Conditions for Oscillation (Barkhausen Criterion)

CONDITIONS FOR OSCILLATION (BARKHAUSEN CRITERION)

Mechanism for Start of Oscillations

The oscillators circuit is set into oscillations by a random variation caused in the base current due to noise component or a small variation in the dc power supply. The noise components ie extremely small random electrical voltages and currents and currents are always present in any conductor, tube or transistor. Even when no external signal is applied, the ever-present noise will cause some small signal at the output of the amplifier when the amplifier is tuned at a particular frequency f_o, the output signal caused by noise signals will be predominantly at f_o. If a small fraction (β) of the output signal is fedback to the input with proper phase, relation then this feedback signal will be amplified by the amplifier. If the amplifier has a gain of more than 1/β  then the output increases and thereby the feedback signal becomes larger. This process continues and the output goes on increasing. But as the signal level increases the gain of the amplifier decreases and at particular value of output, the gain of the amplifier is reduced exactly equal to 1/β. Then the output voltage remains constant at frequency f_o, called frequency of oscillations.

The essential conditions for maintaining oscillations are

1. |Aβ|= 1, ie., the magnitude of loop gain must be unity.

2. The total phase shift around the closed loop is zero (or) 360°.

Practical Considerations

The condition |Aβ|= 1 gives a single and precise value of Aβ which should be set through out the operation of the oscillator circuit. But in practice, as transistor characteristics and performance of other circuit components change with time, |Aβ| will become greater or less than unity. Hence, in all practical circuits |Aβ| should be set greater than unity so that the amplitude of oscillation will continue to increase without limit but such an increase in amplitude is limited by the onset of the nonlinearity of operation in the active devices associated with the amplifier as shown in Fig. 4.12.

In this circuit, Aβ is larger than unity for positive feedback. This onset of nonlinearity is an essential feature of all practical oscillators.