## oscillators-Barkhausen criterion

An oscillator is an electronic device which generates sinusoidal waves when excited by a DC input supply voltage. There are two types of approaches to generate sine waves

• Using resonance phenomena (This can be implemented with a separate circuit or using the non linearity of the device itself)
• By appropriately shaping a triangular waveform.

Multivibrator is a circuit which generate non sinusoidal wave forms such as square, triangular, pulse e.t.c.Oscillators are circuits which generates sinusoidal wave forms. Multi vibrators are basic building blocks in function generators and nonlinear oscillators whereas oscillators are basic building blocks in inverters.

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## Barkhausen criterion

The frequency of oscillation at which sinusoidal oscillator operates is the frequency for which the total shift introduced, as the signal proceeds from the input terminals, through the amplifier and feedback network, and back again to the input, is precisely zero(or an integral multiple of 2*Π).

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Stated simply the condition A*β = -1 at ω= ωo, i.e. the magnitude of loop gain should be one and phase of loop gain should be unity ( the feedback network introduces 1800 phase shift, the other 1800 phase shift is provided by mixer ) is called Barkhausen criterion.

A closed loop system with negative feedback can be represented by a transfer function = A/(1+A*β). Often feedback network consists of only resistive elements and is independent of frequency but amplifier gain is a function of frequency. Hence the loop gain A*β is a function of frequency. There may exist a frequency ωo at which its magnitude is one and phase is 1800 i.e. A*β = -1 (Barkhausen criterion). At that frequency overall gain of system is very large theoretically infinite. Noise at the input of amplifier consists of all frequencies with negligible amplitudes. For all frequencies other than the oscillator frequencies the amplifier gain will not be enough to elevate them to significant amplitudes. But at that frequency where oscillator oscillates it provides very large gain and the amplitude of corresponding sine wave will be limited by the nonlinearity of the active device.

The frequency of oscillation depends mostly on few circuit parameters such as passive elements such as resistance, inductance, and capacitance e.t.c. The principle cause of drift of these circuit parameters is temperature. Therefore compensation measures should be taken for balancing temperature induced variations.