# How is a sine wave created by an oscillator?

How is a sine wave created by an oscillator?

I mean generally, we have a voltage that changes its polarity according to frequency, but at the output we have a sine wave (example Wien bridge oscillator) - how does this happen?

Can anyone prove that with mathematics or ideas that the output wave is a sine wave?

The idea behind such oscillators is pretty simple - make the positive feedback (that causes the oscillator to oscillate) different for the different frequencies. So, if you can make the positive feedback to be >1 only for one exact frequency, then the oscillator will be able to oscillate only on this frequency and this way the output signal will be sinusoidal function (because any other form of the signal is a mix of several sinusoidal signals with different frequencies).

Mentioned Wien bridge, is actually band pass filter that will mostly pass one frequency and will attenuate all other frequencies. Note, that the gain of the amplifier used is very important here - if the gain is too high, even the suppressed frequencies will give a total gain >1 and the oscillator will generate some complex signal, containing several sinusoidal harmonics.

That is why the typical circuit of such generator contains automatic gain regulator that to keep the gain as lower as possible (but more than 1 for the needed frequency). In the most simple schematics, this system consists of single light bulb, that changes its resistance, dependent of the current through it.

For an oscillator to oscillate at a steady frequency it must have an input that is fed with a fraction of the output voltage that will exactly reinforce the signal at the output. This is known as positive feedback.

This is achieved by either a delaying mechanism or a phase shifting mechanism. A delaying mechanism is sometimes used for a square wave oscillator and a phase shift is usually used in a sinewave oscillator.

If the phase shift is frequency dependant there will be only one frequency that meets the criterion for exact positive feed back and this will produce a sustained sinewave at its output$^1$.

The phase shift mechanism can be made from a Wien bridge array of resistors and capacitors or, it can be made from several resistor-capacitor combinations. Either way, both produce one frequency that is the correct phase angle for exact positive feedback and both are easily analysed mathematically.

$^1$ Other criteria must be met for the amplitude of the sinewave to be and remain stable.

Oscillator produce sine wave ,due to the random motion of electrons and the signals produced by the random motion of electrons have noise.

Due to positive feedback ,noise are attenuated.Only certain frequency of signal is generated

Every oscillator must satisfy

Barkhausen stability criterion http://en.wikipedia.org/wiki/Barkhausen_stability_criterion

For example: Wien bridge oscillator

The frequency of oscillation is given by: f = 1(2*pi*R*C).

Brief description on wein bridge oscillator is on http://en.wikipedia.org/wiki/Wien_bridge_oscillator