Oscillators

 Introduction of Oscillators and Barkhausen Criterion

Introduction

■       A Circuit which can deliver electrical energy of some specific frequency is called oscillator.

■       The waveforms produced may be sinusoidal or non-sinusoidal.

■       An oscillator receives D.C. energy and changes it into A.C. energy of desired frequency.

■       The frequency of oscillator depends on components of the oscillator.

■       There is no need of external input signal in oscillators, it produces output signal by its own.

■       This output can be used as energy source for other electrical circuits.

■       An amplifier has negative feedback, where as an oscillator has negative as well as positive feedback.

■       Concept of Feedback

■       The process of adding fraction of output to the input is called feedback.

■       There are two types of feedback - 1) positive feedback 2) negative feedback

      Positive feedback enhances or amplifies an effect by it having an influence on the process which gave rise to it.

      Negative feedback Subtracts a fraction of its output from its input  having an influence on the process which gave decrease to it.

■       Oscillator is having the positive feedback due to which oscillations can sustain without any input signal.

        

Barkhausen Criterion


In the above circuit the basic inverting amplifier produces phase shift of 1800  between input and output, and additional phase shift of 1800 must be provided by feedback network, so that total phase shift around the loop becomes 3600 

In the above circuit, consisder a fictitious voltage vi applied at the input of the amplifier, hence we get, V0 = AVi

Feedback voltage Vf is given by,

Vf = βV0

Therefore, we get Vf  = β AVi

For the oscillator, Vf must act as Vi. In this condition, Vf  drives the circuit and without external input, circuit works as an oscillator.

The circuit works as an oscillator, if the following two conditions are satisfied. It is known as Berkhausen Criterion for oscillations.

■       A) The magnitude of product of the loop gain of the amplifier (A) and the magnitude of the feedback factor β is unity,

    i.e. | Aβ | = 1

■       B) the total phase shift around a loop is 00 or 3600   

When these two conditions are satisfied, it produces sustained oscillations of constant frequency and amplitude, as shown if following fig.


If, | Aβ | > 1 and total phase shift is 00 or 3600 , then the output oscillations are of growing type as shown in following fig.  


If, | Aβ | < 1 and total phase shift is 00 or 3600 , then the output oscillations are of decaying type as shown in following fig., in such case amplitude decreases exponentially and the oscillations finally ceases.


 

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