Oscillators are heart of electronics devices. They provide constant and consistent signal to drive the electronics circuit which can be both digital or analog type. The basic theory of oscillator is an amplifier with controlled positive feedback. The feedback generates signals such that no input signal is required and the whole system performs self-oscillation.

Consider the following circuit where A is the amplifier and B is the feedback circuit. The feedback circuit is usually LC tuned circuit so that it resonant at a particular frequency.

The Theory behind Osillators
For illustration, initially the amplifier A is driven by an input sinusoidal signal vin. The feedback is not connected to the input of the amplifier. That is the output of B at y is not connected to x of the amplifier input.

Now we connect x to y.

The Theory behind Osillators


Here, the input signal vin gets amplified by the amplifier A and the output is.

vout = A*vin

This output vout enters the feedback circuit and the output from here is given by,

vf = B*(vout)
or,
vf = B(A*vin)

The oscillation will be established if
(1) the feedback circuit B is such that, (1) its output signal vf is in phase with its input signal vout and,
(2) the amplifier A produces amplification such that the attenuation through the loop is compensated in such a way that the product A*B is unity.

 Read more on the theory of osillator in electronic principles malvino 8th edition pdf.

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