Experiments With Oscillators

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DEPARTMENT OF PHYSICS, UOC, SRI LANKA

Experiments With

Oscillators

Prasan Hettiarachchi

11/21/2011

The following content is from a very old report of a practical assignment I had to do when I was in my

2nd undergraduate year. It can contain a lot of errors. But here it is copied because information in this

report might be helpful to students who just start learning about practical oscillator circuits in

Electronics subjects.This report has some figures/text directly taken from IC manufacturer datasheetsand also from application notes provided with these ICs.All the simulations were done using Electronics

Workbench V5


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Experiments With Oscillators

The following content is from a very old report of a practical assignment I had to do when I was

in my 2nd undergraduate year. It can contain a lot of errors. But here it is copied because

information in this report might be helpful to students who just start learning about practical

oscillator circuits in Electronics subjects.This report has some figures/text directly taken from

IC manufacturer datasheets and also from application notes provided with these ICs.All the

simulations were done using Electronics Workbench V5

Introduction

In this experiment I implemented various oscillators andobserved their characteristics. My focus was basically on sinewave generation techniques with TL084 QUAD OP-AMP IC and squarewave generation using popular 555 IC.

Oscillator Definition

Oscillators are circuits that produce specific, periodicwaveforms such as square, triangular, saw-tooth or sinusoidal.There are two main classes of oscillators: relaxation andsinusoidal. Relaxation oscillators generate the triangular, saw-tooth and other non-sinusoidal waveforms. Sinusoidal oscillatorsconsist of amplifiers with external components used to generateoscillation or crystals that internally generate theoscillation.

Part I: Sine wave oscillators

Sine wave oscillators are used as references or test waveformsby many circuits. A pure sine wave has only a single orfundamental frequency. Ideally no harmonics are present.

Op-amp oscillators are circuits that are unstable. Oscillatorsare useful for generating uniform signals that are used as areference in such applications as audio, function generators,digital systems, and communication systems.

Two general classes of oscillators exist: sinusoidal and

relaxation. Sinusoidal oscillators consist of amplifiers with RCor LC circuits that have adjustable oscillation frequencies, orcrystals that have a fixed oscillation frequency. Relaxationoscillators generate triangular, saw-tooth, square, pulse, orexponential waveforms.

Op-amp sine-wave oscillators operate without an externally-applied input signal. Instead, some combination of positive andnegative feedback is used to drive the op amp into an unstablestate, causing the output to cycle back and forth between thesupply voltages at a continuous rate. The frequency and

amplitude of oscillation are set by the arrangement of passive


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and active components around a central op amp. Op-amposcillators are restricted to the lower end of the frequencyspectrum because op amps do not have the required bandwidth toachieve low phase shift at high frequencies. Crystal oscillatorsare used in high-frequency applications up to the hundreds ofMHz range.

Requirement for oscillation

Canonical Form of a Feedback System with Positive or Negative FeedbackHere the simplest form of a negative feedback system is used todemonstrate the requirements for oscillation to occur. Figure 1shows the block diagram for this system in which Vin is theinput voltage, Vout is the output voltage from the amplifiergain block (A), and is the signal called the feedback factorthat is fed back to the summing junction. E represents the errorterm that is equal to the summation of the feedback factor and

the input voltage.

out

in out

out

in out

out

in

V E A

E V V

VV V

A

V A

V A A

Oscillators do not require an externally-applied input signal;instead, they use some fraction of the output signal created bythe feedback network as the input signal.

Oscillation results when the feedback system is not able to finda stable steady-state because its transfer function can not besatisfied. The system goes unstable when the denominator in last


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equation becomes zero, i.e., when 1 + A= 0, or A= 1. The keyto designing an oscillator is ensuring that A= 1.

Satisfying this criterion requires that the magnitude of theloop gain is unity with a corresponding phase shift of 180 asindicated by the minus sign. This is called the Barkhausencriterion. For positive feedback configuration term A=1 with 0

or 360 phase shift.

At this stage, one of three things can occur: Nonlinearity in saturation or cutoff causes the system to

become stable and lock up at the current power rail. The initial change causes the system to saturate (or

cutoff) and stay that way for a long time before it becomeslinear and heads for the opposite power rail.

The system stays linear and reverses direction, heading forthe opposite power rail.

The second alternative produces highly distorted oscillations(usually quasi-square waves), the resulting oscillators beingcalled relaxation oscillators. The third produces a sine-waveoscillator.

Wein Bridge Oscillator

The Wien Bridge is one of the simplest and best knownoscillators. Figure shows the basic Wien Bridge circuitconfiguration. Advantages of the circuit are this circuit hasonly a few components and good frequency stability. The majordrawback of the circuit is that the output amplitude is at thesupply voltages, which saturates the op-amp and causes highoutput distortion.


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Because this circuit uses both negative and positive feedback wehave to derive an equation for the voltage gain of theamplifier. Here we first consider the positive feedback loop

consisting of 3Z and 4Z to find V+. Then we consider thenegative feedback path and find the Vout.


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4

3 4

1 2

1

4 1 2

3 4 1

test

out

out

test

ZV V

Z Z

Z ZV V

Z

V Z Z Z

V Z Z Z

For Wein Bridge oscillator Z1=RG, Z2=RF, Z3=R+1/j0, Z4=R||j0where 0 is the oscillating frequency. Substituting in above

equation we get1/ 3

. Therefore to satisfy the oscillationvoltage gain of the amplifier = 3 i.e. RF=2RG.

But practically if we design a circuit with voltage gain ofexactly 3, oscillations does not begin automatically. To startthe oscillations I used a switch witch momentarily connectinverting input of OP-amp to ground. This started oscillationsbut oscillation quickly decayed and stopped. Therefore tomaintain sustained oscillations I had to use a voltage gain ofat least 3.06. This can be explained because none of thecomponents used are ideal and there is a loss of energy in RC

networks, oscilloscope cables an op-amp itself.


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Figure: My design of wein bridge oscillator (This design

was used both for simulation and experiment)

Figure: Starting oscillations with a switch


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Figure: Decaying Oscillations when gain is exactly 3

These facts caused us to use a voltage gain of more than 3 tokeep oscillations and further higher gain to start oscillations(Oscillations start automatically due to noise). But there is amajor drawback of using higher voltage gain. Higher the voltagegain, higher the distortion. Theoretically if voltage gain ismore than 3 oscillations should not occur. But practically,since oscillator oscillates very close to supply rails, highergain force the op-amp to a non linear region and it stilloscillates producing remarkable distortion. This is illustrated

in following pictures.

Figure: Stating oscillations automatically with higher gain.


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Figure: Distorted wave forms

Solution: Use Automatic Gain Control

So to maintain an undistorted sine wave we have to use some formof an AGC with the amplifier gain. These can be done in twoways.

Using non-linear feedback. We can use positive temperaturecoefficient device like a lamp for RG.

Using a separate AGC feedback circuit.

Figure: Single supply Wein Bridge oscillator with AGC.


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The Phase Shift Oscillator

The 1800 phase shift and the condition A= 1 is introduced byactive and passive components in any oscillator. In a phaseshift oscillator we chose passive components to get the desiredphase shift while keeping phase shift of active componentsconstant. Since op-amps work best in low frequency spectrum RCnetworks are the preferred phase shift devices.

The following graph shows the phase shift introduced by RCnetworks with oscillating frequency.The rate of change of phasewith frequency, d/d, determines frequency stability. Whenbuffered RC sections (an op amp buffer provides high input andlow output impedance) are cascaded, the phase shift multipliesby the number of sections, n.

So this graph shows us to get an 1800 phase shift we need atleast two RC sections. But frequency stability is very low insuch design. Therefore we use three RC sections. If we want toget good results we have to use buffered RC sections since RCsections can load each other causing higher voltage gain from

the op-amp.


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Figure: The phase shift oscillator (This design was used

both for the simulation and experiment.)

The normal assumption is that the phase shift sections areindependent of each other.

Then using above Equation the loop phase shift is 1800, when

the phase shift of each section is 600.

This occurs when =2f = 1.732/RC because the tangent of 600 =1.732.

The magnitude of at this point is (1/2)3. So the gain, A, mustbe equal to 8 for the system gain to be equal to one.

Therefore theoretical gain of op-amp = 8 The practical gain to start an oscillation = 32.4 The practical gain to keep oscillation = 31.6 Theoretical frequency = 2.76 Khz Practical frequency = 3.78 Khz

The main reason for this is RC sections are not buffered. Thatis they load each other. Also the tolerance of the values ofcomponents can vary the results. But still there is a remarkablereduction in distortion comparing to the wein bridge oscillator.


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Figure: Start of phase shift oscillator

Figure: Output of phase shift oscillator

Figure: Oscillation cease when gain reduces


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Phase shift oscillator with buffered RC network.

The buffered phase shift oscillator is much improved over theun-buffered version. The buffers prevent the RC sections fromloading each other; hence the buffered phase shift oscillatorperforms closer to the calculated frequency and gain. The gainsetting resistor, RG, loads the third RC section. If the fourthbuffer in a quad op amp buffers this RC section, the performancebecomes ideal.


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PART II: Square Wave Generation with 555 Timer.

The LM555/NE555/SA555 is a highly stable controller capable ofproducing accurate timing pulses. With monostable operation, thetime delay is controlled by one external resistor and one

capacitor. With astable operation, the frequency and duty cycleare accurately controlled with two external resistors and onecapacitor.

The astable multivibrator:

Astable operation: following figure shows the 555 connected as

an astable multivibrator. Both the trigger and threshold inputs(pins 2 and 6) to the two comparators are connected together andto the external capacitor. The capacitor charges toward thesupply voltage through the two resistors, R1 and R2. Thedischarge pin (7) connected to the internal transistor isconnected to the junction of those two resistors.

When power is first applied to the circuit, the capacitor willbe uncharged, therefore, both the trigger and threshold inputswill be near zero volts. The lower comparator sets the controlflip-flop causing the output to switch high. That also turns offtransistor T1. That allows the capacitor to begin chargingthrough R1 and R2. As soon as the charge on the capacitorreaches 2/3 of the supply voltage, the upper comparator willtrigger causing the flip-flop to reset. That causes the outputto switch low. Transistor T1 also conducts. The effect of T1conducting causes resistor R2 to be connected across theexternal capacitor. Resistor R2 is effectively connected to

ground through internal transistor T1. The result of that isthat the capacitor now begins to discharge through R2.


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Figure: Astable Multivibrator

Frequency of operation

f = 1/(0.693C x (R1 + 2R2))

Off and On time periods

t1 = 0.693(R1+R2)Ct2 = 0.693 x R2 x C

And the duty cycle is

D = t1/t = (R1 + R2) / (R1 + 2R2) (This shows that D > 50)

Figure: AMV circuit 1 (Used both in simulation and experiment)


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Figure: Output and capacitor waveform

Astable Multivibrator II with 50% duty cycle

Even though its quite difficult to calculate the duty cycle ofthis AMV it can be shown that it can produce a duty cycle of50%.

1

1 2 1 2

1 2 1 2

0.693

2ln

2

on

off

T R C

R R R RT C

R R R R


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50% duty cycle gives

2 1 2

1 2 1 2

2

ln 0.6932

R R R

R R R R

An interesting phenomena occurs when R1


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Astable multivibrator-3 with adjustable duty cycle

Figure: AMV with 50% duty cycle(Here it can be adjusted to any

value)

Frequency of operation

f = 1/(0.693 x C x (R1 + R2))

Duty Cycle

D = t1/t = R1 / (R1 + R2)


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Figure: AMV waveforms (threshold voltage is distorted due to

the non linearity of diodes.)

555 as a Voltage controlled Oscillator

In this configuration a basic AMV is changed to work as a VCOusing the control input of 555 IC. But there is one constraint.That is we cannot get larger frequency spectrum. Circuit hasgood linearity in the region it operates.

Figure: VCO (In experiment a function generator was used as the

AC voltage source)

Figure: Output waveform and control voltage of VCO


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Pulse Width Modulation using 555

Another two useful applications of 555 IC are PWM and frequencydividing. Both of these circuits are based on monostableoperation of 555 IC. So the monostable mode of 555 is explainedbelow.

Figure: The MMV block diagram

T = 1.1 x RC

Figure: The PWM circuit (this design was used for both

simulation and experiment)


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Figure: Output and control voltages of PWM

In this circuit theres a considerable distortion in the actualcircuit. In actual experiment when we change the control voltagenot only the pulse width but the frequency of the output is alsochanged.

555 as a frequency divider

Figure: Schematic of the frequency divider circuit.

This circuit can be used to divide the frequency of a givenpulse when the monostable time period is greater than the timeperiod of the given pulse. This is shown in the followingpicture.


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Experiments With Oscillators