; is no longer satisfied. This is evident from theexpression

where K2 is a constant determined by the resistances R2­

Rs. By fixing the value of K2 at some particular value (i.e.,after choosing a linear region), the required time periodcan be obtained with proper choice of R; and C, i.e., fre­quency of oscillations is decided. Equation (11) has beenplotted in Fig. 4 and the slope of the line divided by thecapacitor value gives us the value of K2 for a particularduty cycle.

V. DISCUSSION

On oscilloscope we observed that high-frequency pulses( - 1.5 MHz) do not look like exact square pulses. It ismainly due to finite rise and fall times of the pulses ob­tained from the op amp even though we used the op ampin the comparator mode. Moreover, the transistor used

output state of the op amp goes from high to low, thetransistor Q3 sets in conduction and charges the capacitorbypassing the resistance Rc • Thus in this way the chargingtime of the capacitor is independent of resistance R; andhence the assumption RI » R; is no longer needed. Ex­perimentally the circuit was tested and it was observedthat the frequency of oscillations is independent of resis­tance Rca

t, ( Rc )-ex 1+-.td R1

Now if the frequency is increased with the help of presetRI, it obviously means that we have to decrease the valueof RI which in tum means an increase in the factor R; / RI.

Hence tc / td goes on increasing as we go on decreasingRI • Thus the user is advised to choose R1 » R; in thecircuit of Fig. 1.

B. Sawtooth Wave Oscillator

Sawtooth wave frequencies were generated right from-- 2 MHz to very low frequencies and observations havebeen tabulated in Table II. From Table II, it seems thatthe experimental values for K2 obtained from the slopesof Fig. 4(a) and (b) tally fairly well with calculated value.

IV. MODIFIED CIRCUIT

A new modified circuit (Fig. 2) is developed to over­come the limitations caused by the condition R1 » R; inthe circuit of Fig. 1. In this modified circuit the chargingof the capacitor does not take place via Rc . As soon as the

Values of K 2 obtained from slopes ofFig. 4(a) and (b) are

(a) K2 ::= 1.8 X 10-2 whenC = 2.2 kpf

(b) K2 ::= 1.4 X 10- 2 whenC = 0.22 Ilf

Value of K2 , calculated bysubstituting R2-Rs in (11), is

KARNAL et al.: SAWTOOTH WAVE; SQUARE-WAVE OSCILLATOR

was the SL-IOO, in which the response deteriorates athigher frequencies as it is not a high-frequency transistor.Whereas in the case of sawtooth waves of high frequency( - 800 kHz) we observed that the slope of the pulses isnot straight and also that the fall is not sharp but the lin­earity of the pulses as well as sharp fall go on improvingwith the decrease in frequency right from 800 kHz down-.wards. But, as we shift towards extremely low frequen-

123

cies, approximately 20 Hz and below, the linearity of thepulse goes on deteriorating again due to slow charging ofthe capacitor.

REFERENCES

[1] G. B. Clayton, Operational Amplifier, 2nd ed. London: Butterworth,1979, pp. 263-289.