# RC phase shift oscillator

##### introduction

RC phase shift oscillator is a sinusoidal oscillator. RC phase shift oscillator consists of amplifying stage and three RC cascaded network which work as feedback network. Amplifying stage consist of an active device (like a BJT, FET or Op amp) and biasing network.  RC cascaded network takes output of amplifying stage as an input and provide feedback voltage back to amplifying stage.

##### what is oscillator?

Oscillator is an electronics circuit use to generate voltage or current waveform of fixed amplitude and frequency without any external voltage. The waveform can be sinusoidal, square, or can be saw tooth wave. Or we can say it produce ac waveform using dc voltage. Oscillators are used in computer, microprocessor, microcontroller, function generator, in electronics communication circuit, etc.

##### necessary condition for oscillation

Oscillator uses amplifier whose output voltage is feedback through a feedback network. The feedback voltage must have a proper magnitude and phase so that the circuit produces desired waveform. Mostly oscillator uses positive feedback mechanism.

The necessary conditions are:

Loop gain, i.e. Aβ =1 and

Total Phase shift, θ = 0o or 360o

In words, the loop gain of the circuit must be near to or equal to 1. Second, the total phase shift of loop gain of the circuit must 0 degree or 360 degree. This condition are known as Barkhausen criterion for sustain oscillation. Practically Aβ > 1

##### types of oscillator

If the generated output voltage waveform of an oscillator is in sinusoidal form, then the oscillator is Sinusoidal wave oscillator. It produces sine or cosine wave.

Similarly, if the generated output voltage waveform is square form, then the oscillator is square wave oscillator.

So it can depend upon the type of waveform it generates.

It can also classify depending upon the component is used.

##### Working of oscillator circuit

Consider the above circuit diagram. From the circuit,

V = Vin + VF

VO = VA

VF = β VO

And VO = ( Vin + VF ) A

Or,  VO = ( Vin + βVO) A

Or,  VO/Vin = A/ ( 1 – Aβ )

This is the closed loop gain of the circuit, VO/Vin = A/ ( 1 – Aβ ). If Aβ = 1 the the closed loop gain will become infinity. So a infinitesimal voltage can give us a measurable value of voltage. The infinitesimal voltage is noise from the circuit. And thus this circuit operates as an oscillator.

##### what is RC Phase Shift Oscillator

RC phase shift oscillator is a sinusoidal oscillator.

RC phase shift oscillator consists of amplifying stage and three RC cascaded network which work as feedback network. Amplifying stage consist of an active device (like a BJT, FET or Op amp) and biasing network.  RC cascaded network takes output of amplifying stage as an input and provide feedback voltage back to amplifying stage.

Amplifying stage provide amplifying  signal having 180O phase shift to RC network and RC network provide further 180O phase shift back to the amplifying stage. So overall the circuit provide 360O phase shift i.e. positive feedback. There are three RC cascaded network, each RC network provide 60O phase shift ideally and therefore three RC network gives 180O phase shift.

##### RC phase shift oscillator using Op Amp

In the given RC Phase Shift Oscillator circuit diagram, Op amp amplifier circuit provide 180O phase shifted signal to the RC network as op amp used in inverting mode.  And RC cascaded network work as feedback circuit. Each RC combination gives 60O phase shift at specific frequency and all three network provide 360O phase shift.

The frequency at which RC network gives us 180O phases shift is given by

So amplifier gain must be equal to greater than 29.

##### RC Phase Shift Oscillator Using BJT

In the given RC Phase Shift Oscillator circuit diagram, BJT amplifier circuit provide 180O phase shifted signal to the RC network.  And RC cascaded network work as feedback circuit. Each RC combination gives 60O phase shift at specific frequency and all three network provide 360O phase shift.

The frequency at which RC network gives us 180O  phases shift is given by ##### RC Phase Shift Oscillator Using JFET or FET

In the given RC Phase Shift Oscillator circuit diagram, amplifier stage uses self biasing network for FET.

FET amplifier circuit provide 180O phase shifted signal to the RC network.  And RC cascaded network work as feedback circuit. Each RC combination gives 60O phase shift at specific frequency and all three network provide 360O phase shift.

The frequency at which RC network gives us 180phases shift is given by |A| = gmR||  where R|| = RDrD / ( RD + rD )

Since, we know practically Aβ > 1 for oscillator

So amplifier gain must be equal to greater than 29.