The oscillators are the devices that generate oscillatory (AC) output from given DC input. There are different kinds of oscillators based on the output waveform they generate. Like

· Sinusoidal oscillators – they generate sinusoidal (sine) wave output

· Square wave oscillators – they generate square (or rectangular) wave output

· Triangular wave oscillators – they generate triangle or sawtooth wave output

· The most widely used oscillators are sine wave oscillators. Such oscillators are used in

· Transmitters – to generate carrier signal for transmission

· Receivers – to generate local carrier signal to extract IF (intermediate frequency) from mixer

· Modulators – to generate carrier for information signal and generate modulated wave

· RADAR and SONAR – to generate signal that will be transmitted and received back

· RF (Radio Frequency) or AF (Audio Frequency) signal generators

Thus we may list out number of such applications where sine wave oscillators are used. In addition I would say the signal communication is impossible without oscillators.

There are different kinds of Sine wave oscillators based on the components used or based on the output frequency that they generate

1. Based on components means if they produce oscillation using resistors (R) and capacitors (C) then they are called RC oscillators and if they use inductor (L) and capacitor (C) then they are termed as LC oscillators

2. Based on output frequency means if they generate frequency in audio range (20 Hz – 20 KHz) then they are Audio Frequency (AF) oscillators. If they generate frequency in low range (100 – 200 KHz) then they are called Low Frequency (LF) oscillators and last, if they generate frequency in high range (in MHz or GHz) then they are termed as High frequency (HF) or Radio Frequency (RF) oscillators.

I am presenting here two such **sine-wave oscillators** that uses RC components to generate oscillations and they can generate frequency in AF range as well as RF range. The two oscillators are

1. RC phase shift oscillator

2. Wien bridge oscillator

Both are built using op-amp and it is very easy to build them on bread board or on general PCB with few additional components. So let us first gather the required components, instruments and apparatus.

__Instruments required:__

· CRO or DSO

· Dual power supply (+15 V & -15 V)

__Apparatus required:__

· Connecting wires

· CRO probes

· Bread board

__Components required:__

· LM741 IC

· Resistors - 1 K, 47 KΩ (pot), 1.2 KΩ, 10 KΩ, 22 KΩ

· Capacitors – 0.1 µF

Let us first start with RC phase shift oscillator

__RC Phase shift oscillator:__

RC oscillator is build using an amplifier and a RC network in feedback. For any oscillator the two prime requirements to generate sustained and constant oscillations are

1. The total phase shift around loop must be 0 degree

2. The loop gain should be equal or greater than unity

This is also known as “*Barkhausen Criterion*”

In RC phase shift oscillator op-amp is used as an amplifier in inverting configuration. So it gives 180^{o} phase shift in its output. So the RC feedback network following the amplifier has to produce additional 180^{o }phase shift to make total phase shift 0^{o}. Now look at RC circuit given below

The output

V_{out} = I×R

Where

I = V_{in} / Z

Now

V_{in} = V_{m}sin(2πft)

And

Z = R – j / 2πFC = R – jXc

(Xc = 1/2 πFC)

From this, the magnitude of Z is

|Z| = √(R^{2} + Xc^{2})

And phase angle of Z is

α = tan^{-1 }(-Xc/R)

So finally

I = __(Vm / √2)__ = |I|__/ __(+α)

|Z| __/ __(- α)

The positive angle in above equation indicates the current leads input voltage by angle α^{o}. Because output voltage

V_{out} = I×R

It is in phase with current. So output voltage also leads input by angle α^{o}. This angle can be between 0^{o} to 90^{o}. But the RC values are selected such that α = 60^{o}

Thus 1 RC network gives phase shift of 60^{o}. If 3 RC networks are connected in feedback circuit. Each will give phase shift of 60^{o}. So total phase shift will be 3×60 = 180^{o}. Now op-amp gives 180^{o }and RC ladder network gives additional 180^{o }so total of 360^{o} = 0^{o} phase shift means - 1^{st} condition is satisfied.

As per the second conditions to generate sustained oscillation it is required that loop gain must be greater or equal to unity

AB ≥ 1

Where A = op-amp gain

And B = feedback gain

But the gain of RC ladder (feedback) network B = 1/29

So

AB ≥ 1

A ≥ 1/B

Means

A ≥ 29

So we have to adjust op-amp gain such a way that it should be slightly more than 29. When these two conditions are satisfied the circuit will generate sustained oscillation. The oscillation frequency is give by equation

F = 1 / 2πRC√6

__Circuit description:__

(See the circuit diagram tab 1 for RC Phase Shift Oscillator Circuit)

· Non inverting terminal of IC LM741 is connected to ground

· A 47 K pot is connected between inverting terminal and output terminal to adjust loop gain and generate sustained oscillation

· Three identical RC networks are connected in series in feedback path as shown.

· Pin 7 is given +Vcc of +15 V and pin 4 is given –Vee of -15 V as shown

__Circuit operation:__

The circuit will generate sine wave output when op-amp gain is adjusted to slightly more than 29. Now op-amp gain is

A = -R1 / R5

But R5 = 1 K and R1 is pot of 47 K. So by tuning pot R1 we can adjust A as greater or equal to 29 to generate sustained oscillation of constant amplitude.

The circuit oscillates at a frequency

F = 1 / 2πRC√6

Substituting values

F = 1 / 2×3.14×1000×100×10^{-9}×2.45

F = 650 Hz

So we get sine wave output of around 650 Hz.

Now after understanding the theory, working principle and circuit operation you will be excited to build and test the circuit. So here is step by step test procedure to follow

__Procedure to test the circuit:__

· Wire up the circuit on bread board or on general PCB

· Connect the output of circuit to DSO / CRO using CRO probe

· Give +15 V ,-15 V, and ground to circuit from power supply

· Switch on power supply

· Adjust pot R1 till the circuit generates sustained sine wave oscillation

· Observe sine wave output and find out its frequency

Here are the photographs of circuit prepare on bread board and test setup.

*Fig. 1: Prototype of LM741 OPAMP IC based RC Phase Shift Sine Wave Oscillator*

*Fig. 2: Image showing Output from LM741 OPAMP IC based RC Phase Shift Sine Wave Oscillator on an Oscilloscope*

When you build and test the circuit you will get the output sine wave on DSO as shown in photograph. You can also observe the frequency of oscillation is 694 Hz that is near to calculated theoretical value from equation.

*Fig. 3: Image showing Output Waveform from LM741 OPAMP IC based RC Phase Shift Sine Wave Oscillator on an Oscilloscope*

Now let us move forward to next oscillator

## Wien Bridge Oscillator

Wien bridge oscillator is a combination of op-amp as an amplifier and a **Wien bridge network **in feedback path. Wien bridge network is made up of four arms. In one arm there is series RC network. In the adjoining arm there is parallel RC network. These two arms are called frequency sensitive arms. Rest two arms consist of two fixed value resistor. This type of network is called lead-lag network because at low frequency it acts like a lead and at high frequency it act like lag. For the circuit to produce sustained oscillation again we have to check Barkhausen criteria.

1. The total phase shift around loop is zero

2. The loop gain should be greater than or equal to unity

In this circuit the amplifier does not produce any phase shift. The wein bridge network is balanced to achieve 0 phase shift. So the 1^{st} condition satisfies. For second condition

AB ≥ 1

Where A = op-amp gain

And B = feedback network gain

But the gain of Wien bridge (feedback) network

B = 1/3

So

AB ≥ 1

A ≥ 1/B

Means

A ≥ 3

So the op-amp gain is adjusted to be greater than or equal to 3. When these two conditions are satisfied the circuit will generate sine wave of frequency

F = 1 / 2π√(R_{1}R_{2}C_{1}C_{2})

But practically

R_{1} = R_{2} = R and C_{1} = C_{2} = C

Then

F = 1 / 2πRC

__Circuit description:__

As shown in schematic there are four arms of Wien bridge

· One arm made up of series connection of R2 and C1

· Second arm made up of parallel connection of R1 and C2

· Third and fourth arm are resistance R3 and R4

· The feedback taken across parallel RC network is applied to non inverting terminal

· Another feedback is taken across resistance R3 and applied to inverting terminal

· The output is taken from output pin number 6

· Pin 7 is given +Vcc of +15 V and pin 4 is given –Vee of -15 V as shown

__Circuit operation:__

The circuit will generate sine wave when wien bridge is in balance condition and op-amp gain will be

A ≥ 3

But

A = 1 + R4/R3

So

1 + R4/R3 ≥ 3

R4/R3 ≥ 2

R4 ≥ 2 R3

R3 is selected as 10 KΩ. So R4 will be 20 KΩ. But R4 is kept slightly more than 2 R3 to make loop gain slightly more than unity. So and R4 = 22 KΩ

The circuit generates sine wave of frequency

F = 1 / 2πRC

Substituting values

R = 1200 Ω and C = 100 nF

F = 1 / 2×3.14×1200×100×10^{-9}

F = 1.327 KHz

Now it’s time to build and test the circuit. Once again follow the same step by step procedure given before. Here are the photographs of circuit built on bread board and required test set up with power supply and DSO.

*Fig. 4: Image showing circuit connections of LM741 IC for making Wien Bridge Oscillator on a breadboard*

*Fig. 5: Image showing Output from LM741 IC based Wien Bridge Sine Wave Oscillator on an Oscilloscope*

You can observe the sine output on DSO as given in the photograph. Observe the practical value of frequency 1.48 KHz matches with calculated theoretical value using equations.

*Fig. 6: Image showing Output Waveform from LM741 IC based Wien Bridge Sine Wave Oscillator on an Oscilloscope*

__Applications:__

RC phase shift oscillators can generate output frequency in audio range (20 Hz – 20 KHz ) as well as in low range around 100 – 300 KHZ

**Wien bridge oscillators** are preferred to generate output frequency is audio range only.

.

## Comments

## how to convert the square

how to convert the square wave into sine wave i design the inveter whose output wave form is square wave now i want to convert into sine wave plz guide me and give me the circuit diagram step by step discription i am will be very thankful for this kindness

## You could try filtering the

You could try filtering the output? a high order LP filter would give an approximate sinusoid (with the harmonics still there, just highly attenuated)